topology.continuous_function.compact
⟷
Mathlib.Topology.ContinuousFunction.Compact
The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.
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mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -350,12 +350,12 @@ def linearIsometryBoundedOfCompact : C(α, E) ≃ₗᵢ[𝕜] α →ᵇ E :=
variable {α E}
-#print ContinuousMap.evalClm /-
+#print ContinuousMap.evalCLM /-
-- to match bounded_continuous_function.eval_clm
/-- The evaluation at a point, as a continuous linear map from `C(α, 𝕜)` to `𝕜`. -/
-def evalClm (x : α) : C(α, E) →L[𝕜] E :=
- (evalClm 𝕜 x).comp (linearIsometryBoundedOfCompact α E 𝕜).toLinearIsometry.toContinuousLinearMap
-#align continuous_map.eval_clm ContinuousMap.evalClm
+def evalCLM (x : α) : C(α, E) →L[𝕜] E :=
+ (evalCLM 𝕜 x).comp (linearIsometryBoundedOfCompact α E 𝕜).toLinearIsometry.toContinuousLinearMap
+#align continuous_map.eval_clm ContinuousMap.evalCLM
-/
end
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -295,7 +295,7 @@ theorem apply_le_norm (f : C(α, ℝ)) (x : α) : f x ≤ ‖f‖ :=
#print ContinuousMap.neg_norm_le_apply /-
theorem neg_norm_le_apply (f : C(α, ℝ)) (x : α) : -‖f‖ ≤ f x :=
- le_trans (neg_le_neg (f.norm_coe_le_norm x)) (neg_le.mp (neg_le_abs_self (f x)))
+ le_trans (neg_le_neg (f.norm_coe_le_norm x)) (neg_le.mp (neg_le_abs (f x)))
#align continuous_map.neg_norm_le_apply ContinuousMap.neg_norm_le_apply
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -170,6 +170,8 @@ end
instance [CompleteSpace β] : CompleteSpace C(α, β) :=
(isometryEquivBoundedOfCompact α β).CompleteSpace
+/- warning: continuous_map.continuous_eval clashes with continuous_map.continuous_eval' -> ContinuousMap.continuous_eval
+Case conversion may be inaccurate. Consider using '#align continuous_map.continuous_eval ContinuousMap.continuous_evalₓ'. -/
#print ContinuousMap.continuous_eval /-
/-- See also `continuous_map.continuous_eval'` -/
@[continuity]
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -591,7 +591,7 @@ theorem summable_of_locally_summable_norm {ι : Type _} {F : ι → C(X, E)}
lift K to compacts X using hK
have A : ∀ s : Finset ι, restrict (↑K) (∑ i in s, F i) = ∑ i in s, restrict K (F i) := by intro s;
ext1 x; simp
- simpa only [HasSum, A] using summable_of_summable_norm (hF K)
+ simpa only [HasSum, A] using Summable.of_norm (hF K)
#align continuous_map.summable_of_locally_summable_norm ContinuousMap.summable_of_locally_summable_norm
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,10 +3,10 @@ Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
-import Mathbin.Topology.ContinuousFunction.Bounded
-import Mathbin.Topology.UniformSpace.Compact
-import Mathbin.Topology.CompactOpen
-import Mathbin.Topology.Sets.Compacts
+import Topology.ContinuousFunction.Bounded
+import Topology.UniformSpace.Compact
+import Topology.CompactOpen
+import Topology.Sets.Compacts
#align_import topology.continuous_function.compact from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"
mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504
@@ -318,7 +318,7 @@ variable {R : Type _} [NormedRing R]
instance : NormedRing C(α, R) :=
{ (inferInstance : NormedAddCommGroup C(α, R)), ContinuousMap.ring with
- norm_mul := fun f g => norm_mul_le (mkOfCompact f) (mkOfCompact g) }
+ norm_hMul := fun f g => norm_mul_le (mkOfCompact f) (mkOfCompact g) }
end
@@ -633,20 +633,20 @@ variable {α : Type _} {β : Type _}
variable [TopologicalSpace α] [NormedRing β] [StarRing β]
instance [CompactSpace α] [CstarRing β] : CstarRing C(α, β)
- where norm_star_mul_self := by
+ where norm_star_hMul_self := by
intro f
refine' le_antisymm _ _
· rw [← sq, ContinuousMap.norm_le _ (sq_nonneg _)]
intro x
simp only [ContinuousMap.coe_mul, coe_star, Pi.mul_apply, Pi.star_apply,
- CstarRing.norm_star_mul_self, ← sq]
+ CstarRing.norm_star_hMul_self, ← sq]
refine' sq_le_sq' _ _
· linarith [norm_nonneg (f x), norm_nonneg f]
· exact ContinuousMap.norm_coe_le_norm f x
· rw [← sq, ← Real.le_sqrt (norm_nonneg _) (norm_nonneg _),
ContinuousMap.norm_le _ (Real.sqrt_nonneg _)]
intro x
- rw [Real.le_sqrt (norm_nonneg _) (norm_nonneg _), sq, ← CstarRing.norm_star_mul_self]
+ rw [Real.le_sqrt (norm_nonneg _) (norm_nonneg _), sq, ← CstarRing.norm_star_hMul_self]
exact ContinuousMap.norm_coe_le_norm (star f * f) x
end CstarRing
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,17 +2,14 @@
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module topology.continuous_function.compact
-! leanprover-community/mathlib commit 0b7c740e25651db0ba63648fbae9f9d6f941e31b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Topology.ContinuousFunction.Bounded
import Mathbin.Topology.UniformSpace.Compact
import Mathbin.Topology.CompactOpen
import Mathbin.Topology.Sets.Compacts
+#align_import topology.continuous_function.compact from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"
+
/-!
# Continuous functions on a compact space
mathlib commit https://github.com/leanprover-community/mathlib/commit/728ef9dbb281241906f25cbeb30f90d83e0bb451
@@ -181,6 +181,8 @@ theorem continuous_eval : Continuous fun p : C(α, β) × α => p.1 p.2 :=
#align continuous_map.continuous_eval ContinuousMap.continuous_eval
-/
+/- warning: continuous_map.continuous_eval_const clashes with continuous_map.continuous_eval_const' -> ContinuousMap.continuous_eval_const
+Case conversion may be inaccurate. Consider using '#align continuous_map.continuous_eval_const ContinuousMap.continuous_eval_constₓ'. -/
#print ContinuousMap.continuous_eval_const /-
/-- See also `continuous_map.continuous_eval_const` -/
@[continuity]
@@ -189,6 +191,8 @@ theorem continuous_eval_const (x : α) : Continuous fun f : C(α, β) => f x :=
#align continuous_map.continuous_eval_const ContinuousMap.continuous_eval_const
-/
+/- warning: continuous_map.continuous_coe clashes with continuous_map.continuous_coe' -> ContinuousMap.continuous_coe
+Case conversion may be inaccurate. Consider using '#align continuous_map.continuous_coe ContinuousMap.continuous_coeₓ'. -/
#print ContinuousMap.continuous_coe /-
/-- See also `continuous_map.continuous_coe'` -/
theorem continuous_coe : @Continuous C(α, β) (α → β) _ _ coeFn :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -60,6 +60,7 @@ def equivBoundedOfCompact : C(α, β) ≃ (α →ᵇ β) :=
#align continuous_map.equiv_bounded_of_compact ContinuousMap.equivBoundedOfCompact
-/
+#print ContinuousMap.uniformInducing_equivBoundedOfCompact /-
theorem uniformInducing_equivBoundedOfCompact : UniformInducing (equivBoundedOfCompact α β) :=
UniformInducing.mk'
(by
@@ -72,11 +73,15 @@ theorem uniformInducing_equivBoundedOfCompact : UniformInducing (equivBoundedOfC
⟨⟨Set.univ, {p | dist p.1 p.2 ≤ ε}⟩, ⟨isCompact_univ, ⟨ε, hε, fun _ h => h⟩⟩,
fun ⟨f, g⟩ h => hs _ _ (ht ((dist_le hε.le).mpr fun x => h x (mem_univ x)))⟩⟩)
#align continuous_map.uniform_inducing_equiv_bounded_of_compact ContinuousMap.uniformInducing_equivBoundedOfCompact
+-/
+#print ContinuousMap.uniformEmbedding_equivBoundedOfCompact /-
theorem uniformEmbedding_equivBoundedOfCompact : UniformEmbedding (equivBoundedOfCompact α β) :=
{ uniformInducing_equivBoundedOfCompact α β with inj := (equivBoundedOfCompact α β).Injective }
#align continuous_map.uniform_embedding_equiv_bounded_of_compact ContinuousMap.uniformEmbedding_equivBoundedOfCompact
+-/
+#print ContinuousMap.addEquivBoundedOfCompact /-
/-- When `α` is compact, the bounded continuous maps `α →ᵇ 𝕜` are
additively equivalent to `C(α, 𝕜)`.
-/
@@ -84,10 +89,12 @@ additively equivalent to `C(α, 𝕜)`.
def addEquivBoundedOfCompact [AddMonoid β] [LipschitzAdd β] : C(α, β) ≃+ (α →ᵇ β) :=
({ toContinuousMapAddHom α β, (equivBoundedOfCompact α β).symm with } : (α →ᵇ β) ≃+ C(α, β)).symm
#align continuous_map.add_equiv_bounded_of_compact ContinuousMap.addEquivBoundedOfCompact
+-/
instance : MetricSpace C(α, β) :=
(uniformEmbedding_equivBoundedOfCompact α β).comapMetricSpace _
+#print ContinuousMap.isometryEquivBoundedOfCompact /-
/-- When `α` is compact, and `β` is a metric space, the bounded continuous maps `α →ᵇ β` are
isometric to `C(α, β)`.
-/
@@ -97,20 +104,25 @@ def isometryEquivBoundedOfCompact : C(α, β) ≃ᵢ (α →ᵇ β)
isometry_toFun x y := rfl
toEquiv := equivBoundedOfCompact α β
#align continuous_map.isometry_equiv_bounded_of_compact ContinuousMap.isometryEquivBoundedOfCompact
+-/
end
+#print BoundedContinuousFunction.dist_mkOfCompact /-
@[simp]
theorem BoundedContinuousFunction.dist_mkOfCompact (f g : C(α, β)) :
dist (mkOfCompact f) (mkOfCompact g) = dist f g :=
rfl
#align bounded_continuous_function.dist_mk_of_compact BoundedContinuousFunction.dist_mkOfCompact
+-/
+#print BoundedContinuousFunction.dist_toContinuousMap /-
@[simp]
theorem BoundedContinuousFunction.dist_toContinuousMap (f g : α →ᵇ β) :
dist f.toContinuousMap g.toContinuousMap = dist f g :=
rfl
#align bounded_continuous_function.dist_to_continuous_map BoundedContinuousFunction.dist_toContinuousMap
+-/
open BoundedContinuousFunction
@@ -118,68 +130,90 @@ section
variable {α β} {f g : C(α, β)} {C : ℝ}
+#print ContinuousMap.dist_apply_le_dist /-
/-- The pointwise distance is controlled by the distance between functions, by definition. -/
theorem dist_apply_le_dist (x : α) : dist (f x) (g x) ≤ dist f g := by
simp only [← dist_mk_of_compact, dist_coe_le_dist, ← mk_of_compact_apply]
#align continuous_map.dist_apply_le_dist ContinuousMap.dist_apply_le_dist
+-/
+#print ContinuousMap.dist_le /-
/-- The distance between two functions is controlled by the supremum of the pointwise distances -/
theorem dist_le (C0 : (0 : ℝ) ≤ C) : dist f g ≤ C ↔ ∀ x : α, dist (f x) (g x) ≤ C := by
simp only [← dist_mk_of_compact, dist_le C0, mk_of_compact_apply]
#align continuous_map.dist_le ContinuousMap.dist_le
+-/
+#print ContinuousMap.dist_le_iff_of_nonempty /-
theorem dist_le_iff_of_nonempty [Nonempty α] : dist f g ≤ C ↔ ∀ x, dist (f x) (g x) ≤ C := by
simp only [← dist_mk_of_compact, dist_le_iff_of_nonempty, mk_of_compact_apply]
#align continuous_map.dist_le_iff_of_nonempty ContinuousMap.dist_le_iff_of_nonempty
+-/
+#print ContinuousMap.dist_lt_iff_of_nonempty /-
theorem dist_lt_iff_of_nonempty [Nonempty α] : dist f g < C ↔ ∀ x : α, dist (f x) (g x) < C := by
simp only [← dist_mk_of_compact, dist_lt_iff_of_nonempty_compact, mk_of_compact_apply]
#align continuous_map.dist_lt_iff_of_nonempty ContinuousMap.dist_lt_iff_of_nonempty
+-/
+#print ContinuousMap.dist_lt_of_nonempty /-
theorem dist_lt_of_nonempty [Nonempty α] (w : ∀ x : α, dist (f x) (g x) < C) : dist f g < C :=
dist_lt_iff_of_nonempty.2 w
#align continuous_map.dist_lt_of_nonempty ContinuousMap.dist_lt_of_nonempty
+-/
+#print ContinuousMap.dist_lt_iff /-
theorem dist_lt_iff (C0 : (0 : ℝ) < C) : dist f g < C ↔ ∀ x : α, dist (f x) (g x) < C := by
simp only [← dist_mk_of_compact, dist_lt_iff_of_compact C0, mk_of_compact_apply]
#align continuous_map.dist_lt_iff ContinuousMap.dist_lt_iff
+-/
end
instance [CompleteSpace β] : CompleteSpace C(α, β) :=
(isometryEquivBoundedOfCompact α β).CompleteSpace
+#print ContinuousMap.continuous_eval /-
/-- See also `continuous_map.continuous_eval'` -/
@[continuity]
theorem continuous_eval : Continuous fun p : C(α, β) × α => p.1 p.2 :=
continuous_eval.comp ((isometryEquivBoundedOfCompact α β).Continuous.Prod_map continuous_id)
#align continuous_map.continuous_eval ContinuousMap.continuous_eval
+-/
+#print ContinuousMap.continuous_eval_const /-
/-- See also `continuous_map.continuous_eval_const` -/
@[continuity]
theorem continuous_eval_const (x : α) : Continuous fun f : C(α, β) => f x :=
continuous_eval.comp (continuous_id.prod_mk continuous_const)
#align continuous_map.continuous_eval_const ContinuousMap.continuous_eval_const
+-/
+#print ContinuousMap.continuous_coe /-
/-- See also `continuous_map.continuous_coe'` -/
theorem continuous_coe : @Continuous C(α, β) (α → β) _ _ coeFn :=
continuous_pi continuous_eval_const
#align continuous_map.continuous_coe ContinuousMap.continuous_coe
+-/
-- TODO at some point we will need lemmas characterising this norm!
-- At the moment the only way to reason about it is to transfer `f : C(α,E)` back to `α →ᵇ E`.
instance : Norm C(α, E) where norm x := dist x 0
+#print BoundedContinuousFunction.norm_mkOfCompact /-
@[simp]
theorem BoundedContinuousFunction.norm_mkOfCompact (f : C(α, E)) : ‖mkOfCompact f‖ = ‖f‖ :=
rfl
#align bounded_continuous_function.norm_mk_of_compact BoundedContinuousFunction.norm_mkOfCompact
+-/
+#print BoundedContinuousFunction.norm_toContinuousMap_eq /-
@[simp]
theorem BoundedContinuousFunction.norm_toContinuousMap_eq (f : α →ᵇ E) :
‖f.toContinuousMap‖ = ‖f‖ :=
rfl
#align bounded_continuous_function.norm_to_continuous_map_eq BoundedContinuousFunction.norm_toContinuousMap_eq
+-/
open BoundedContinuousFunction
@@ -198,58 +232,82 @@ section
variable (f : C(α, E))
+#print ContinuousMap.norm_coe_le_norm /-
-- The corresponding lemmas for `bounded_continuous_function` are stated with `{f}`,
-- and so can not be used in dot notation.
theorem norm_coe_le_norm (x : α) : ‖f x‖ ≤ ‖f‖ :=
(mkOfCompact f).norm_coe_le_norm x
#align continuous_map.norm_coe_le_norm ContinuousMap.norm_coe_le_norm
+-/
+#print ContinuousMap.dist_le_two_norm /-
/-- Distance between the images of any two points is at most twice the norm of the function. -/
theorem dist_le_two_norm (x y : α) : dist (f x) (f y) ≤ 2 * ‖f‖ :=
(mkOfCompact f).dist_le_two_norm x y
#align continuous_map.dist_le_two_norm ContinuousMap.dist_le_two_norm
+-/
+#print ContinuousMap.norm_le /-
/-- The norm of a function is controlled by the supremum of the pointwise norms -/
theorem norm_le {C : ℝ} (C0 : (0 : ℝ) ≤ C) : ‖f‖ ≤ C ↔ ∀ x : α, ‖f x‖ ≤ C :=
@BoundedContinuousFunction.norm_le _ _ _ _ (mkOfCompact f) _ C0
#align continuous_map.norm_le ContinuousMap.norm_le
+-/
+#print ContinuousMap.norm_le_of_nonempty /-
theorem norm_le_of_nonempty [Nonempty α] {M : ℝ} : ‖f‖ ≤ M ↔ ∀ x, ‖f x‖ ≤ M :=
@BoundedContinuousFunction.norm_le_of_nonempty _ _ _ _ _ (mkOfCompact f) _
#align continuous_map.norm_le_of_nonempty ContinuousMap.norm_le_of_nonempty
+-/
+#print ContinuousMap.norm_lt_iff /-
theorem norm_lt_iff {M : ℝ} (M0 : 0 < M) : ‖f‖ < M ↔ ∀ x, ‖f x‖ < M :=
@BoundedContinuousFunction.norm_lt_iff_of_compact _ _ _ _ _ (mkOfCompact f) _ M0
#align continuous_map.norm_lt_iff ContinuousMap.norm_lt_iff
+-/
+#print ContinuousMap.nnnorm_lt_iff /-
theorem nnnorm_lt_iff {M : ℝ≥0} (M0 : 0 < M) : ‖f‖₊ < M ↔ ∀ x : α, ‖f x‖₊ < M :=
f.norm_lt_iff M0
#align continuous_map.nnnorm_lt_iff ContinuousMap.nnnorm_lt_iff
+-/
+#print ContinuousMap.norm_lt_iff_of_nonempty /-
theorem norm_lt_iff_of_nonempty [Nonempty α] {M : ℝ} : ‖f‖ < M ↔ ∀ x, ‖f x‖ < M :=
@BoundedContinuousFunction.norm_lt_iff_of_nonempty_compact _ _ _ _ _ _ (mkOfCompact f) _
#align continuous_map.norm_lt_iff_of_nonempty ContinuousMap.norm_lt_iff_of_nonempty
+-/
+#print ContinuousMap.nnnorm_lt_iff_of_nonempty /-
theorem nnnorm_lt_iff_of_nonempty [Nonempty α] {M : ℝ≥0} : ‖f‖₊ < M ↔ ∀ x, ‖f x‖₊ < M :=
f.norm_lt_iff_of_nonempty
#align continuous_map.nnnorm_lt_iff_of_nonempty ContinuousMap.nnnorm_lt_iff_of_nonempty
+-/
+#print ContinuousMap.apply_le_norm /-
theorem apply_le_norm (f : C(α, ℝ)) (x : α) : f x ≤ ‖f‖ :=
le_trans (le_abs.mpr (Or.inl (le_refl (f x)))) (f.norm_coe_le_norm x)
#align continuous_map.apply_le_norm ContinuousMap.apply_le_norm
+-/
+#print ContinuousMap.neg_norm_le_apply /-
theorem neg_norm_le_apply (f : C(α, ℝ)) (x : α) : -‖f‖ ≤ f x :=
le_trans (neg_le_neg (f.norm_coe_le_norm x)) (neg_le.mp (neg_le_abs_self (f x)))
#align continuous_map.neg_norm_le_apply ContinuousMap.neg_norm_le_apply
+-/
+#print ContinuousMap.norm_eq_iSup_norm /-
theorem norm_eq_iSup_norm : ‖f‖ = ⨆ x : α, ‖f x‖ :=
(mkOfCompact f).norm_eq_iSup_norm
#align continuous_map.norm_eq_supr_norm ContinuousMap.norm_eq_iSup_norm
+-/
+#print ContinuousMap.norm_restrict_mono_set /-
theorem norm_restrict_mono_set {X : Type _} [TopologicalSpace X] (f : C(X, E))
{K L : TopologicalSpace.Compacts X} (hKL : K ≤ L) : ‖f.restrict K‖ ≤ ‖f.restrict L‖ :=
(norm_le _ (norm_nonneg _)).mpr fun x => norm_coe_le_norm (f.restrict L) <| Set.inclusion hKL x
#align continuous_map.norm_restrict_mono_set ContinuousMap.norm_restrict_mono_set
+-/
end
@@ -273,6 +331,7 @@ section
variable (α 𝕜 E)
+#print ContinuousMap.linearIsometryBoundedOfCompact /-
/-- When `α` is compact and `𝕜` is a normed field,
the `𝕜`-algebra of bounded continuous maps `α →ᵇ β` is
`𝕜`-linearly isometric to `C(α, β)`.
@@ -284,17 +343,21 @@ def linearIsometryBoundedOfCompact : C(α, E) ≃ₗᵢ[𝕜] α →ᵇ E :=
map_smul' := fun c f => by ext; simp
norm_map' := fun f => rfl }
#align continuous_map.linear_isometry_bounded_of_compact ContinuousMap.linearIsometryBoundedOfCompact
+-/
variable {α E}
+#print ContinuousMap.evalClm /-
-- to match bounded_continuous_function.eval_clm
/-- The evaluation at a point, as a continuous linear map from `C(α, 𝕜)` to `𝕜`. -/
def evalClm (x : α) : C(α, E) →L[𝕜] E :=
(evalClm 𝕜 x).comp (linearIsometryBoundedOfCompact α E 𝕜).toLinearIsometry.toContinuousLinearMap
#align continuous_map.eval_clm ContinuousMap.evalClm
+-/
end
+#print ContinuousMap.linearIsometryBoundedOfCompact_symm_apply /-
-- this lemma and the next are the analogues of those autogenerated by `@[simps]` for
-- `equiv_bounded_of_compact`, `add_equiv_bounded_of_compact`
@[simp]
@@ -302,31 +365,40 @@ theorem linearIsometryBoundedOfCompact_symm_apply (f : α →ᵇ E) :
(linearIsometryBoundedOfCompact α E 𝕜).symm f = f.toContinuousMap :=
rfl
#align continuous_map.linear_isometry_bounded_of_compact_symm_apply ContinuousMap.linearIsometryBoundedOfCompact_symm_apply
+-/
+#print ContinuousMap.linearIsometryBoundedOfCompact_apply_apply /-
@[simp]
theorem linearIsometryBoundedOfCompact_apply_apply (f : C(α, E)) (a : α) :
(linearIsometryBoundedOfCompact α E 𝕜 f) a = f a :=
rfl
#align continuous_map.linear_isometry_bounded_of_compact_apply_apply ContinuousMap.linearIsometryBoundedOfCompact_apply_apply
+-/
+#print ContinuousMap.linearIsometryBoundedOfCompact_toIsometryEquiv /-
@[simp]
theorem linearIsometryBoundedOfCompact_toIsometryEquiv :
(linearIsometryBoundedOfCompact α E 𝕜).toIsometryEquiv = isometryEquivBoundedOfCompact α E :=
rfl
#align continuous_map.linear_isometry_bounded_of_compact_to_isometry_equiv ContinuousMap.linearIsometryBoundedOfCompact_toIsometryEquiv
+-/
+#print ContinuousMap.linearIsometryBoundedOfCompact_toAddEquiv /-
@[simp]
theorem linearIsometryBoundedOfCompact_toAddEquiv :
(linearIsometryBoundedOfCompact α E 𝕜).toLinearEquiv.toAddEquiv =
addEquivBoundedOfCompact α E :=
rfl
#align continuous_map.linear_isometry_bounded_of_compact_to_add_equiv ContinuousMap.linearIsometryBoundedOfCompact_toAddEquiv
+-/
+#print ContinuousMap.linearIsometryBoundedOfCompact_of_compact_toEquiv /-
@[simp]
theorem linearIsometryBoundedOfCompact_of_compact_toEquiv :
(linearIsometryBoundedOfCompact α E 𝕜).toLinearEquiv.toEquiv = equivBoundedOfCompact α E :=
rfl
#align continuous_map.linear_isometry_bounded_of_compact_of_compact_to_equiv ContinuousMap.linearIsometryBoundedOfCompact_of_compact_toEquiv
+-/
end
@@ -354,11 +426,14 @@ We now set up some declarations making it convenient to use uniform continuity.
-/
+#print ContinuousMap.uniform_continuity /-
theorem uniform_continuity (f : C(α, β)) (ε : ℝ) (h : 0 < ε) :
∃ δ > 0, ∀ {x y}, dist x y < δ → dist (f x) (f y) < ε :=
Metric.uniformContinuous_iff.mp (CompactSpace.uniformContinuous_of_continuous f.Continuous) ε h
#align continuous_map.uniform_continuity ContinuousMap.uniform_continuity
+-/
+#print ContinuousMap.modulus /-
-- This definition allows us to separate the choice of some `δ`,
-- and the corresponding use of `dist a b < δ → dist (f a) (f b) < ε`,
-- even across different declarations.
@@ -367,15 +442,20 @@ theorem uniform_continuity (f : C(α, β)) (ε : ℝ) (h : 0 < ε) :
def modulus (f : C(α, β)) (ε : ℝ) (h : 0 < ε) : ℝ :=
Classical.choose (uniform_continuity f ε h)
#align continuous_map.modulus ContinuousMap.modulus
+-/
+#print ContinuousMap.modulus_pos /-
theorem modulus_pos (f : C(α, β)) {ε : ℝ} {h : 0 < ε} : 0 < f.modulus ε h :=
(Classical.choose_spec (uniform_continuity f ε h)).fst
#align continuous_map.modulus_pos ContinuousMap.modulus_pos
+-/
+#print ContinuousMap.dist_lt_of_dist_lt_modulus /-
theorem dist_lt_of_dist_lt_modulus (f : C(α, β)) (ε : ℝ) (h : 0 < ε) {a b : α}
(w : dist a b < f.modulus ε h) : dist (f a) (f b) < ε :=
(Classical.choose_spec (uniform_continuity f ε h)).snd w
#align continuous_map.dist_lt_of_dist_lt_modulus ContinuousMap.dist_lt_of_dist_lt_modulus
+-/
end UniformContinuity
@@ -390,6 +470,7 @@ variable [NormedAddCommGroup β] [NormedSpace 𝕜 β] [NormedAddCommGroup γ] [
open ContinuousMap
+#print ContinuousLinearMap.compLeftContinuousCompact /-
/-- Postcomposition of continuous functions into a normed module by a continuous linear map is a
continuous linear map.
Transferred version of `continuous_linear_map.comp_left_continuous_bounded`,
@@ -401,18 +482,23 @@ protected def ContinuousLinearMap.compLeftContinuousCompact (g : β →L[𝕜]
(g.compLeftContinuousBounded X).comp <|
(linearIsometryBoundedOfCompact X β 𝕜).toLinearIsometry.toContinuousLinearMap
#align continuous_linear_map.comp_left_continuous_compact ContinuousLinearMap.compLeftContinuousCompact
+-/
+#print ContinuousLinearMap.toLinear_compLeftContinuousCompact /-
@[simp]
theorem ContinuousLinearMap.toLinear_compLeftContinuousCompact (g : β →L[𝕜] γ) :
(g.compLeftContinuousCompact X : C(X, β) →ₗ[𝕜] C(X, γ)) = g.compLeftContinuous 𝕜 X := by ext f;
rfl
#align continuous_linear_map.to_linear_comp_left_continuous_compact ContinuousLinearMap.toLinear_compLeftContinuousCompact
+-/
+#print ContinuousLinearMap.compLeftContinuousCompact_apply /-
@[simp]
theorem ContinuousLinearMap.compLeftContinuousCompact_apply (g : β →L[𝕜] γ) (f : C(X, β)) (x : X) :
g.compLeftContinuousCompact X f x = g (f x) :=
rfl
#align continuous_linear_map.comp_left_continuous_compact_apply ContinuousLinearMap.compLeftContinuousCompact_apply
+-/
end CompLeft
@@ -448,12 +534,14 @@ def compRightContinuousMap {X Y : Type _} (T : Type _) [TopologicalSpace X] [Com
#align continuous_map.comp_right_continuous_map ContinuousMap.compRightContinuousMap
-/
+#print ContinuousMap.compRightContinuousMap_apply /-
@[simp]
theorem compRightContinuousMap_apply {X Y : Type _} (T : Type _) [TopologicalSpace X]
[CompactSpace X] [TopologicalSpace Y] [CompactSpace Y] [MetricSpace T] (f : C(X, Y))
(g : C(Y, T)) : (compRightContinuousMap T f) g = g.comp f :=
rfl
#align continuous_map.comp_right_continuous_map_apply ContinuousMap.compRightContinuousMap_apply
+-/
#print ContinuousMap.compRightHomeomorph /-
/-- Precomposition by a homeomorphism is itself a homeomorphism between spaces of continuous maps.
@@ -468,12 +556,14 @@ def compRightHomeomorph {X Y : Type _} (T : Type _) [TopologicalSpace X] [Compac
#align continuous_map.comp_right_homeomorph ContinuousMap.compRightHomeomorph
-/
+#print ContinuousMap.compRightAlgHom_continuous /-
theorem compRightAlgHom_continuous {X Y : Type _} (R A : Type _) [TopologicalSpace X]
[CompactSpace X] [TopologicalSpace Y] [CompactSpace Y] [CommSemiring R] [Semiring A]
[MetricSpace A] [TopologicalSemiring A] [Algebra R A] (f : C(X, Y)) :
Continuous (compRightAlgHom R A f) :=
map_continuous (compRightContinuousMap A f)
#align continuous_map.comp_right_alg_hom_continuous ContinuousMap.compRightAlgHom_continuous
+-/
end CompRight
@@ -492,6 +582,7 @@ variable {X : Type _} [TopologicalSpace X] [T2Space X] [LocallyCompactSpace X]
variable {E : Type _} [NormedAddCommGroup E] [CompleteSpace E]
+#print ContinuousMap.summable_of_locally_summable_norm /-
theorem summable_of_locally_summable_norm {ι : Type _} {F : ι → C(X, E)}
(hF : ∀ K : Compacts X, Summable fun i => ‖(F i).restrict K‖) : Summable F :=
by
@@ -501,6 +592,7 @@ theorem summable_of_locally_summable_norm {ι : Type _} {F : ι → C(X, E)}
ext1 x; simp
simpa only [HasSum, A] using summable_of_summable_norm (hF K)
#align continuous_map.summable_of_locally_summable_norm ContinuousMap.summable_of_locally_summable_norm
+-/
end LocalNormalConvergence
@@ -519,10 +611,12 @@ variable {α : Type _} {β : Type _}
variable [TopologicalSpace α] [NormedAddCommGroup β] [StarAddMonoid β] [NormedStarGroup β]
+#print BoundedContinuousFunction.mkOfCompact_star /-
theorem BoundedContinuousFunction.mkOfCompact_star [CompactSpace α] (f : C(α, β)) :
mkOfCompact (star f) = star (mkOfCompact f) :=
rfl
#align bounded_continuous_function.mk_of_compact_star BoundedContinuousFunction.mkOfCompact_star
+-/
instance [CompactSpace α] : NormedStarGroup C(α, β)
where norm_star f := by
mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297
@@ -66,10 +66,10 @@ theorem uniformInducing_equivBoundedOfCompact : UniformInducing (equivBoundedOfC
simp only [has_basis_compact_convergence_uniformity.mem_iff, uniformity_basis_dist_le.mem_iff]
exact fun s =>
⟨fun ⟨⟨a, b⟩, ⟨ha, ⟨ε, hε, hb⟩⟩, hs⟩ =>
- ⟨{ p | ∀ x, (p.1 x, p.2 x) ∈ b }, ⟨ε, hε, fun _ h x => hb ((dist_le hε.le).mp h x)⟩,
+ ⟨{p | ∀ x, (p.1 x, p.2 x) ∈ b}, ⟨ε, hε, fun _ h x => hb ((dist_le hε.le).mp h x)⟩,
fun f g h => hs fun x hx => h x⟩,
fun ⟨t, ⟨ε, hε, ht⟩, hs⟩ =>
- ⟨⟨Set.univ, { p | dist p.1 p.2 ≤ ε }⟩, ⟨isCompact_univ, ⟨ε, hε, fun _ h => h⟩⟩,
+ ⟨⟨Set.univ, {p | dist p.1 p.2 ≤ ε}⟩, ⟨isCompact_univ, ⟨ε, hε, fun _ h => h⟩⟩,
fun ⟨f, g⟩ h => hs _ _ (ht ((dist_le hε.le).mpr fun x => h x (mem_univ x)))⟩⟩)
#align continuous_map.uniform_inducing_equiv_bounded_of_compact ContinuousMap.uniformInducing_equivBoundedOfCompact
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -443,7 +443,7 @@ def compRightContinuousMap {X Y : Type _} (T : Type _) [TopologicalSpace X] [Com
refine' metric.continuous_iff.mpr _
intro g ε ε_pos
refine' ⟨ε, ε_pos, fun g' h => _⟩
- rw [ContinuousMap.dist_lt_iff ε_pos] at h⊢
+ rw [ContinuousMap.dist_lt_iff ε_pos] at h ⊢
· exact fun x => h (f x)
#align continuous_map.comp_right_continuous_map ContinuousMap.compRightContinuousMap
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -34,7 +34,7 @@ you should restate it here. You can also use
noncomputable section
-open Topology Classical NNReal BoundedContinuousFunction BigOperators
+open scoped Topology Classical NNReal BoundedContinuousFunction BigOperators
open Set Filter Metric
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -60,12 +60,6 @@ def equivBoundedOfCompact : C(α, β) ≃ (α →ᵇ β) :=
#align continuous_map.equiv_bounded_of_compact ContinuousMap.equivBoundedOfCompact
-/
-/- warning: continuous_map.uniform_inducing_equiv_bounded_of_compact -> ContinuousMap.uniformInducing_equivBoundedOfCompact is a dubious translation:
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theorem uniformInducing_equivBoundedOfCompact : UniformInducing (equivBoundedOfCompact α β) :=
UniformInducing.mk'
(by
@@ -79,22 +73,10 @@ theorem uniformInducing_equivBoundedOfCompact : UniformInducing (equivBoundedOfC
fun ⟨f, g⟩ h => hs _ _ (ht ((dist_le hε.le).mpr fun x => h x (mem_univ x)))⟩⟩)
#align continuous_map.uniform_inducing_equiv_bounded_of_compact ContinuousMap.uniformInducing_equivBoundedOfCompact
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theorem uniformEmbedding_equivBoundedOfCompact : UniformEmbedding (equivBoundedOfCompact α β) :=
{ uniformInducing_equivBoundedOfCompact α β with inj := (equivBoundedOfCompact α β).Injective }
#align continuous_map.uniform_embedding_equiv_bounded_of_compact ContinuousMap.uniformEmbedding_equivBoundedOfCompact
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/-- When `α` is compact, the bounded continuous maps `α →ᵇ 𝕜` are
additively equivalent to `C(α, 𝕜)`.
-/
@@ -106,12 +88,6 @@ def addEquivBoundedOfCompact [AddMonoid β] [LipschitzAdd β] : C(α, β) ≃+ (
instance : MetricSpace C(α, β) :=
(uniformEmbedding_equivBoundedOfCompact α β).comapMetricSpace _
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/-- When `α` is compact, and `β` is a metric space, the bounded continuous maps `α →ᵇ β` are
isometric to `C(α, β)`.
-/
@@ -124,24 +100,12 @@ def isometryEquivBoundedOfCompact : C(α, β) ≃ᵢ (α →ᵇ β)
end
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@[simp]
theorem BoundedContinuousFunction.dist_mkOfCompact (f g : C(α, β)) :
dist (mkOfCompact f) (mkOfCompact g) = dist f g :=
rfl
#align bounded_continuous_function.dist_mk_of_compact BoundedContinuousFunction.dist_mkOfCompact
-/- warning: bounded_continuous_function.dist_to_continuous_map -> BoundedContinuousFunction.dist_toContinuousMap is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.dist_to_continuous_map BoundedContinuousFunction.dist_toContinuousMapₓ'. -/
@[simp]
theorem BoundedContinuousFunction.dist_toContinuousMap (f g : α →ᵇ β) :
dist f.toContinuousMap g.toContinuousMap = dist f g :=
@@ -154,64 +118,28 @@ section
variable {α β} {f g : C(α, β)} {C : ℝ}
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/-- The pointwise distance is controlled by the distance between functions, by definition. -/
theorem dist_apply_le_dist (x : α) : dist (f x) (g x) ≤ dist f g := by
simp only [← dist_mk_of_compact, dist_coe_le_dist, ← mk_of_compact_apply]
#align continuous_map.dist_apply_le_dist ContinuousMap.dist_apply_le_dist
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/-- The distance between two functions is controlled by the supremum of the pointwise distances -/
theorem dist_le (C0 : (0 : ℝ) ≤ C) : dist f g ≤ C ↔ ∀ x : α, dist (f x) (g x) ≤ C := by
simp only [← dist_mk_of_compact, dist_le C0, mk_of_compact_apply]
#align continuous_map.dist_le ContinuousMap.dist_le
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theorem dist_le_iff_of_nonempty [Nonempty α] : dist f g ≤ C ↔ ∀ x, dist (f x) (g x) ≤ C := by
simp only [← dist_mk_of_compact, dist_le_iff_of_nonempty, mk_of_compact_apply]
#align continuous_map.dist_le_iff_of_nonempty ContinuousMap.dist_le_iff_of_nonempty
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theorem dist_lt_iff_of_nonempty [Nonempty α] : dist f g < C ↔ ∀ x : α, dist (f x) (g x) < C := by
simp only [← dist_mk_of_compact, dist_lt_iff_of_nonempty_compact, mk_of_compact_apply]
#align continuous_map.dist_lt_iff_of_nonempty ContinuousMap.dist_lt_iff_of_nonempty
-/- warning: continuous_map.dist_lt_of_nonempty -> ContinuousMap.dist_lt_of_nonempty is a dubious translation:
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theorem dist_lt_of_nonempty [Nonempty α] (w : ∀ x : α, dist (f x) (g x) < C) : dist f g < C :=
dist_lt_iff_of_nonempty.2 w
#align continuous_map.dist_lt_of_nonempty ContinuousMap.dist_lt_of_nonempty
-/- warning: continuous_map.dist_lt_iff -> ContinuousMap.dist_lt_iff is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align continuous_map.dist_lt_iff ContinuousMap.dist_lt_iffₓ'. -/
theorem dist_lt_iff (C0 : (0 : ℝ) < C) : dist f g < C ↔ ∀ x : α, dist (f x) (g x) < C := by
simp only [← dist_mk_of_compact, dist_lt_iff_of_compact C0, mk_of_compact_apply]
#align continuous_map.dist_lt_iff ContinuousMap.dist_lt_iff
@@ -221,36 +149,18 @@ end
instance [CompleteSpace β] : CompleteSpace C(α, β) :=
(isometryEquivBoundedOfCompact α β).CompleteSpace
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/-- See also `continuous_map.continuous_eval'` -/
@[continuity]
theorem continuous_eval : Continuous fun p : C(α, β) × α => p.1 p.2 :=
continuous_eval.comp ((isometryEquivBoundedOfCompact α β).Continuous.Prod_map continuous_id)
#align continuous_map.continuous_eval ContinuousMap.continuous_eval
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-Case conversion may be inaccurate. Consider using '#align continuous_map.continuous_eval_const ContinuousMap.continuous_eval_constₓ'. -/
/-- See also `continuous_map.continuous_eval_const` -/
@[continuity]
theorem continuous_eval_const (x : α) : Continuous fun f : C(α, β) => f x :=
continuous_eval.comp (continuous_id.prod_mk continuous_const)
#align continuous_map.continuous_eval_const ContinuousMap.continuous_eval_const
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-Case conversion may be inaccurate. Consider using '#align continuous_map.continuous_coe ContinuousMap.continuous_coeₓ'. -/
/-- See also `continuous_map.continuous_coe'` -/
theorem continuous_coe : @Continuous C(α, β) (α → β) _ _ coeFn :=
continuous_pi continuous_eval_const
@@ -260,23 +170,11 @@ theorem continuous_coe : @Continuous C(α, β) (α → β) _ _ coeFn :=
-- At the moment the only way to reason about it is to transfer `f : C(α,E)` back to `α →ᵇ E`.
instance : Norm C(α, E) where norm x := dist x 0
-/- warning: bounded_continuous_function.norm_mk_of_compact -> BoundedContinuousFunction.norm_mkOfCompact is a dubious translation:
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@[simp]
theorem BoundedContinuousFunction.norm_mkOfCompact (f : C(α, E)) : ‖mkOfCompact f‖ = ‖f‖ :=
rfl
#align bounded_continuous_function.norm_mk_of_compact BoundedContinuousFunction.norm_mkOfCompact
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@[simp]
theorem BoundedContinuousFunction.norm_toContinuousMap_eq (f : α →ᵇ E) :
‖f.toContinuousMap‖ = ‖f‖ :=
@@ -300,123 +198,54 @@ section
variable (f : C(α, E))
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-- The corresponding lemmas for `bounded_continuous_function` are stated with `{f}`,
-- and so can not be used in dot notation.
theorem norm_coe_le_norm (x : α) : ‖f x‖ ≤ ‖f‖ :=
(mkOfCompact f).norm_coe_le_norm x
#align continuous_map.norm_coe_le_norm ContinuousMap.norm_coe_le_norm
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/-- Distance between the images of any two points is at most twice the norm of the function. -/
theorem dist_le_two_norm (x y : α) : dist (f x) (f y) ≤ 2 * ‖f‖ :=
(mkOfCompact f).dist_le_two_norm x y
#align continuous_map.dist_le_two_norm ContinuousMap.dist_le_two_norm
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/-- The norm of a function is controlled by the supremum of the pointwise norms -/
theorem norm_le {C : ℝ} (C0 : (0 : ℝ) ≤ C) : ‖f‖ ≤ C ↔ ∀ x : α, ‖f x‖ ≤ C :=
@BoundedContinuousFunction.norm_le _ _ _ _ (mkOfCompact f) _ C0
#align continuous_map.norm_le ContinuousMap.norm_le
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theorem norm_le_of_nonempty [Nonempty α] {M : ℝ} : ‖f‖ ≤ M ↔ ∀ x, ‖f x‖ ≤ M :=
@BoundedContinuousFunction.norm_le_of_nonempty _ _ _ _ _ (mkOfCompact f) _
#align continuous_map.norm_le_of_nonempty ContinuousMap.norm_le_of_nonempty
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theorem norm_lt_iff {M : ℝ} (M0 : 0 < M) : ‖f‖ < M ↔ ∀ x, ‖f x‖ < M :=
@BoundedContinuousFunction.norm_lt_iff_of_compact _ _ _ _ _ (mkOfCompact f) _ M0
#align continuous_map.norm_lt_iff ContinuousMap.norm_lt_iff
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-Case conversion may be inaccurate. Consider using '#align continuous_map.nnnorm_lt_iff ContinuousMap.nnnorm_lt_iffₓ'. -/
theorem nnnorm_lt_iff {M : ℝ≥0} (M0 : 0 < M) : ‖f‖₊ < M ↔ ∀ x : α, ‖f x‖₊ < M :=
f.norm_lt_iff M0
#align continuous_map.nnnorm_lt_iff ContinuousMap.nnnorm_lt_iff
-/- warning: continuous_map.norm_lt_iff_of_nonempty -> ContinuousMap.norm_lt_iff_of_nonempty is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align continuous_map.norm_lt_iff_of_nonempty ContinuousMap.norm_lt_iff_of_nonemptyₓ'. -/
theorem norm_lt_iff_of_nonempty [Nonempty α] {M : ℝ} : ‖f‖ < M ↔ ∀ x, ‖f x‖ < M :=
@BoundedContinuousFunction.norm_lt_iff_of_nonempty_compact _ _ _ _ _ _ (mkOfCompact f) _
#align continuous_map.norm_lt_iff_of_nonempty ContinuousMap.norm_lt_iff_of_nonempty
-/- warning: continuous_map.nnnorm_lt_iff_of_nonempty -> ContinuousMap.nnnorm_lt_iff_of_nonempty is a dubious translation:
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theorem nnnorm_lt_iff_of_nonempty [Nonempty α] {M : ℝ≥0} : ‖f‖₊ < M ↔ ∀ x, ‖f x‖₊ < M :=
f.norm_lt_iff_of_nonempty
#align continuous_map.nnnorm_lt_iff_of_nonempty ContinuousMap.nnnorm_lt_iff_of_nonempty
-/- warning: continuous_map.apply_le_norm -> ContinuousMap.apply_le_norm is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align continuous_map.apply_le_norm ContinuousMap.apply_le_normₓ'. -/
theorem apply_le_norm (f : C(α, ℝ)) (x : α) : f x ≤ ‖f‖ :=
le_trans (le_abs.mpr (Or.inl (le_refl (f x)))) (f.norm_coe_le_norm x)
#align continuous_map.apply_le_norm ContinuousMap.apply_le_norm
-/- warning: continuous_map.neg_norm_le_apply -> ContinuousMap.neg_norm_le_apply is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align continuous_map.neg_norm_le_apply ContinuousMap.neg_norm_le_applyₓ'. -/
theorem neg_norm_le_apply (f : C(α, ℝ)) (x : α) : -‖f‖ ≤ f x :=
le_trans (neg_le_neg (f.norm_coe_le_norm x)) (neg_le.mp (neg_le_abs_self (f x)))
#align continuous_map.neg_norm_le_apply ContinuousMap.neg_norm_le_apply
-/- warning: continuous_map.norm_eq_supr_norm -> ContinuousMap.norm_eq_iSup_norm is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align continuous_map.norm_eq_supr_norm ContinuousMap.norm_eq_iSup_normₓ'. -/
theorem norm_eq_iSup_norm : ‖f‖ = ⨆ x : α, ‖f x‖ :=
(mkOfCompact f).norm_eq_iSup_norm
#align continuous_map.norm_eq_supr_norm ContinuousMap.norm_eq_iSup_norm
-/- warning: continuous_map.norm_restrict_mono_set -> ContinuousMap.norm_restrict_mono_set is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_map.norm_restrict_mono_set ContinuousMap.norm_restrict_mono_setₓ'. -/
theorem norm_restrict_mono_set {X : Type _} [TopologicalSpace X] (f : C(X, E))
{K L : TopologicalSpace.Compacts X} (hKL : K ≤ L) : ‖f.restrict K‖ ≤ ‖f.restrict L‖ :=
(norm_le _ (norm_nonneg _)).mpr fun x => norm_coe_le_norm (f.restrict L) <| Set.inclusion hKL x
@@ -444,9 +273,6 @@ section
variable (α 𝕜 E)
-/- warning: continuous_map.linear_isometry_bounded_of_compact -> ContinuousMap.linearIsometryBoundedOfCompact is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_map.linear_isometry_bounded_of_compact ContinuousMap.linearIsometryBoundedOfCompactₓ'. -/
/-- When `α` is compact and `𝕜` is a normed field,
the `𝕜`-algebra of bounded continuous maps `α →ᵇ β` is
`𝕜`-linearly isometric to `C(α, β)`.
@@ -461,9 +287,6 @@ def linearIsometryBoundedOfCompact : C(α, E) ≃ₗᵢ[𝕜] α →ᵇ E :=
variable {α E}
-/- warning: continuous_map.eval_clm -> ContinuousMap.evalClm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_map.eval_clm ContinuousMap.evalClmₓ'. -/
-- to match bounded_continuous_function.eval_clm
/-- The evaluation at a point, as a continuous linear map from `C(α, 𝕜)` to `𝕜`. -/
def evalClm (x : α) : C(α, E) →L[𝕜] E :=
@@ -472,9 +295,6 @@ def evalClm (x : α) : C(α, E) →L[𝕜] E :=
end
-/- warning: continuous_map.linear_isometry_bounded_of_compact_symm_apply -> ContinuousMap.linearIsometryBoundedOfCompact_symm_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_map.linear_isometry_bounded_of_compact_symm_apply ContinuousMap.linearIsometryBoundedOfCompact_symm_applyₓ'. -/
-- this lemma and the next are the analogues of those autogenerated by `@[simps]` for
-- `equiv_bounded_of_compact`, `add_equiv_bounded_of_compact`
@[simp]
@@ -483,27 +303,18 @@ theorem linearIsometryBoundedOfCompact_symm_apply (f : α →ᵇ E) :
rfl
#align continuous_map.linear_isometry_bounded_of_compact_symm_apply ContinuousMap.linearIsometryBoundedOfCompact_symm_apply
-/- warning: continuous_map.linear_isometry_bounded_of_compact_apply_apply -> ContinuousMap.linearIsometryBoundedOfCompact_apply_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_map.linear_isometry_bounded_of_compact_apply_apply ContinuousMap.linearIsometryBoundedOfCompact_apply_applyₓ'. -/
@[simp]
theorem linearIsometryBoundedOfCompact_apply_apply (f : C(α, E)) (a : α) :
(linearIsometryBoundedOfCompact α E 𝕜 f) a = f a :=
rfl
#align continuous_map.linear_isometry_bounded_of_compact_apply_apply ContinuousMap.linearIsometryBoundedOfCompact_apply_apply
-/- warning: continuous_map.linear_isometry_bounded_of_compact_to_isometry_equiv -> ContinuousMap.linearIsometryBoundedOfCompact_toIsometryEquiv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_map.linear_isometry_bounded_of_compact_to_isometry_equiv ContinuousMap.linearIsometryBoundedOfCompact_toIsometryEquivₓ'. -/
@[simp]
theorem linearIsometryBoundedOfCompact_toIsometryEquiv :
(linearIsometryBoundedOfCompact α E 𝕜).toIsometryEquiv = isometryEquivBoundedOfCompact α E :=
rfl
#align continuous_map.linear_isometry_bounded_of_compact_to_isometry_equiv ContinuousMap.linearIsometryBoundedOfCompact_toIsometryEquiv
-/- warning: continuous_map.linear_isometry_bounded_of_compact_to_add_equiv -> ContinuousMap.linearIsometryBoundedOfCompact_toAddEquiv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_map.linear_isometry_bounded_of_compact_to_add_equiv ContinuousMap.linearIsometryBoundedOfCompact_toAddEquivₓ'. -/
@[simp]
theorem linearIsometryBoundedOfCompact_toAddEquiv :
(linearIsometryBoundedOfCompact α E 𝕜).toLinearEquiv.toAddEquiv =
@@ -511,9 +322,6 @@ theorem linearIsometryBoundedOfCompact_toAddEquiv :
rfl
#align continuous_map.linear_isometry_bounded_of_compact_to_add_equiv ContinuousMap.linearIsometryBoundedOfCompact_toAddEquiv
-/- warning: continuous_map.linear_isometry_bounded_of_compact_of_compact_to_equiv -> ContinuousMap.linearIsometryBoundedOfCompact_of_compact_toEquiv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_map.linear_isometry_bounded_of_compact_of_compact_to_equiv ContinuousMap.linearIsometryBoundedOfCompact_of_compact_toEquivₓ'. -/
@[simp]
theorem linearIsometryBoundedOfCompact_of_compact_toEquiv :
(linearIsometryBoundedOfCompact α E 𝕜).toLinearEquiv.toEquiv = equivBoundedOfCompact α E :=
@@ -546,20 +354,11 @@ We now set up some declarations making it convenient to use uniform continuity.
-/
-/- warning: continuous_map.uniform_continuity -> ContinuousMap.uniform_continuity is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_map.uniform_continuity ContinuousMap.uniform_continuityₓ'. -/
theorem uniform_continuity (f : C(α, β)) (ε : ℝ) (h : 0 < ε) :
∃ δ > 0, ∀ {x y}, dist x y < δ → dist (f x) (f y) < ε :=
Metric.uniformContinuous_iff.mp (CompactSpace.uniformContinuous_of_continuous f.Continuous) ε h
#align continuous_map.uniform_continuity ContinuousMap.uniform_continuity
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-Case conversion may be inaccurate. Consider using '#align continuous_map.modulus ContinuousMap.modulusₓ'. -/
-- This definition allows us to separate the choice of some `δ`,
-- and the corresponding use of `dist a b < δ → dist (f a) (f b) < ε`,
-- even across different declarations.
@@ -569,22 +368,10 @@ def modulus (f : C(α, β)) (ε : ℝ) (h : 0 < ε) : ℝ :=
Classical.choose (uniform_continuity f ε h)
#align continuous_map.modulus ContinuousMap.modulus
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-Case conversion may be inaccurate. Consider using '#align continuous_map.modulus_pos ContinuousMap.modulus_posₓ'. -/
theorem modulus_pos (f : C(α, β)) {ε : ℝ} {h : 0 < ε} : 0 < f.modulus ε h :=
(Classical.choose_spec (uniform_continuity f ε h)).fst
#align continuous_map.modulus_pos ContinuousMap.modulus_pos
-/- warning: continuous_map.dist_lt_of_dist_lt_modulus -> ContinuousMap.dist_lt_of_dist_lt_modulus is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align continuous_map.dist_lt_of_dist_lt_modulus ContinuousMap.dist_lt_of_dist_lt_modulusₓ'. -/
theorem dist_lt_of_dist_lt_modulus (f : C(α, β)) (ε : ℝ) (h : 0 < ε) {a b : α}
(w : dist a b < f.modulus ε h) : dist (f a) (f b) < ε :=
(Classical.choose_spec (uniform_continuity f ε h)).snd w
@@ -603,9 +390,6 @@ variable [NormedAddCommGroup β] [NormedSpace 𝕜 β] [NormedAddCommGroup γ] [
open ContinuousMap
-/- warning: continuous_linear_map.comp_left_continuous_compact -> ContinuousLinearMap.compLeftContinuousCompact is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_left_continuous_compact ContinuousLinearMap.compLeftContinuousCompactₓ'. -/
/-- Postcomposition of continuous functions into a normed module by a continuous linear map is a
continuous linear map.
Transferred version of `continuous_linear_map.comp_left_continuous_bounded`,
@@ -618,18 +402,12 @@ protected def ContinuousLinearMap.compLeftContinuousCompact (g : β →L[𝕜]
(linearIsometryBoundedOfCompact X β 𝕜).toLinearIsometry.toContinuousLinearMap
#align continuous_linear_map.comp_left_continuous_compact ContinuousLinearMap.compLeftContinuousCompact
-/- warning: continuous_linear_map.to_linear_comp_left_continuous_compact -> ContinuousLinearMap.toLinear_compLeftContinuousCompact is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.to_linear_comp_left_continuous_compact ContinuousLinearMap.toLinear_compLeftContinuousCompactₓ'. -/
@[simp]
theorem ContinuousLinearMap.toLinear_compLeftContinuousCompact (g : β →L[𝕜] γ) :
(g.compLeftContinuousCompact X : C(X, β) →ₗ[𝕜] C(X, γ)) = g.compLeftContinuous 𝕜 X := by ext f;
rfl
#align continuous_linear_map.to_linear_comp_left_continuous_compact ContinuousLinearMap.toLinear_compLeftContinuousCompact
-/- warning: continuous_linear_map.comp_left_continuous_compact_apply -> ContinuousLinearMap.compLeftContinuousCompact_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_left_continuous_compact_apply ContinuousLinearMap.compLeftContinuousCompact_applyₓ'. -/
@[simp]
theorem ContinuousLinearMap.compLeftContinuousCompact_apply (g : β →L[𝕜] γ) (f : C(X, β)) (x : X) :
g.compLeftContinuousCompact X f x = g (f x) :=
@@ -670,12 +448,6 @@ def compRightContinuousMap {X Y : Type _} (T : Type _) [TopologicalSpace X] [Com
#align continuous_map.comp_right_continuous_map ContinuousMap.compRightContinuousMap
-/
-/- warning: continuous_map.comp_right_continuous_map_apply -> ContinuousMap.compRightContinuousMap_apply is a dubious translation:
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(PseudoMetricSpace.toUniformSpace.{u1} T (MetricSpace.toPseudoMetricSpace.{u1} T _inst_5)))) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : ContinuousMap.{u2, u1} Y T _inst_3 (UniformSpace.toTopologicalSpace.{u1} T (PseudoMetricSpace.toUniformSpace.{u1} T (MetricSpace.toPseudoMetricSpace.{u1} T _inst_5)))) => ContinuousMap.{u3, u1} X T _inst_1 (UniformSpace.toTopologicalSpace.{u1} T (PseudoMetricSpace.toUniformSpace.{u1} T (MetricSpace.toPseudoMetricSpace.{u1} T _inst_5)))) _x) (ContinuousMapClass.toFunLike.{max (max u3 u2) u1, max u2 u1, max u3 u1} (ContinuousMap.{max u1 u2, max u1 u3} (ContinuousMap.{u2, u1} Y T _inst_3 (UniformSpace.toTopologicalSpace.{u1} T (PseudoMetricSpace.toUniformSpace.{u1} T (MetricSpace.toPseudoMetricSpace.{u1} T _inst_5)))) (ContinuousMap.{u3, u1} X T _inst_1 (UniformSpace.toTopologicalSpace.{u1} T (PseudoMetricSpace.toUniformSpace.{u1} T (MetricSpace.toPseudoMetricSpace.{u1} T _inst_5)))) (ContinuousMap.compactOpen.{u2, u1} Y T _inst_3 (UniformSpace.toTopologicalSpace.{u1} T (PseudoMetricSpace.toUniformSpace.{u1} T (MetricSpace.toPseudoMetricSpace.{u1} T _inst_5)))) (ContinuousMap.compactOpen.{u3, u1} X T _inst_1 (UniformSpace.toTopologicalSpace.{u1} T (PseudoMetricSpace.toUniformSpace.{u1} T (MetricSpace.toPseudoMetricSpace.{u1} T _inst_5))))) (ContinuousMap.{u2, u1} Y T _inst_3 (UniformSpace.toTopologicalSpace.{u1} T (PseudoMetricSpace.toUniformSpace.{u1} T (MetricSpace.toPseudoMetricSpace.{u1} T _inst_5)))) (ContinuousMap.{u3, u1} X T _inst_1 (UniformSpace.toTopologicalSpace.{u1} T (PseudoMetricSpace.toUniformSpace.{u1} T (MetricSpace.toPseudoMetricSpace.{u1} T _inst_5)))) (ContinuousMap.compactOpen.{u2, u1} Y T _inst_3 (UniformSpace.toTopologicalSpace.{u1} T (PseudoMetricSpace.toUniformSpace.{u1} T (MetricSpace.toPseudoMetricSpace.{u1} T _inst_5)))) (ContinuousMap.compactOpen.{u3, u1} X T _inst_1 (UniformSpace.toTopologicalSpace.{u1} T (PseudoMetricSpace.toUniformSpace.{u1} T (MetricSpace.toPseudoMetricSpace.{u1} T _inst_5)))) (ContinuousMap.instContinuousMapClassContinuousMap.{max u2 u1, max u3 u1} (ContinuousMap.{u2, u1} Y T _inst_3 (UniformSpace.toTopologicalSpace.{u1} T (PseudoMetricSpace.toUniformSpace.{u1} T (MetricSpace.toPseudoMetricSpace.{u1} T _inst_5)))) (ContinuousMap.{u3, u1} X T _inst_1 (UniformSpace.toTopologicalSpace.{u1} T (PseudoMetricSpace.toUniformSpace.{u1} T (MetricSpace.toPseudoMetricSpace.{u1} T _inst_5)))) (ContinuousMap.compactOpen.{u2, u1} Y T _inst_3 (UniformSpace.toTopologicalSpace.{u1} T (PseudoMetricSpace.toUniformSpace.{u1} T (MetricSpace.toPseudoMetricSpace.{u1} T _inst_5)))) (ContinuousMap.compactOpen.{u3, u1} X T _inst_1 (UniformSpace.toTopologicalSpace.{u1} T (PseudoMetricSpace.toUniformSpace.{u1} T (MetricSpace.toPseudoMetricSpace.{u1} T _inst_5)))))) (ContinuousMap.compRightContinuousMap.{u3, u2, u1} X Y T _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f) g) (ContinuousMap.comp.{u3, u2, u1} X Y T _inst_1 _inst_3 (UniformSpace.toTopologicalSpace.{u1} T (PseudoMetricSpace.toUniformSpace.{u1} T (MetricSpace.toPseudoMetricSpace.{u1} T _inst_5))) g f)
-Case conversion may be inaccurate. Consider using '#align continuous_map.comp_right_continuous_map_apply ContinuousMap.compRightContinuousMap_applyₓ'. -/
@[simp]
theorem compRightContinuousMap_apply {X Y : Type _} (T : Type _) [TopologicalSpace X]
[CompactSpace X] [TopologicalSpace Y] [CompactSpace Y] [MetricSpace T] (f : C(X, Y))
@@ -696,9 +468,6 @@ def compRightHomeomorph {X Y : Type _} (T : Type _) [TopologicalSpace X] [Compac
#align continuous_map.comp_right_homeomorph ContinuousMap.compRightHomeomorph
-/
-/- warning: continuous_map.comp_right_alg_hom_continuous -> ContinuousMap.compRightAlgHom_continuous is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_map.comp_right_alg_hom_continuous ContinuousMap.compRightAlgHom_continuousₓ'. -/
theorem compRightAlgHom_continuous {X Y : Type _} (R A : Type _) [TopologicalSpace X]
[CompactSpace X] [TopologicalSpace Y] [CompactSpace Y] [CommSemiring R] [Semiring A]
[MetricSpace A] [TopologicalSemiring A] [Algebra R A] (f : C(X, Y)) :
@@ -723,9 +492,6 @@ variable {X : Type _} [TopologicalSpace X] [T2Space X] [LocallyCompactSpace X]
variable {E : Type _} [NormedAddCommGroup E] [CompleteSpace E]
-/- warning: continuous_map.summable_of_locally_summable_norm -> ContinuousMap.summable_of_locally_summable_norm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_map.summable_of_locally_summable_norm ContinuousMap.summable_of_locally_summable_normₓ'. -/
theorem summable_of_locally_summable_norm {ι : Type _} {F : ι → C(X, E)}
(hF : ∀ K : Compacts X, Summable fun i => ‖(F i).restrict K‖) : Summable F :=
by
@@ -753,12 +519,6 @@ variable {α : Type _} {β : Type _}
variable [TopologicalSpace α] [NormedAddCommGroup β] [StarAddMonoid β] [NormedStarGroup β]
-/- warning: bounded_continuous_function.mk_of_compact_star -> BoundedContinuousFunction.mkOfCompact_star is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : NormedAddCommGroup.{u2} β] [_inst_3 : StarAddMonoid.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (NormedAddGroup.toAddGroup.{u2} β (NormedAddCommGroup.toNormedAddGroup.{u2} β _inst_2))))] [_inst_4 : NormedStarGroup.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β _inst_2) _inst_3] [_inst_5 : CompactSpace.{u1} α _inst_1] (f : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β _inst_2))))), Eq.{succ (max u1 u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β _inst_2))) (BoundedContinuousFunction.mkOfCompact.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β _inst_2)) _inst_5 (Star.star.{max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β _inst_2))))) (ContinuousMap.hasStar.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β _inst_2)))) (InvolutiveStar.toHasStar.{u2} β (StarAddMonoid.toHasInvolutiveStar.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β _inst_2))))) _inst_3)) (NormedStarGroup.to_continuousStar.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β _inst_2) _inst_3 _inst_4)) f)) (Star.star.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β _inst_2))) (InvolutiveStar.toHasStar.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β _inst_2))) (StarAddMonoid.toHasInvolutiveStar.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β _inst_2))) (BoundedContinuousFunction.addMonoid.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β _inst_2)) (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β _inst_2))))) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β _inst_2))) (BoundedContinuousFunction.starAddMonoid.{u1, u2} α β _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β _inst_2) _inst_3 _inst_4))) (BoundedContinuousFunction.mkOfCompact.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β _inst_2)) _inst_5 f))
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- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : NormedAddCommGroup.{u1} β] [_inst_3 : StarAddMonoid.{u1} β (SubNegMonoid.toAddMonoid.{u1} β (AddGroup.toSubNegMonoid.{u1} β (NormedAddGroup.toAddGroup.{u1} β (NormedAddCommGroup.toNormedAddGroup.{u1} β _inst_2))))] [_inst_4 : NormedStarGroup.{u1} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} β _inst_2) _inst_3] [_inst_5 : CompactSpace.{u2} α _inst_1] (f : ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} β _inst_2))))), Eq.{max (succ u2) (succ u1)} (BoundedContinuousFunction.{u2, u1} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} β _inst_2))) (BoundedContinuousFunction.mkOfCompact.{u2, u1} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} β _inst_2)) _inst_5 (Star.star.{max u1 u2} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} β _inst_2))))) (ContinuousMap.instStarContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} β _inst_2)))) (InvolutiveStar.toStar.{u1} β (StarAddMonoid.toInvolutiveStar.{u1} β (SubNegMonoid.toAddMonoid.{u1} β (AddGroup.toSubNegMonoid.{u1} β (NormedAddGroup.toAddGroup.{u1} β (NormedAddCommGroup.toNormedAddGroup.{u1} β _inst_2)))) _inst_3)) (NormedStarGroup.to_continuousStar.{u1} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} β _inst_2) _inst_3 _inst_4)) f)) (Star.star.{max u1 u2} (BoundedContinuousFunction.{u2, u1} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} β _inst_2))) (InvolutiveStar.toStar.{max u2 u1} (BoundedContinuousFunction.{u2, u1} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} β _inst_2))) (StarAddMonoid.toInvolutiveStar.{max u2 u1} (BoundedContinuousFunction.{u2, u1} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} β _inst_2))) (BoundedContinuousFunction.addMonoid.{u2, u1} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} β _inst_2)) (SubNegMonoid.toAddMonoid.{u1} β (AddGroup.toSubNegMonoid.{u1} β (NormedAddGroup.toAddGroup.{u1} β (NormedAddCommGroup.toNormedAddGroup.{u1} β _inst_2)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u1} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} β _inst_2))) (BoundedContinuousFunction.starAddMonoid.{u2, u1} α β _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} β _inst_2) _inst_3 _inst_4))) (BoundedContinuousFunction.mkOfCompact.{u2, u1} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} β _inst_2)) _inst_5 f))
-Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.mk_of_compact_star BoundedContinuousFunction.mkOfCompact_starₓ'. -/
theorem BoundedContinuousFunction.mkOfCompact_star [CompactSpace α] (f : C(α, β)) :
mkOfCompact (star f) = star (mkOfCompact f) :=
rfl
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -55,11 +55,7 @@ equivalent to `C(α, β)`.
-/
@[simps (config := { fullyApplied := false })]
def equivBoundedOfCompact : C(α, β) ≃ (α →ᵇ β) :=
- ⟨mkOfCompact, BoundedContinuousFunction.toContinuousMap, fun f =>
- by
- ext
- rfl, fun f => by
- ext
+ ⟨mkOfCompact, BoundedContinuousFunction.toContinuousMap, fun f => by ext; rfl, fun f => by ext;
rfl⟩
#align continuous_map.equiv_bounded_of_compact ContinuousMap.equivBoundedOfCompact
-/
@@ -459,9 +455,7 @@ def linearIsometryBoundedOfCompact : C(α, E) ≃ₗᵢ[𝕜] α →ᵇ E :=
{
addEquivBoundedOfCompact α
E with
- map_smul' := fun c f => by
- ext
- simp
+ map_smul' := fun c f => by ext; simp
norm_map' := fun f => rfl }
#align continuous_map.linear_isometry_bounded_of_compact ContinuousMap.linearIsometryBoundedOfCompact
@@ -629,9 +623,7 @@ protected def ContinuousLinearMap.compLeftContinuousCompact (g : β →L[𝕜]
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.to_linear_comp_left_continuous_compact ContinuousLinearMap.toLinear_compLeftContinuousCompactₓ'. -/
@[simp]
theorem ContinuousLinearMap.toLinear_compLeftContinuousCompact (g : β →L[𝕜] γ) :
- (g.compLeftContinuousCompact X : C(X, β) →ₗ[𝕜] C(X, γ)) = g.compLeftContinuous 𝕜 X :=
- by
- ext f
+ (g.compLeftContinuousCompact X : C(X, β) →ₗ[𝕜] C(X, γ)) = g.compLeftContinuous 𝕜 X := by ext f;
rfl
#align continuous_linear_map.to_linear_comp_left_continuous_compact ContinuousLinearMap.toLinear_compLeftContinuousCompact
@@ -739,11 +731,8 @@ theorem summable_of_locally_summable_norm {ι : Type _} {F : ι → C(X, E)}
by
refine' (ContinuousMap.exists_tendsto_compactOpen_iff_forall _).2 fun K hK => _
lift K to compacts X using hK
- have A : ∀ s : Finset ι, restrict (↑K) (∑ i in s, F i) = ∑ i in s, restrict K (F i) :=
- by
- intro s
- ext1 x
- simp
+ have A : ∀ s : Finset ι, restrict (↑K) (∑ i in s, F i) = ∑ i in s, restrict K (F i) := by intro s;
+ ext1 x; simp
simpa only [HasSum, A] using summable_of_summable_norm (hF K)
#align continuous_map.summable_of_locally_summable_norm ContinuousMap.summable_of_locally_summable_norm
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
! This file was ported from Lean 3 source module topology.continuous_function.compact
-! leanprover-community/mathlib commit d3af0609f6db8691dffdc3e1fb7feb7da72698f2
+! leanprover-community/mathlib commit 0b7c740e25651db0ba63648fbae9f9d6f941e31b
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -16,6 +16,9 @@ import Mathbin.Topology.Sets.Compacts
/-!
# Continuous functions on a compact space
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
Continuous functions `C(α, β)` from a compact space `α` to a metric space `β`
are automatically bounded, and so acquire various structures inherited from `α →ᵇ β`.
@@ -416,10 +419,7 @@ theorem norm_eq_iSup_norm : ‖f‖ = ⨆ x : α, ‖f x‖ :=
#align continuous_map.norm_eq_supr_norm ContinuousMap.norm_eq_iSup_norm
/- warning: continuous_map.norm_restrict_mono_set -> ContinuousMap.norm_restrict_mono_set is a dubious translation:
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HasLiftT.{succ u2, succ u2} a b] => self.0) (TopologicalSpace.Compacts.{u2} X _inst_5) (Set.{u2} X) (HasLiftT.mk.{succ u2, succ u2} (TopologicalSpace.Compacts.{u2} X _inst_5) (Set.{u2} X) (CoeTCₓ.coe.{succ u2, succ u2} (TopologicalSpace.Compacts.{u2} X _inst_5) (Set.{u2} X) (SetLike.Set.hasCoeT.{u2, u2} (TopologicalSpace.Compacts.{u2} X _inst_5) X (TopologicalSpace.Compacts.setLike.{u2} X _inst_5)))) L) f)))
-but is expected to have type
- forall {E : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} E] {X : Type.{u2}} [_inst_5 : TopologicalSpace.{u2} X] (f : ContinuousMap.{u2, u1} X E _inst_5 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) {K : TopologicalSpace.Compacts.{u2} X _inst_5} {L : TopologicalSpace.Compacts.{u2} X _inst_5}, (LE.le.{u2} (TopologicalSpace.Compacts.{u2} X _inst_5) (Preorder.toLE.{u2} (TopologicalSpace.Compacts.{u2} X _inst_5) (PartialOrder.toPreorder.{u2} (TopologicalSpace.Compacts.{u2} X _inst_5) (SemilatticeSup.toPartialOrder.{u2} (TopologicalSpace.Compacts.{u2} X _inst_5) (TopologicalSpace.Compacts.instSemilatticeSupCompacts.{u2} X _inst_5)))) K L) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{max u1 u2} (ContinuousMap.{u2, u1} (Set.Elem.{u2} X (SetLike.coe.{u2, u2} (TopologicalSpace.Compacts.{u2} X _inst_5) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u2} X _inst_5) K)) E (instTopologicalSpaceSubtype.{u2} X (fun (x : X) => Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) x (SetLike.coe.{u2, u2} (TopologicalSpace.Compacts.{u2} X _inst_5) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u2} X _inst_5) K)) _inst_5) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) (ContinuousMap.instNormContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u2, u1} (Set.Elem.{u2} X (SetLike.coe.{u2, u2} (TopologicalSpace.Compacts.{u2} X _inst_5) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u2} X _inst_5) K)) E (instTopologicalSpaceSubtype.{u2} X (fun (x : X) => Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) x (SetLike.coe.{u2, u2} (TopologicalSpace.Compacts.{u2} X _inst_5) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u2} X _inst_5) K)) _inst_5) (TopologicalSpace.Compacts.instCompactSpaceSubtypeMemCompactsInstMembershipInstSetLikeCompactsInstTopologicalSpaceSubtype.{u2} X _inst_5 K) _inst_4) (ContinuousMap.restrict.{u2, u1} X E _inst_5 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4)))) (SetLike.coe.{u2, u2} (TopologicalSpace.Compacts.{u2} X _inst_5) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u2} X _inst_5) K) f)) (Norm.norm.{max u1 u2} (ContinuousMap.{u2, u1} (Set.Elem.{u2} X (SetLike.coe.{u2, u2} (TopologicalSpace.Compacts.{u2} X _inst_5) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u2} X _inst_5) L)) E (instTopologicalSpaceSubtype.{u2} X (fun (x : X) => Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) x (SetLike.coe.{u2, u2} (TopologicalSpace.Compacts.{u2} X _inst_5) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u2} X _inst_5) L)) _inst_5) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) (ContinuousMap.instNormContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u2, u1} (Set.Elem.{u2} X (SetLike.coe.{u2, u2} (TopologicalSpace.Compacts.{u2} X _inst_5) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u2} X _inst_5) L)) E (instTopologicalSpaceSubtype.{u2} X (fun (x : X) => Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) x (SetLike.coe.{u2, u2} (TopologicalSpace.Compacts.{u2} X _inst_5) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u2} X _inst_5) L)) _inst_5) (TopologicalSpace.Compacts.instCompactSpaceSubtypeMemCompactsInstMembershipInstSetLikeCompactsInstTopologicalSpaceSubtype.{u2} X _inst_5 L) _inst_4) (ContinuousMap.restrict.{u2, u1} X E _inst_5 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4)))) (SetLike.coe.{u2, u2} (TopologicalSpace.Compacts.{u2} X _inst_5) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u2} X _inst_5) L) f)))
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_map.norm_restrict_mono_set ContinuousMap.norm_restrict_mono_setₓ'. -/
theorem norm_restrict_mono_set {X : Type _} [TopologicalSpace X] (f : C(X, E))
{K L : TopologicalSpace.Compacts X} (hKL : K ≤ L) : ‖f.restrict K‖ ≤ ‖f.restrict L‖ :=
@@ -449,10 +449,7 @@ section
variable (α 𝕜 E)
/- warning: continuous_map.linear_isometry_bounded_of_compact -> ContinuousMap.linearIsometryBoundedOfCompact is a dubious translation:
-lean 3 declaration is
- forall (α : Type.{u1}) (E : Type.{u2}) [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_4 : NormedAddCommGroup.{u2} E] (𝕜 : Type.{u3}) [_inst_5 : NormedField.{u3} 𝕜] [_inst_6 : NormedSpace.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)], LinearIsometryEquiv.{u3, u3, max u1 u2, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))))) (ContinuousMap.linearIsometryBoundedOfCompact._proof_1.{u3} 𝕜 _inst_5) (ContinuousMap.linearIsometryBoundedOfCompact._proof_2.{u3} 𝕜 _inst_5) (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.normedAddCommGroup.{u1, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.seminormedAddCommGroup.{u1, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (ContinuousMap.module.{u1, u3, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.linearIsometryBoundedOfCompact._proof_3.{u2} E _inst_4) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_4.{u2, u3} E _inst_4 𝕜 _inst_5 _inst_6)) (BoundedContinuousFunction.module.{u1, u2, u3} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u3} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_5.{u2, u3} E _inst_4 𝕜 _inst_5 _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_6.{u2} E _inst_4))
-but is expected to have type
- forall (α : Type.{u1}) (E : Type.{u2}) [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_4 : NormedAddCommGroup.{u2} E] (𝕜 : Type.{u3}) [_inst_5 : NormedField.{u3} 𝕜] [_inst_6 : NormedSpace.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)], LinearIsometryEquiv.{u3, u3, max u2 u1, max u2 u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5)))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5)))))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5))))) (RingHomInvPair.ids.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5))))) (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u1, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.seminormedAddCommGroup.{u1, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (ContinuousMap.module.{u1, u3, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u3, u2} 𝕜 E (UniformSpace.toTopologicalSpace.{u3} 𝕜 (PseudoMetricSpace.toUniformSpace.{u3} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u3} 𝕜 (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (MonoidWithZero.toZero.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u3, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u3} 𝕜 (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (MonoidWithZero.toZero.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (BoundedContinuousFunction.module.{u1, u2, u3} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u3} 𝕜 (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_map.linear_isometry_bounded_of_compact ContinuousMap.linearIsometryBoundedOfCompactₓ'. -/
/-- When `α` is compact and `𝕜` is a normed field,
the `𝕜`-algebra of bounded continuous maps `α →ᵇ β` is
@@ -471,10 +468,7 @@ def linearIsometryBoundedOfCompact : C(α, E) ≃ₗᵢ[𝕜] α →ᵇ E :=
variable {α E}
/- warning: continuous_map.eval_clm -> ContinuousMap.evalClm is a dubious translation:
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- forall {α : Type.{u1}} {E : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_4 : NormedAddCommGroup.{u2} E] (𝕜 : Type.{u3}) [_inst_5 : NormedField.{u3} 𝕜] [_inst_6 : NormedSpace.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)], α -> (ContinuousLinearMap.{u3, u3, max u2 u1, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5)))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5)))))) (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.compactOpen.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instAddCommMonoidContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (TopologicalAddGroup.toContinuousAdd.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.module.{u1, u3, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (TopologicalAddGroup.toContinuousAdd.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u3, u2} 𝕜 E (UniformSpace.toTopologicalSpace.{u3} 𝕜 (PseudoMetricSpace.toUniformSpace.{u3} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u3} 𝕜 (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (MonoidWithZero.toZero.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E 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(SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (MonoidWithZero.toZero.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_map.eval_clm ContinuousMap.evalClmₓ'. -/
-- to match bounded_continuous_function.eval_clm
/-- The evaluation at a point, as a continuous linear map from `C(α, 𝕜)` to `𝕜`. -/
@@ -485,10 +479,7 @@ def evalClm (x : α) : C(α, E) →L[𝕜] E :=
end
/- warning: continuous_map.linear_isometry_bounded_of_compact_symm_apply -> ContinuousMap.linearIsometryBoundedOfCompact_symm_apply is a dubious translation:
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(MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (fun (_x : BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) => ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) _x) (ContinuousMapClass.toFunLike.{max u3 u2, max u3 u2, max u3 u2} (LinearIsometryEquiv.{u1, u1, max u3 u2, max u3 u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (UniformSpace.toTopologicalSpace.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (PseudoMetricSpace.toUniformSpace.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (SeminormedAddCommGroup.toPseudoMetricSpace.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (UniformSpace.toTopologicalSpace.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (PseudoMetricSpace.toUniformSpace.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4))))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max 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_inst_4))) (UniformSpace.toTopologicalSpace.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (PseudoMetricSpace.toUniformSpace.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (SeminormedAddCommGroup.toPseudoMetricSpace.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (AddCommGroup.toAddCommMonoid.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (SeminormedAddCommGroup.toAddCommGroup.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (UniformSpace.toTopologicalSpace.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (PseudoMetricSpace.toUniformSpace.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E 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(SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{u1, u1, max u3 u2, max u3 u2, max u3 u2} 𝕜 𝕜 (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (LinearIsometryEquiv.{u1, u1, max u3 u2, max u3 u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.{u3, u2} α E _inst_1 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(NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (SemilinearIsometryEquivClass.instSemilinearIsometryClass.{u1, u1, max u3 u2, max u3 u2, max u3 u2} 𝕜 𝕜 (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (LinearIsometryEquiv.{u1, u1, max u3 u2, max u3 u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (LinearIsometryEquiv.instSemilinearIsometryEquivClassLinearIsometryEquiv.{u1, u1, max u3 u2, max u3 u2} 𝕜 𝕜 (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))))))) (LinearIsometryEquiv.symm.{u1, u1, max u3 u2, max u3 u2} 𝕜 𝕜 (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (ContinuousMap.module.{u3, u1, u2} α 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_inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E 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(SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.linearIsometryBoundedOfCompact.{u3, u2, u1} α E _inst_1 _inst_2 _inst_4 𝕜 _inst_5 _inst_6)) f) (BoundedContinuousFunction.toContinuousMap.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) f)
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_map.linear_isometry_bounded_of_compact_symm_apply ContinuousMap.linearIsometryBoundedOfCompact_symm_applyₓ'. -/
-- this lemma and the next are the analogues of those autogenerated by `@[simps]` for
-- `equiv_bounded_of_compact`, `add_equiv_bounded_of_compact`
@@ -499,10 +490,7 @@ theorem linearIsometryBoundedOfCompact_symm_apply (f : α →ᵇ E) :
#align continuous_map.linear_isometry_bounded_of_compact_symm_apply ContinuousMap.linearIsometryBoundedOfCompact_symm_apply
/- warning: continuous_map.linear_isometry_bounded_of_compact_apply_apply -> ContinuousMap.linearIsometryBoundedOfCompact_apply_apply is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {E : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_4 : NormedAddCommGroup.{u2} E] {𝕜 : Type.{u3}} [_inst_5 : NormedField.{u3} 𝕜] [_inst_6 : NormedSpace.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] (f : ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (a : α), Eq.{succ u2} E (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (fun (_x : BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) => α -> E) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearIsometryEquiv.{u3, u3, max u1 u2, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))))) (ContinuousMap.linearIsometryBoundedOfCompact._proof_1.{u3} 𝕜 _inst_5) (ContinuousMap.linearIsometryBoundedOfCompact._proof_2.{u3} 𝕜 _inst_5) (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.normedAddCommGroup.{u1, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.seminormedAddCommGroup.{u1, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (ContinuousMap.module.{u1, u3, u2} α 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E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_5.{u2, u3} E _inst_4 𝕜 _inst_5 _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_6.{u2} E _inst_4))) (fun (_x : LinearIsometryEquiv.{u3, u3, max u1 u2, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 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(NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E 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(NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (fun (_x : ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) => BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) _x) (ContinuousMapClass.toFunLike.{max u3 u2, max u3 u2, max u3 u2} (LinearIsometryEquiv.{u1, u1, max u2 u3, max u2 u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (UniformSpace.toTopologicalSpace.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (PseudoMetricSpace.toUniformSpace.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4))))) (UniformSpace.toTopologicalSpace.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (PseudoMetricSpace.toUniformSpace.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (SeminormedAddCommGroup.toPseudoMetricSpace.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u2, u1, u1, max u3 u2, max u3 u2} (LinearIsometryEquiv.{u1, u1, max u2 u3, max u2 u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E 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(AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (UniformSpace.toTopologicalSpace.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (PseudoMetricSpace.toUniformSpace.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4))))) (AddCommGroup.toAddCommMonoid.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (SeminormedAddCommGroup.toAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (UniformSpace.toTopologicalSpace.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (PseudoMetricSpace.toUniformSpace.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (SeminormedAddCommGroup.toPseudoMetricSpace.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (AddCommGroup.toAddCommMonoid.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (SeminormedAddCommGroup.toAddCommGroup.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{u1, u1, max u3 u2, max u3 u2, max u3 u2} 𝕜 𝕜 (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (LinearIsometryEquiv.{u1, u1, max u2 u3, max u2 u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (SemilinearIsometryEquivClass.instSemilinearIsometryClass.{u1, u1, max u3 u2, max u3 u2, max u3 u2} 𝕜 𝕜 (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (LinearIsometryEquiv.{u1, u1, max u2 u3, max u2 u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) 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(NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (LinearIsometryEquiv.instSemilinearIsometryEquivClassLinearIsometryEquiv.{u1, u1, max u3 u2, max u3 u2} 𝕜 𝕜 (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))))))) (ContinuousMap.linearIsometryBoundedOfCompact.{u3, u2, u1} α E _inst_1 _inst_2 _inst_4 𝕜 _inst_5 _inst_6) f) a) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) α (fun (_x : α) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => E) _x) (ContinuousMapClass.toFunLike.{max u3 u2, u3, u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (ContinuousMap.instContinuousMapClassContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))))) f a)
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_map.linear_isometry_bounded_of_compact_apply_apply ContinuousMap.linearIsometryBoundedOfCompact_apply_applyₓ'. -/
@[simp]
theorem linearIsometryBoundedOfCompact_apply_apply (f : C(α, E)) (a : α) :
@@ -511,10 +499,7 @@ theorem linearIsometryBoundedOfCompact_apply_apply (f : C(α, E)) (a : α) :
#align continuous_map.linear_isometry_bounded_of_compact_apply_apply ContinuousMap.linearIsometryBoundedOfCompact_apply_apply
/- warning: continuous_map.linear_isometry_bounded_of_compact_to_isometry_equiv -> ContinuousMap.linearIsometryBoundedOfCompact_toIsometryEquiv is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {E : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_4 : NormedAddCommGroup.{u2} E] {𝕜 : Type.{u3}} [_inst_5 : NormedField.{u3} 𝕜] [_inst_6 : NormedSpace.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)], Eq.{succ (max u1 u2)} (IsometryEquiv.{max u1 u2, max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (PseudoMetricSpace.toPseudoEMetricSpace.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.normedAddCommGroup.{u1, u2} α E _inst_1 _inst_2 _inst_4)))) (PseudoMetricSpace.toPseudoEMetricSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (SeminormedAddCommGroup.toPseudoMetricSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (BoundedContinuousFunction.seminormedAddCommGroup.{u1, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (LinearIsometryEquiv.toIsometryEquiv.{u3, u3, max u1 u2, max u1 u2} 𝕜 𝕜 (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))))) (ContinuousMap.linearIsometryBoundedOfCompact._proof_1.{u3} 𝕜 _inst_5) (ContinuousMap.linearIsometryBoundedOfCompact._proof_2.{u3} 𝕜 _inst_5) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.normedAddCommGroup.{u1, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.seminormedAddCommGroup.{u1, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (ContinuousMap.module.{u1, u3, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.linearIsometryBoundedOfCompact._proof_3.{u2} E _inst_4) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_4.{u2, u3} E _inst_4 𝕜 _inst_5 _inst_6)) (BoundedContinuousFunction.module.{u1, u2, u3} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u3} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_5.{u2, u3} E _inst_4 𝕜 _inst_5 _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_6.{u2} E _inst_4)) (ContinuousMap.linearIsometryBoundedOfCompact.{u1, u2, u3} α E _inst_1 _inst_2 _inst_4 𝕜 _inst_5 _inst_6)) (ContinuousMap.isometryEquivBoundedOfCompact.{u1, u2} α E _inst_1 _inst_2 (NormedAddCommGroup.toMetricSpace.{u2} E _inst_4))
-but is expected to have type
- forall {α : Type.{u3}} {E : Type.{u2}} [_inst_1 : TopologicalSpace.{u3} α] [_inst_2 : CompactSpace.{u3} α _inst_1] [_inst_4 : NormedAddCommGroup.{u2} E] {𝕜 : Type.{u1}} [_inst_5 : NormedField.{u1} 𝕜] [_inst_6 : NormedSpace.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)], Eq.{max (succ u3) (succ u2)} (IsometryEquiv.{max u3 u2, max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (PseudoMetricSpace.toPseudoEMetricSpace.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)))) (PseudoMetricSpace.toPseudoEMetricSpace.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (SeminormedAddCommGroup.toPseudoMetricSpace.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (LinearIsometryEquiv.toIsometryEquiv.{u1, u1, max u3 u2, max u3 u2} 𝕜 𝕜 (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.linearIsometryBoundedOfCompact.{u3, u2, u1} α E _inst_1 _inst_2 _inst_4 𝕜 _inst_5 _inst_6)) (ContinuousMap.isometryEquivBoundedOfCompact.{u3, u2} α E _inst_1 _inst_2 (NormedAddCommGroup.toMetricSpace.{u2} E _inst_4))
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_map.linear_isometry_bounded_of_compact_to_isometry_equiv ContinuousMap.linearIsometryBoundedOfCompact_toIsometryEquivₓ'. -/
@[simp]
theorem linearIsometryBoundedOfCompact_toIsometryEquiv :
@@ -523,10 +508,7 @@ theorem linearIsometryBoundedOfCompact_toIsometryEquiv :
#align continuous_map.linear_isometry_bounded_of_compact_to_isometry_equiv ContinuousMap.linearIsometryBoundedOfCompact_toIsometryEquiv
/- warning: continuous_map.linear_isometry_bounded_of_compact_to_add_equiv -> ContinuousMap.linearIsometryBoundedOfCompact_toAddEquiv is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {E : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_4 : NormedAddCommGroup.{u2} E] {𝕜 : Type.{u3}} [_inst_5 : NormedField.{u3} 𝕜] [_inst_6 : NormedSpace.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)], Eq.{succ (max u1 u2)} (AddEquiv.{max u1 u2, max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (AddZeroClass.toHasAdd.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (AddMonoid.toAddZeroClass.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (AddCommGroup.toAddCommMonoid.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (SeminormedAddCommGroup.toAddCommGroup.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 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E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_5.{u2, u3} E _inst_4 𝕜 _inst_5 _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_6.{u2} E _inst_4)) (ContinuousMap.linearIsometryBoundedOfCompact.{u1, u2, u3} α E _inst_1 _inst_2 _inst_4 𝕜 _inst_5 _inst_6))) (ContinuousMap.addEquivBoundedOfCompact.{u1, u2} α E _inst_1 _inst_2 (NormedAddCommGroup.toMetricSpace.{u2} E _inst_4) (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))
-but is expected to have type
- forall {α : Type.{u3}} {E : Type.{u2}} [_inst_1 : TopologicalSpace.{u3} α] [_inst_2 : CompactSpace.{u3} α _inst_1] [_inst_4 : NormedAddCommGroup.{u2} E] {𝕜 : Type.{u1}} [_inst_5 : NormedField.{u1} 𝕜] [_inst_6 : NormedSpace.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)], Eq.{max (succ u3) (succ u2)} (AddEquiv.{max u3 u2, max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.instAdd.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_4)))))) (TopologicalAddGroup.toContinuousAdd.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (BoundedContinuousFunction.instAddBoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (AddEquivClass.toAddEquiv.{max u3 u2, max u3 u2, max u3 u2} (LinearEquiv.{u1, u1, max u3 u2, max u3 u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u1} 𝕜 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(SeminormedAddCommGroup.toAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)))) (AddCommGroup.toAddCommMonoid.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (SeminormedAddCommGroup.toAddCommGroup.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.instAdd.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_4)))))) (TopologicalAddGroup.toContinuousAdd.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (BoundedContinuousFunction.instAddBoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (SemilinearEquivClass.toAddEquivClass.{max u3 u2, u1, u1, max u3 u2, max u3 u2} (LinearEquiv.{u1, u1, max u3 u2, max u3 u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (AddCommGroup.toAddCommMonoid.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (SeminormedAddCommGroup.toAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)))) (AddCommGroup.toAddCommMonoid.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (SeminormedAddCommGroup.toAddCommGroup.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.instAddCommMonoidContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (TopologicalAddGroup.toContinuousAdd.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max u3 u2, max u3 u2} 𝕜 𝕜 (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (SeminormedAddCommGroup.toAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)))) (AddCommGroup.toAddCommMonoid.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (SeminormedAddCommGroup.toAddCommGroup.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E 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(SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))))) (LinearIsometryEquiv.toLinearEquiv.{u1, u1, max u3 u2, max u3 u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.linearIsometryBoundedOfCompact.{u3, u2, u1} α E _inst_1 _inst_2 _inst_4 𝕜 _inst_5 _inst_6))) (ContinuousMap.addEquivBoundedOfCompact.{u3, u2} α E _inst_1 _inst_2 (NormedAddCommGroup.toMetricSpace.{u2} E _inst_4) (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_map.linear_isometry_bounded_of_compact_to_add_equiv ContinuousMap.linearIsometryBoundedOfCompact_toAddEquivₓ'. -/
@[simp]
theorem linearIsometryBoundedOfCompact_toAddEquiv :
@@ -536,10 +518,7 @@ theorem linearIsometryBoundedOfCompact_toAddEquiv :
#align continuous_map.linear_isometry_bounded_of_compact_to_add_equiv ContinuousMap.linearIsometryBoundedOfCompact_toAddEquiv
/- warning: continuous_map.linear_isometry_bounded_of_compact_of_compact_to_equiv -> ContinuousMap.linearIsometryBoundedOfCompact_of_compact_toEquiv is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {E : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_4 : NormedAddCommGroup.{u2} E] {𝕜 : Type.{u3}} [_inst_5 : NormedField.{u3} 𝕜] [_inst_6 : NormedSpace.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)], Eq.{succ (max u1 u2)} (Equiv.{succ (max u1 u2), succ (max u1 u2)} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (LinearEquiv.toEquiv.{u3, u3, max u1 u2, max u1 u2} 𝕜 𝕜 (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (SeminormedAddCommGroup.toAddCommGroup.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.normedAddCommGroup.{u1, u2} α E _inst_1 _inst_2 _inst_4)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (SeminormedAddCommGroup.toAddCommGroup.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (BoundedContinuousFunction.seminormedAddCommGroup.{u1, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (ContinuousMap.module.{u1, u3, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.linearIsometryBoundedOfCompact._proof_3.{u2} E _inst_4) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_4.{u2, u3} E _inst_4 𝕜 _inst_5 _inst_6)) (BoundedContinuousFunction.module.{u1, u2, u3} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u3} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_5.{u2, u3} E _inst_4 𝕜 _inst_5 _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_6.{u2} E _inst_4)) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))))) (ContinuousMap.linearIsometryBoundedOfCompact._proof_1.{u3} 𝕜 _inst_5) (ContinuousMap.linearIsometryBoundedOfCompact._proof_2.{u3} 𝕜 _inst_5) (LinearIsometryEquiv.toLinearEquiv.{u3, u3, max u1 u2, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))))) (ContinuousMap.linearIsometryBoundedOfCompact._proof_1.{u3} 𝕜 _inst_5) (ContinuousMap.linearIsometryBoundedOfCompact._proof_2.{u3} 𝕜 _inst_5) (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.normedAddCommGroup.{u1, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.seminormedAddCommGroup.{u1, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (ContinuousMap.module.{u1, u3, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E 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E _inst_4)) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_5.{u2, u3} E _inst_4 𝕜 _inst_5 _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_6.{u2} E _inst_4)) (ContinuousMap.linearIsometryBoundedOfCompact.{u1, u2, u3} α E _inst_1 _inst_2 _inst_4 𝕜 _inst_5 _inst_6))) (ContinuousMap.equivBoundedOfCompact.{u1, u2} α E _inst_1 _inst_2 (NormedAddCommGroup.toMetricSpace.{u2} E _inst_4))
-but is expected to have type
- forall {α : Type.{u3}} {E : Type.{u2}} [_inst_1 : TopologicalSpace.{u3} α] [_inst_2 : CompactSpace.{u3} α _inst_1] [_inst_4 : NormedAddCommGroup.{u2} E] {𝕜 : Type.{u1}} [_inst_5 : NormedField.{u1} 𝕜] [_inst_6 : NormedSpace.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)], Eq.{max (succ u3) (succ u2)} (Equiv.{succ (max u3 u2), succ (max u3 u2)} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (LinearEquiv.toEquiv.{u1, u1, max u3 u2, max u3 u2} 𝕜 𝕜 (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} 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E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E 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(BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (LinearIsometryEquiv.toLinearEquiv.{u1, u1, max u3 u2, max u3 u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.linearIsometryBoundedOfCompact.{u3, u2, u1} α E _inst_1 _inst_2 _inst_4 𝕜 _inst_5 _inst_6))) (ContinuousMap.equivBoundedOfCompact.{u3, u2} α E _inst_1 _inst_2 (NormedAddCommGroup.toMetricSpace.{u2} E _inst_4))
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_map.linear_isometry_bounded_of_compact_of_compact_to_equiv ContinuousMap.linearIsometryBoundedOfCompact_of_compact_toEquivₓ'. -/
@[simp]
theorem linearIsometryBoundedOfCompact_of_compact_toEquiv :
@@ -574,10 +553,7 @@ We now set up some declarations making it convenient to use uniform continuity.
/- warning: continuous_map.uniform_continuity -> ContinuousMap.uniform_continuity is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : MetricSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)))] [_inst_3 : MetricSpace.{u2} β] (f : ContinuousMap.{u1, u2} α β (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))) (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (ε : Real), (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε) -> (Exists.{1} Real (fun (δ : Real) => Exists.{0} (GT.gt.{0} Real Real.hasLt δ (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (fun (H : GT.gt.{0} Real Real.hasLt δ (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) => forall {x : α} {y : α}, (LT.lt.{0} Real Real.hasLt (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) x y) δ) -> (LT.lt.{0} Real Real.hasLt (Dist.dist.{u2} β (PseudoMetricSpace.toHasDist.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} α β (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))) (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (fun (_x : ContinuousMap.{u1, u2} α β (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))) (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) => α -> β) (ContinuousMap.hasCoeToFun.{u1, u2} α β (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))) (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} α β (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))) (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (fun (_x : ContinuousMap.{u1, u2} α β (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))) (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) => α -> β) (ContinuousMap.hasCoeToFun.{u1, u2} α β (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))) (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) f y)) ε))))
-but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : MetricSpace.{u2} α] [_inst_2 : CompactSpace.{u2} α (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1)))] [_inst_3 : MetricSpace.{u1} β] (f : ContinuousMap.{u2, u1} α β (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1))) (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) (ε : Real), (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) -> (Exists.{1} Real (fun (δ : Real) => And (GT.gt.{0} Real Real.instLTReal δ (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (forall {x : α} {y : α}, (LT.lt.{0} Real Real.instLTReal (Dist.dist.{u2} α (PseudoMetricSpace.toDist.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1)) x y) δ) -> (LT.lt.{0} Real Real.instLTReal (Dist.dist.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) x) (PseudoMetricSpace.toDist.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) x) (MetricSpace.toPseudoMetricSpace.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) x) _inst_3)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousMap.{u2, u1} α β (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1))) (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) α (fun (a : α) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) a) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousMap.{u2, u1} α β (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1))) (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) α β (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1))) (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3))) (ContinuousMap.instContinuousMapClassContinuousMap.{u2, u1} α β (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1))) (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3))))) f x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousMap.{u2, u1} α β (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1))) (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) α (fun (a : α) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) a) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousMap.{u2, u1} α β (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1))) (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) α β (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1))) (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3))) (ContinuousMap.instContinuousMapClassContinuousMap.{u2, u1} α β (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1))) (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3))))) f y)) ε))))
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_map.uniform_continuity ContinuousMap.uniform_continuityₓ'. -/
theorem uniform_continuity (f : C(α, β)) (ε : ℝ) (h : 0 < ε) :
∃ δ > 0, ∀ {x y}, dist x y < δ → dist (f x) (f y) < ε :=
@@ -634,10 +610,7 @@ variable [NormedAddCommGroup β] [NormedSpace 𝕜 β] [NormedAddCommGroup γ] [
open ContinuousMap
/- warning: continuous_linear_map.comp_left_continuous_compact -> ContinuousLinearMap.compLeftContinuousCompact is a dubious translation:
-lean 3 declaration is
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(Semiring.toNonAssocSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) γ (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7)) -> (ContinuousLinearMap.{u2, u2, max u1 u3, max u1 u4} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.compactOpen.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.addCommMonoid.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (ContinuousLinearMap.compLeftContinuousCompact._proof_1.{u3} β _inst_4)) (ContinuousMap.{u1, u4} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))))) (ContinuousMap.compactOpen.{u1, u4} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))))) (ContinuousMap.addCommMonoid.{u1, u4} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (ContinuousLinearMap.compLeftContinuousCompact._proof_2.{u4} γ _inst_6)) (ContinuousMap.module.{u1, u2, u3} X _inst_1 𝕜 β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (ContinuousLinearMap.compLeftContinuousCompact._proof_3.{u3} β _inst_4) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (ContinuousLinearMap.compLeftContinuousCompact._proof_4.{u2, u3} 𝕜 β _inst_3 _inst_4 _inst_5)) (ContinuousMap.module.{u1, u2, u4} X _inst_1 𝕜 γ (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (ContinuousLinearMap.compLeftContinuousCompact._proof_5.{u4} γ _inst_6) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7) (ContinuousLinearMap.compLeftContinuousCompact._proof_6.{u2, u4} 𝕜 γ _inst_3 _inst_6 _inst_7)))
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- forall (X : Type.{u1}) {𝕜 : Type.{u2}} {β : Type.{u3}} {γ : Type.{u4}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : CompactSpace.{u1} X _inst_1] [_inst_3 : NontriviallyNormedField.{u2} 𝕜] [_inst_4 : NormedAddCommGroup.{u3} β] [_inst_5 : NormedSpace.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)] [_inst_6 : NormedAddCommGroup.{u4} γ] [_inst_7 : NormedSpace.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)], (ContinuousLinearMap.{u2, u2, u3, u4} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) γ (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7)) -> (ContinuousLinearMap.{u2, u2, max u3 u1, max u4 u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.compactOpen.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.instAddCommMonoidContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (TopologicalAddGroup.toContinuousAdd.{u3} β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (ContinuousMap.{u1, u4} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))))) (ContinuousMap.compactOpen.{u1, u4} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))))) (ContinuousMap.instAddCommMonoidContinuousMap.{u1, u4} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (TopologicalAddGroup.toContinuousAdd.{u4} γ (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (NormedAddGroup.toAddGroup.{u4} γ (NormedAddCommGroup.toNormedAddGroup.{u4} γ _inst_6)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (ContinuousMap.module.{u1, u2, u3} X _inst_1 𝕜 β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (TopologicalAddGroup.toContinuousAdd.{u3} β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (ContinuousSMul.continuousConstSMul.{u2, u3} 𝕜 β (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (SMulZeroClass.toSMul.{u2, u3} 𝕜 β (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕜 β (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 β (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (Module.toMulActionWithZero.{u2, u3} 𝕜 β (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (BoundedSMul.continuousSMul.{u2, u3} 𝕜 β (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (NegZeroClass.toZero.{u3} β (SubNegZeroMonoid.toNegZeroClass.{u3} β (SubtractionMonoid.toSubNegZeroMonoid.{u3} β (SubtractionCommMonoid.toSubtractionMonoid.{u3} β (AddCommGroup.toDivisionAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))))) (SMulZeroClass.toSMul.{u2, u3} 𝕜 β (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕜 β (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 β (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (Module.toMulActionWithZero.{u2, u3} 𝕜 β (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (NormedSpace.boundedSMul.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5)))) (ContinuousMap.module.{u1, u2, u4} X _inst_1 𝕜 γ (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (TopologicalAddGroup.toContinuousAdd.{u4} γ (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (NormedAddGroup.toAddGroup.{u4} γ (NormedAddCommGroup.toNormedAddGroup.{u4} γ _inst_6)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7) (ContinuousSMul.continuousConstSMul.{u2, u4} 𝕜 γ (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (SMulZeroClass.toSMul.{u2, u4} 𝕜 γ (AddMonoid.toZero.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)))) (SMulWithZero.toSMulZeroClass.{u2, u4} 𝕜 γ (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)))) (MulActionWithZero.toSMulWithZero.{u2, u4} 𝕜 γ (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)))) (Module.toMulActionWithZero.{u2, u4} 𝕜 γ (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7))))) (BoundedSMul.continuousSMul.{u2, u4} 𝕜 γ (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (NegZeroClass.toZero.{u4} γ (SubNegZeroMonoid.toNegZeroClass.{u4} γ (SubtractionMonoid.toSubNegZeroMonoid.{u4} γ (SubtractionCommMonoid.toSubtractionMonoid.{u4} γ (AddCommGroup.toDivisionAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)))))) (SMulZeroClass.toSMul.{u2, u4} 𝕜 γ (AddMonoid.toZero.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)))) (SMulWithZero.toSMulZeroClass.{u2, u4} 𝕜 γ (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)))) (MulActionWithZero.toSMulWithZero.{u2, u4} 𝕜 γ (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)))) (Module.toMulActionWithZero.{u2, u4} 𝕜 γ (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7))))) (NormedSpace.boundedSMul.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7)))))
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_left_continuous_compact ContinuousLinearMap.compLeftContinuousCompactₓ'. -/
/-- Postcomposition of continuous functions into a normed module by a continuous linear map is a
continuous linear map.
@@ -652,10 +625,7 @@ protected def ContinuousLinearMap.compLeftContinuousCompact (g : β →L[𝕜]
#align continuous_linear_map.comp_left_continuous_compact ContinuousLinearMap.compLeftContinuousCompact
/- warning: continuous_linear_map.to_linear_comp_left_continuous_compact -> ContinuousLinearMap.toLinear_compLeftContinuousCompact is a dubious translation:
-lean 3 declaration is
- forall (X : Type.{u1}) {𝕜 : Type.{u2}} {β : Type.{u3}} {γ : Type.{u4}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : CompactSpace.{u1} X _inst_1] [_inst_3 : NontriviallyNormedField.{u2} 𝕜] [_inst_4 : NormedAddCommGroup.{u3} β] [_inst_5 : NormedSpace.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)] [_inst_6 : NormedAddCommGroup.{u4} γ] [_inst_7 : NormedSpace.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)] (g : ContinuousLinearMap.{u2, u2, u3, u4} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) γ (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7)), Eq.{max (succ (max u1 u3)) (succ (max u1 u4))} (LinearMap.{u2, u2, max u1 u3, max u1 u4} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.{u1, u4} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))))) (ContinuousMap.addCommMonoid.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (LipschitzAdd.continuousAdd.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)) (SubNegMonoid.toAddMonoid.{u3} β (AddGroup.toSubNegMonoid.{u3} β (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (ContinuousMap.addCommMonoid.{u1, u4} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (LipschitzAdd.continuousAdd.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)) (SubNegMonoid.toAddMonoid.{u4} γ (AddGroup.toSubNegMonoid.{u4} γ (NormedAddGroup.toAddGroup.{u4} γ (NormedAddCommGroup.toNormedAddGroup.{u4} γ _inst_6)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (ContinuousMap.module.{u1, u2, u3} X _inst_1 𝕜 β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (LipschitzAdd.continuousAdd.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)) (SubNegMonoid.toAddMonoid.{u3} β (AddGroup.toSubNegMonoid.{u3} β (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (ContinuousSMul.continuousConstSMul.{u2, u3} 𝕜 β (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (SMulZeroClass.toHasSmul.{u2, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (SMulWithZero.toSmulZeroClass.{u2, u3} 𝕜 β (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 β (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 β (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (BoundedSMul.continuousSMul.{u2, u3} 𝕜 β (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)) (MulZeroClass.toHasZero.{u2} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (SubNegMonoid.toAddMonoid.{u3} β (AddGroup.toSubNegMonoid.{u3} β (SeminormedAddGroup.toAddGroup.{u3} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))))) (SMulZeroClass.toHasSmul.{u2, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (SMulWithZero.toSmulZeroClass.{u2, u3} 𝕜 β (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 β (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 β (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (NormedSpace.boundedSMul.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5)))) (ContinuousMap.module.{u1, u2, u4} X _inst_1 𝕜 γ (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (LipschitzAdd.continuousAdd.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)) (SubNegMonoid.toAddMonoid.{u4} γ (AddGroup.toSubNegMonoid.{u4} γ (NormedAddGroup.toAddGroup.{u4} γ (NormedAddCommGroup.toNormedAddGroup.{u4} γ _inst_6)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7) (ContinuousSMul.continuousConstSMul.{u2, u4} 𝕜 γ (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (SMulZeroClass.toHasSmul.{u2, u4} 𝕜 γ (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (SMulWithZero.toSmulZeroClass.{u2, u4} 𝕜 γ (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (MulActionWithZero.toSMulWithZero.{u2, u4} 𝕜 γ (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (Module.toMulActionWithZero.{u2, u4} 𝕜 γ (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7))))) (BoundedSMul.continuousSMul.{u2, u4} 𝕜 γ (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)) (MulZeroClass.toHasZero.{u2} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (SubNegMonoid.toAddMonoid.{u4} γ (AddGroup.toSubNegMonoid.{u4} γ (SeminormedAddGroup.toAddGroup.{u4} γ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))))))) (SMulZeroClass.toHasSmul.{u2, u4} 𝕜 γ (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (SMulWithZero.toSmulZeroClass.{u2, u4} 𝕜 γ (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 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_inst_7))) (LinearMap.{u2, u2, max u1 u3, max u1 u4} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.{u1, u4} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u4} γ 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(NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (SMulZeroClass.toHasSmul.{u2, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (SMulWithZero.toSmulZeroClass.{u2, u3} 𝕜 β (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u3} β 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(NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (BoundedSMul.continuousSMul.{u2, u3} 𝕜 β (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)) (MulZeroClass.toHasZero.{u2} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (SubNegMonoid.toAddMonoid.{u3} β (AddGroup.toSubNegMonoid.{u3} β (SeminormedAddGroup.toAddGroup.{u3} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))))) (SMulZeroClass.toHasSmul.{u2, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (SMulWithZero.toSmulZeroClass.{u2, u3} 𝕜 β (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 β (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 β (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (NormedSpace.boundedSMul.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5)))) (ContinuousMap.module.{u1, u2, u4} X _inst_1 𝕜 γ (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (LipschitzAdd.continuousAdd.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)) (SubNegMonoid.toAddMonoid.{u4} γ (AddGroup.toSubNegMonoid.{u4} γ (NormedAddGroup.toAddGroup.{u4} γ (NormedAddCommGroup.toNormedAddGroup.{u4} γ _inst_6)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7) (ContinuousSMul.continuousConstSMul.{u2, u4} 𝕜 γ (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (SMulZeroClass.toHasSmul.{u2, u4} 𝕜 γ (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (SMulWithZero.toSmulZeroClass.{u2, u4} 𝕜 γ (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (MulActionWithZero.toSMulWithZero.{u2, u4} 𝕜 γ (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (Module.toMulActionWithZero.{u2, u4} 𝕜 γ (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7))))) (BoundedSMul.continuousSMul.{u2, u4} 𝕜 γ (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)) (MulZeroClass.toHasZero.{u2} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (SubNegMonoid.toAddMonoid.{u4} γ (AddGroup.toSubNegMonoid.{u4} γ (SeminormedAddGroup.toAddGroup.{u4} γ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))))))) (SMulZeroClass.toHasSmul.{u2, u4} 𝕜 γ (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (SMulWithZero.toSmulZeroClass.{u2, u4} 𝕜 γ (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 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(NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7))))) (NormedSpace.boundedSMul.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7))))) (HasLiftT.mk.{max (succ (max u1 u3)) (succ (max u1 u4)), max (succ (max u1 u3)) (succ (max u1 u4))} (ContinuousLinearMap.{u2, u2, max u1 u3, max u1 u4} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) 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(NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)) (MulZeroClass.toHasZero.{u2} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (SubNegMonoid.toAddMonoid.{u3} β (AddGroup.toSubNegMonoid.{u3} β (SeminormedAddGroup.toAddGroup.{u3} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))))) (SMulZeroClass.toHasSmul.{u2, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β 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(NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (LipschitzAdd.continuousAdd.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)) (SubNegMonoid.toAddMonoid.{u4} γ (AddGroup.toSubNegMonoid.{u4} γ (NormedAddGroup.toAddGroup.{u4} γ (NormedAddCommGroup.toNormedAddGroup.{u4} γ _inst_6)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7) (ContinuousSMul.continuousConstSMul.{u2, u4} 𝕜 γ (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (SMulZeroClass.toHasSmul.{u2, u4} 𝕜 γ (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (SMulWithZero.toSmulZeroClass.{u2, u4} 𝕜 γ (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (MulActionWithZero.toSMulWithZero.{u2, u4} 𝕜 γ (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (Module.toMulActionWithZero.{u2, u4} 𝕜 γ (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7))))) (BoundedSMul.continuousSMul.{u2, u4} 𝕜 γ (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)) (MulZeroClass.toHasZero.{u2} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (SubNegMonoid.toAddMonoid.{u4} γ (AddGroup.toSubNegMonoid.{u4} γ (SeminormedAddGroup.toAddGroup.{u4} γ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))))))) (SMulZeroClass.toHasSmul.{u2, u4} 𝕜 γ (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (SMulWithZero.toSmulZeroClass.{u2, u4} 𝕜 γ (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (MulActionWithZero.toSMulWithZero.{u2, u4} 𝕜 γ (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (Module.toMulActionWithZero.{u2, u4} 𝕜 γ (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7))))) (NormedSpace.boundedSMul.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7))))) (CoeTCₓ.coe.{max (succ (max u1 u3)) (succ (max u1 u4)), max (succ (max u1 u3)) (succ (max u1 u4))} (ContinuousLinearMap.{u2, u2, max u1 u3, max u1 u4} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (ContinuousMap.{u1, u3} X β _inst_1 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(SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))))) (ContinuousMap.compactOpen.{u1, u4} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))))) (ContinuousMap.addCommMonoid.{u1, u4} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (ContinuousLinearMap.compLeftContinuousCompact._proof_2.{u4} γ _inst_6)) (ContinuousMap.module.{u1, u2, u3} X _inst_1 𝕜 β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (ContinuousLinearMap.compLeftContinuousCompact._proof_3.{u3} β _inst_4) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (ContinuousLinearMap.compLeftContinuousCompact._proof_4.{u2, u3} 𝕜 β _inst_3 _inst_4 _inst_5)) (ContinuousMap.module.{u1, u2, u4} X _inst_1 𝕜 γ (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (ContinuousLinearMap.compLeftContinuousCompact._proof_5.{u4} γ _inst_6) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7) (ContinuousLinearMap.compLeftContinuousCompact._proof_6.{u2, u4} 𝕜 γ _inst_3 _inst_6 _inst_7))) (LinearMap.{u2, u2, max u1 u3, max u1 u4} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.{u1, u4} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))))) (ContinuousMap.addCommMonoid.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (LipschitzAdd.continuousAdd.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)) (SubNegMonoid.toAddMonoid.{u3} β (AddGroup.toSubNegMonoid.{u3} β (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (ContinuousMap.addCommMonoid.{u1, u4} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (LipschitzAdd.continuousAdd.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)) (SubNegMonoid.toAddMonoid.{u4} γ (AddGroup.toSubNegMonoid.{u4} γ (NormedAddGroup.toAddGroup.{u4} γ (NormedAddCommGroup.toNormedAddGroup.{u4} γ _inst_6)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (ContinuousMap.module.{u1, u2, u3} X _inst_1 𝕜 β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (LipschitzAdd.continuousAdd.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)) (SubNegMonoid.toAddMonoid.{u3} β (AddGroup.toSubNegMonoid.{u3} β (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (ContinuousSMul.continuousConstSMul.{u2, u3} 𝕜 β (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (SMulZeroClass.toHasSmul.{u2, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (SMulWithZero.toSmulZeroClass.{u2, u3} 𝕜 β (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 β (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 β (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (BoundedSMul.continuousSMul.{u2, u3} 𝕜 β (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)) (MulZeroClass.toHasZero.{u2} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (SubNegMonoid.toAddMonoid.{u3} β (AddGroup.toSubNegMonoid.{u3} β (SeminormedAddGroup.toAddGroup.{u3} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))))) (SMulZeroClass.toHasSmul.{u2, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (SMulWithZero.toSmulZeroClass.{u2, u3} 𝕜 β (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 β (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 β (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (NormedSpace.boundedSMul.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5)))) (ContinuousMap.module.{u1, u2, u4} X _inst_1 𝕜 γ (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (LipschitzAdd.continuousAdd.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)) (SubNegMonoid.toAddMonoid.{u4} γ (AddGroup.toSubNegMonoid.{u4} γ (NormedAddGroup.toAddGroup.{u4} γ (NormedAddCommGroup.toNormedAddGroup.{u4} γ _inst_6)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7) (ContinuousSMul.continuousConstSMul.{u2, u4} 𝕜 γ (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (SMulZeroClass.toHasSmul.{u2, u4} 𝕜 γ (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (SMulWithZero.toSmulZeroClass.{u2, u4} 𝕜 γ (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (MulActionWithZero.toSMulWithZero.{u2, u4} 𝕜 γ (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (Module.toMulActionWithZero.{u2, u4} 𝕜 γ (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7))))) (BoundedSMul.continuousSMul.{u2, u4} 𝕜 γ (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)) (MulZeroClass.toHasZero.{u2} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (SubNegMonoid.toAddMonoid.{u4} γ (AddGroup.toSubNegMonoid.{u4} γ (SeminormedAddGroup.toAddGroup.{u4} γ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))))))) (SMulZeroClass.toHasSmul.{u2, u4} 𝕜 γ (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (SMulWithZero.toSmulZeroClass.{u2, u4} 𝕜 γ (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (MulActionWithZero.toSMulWithZero.{u2, u4} 𝕜 γ (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 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_inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (BoundedSMul.continuousSMul.{u2, u3} 𝕜 β (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)) (MulZeroClass.toHasZero.{u2} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 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(AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 β (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 β (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (NormedSpace.boundedSMul.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5)))) (ContinuousMap.module.{u1, u2, u4} X _inst_1 𝕜 γ (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (LipschitzAdd.continuousAdd.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)) (SubNegMonoid.toAddMonoid.{u4} γ (AddGroup.toSubNegMonoid.{u4} γ (NormedAddGroup.toAddGroup.{u4} γ (NormedAddCommGroup.toNormedAddGroup.{u4} γ _inst_6)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7) (ContinuousSMul.continuousConstSMul.{u2, u4} 𝕜 γ (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (SMulZeroClass.toHasSmul.{u2, u4} 𝕜 γ (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (SMulWithZero.toSmulZeroClass.{u2, u4} 𝕜 γ (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (MulActionWithZero.toSMulWithZero.{u2, u4} 𝕜 γ (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (Module.toMulActionWithZero.{u2, u4} 𝕜 γ (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7))))) (BoundedSMul.continuousSMul.{u2, u4} 𝕜 γ (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)) (MulZeroClass.toHasZero.{u2} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (SubNegMonoid.toAddMonoid.{u4} γ (AddGroup.toSubNegMonoid.{u4} γ (SeminormedAddGroup.toAddGroup.{u4} γ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))))))) (SMulZeroClass.toHasSmul.{u2, u4} 𝕜 γ (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (SMulWithZero.toSmulZeroClass.{u2, u4} 𝕜 γ (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (MulActionWithZero.toSMulWithZero.{u2, u4} 𝕜 γ (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (Module.toMulActionWithZero.{u2, u4} 𝕜 γ (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7))))) (NormedSpace.boundedSMul.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7))))) (ContinuousLinearMap.LinearMap.coe.{u2, u2, max u1 u3, max u1 u4} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.compactOpen.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.addCommMonoid.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (ContinuousLinearMap.compLeftContinuousCompact._proof_1.{u3} β _inst_4)) (ContinuousMap.{u1, u4} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))))) (ContinuousMap.compactOpen.{u1, u4} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))))) (ContinuousMap.addCommMonoid.{u1, u4} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (ContinuousLinearMap.compLeftContinuousCompact._proof_2.{u4} γ _inst_6)) (ContinuousMap.module.{u1, u2, u3} X _inst_1 𝕜 β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (ContinuousLinearMap.compLeftContinuousCompact._proof_3.{u3} β _inst_4) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (ContinuousLinearMap.compLeftContinuousCompact._proof_4.{u2, u3} 𝕜 β _inst_3 _inst_4 _inst_5)) (ContinuousMap.module.{u1, u2, u4} X _inst_1 𝕜 γ (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (ContinuousLinearMap.compLeftContinuousCompact._proof_5.{u4} γ _inst_6) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7) (ContinuousLinearMap.compLeftContinuousCompact._proof_6.{u2, u4} 𝕜 γ _inst_3 _inst_6 _inst_7)))))) (ContinuousLinearMap.compLeftContinuousCompact.{u1, u2, u3, u4} X 𝕜 β γ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 g)) (ContinuousLinearMap.compLeftContinuous.{u2, u3, u4, u1} 𝕜 β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) γ (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (LipschitzAdd.continuousAdd.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)) (SubNegMonoid.toAddMonoid.{u3} β (AddGroup.toSubNegMonoid.{u3} β (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (ContinuousSMul.continuousConstSMul.{u2, u3} 𝕜 β (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (SMulZeroClass.toHasSmul.{u2, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (SMulWithZero.toSmulZeroClass.{u2, u3} 𝕜 β (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 β (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 β (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (BoundedSMul.continuousSMul.{u2, u3} 𝕜 β (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)) (MulZeroClass.toHasZero.{u2} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (SubNegMonoid.toAddMonoid.{u3} β (AddGroup.toSubNegMonoid.{u3} β (SeminormedAddGroup.toAddGroup.{u3} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))))) (SMulZeroClass.toHasSmul.{u2, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (SMulWithZero.toSmulZeroClass.{u2, u3} 𝕜 β (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 β (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 β (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (NormedSpace.boundedSMul.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))) (LipschitzAdd.continuousAdd.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)) (SubNegMonoid.toAddMonoid.{u4} γ (AddGroup.toSubNegMonoid.{u4} γ (NormedAddGroup.toAddGroup.{u4} γ (NormedAddCommGroup.toNormedAddGroup.{u4} γ _inst_6)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7) (ContinuousSMul.continuousConstSMul.{u2, u4} 𝕜 γ (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (SMulZeroClass.toHasSmul.{u2, u4} 𝕜 γ (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (SMulWithZero.toSmulZeroClass.{u2, u4} 𝕜 γ (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (MulActionWithZero.toSMulWithZero.{u2, u4} 𝕜 γ (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (Module.toMulActionWithZero.{u2, u4} 𝕜 γ (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7))))) (BoundedSMul.continuousSMul.{u2, u4} 𝕜 γ (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)) (MulZeroClass.toHasZero.{u2} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (SubNegMonoid.toAddMonoid.{u4} γ (AddGroup.toSubNegMonoid.{u4} γ (SeminormedAddGroup.toAddGroup.{u4} γ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))))))) (SMulZeroClass.toHasSmul.{u2, u4} 𝕜 γ (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (SMulWithZero.toSmulZeroClass.{u2, u4} 𝕜 γ (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (MulActionWithZero.toSMulWithZero.{u2, u4} 𝕜 γ (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (Module.toMulActionWithZero.{u2, u4} 𝕜 γ (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7))))) (NormedSpace.boundedSMul.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7))) X _inst_1 g)
-but is expected to have type
- forall (X : Type.{u1}) {𝕜 : Type.{u4}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : CompactSpace.{u1} X _inst_1] [_inst_3 : NontriviallyNormedField.{u4} 𝕜] [_inst_4 : NormedAddCommGroup.{u3} β] [_inst_5 : NormedSpace.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)] [_inst_6 : NormedAddCommGroup.{u2} γ] [_inst_7 : NormedSpace.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)] (g : ContinuousLinearMap.{u4, u4, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (RingHom.id.{u4} 𝕜 (Semiring.toNonAssocSemiring.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7)), Eq.{max (max (succ u1) (succ u3)) (succ u2)} (LinearMap.{u4, u4, max u1 u3, max u1 u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (RingHom.id.{u4} 𝕜 (Semiring.toNonAssocSemiring.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))))) (ContinuousMap.instAddCommMonoidContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (TopologicalAddGroup.toContinuousAdd.{u3} β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (ContinuousMap.instAddCommMonoidContinuousMap.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (TopologicalAddGroup.toContinuousAdd.{u2} γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (NormedAddGroup.toAddGroup.{u2} γ (NormedAddCommGroup.toNormedAddGroup.{u2} γ _inst_6)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (ContinuousMap.module.{u1, u4, u3} X _inst_1 𝕜 β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (TopologicalAddGroup.toContinuousAdd.{u3} β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (ContinuousSMul.continuousConstSMul.{u4, u3} 𝕜 β (UniformSpace.toTopologicalSpace.{u4} 𝕜 (PseudoMetricSpace.toUniformSpace.{u4} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (SMulZeroClass.toSMul.{u4, u3} 𝕜 β (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 β (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (Module.toMulActionWithZero.{u4, u3} 𝕜 β (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (BoundedSMul.continuousSMul.{u4, u3} 𝕜 β (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)) (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (NegZeroClass.toZero.{u3} β (SubNegZeroMonoid.toNegZeroClass.{u3} β (SubtractionMonoid.toSubNegZeroMonoid.{u3} β (SubtractionCommMonoid.toSubtractionMonoid.{u3} β (AddCommGroup.toDivisionAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))))) (SMulZeroClass.toSMul.{u4, u3} 𝕜 β (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 β (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (Module.toMulActionWithZero.{u4, u3} 𝕜 β (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (NormedSpace.boundedSMul.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5)))) (ContinuousMap.module.{u1, u4, u2} X _inst_1 𝕜 γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (TopologicalAddGroup.toContinuousAdd.{u2} γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (NormedAddGroup.toAddGroup.{u2} γ (NormedAddCommGroup.toNormedAddGroup.{u2} γ _inst_6)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7) (ContinuousSMul.continuousConstSMul.{u4, u2} 𝕜 γ (UniformSpace.toTopologicalSpace.{u4} 𝕜 (PseudoMetricSpace.toUniformSpace.{u4} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 γ (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 γ (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 γ (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (Module.toMulActionWithZero.{u4, u2} 𝕜 γ (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7))))) (BoundedSMul.continuousSMul.{u4, u2} 𝕜 γ (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)) (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (NegZeroClass.toZero.{u2} γ (SubNegZeroMonoid.toNegZeroClass.{u2} γ (SubtractionMonoid.toSubNegZeroMonoid.{u2} γ (SubtractionCommMonoid.toSubtractionMonoid.{u2} γ (AddCommGroup.toDivisionAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 γ (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 γ (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 γ (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (Module.toMulActionWithZero.{u4, u2} 𝕜 γ (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7))))) (NormedSpace.boundedSMul.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7))))) (ContinuousLinearMap.toLinearMap.{u4, u4, max u1 u3, max u1 u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (RingHom.id.{u4} 𝕜 (Semiring.toNonAssocSemiring.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.compactOpen.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.instAddCommMonoidContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (TopologicalAddGroup.toContinuousAdd.{u3} β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (ContinuousMap.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))))) (ContinuousMap.compactOpen.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))))) (ContinuousMap.instAddCommMonoidContinuousMap.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (TopologicalAddGroup.toContinuousAdd.{u2} γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (NormedAddGroup.toAddGroup.{u2} γ (NormedAddCommGroup.toNormedAddGroup.{u2} γ _inst_6)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (ContinuousMap.module.{u1, u4, u3} X _inst_1 𝕜 β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (TopologicalAddGroup.toContinuousAdd.{u3} β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (ContinuousSMul.continuousConstSMul.{u4, u3} 𝕜 β (UniformSpace.toTopologicalSpace.{u4} 𝕜 (PseudoMetricSpace.toUniformSpace.{u4} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (SMulZeroClass.toSMul.{u4, u3} 𝕜 β (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 β (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (Module.toMulActionWithZero.{u4, u3} 𝕜 β (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (BoundedSMul.continuousSMul.{u4, u3} 𝕜 β (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)) (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (NegZeroClass.toZero.{u3} β (SubNegZeroMonoid.toNegZeroClass.{u3} β (SubtractionMonoid.toSubNegZeroMonoid.{u3} β (SubtractionCommMonoid.toSubtractionMonoid.{u3} β (AddCommGroup.toDivisionAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))))) (SMulZeroClass.toSMul.{u4, u3} 𝕜 β (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 β (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (Module.toMulActionWithZero.{u4, u3} 𝕜 β (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (NormedSpace.boundedSMul.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5)))) (ContinuousMap.module.{u1, u4, u2} X _inst_1 𝕜 γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (TopologicalAddGroup.toContinuousAdd.{u2} γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (NormedAddGroup.toAddGroup.{u2} γ (NormedAddCommGroup.toNormedAddGroup.{u2} γ _inst_6)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7) (ContinuousSMul.continuousConstSMul.{u4, u2} 𝕜 γ (UniformSpace.toTopologicalSpace.{u4} 𝕜 (PseudoMetricSpace.toUniformSpace.{u4} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 γ (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 γ (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 γ (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (Module.toMulActionWithZero.{u4, u2} 𝕜 γ (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7))))) (BoundedSMul.continuousSMul.{u4, u2} 𝕜 γ (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)) (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (NegZeroClass.toZero.{u2} γ (SubNegZeroMonoid.toNegZeroClass.{u2} γ (SubtractionMonoid.toSubNegZeroMonoid.{u2} γ (SubtractionCommMonoid.toSubtractionMonoid.{u2} γ (AddCommGroup.toDivisionAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 γ (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 γ (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 γ (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (Module.toMulActionWithZero.{u4, u2} 𝕜 γ (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7))))) (NormedSpace.boundedSMul.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7)))) (ContinuousLinearMap.compLeftContinuousCompact.{u1, u4, u3, u2} X 𝕜 β γ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 g)) (ContinuousLinearMap.compLeftContinuous.{u4, u3, u2, u1} 𝕜 β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (TopologicalAddGroup.toContinuousAdd.{u3} β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (ContinuousSMul.continuousConstSMul.{u4, u3} 𝕜 β (UniformSpace.toTopologicalSpace.{u4} 𝕜 (PseudoMetricSpace.toUniformSpace.{u4} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (SMulZeroClass.toSMul.{u4, u3} 𝕜 β (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 β (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (Module.toMulActionWithZero.{u4, u3} 𝕜 β (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (BoundedSMul.continuousSMul.{u4, u3} 𝕜 β (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)) (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (NegZeroClass.toZero.{u3} β (SubNegZeroMonoid.toNegZeroClass.{u3} β (SubtractionMonoid.toSubNegZeroMonoid.{u3} β (SubtractionCommMonoid.toSubtractionMonoid.{u3} β (AddCommGroup.toDivisionAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))))) (SMulZeroClass.toSMul.{u4, u3} 𝕜 β (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 β (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (Module.toMulActionWithZero.{u4, u3} 𝕜 β (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (NormedSpace.boundedSMul.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))) (TopologicalAddGroup.toContinuousAdd.{u2} γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (NormedAddGroup.toAddGroup.{u2} γ (NormedAddCommGroup.toNormedAddGroup.{u2} γ _inst_6)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7) (ContinuousSMul.continuousConstSMul.{u4, u2} 𝕜 γ (UniformSpace.toTopologicalSpace.{u4} 𝕜 (PseudoMetricSpace.toUniformSpace.{u4} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 γ (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 γ (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 γ (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (Module.toMulActionWithZero.{u4, u2} 𝕜 γ (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7))))) (BoundedSMul.continuousSMul.{u4, u2} 𝕜 γ (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)) (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (NegZeroClass.toZero.{u2} γ (SubNegZeroMonoid.toNegZeroClass.{u2} γ (SubtractionMonoid.toSubNegZeroMonoid.{u2} γ (SubtractionCommMonoid.toSubtractionMonoid.{u2} γ (AddCommGroup.toDivisionAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 γ (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 γ (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 γ (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (Module.toMulActionWithZero.{u4, u2} 𝕜 γ (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7))))) (NormedSpace.boundedSMul.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7))) X _inst_1 g)
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.to_linear_comp_left_continuous_compact ContinuousLinearMap.toLinear_compLeftContinuousCompactₓ'. -/
@[simp]
theorem ContinuousLinearMap.toLinear_compLeftContinuousCompact (g : β →L[𝕜] γ) :
@@ -666,10 +636,7 @@ theorem ContinuousLinearMap.toLinear_compLeftContinuousCompact (g : β →L[𝕜
#align continuous_linear_map.to_linear_comp_left_continuous_compact ContinuousLinearMap.toLinear_compLeftContinuousCompact
/- warning: continuous_linear_map.comp_left_continuous_compact_apply -> ContinuousLinearMap.compLeftContinuousCompact_apply is a dubious translation:
-lean 3 declaration is
- forall (X : Type.{u1}) {𝕜 : Type.{u2}} {β : Type.{u3}} {γ : Type.{u4}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : CompactSpace.{u1} X _inst_1] [_inst_3 : NontriviallyNormedField.{u2} 𝕜] [_inst_4 : NormedAddCommGroup.{u3} β] [_inst_5 : NormedSpace.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)] [_inst_6 : NormedAddCommGroup.{u4} γ] [_inst_7 : NormedSpace.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)] (g : ContinuousLinearMap.{u2, u2, u3, u4} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) γ (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7)) (f : ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (x : X), Eq.{succ u4} γ (coeFn.{max (succ u1) (succ u4), max (succ u1) (succ u4)} (ContinuousMap.{u1, u4} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))))) (fun (_x : ContinuousMap.{u1, u4} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))))) => X -> γ) (ContinuousMap.hasCoeToFun.{u1, u4} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))))) (coeFn.{max (succ (max u1 u3)) (succ (max u1 u4)), max (succ (max u1 u3)) (succ (max u1 u4))} (ContinuousLinearMap.{u2, u2, max u1 u3, max u1 u4} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.compactOpen.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.addCommMonoid.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (ContinuousLinearMap.compLeftContinuousCompact._proof_1.{u3} β _inst_4)) (ContinuousMap.{u1, u4} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))))) (ContinuousMap.compactOpen.{u1, u4} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))))) (ContinuousMap.addCommMonoid.{u1, u4} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (ContinuousLinearMap.compLeftContinuousCompact._proof_2.{u4} γ _inst_6)) (ContinuousMap.module.{u1, u2, u3} X _inst_1 𝕜 β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (ContinuousLinearMap.compLeftContinuousCompact._proof_3.{u3} β _inst_4) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (ContinuousLinearMap.compLeftContinuousCompact._proof_4.{u2, u3} 𝕜 β _inst_3 _inst_4 _inst_5)) (ContinuousMap.module.{u1, u2, u4} X _inst_1 𝕜 γ (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (ContinuousLinearMap.compLeftContinuousCompact._proof_5.{u4} γ _inst_6) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7) (ContinuousLinearMap.compLeftContinuousCompact._proof_6.{u2, u4} 𝕜 γ _inst_3 _inst_6 _inst_7))) (fun (_x : ContinuousLinearMap.{u2, u2, max u1 u3, max u1 u4} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 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(NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7)) g (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (fun (_x : ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) => X -> β) (ContinuousMap.hasCoeToFun.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β 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- forall (X : Type.{u1}) {𝕜 : Type.{u4}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : CompactSpace.{u1} X _inst_1] [_inst_3 : NontriviallyNormedField.{u4} 𝕜] [_inst_4 : NormedAddCommGroup.{u3} β] [_inst_5 : NormedSpace.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)] [_inst_6 : NormedAddCommGroup.{u2} γ] [_inst_7 : NormedSpace.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)] (g : ContinuousLinearMap.{u4, u4, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (RingHom.id.{u4} 𝕜 (Semiring.toNonAssocSemiring.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) 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(SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))))) f) X (fun (_x : X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : X) => γ) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) => ContinuousMap.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))))) f) X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (ContinuousMap.instContinuousMapClassContinuousMap.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u3), max (succ u1) (succ u2)} (ContinuousLinearMap.{u4, u4, max u3 u1, max u2 u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (RingHom.id.{u4} 𝕜 (Semiring.toNonAssocSemiring.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.compactOpen.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.instAddCommMonoidContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (TopologicalAddGroup.toContinuousAdd.{u3} β (UniformSpace.toTopologicalSpace.{u3} β 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(SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (TopologicalAddGroup.toContinuousAdd.{u2} γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (NormedAddGroup.toAddGroup.{u2} γ (NormedAddCommGroup.toNormedAddGroup.{u2} γ _inst_6)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (ContinuousMap.module.{u1, u4, u3} X _inst_1 𝕜 β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 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(SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)) (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (NegZeroClass.toZero.{u3} β (SubNegZeroMonoid.toNegZeroClass.{u3} β (SubtractionMonoid.toSubNegZeroMonoid.{u3} β (SubtractionCommMonoid.toSubtractionMonoid.{u3} β (AddCommGroup.toDivisionAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))))) (SMulZeroClass.toSMul.{u4, u3} 𝕜 β (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 β (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (Module.toMulActionWithZero.{u4, u3} 𝕜 β (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (NormedSpace.boundedSMul.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5)))) (ContinuousMap.module.{u1, u4, u2} X _inst_1 𝕜 γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (TopologicalAddGroup.toContinuousAdd.{u2} γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (NormedAddGroup.toAddGroup.{u2} γ (NormedAddCommGroup.toNormedAddGroup.{u2} γ _inst_6)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7) (ContinuousSMul.continuousConstSMul.{u4, u2} 𝕜 γ (UniformSpace.toTopologicalSpace.{u4} 𝕜 (PseudoMetricSpace.toUniformSpace.{u4} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 γ (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 γ (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 γ (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (Module.toMulActionWithZero.{u4, u2} 𝕜 γ (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7))))) (BoundedSMul.continuousSMul.{u4, u2} 𝕜 γ (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)) (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (NegZeroClass.toZero.{u2} γ (SubNegZeroMonoid.toNegZeroClass.{u2} γ (SubtractionMonoid.toSubNegZeroMonoid.{u2} γ (SubtractionCommMonoid.toSubtractionMonoid.{u2} γ (AddCommGroup.toDivisionAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 γ (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 γ (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 γ (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (Module.toMulActionWithZero.{u4, u2} 𝕜 γ (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7))))) (NormedSpace.boundedSMul.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7))))) (ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (fun (_x : ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) => ContinuousMap.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))))) _x) (ContinuousMapClass.toFunLike.{max (max u1 u3) u2, max u1 u3, max u1 u2} (ContinuousLinearMap.{u4, u4, max u3 u1, max u2 u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (RingHom.id.{u4} 𝕜 (Semiring.toNonAssocSemiring.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.compactOpen.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.instAddCommMonoidContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (TopologicalAddGroup.toContinuousAdd.{u3} β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (ContinuousMap.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))))) (ContinuousMap.compactOpen.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))))) (ContinuousMap.instAddCommMonoidContinuousMap.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (TopologicalAddGroup.toContinuousAdd.{u2} γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (NormedAddGroup.toAddGroup.{u2} γ (NormedAddCommGroup.toNormedAddGroup.{u2} γ _inst_6)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (ContinuousMap.module.{u1, u4, u3} X _inst_1 𝕜 β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (TopologicalAddGroup.toContinuousAdd.{u3} β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (ContinuousSMul.continuousConstSMul.{u4, u3} 𝕜 β (UniformSpace.toTopologicalSpace.{u4} 𝕜 (PseudoMetricSpace.toUniformSpace.{u4} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (SMulZeroClass.toSMul.{u4, u3} 𝕜 β (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 β (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (Module.toMulActionWithZero.{u4, u3} 𝕜 β (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (BoundedSMul.continuousSMul.{u4, u3} 𝕜 β (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)) (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (NegZeroClass.toZero.{u3} β (SubNegZeroMonoid.toNegZeroClass.{u3} β (SubtractionMonoid.toSubNegZeroMonoid.{u3} β (SubtractionCommMonoid.toSubtractionMonoid.{u3} β (AddCommGroup.toDivisionAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))))) (SMulZeroClass.toSMul.{u4, u3} 𝕜 β (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 β (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (Module.toMulActionWithZero.{u4, u3} 𝕜 β (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (NormedSpace.boundedSMul.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5)))) (ContinuousMap.module.{u1, u4, u2} X _inst_1 𝕜 γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (TopologicalAddGroup.toContinuousAdd.{u2} γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (NormedAddGroup.toAddGroup.{u2} γ (NormedAddCommGroup.toNormedAddGroup.{u2} γ _inst_6)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7) (ContinuousSMul.continuousConstSMul.{u4, u2} 𝕜 γ (UniformSpace.toTopologicalSpace.{u4} 𝕜 (PseudoMetricSpace.toUniformSpace.{u4} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 γ (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 γ (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 γ (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (Module.toMulActionWithZero.{u4, u2} 𝕜 γ (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7))))) (BoundedSMul.continuousSMul.{u4, u2} 𝕜 γ (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)) (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (NegZeroClass.toZero.{u2} γ (SubNegZeroMonoid.toNegZeroClass.{u2} γ (SubtractionMonoid.toSubNegZeroMonoid.{u2} γ (SubtractionCommMonoid.toSubtractionMonoid.{u2} γ (AddCommGroup.toDivisionAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 γ (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 γ (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 γ (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (Module.toMulActionWithZero.{u4, u2} 𝕜 γ (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7))))) (NormedSpace.boundedSMul.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7))))) (ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))))) (ContinuousMap.compactOpen.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.compactOpen.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max (max u1 u3) u2, u4, u4, max u1 u3, max u1 u2} (ContinuousLinearMap.{u4, u4, max u3 u1, max u2 u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (RingHom.id.{u4} 𝕜 (Semiring.toNonAssocSemiring.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.compactOpen.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.instAddCommMonoidContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (TopologicalAddGroup.toContinuousAdd.{u3} β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (ContinuousMap.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))))) (ContinuousMap.compactOpen.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))))) (ContinuousMap.instAddCommMonoidContinuousMap.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (TopologicalAddGroup.toContinuousAdd.{u2} γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (NormedAddGroup.toAddGroup.{u2} γ (NormedAddCommGroup.toNormedAddGroup.{u2} γ _inst_6)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (ContinuousMap.module.{u1, u4, u3} X _inst_1 𝕜 β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (TopologicalAddGroup.toContinuousAdd.{u3} β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (ContinuousSMul.continuousConstSMul.{u4, u3} 𝕜 β (UniformSpace.toTopologicalSpace.{u4} 𝕜 (PseudoMetricSpace.toUniformSpace.{u4} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (SMulZeroClass.toSMul.{u4, u3} 𝕜 β (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 β (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (Module.toMulActionWithZero.{u4, u3} 𝕜 β (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (BoundedSMul.continuousSMul.{u4, u3} 𝕜 β (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)) (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (NegZeroClass.toZero.{u3} β (SubNegZeroMonoid.toNegZeroClass.{u3} β (SubtractionMonoid.toSubNegZeroMonoid.{u3} β (SubtractionCommMonoid.toSubtractionMonoid.{u3} β (AddCommGroup.toDivisionAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))))) (SMulZeroClass.toSMul.{u4, u3} 𝕜 β (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 β (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (Module.toMulActionWithZero.{u4, u3} 𝕜 β (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (NormedSpace.boundedSMul.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5)))) (ContinuousMap.module.{u1, u4, u2} X _inst_1 𝕜 γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (TopologicalAddGroup.toContinuousAdd.{u2} γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (NormedAddGroup.toAddGroup.{u2} γ (NormedAddCommGroup.toNormedAddGroup.{u2} γ _inst_6)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7) (ContinuousSMul.continuousConstSMul.{u4, u2} 𝕜 γ (UniformSpace.toTopologicalSpace.{u4} 𝕜 (PseudoMetricSpace.toUniformSpace.{u4} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 γ (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 γ (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 γ (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (Module.toMulActionWithZero.{u4, u2} 𝕜 γ (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7))))) (BoundedSMul.continuousSMul.{u4, u2} 𝕜 γ (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)) (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (NegZeroClass.toZero.{u2} γ (SubNegZeroMonoid.toNegZeroClass.{u2} γ (SubtractionMonoid.toSubNegZeroMonoid.{u2} γ (SubtractionCommMonoid.toSubtractionMonoid.{u2} γ (AddCommGroup.toDivisionAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 γ (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 γ (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 γ (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (Module.toMulActionWithZero.{u4, u2} 𝕜 γ (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7))))) (NormedSpace.boundedSMul.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7))))) 𝕜 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (RingHom.id.{u4} 𝕜 (Semiring.toNonAssocSemiring.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.compactOpen.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.instAddCommMonoidContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (TopologicalAddGroup.toContinuousAdd.{u3} β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (ContinuousMap.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))))) (ContinuousMap.compactOpen.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))))) (ContinuousMap.instAddCommMonoidContinuousMap.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (TopologicalAddGroup.toContinuousAdd.{u2} γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (NormedAddGroup.toAddGroup.{u2} γ (NormedAddCommGroup.toNormedAddGroup.{u2} γ _inst_6)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (ContinuousMap.module.{u1, u4, u3} X _inst_1 𝕜 β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (TopologicalAddGroup.toContinuousAdd.{u3} β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (ContinuousSMul.continuousConstSMul.{u4, u3} 𝕜 β (UniformSpace.toTopologicalSpace.{u4} 𝕜 (PseudoMetricSpace.toUniformSpace.{u4} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (SMulZeroClass.toSMul.{u4, u3} 𝕜 β (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 β (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (Module.toMulActionWithZero.{u4, u3} 𝕜 β (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (BoundedSMul.continuousSMul.{u4, u3} 𝕜 β (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)) (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (NegZeroClass.toZero.{u3} β (SubNegZeroMonoid.toNegZeroClass.{u3} β (SubtractionMonoid.toSubNegZeroMonoid.{u3} β (SubtractionCommMonoid.toSubtractionMonoid.{u3} β (AddCommGroup.toDivisionAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))))) (SMulZeroClass.toSMul.{u4, u3} 𝕜 β (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 β (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (Module.toMulActionWithZero.{u4, u3} 𝕜 β (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (NormedSpace.boundedSMul.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5)))) (ContinuousMap.module.{u1, u4, u2} X _inst_1 𝕜 γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (TopologicalAddGroup.toContinuousAdd.{u2} γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (NormedAddGroup.toAddGroup.{u2} γ (NormedAddCommGroup.toNormedAddGroup.{u2} γ _inst_6)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7) (ContinuousSMul.continuousConstSMul.{u4, u2} 𝕜 γ (UniformSpace.toTopologicalSpace.{u4} 𝕜 (PseudoMetricSpace.toUniformSpace.{u4} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 γ (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 γ (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 γ (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (Module.toMulActionWithZero.{u4, u2} 𝕜 γ (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7))))) (BoundedSMul.continuousSMul.{u4, u2} 𝕜 γ (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)) (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (NegZeroClass.toZero.{u2} γ (SubNegZeroMonoid.toNegZeroClass.{u2} γ (SubtractionMonoid.toSubNegZeroMonoid.{u2} γ (SubtractionCommMonoid.toSubtractionMonoid.{u2} γ (AddCommGroup.toDivisionAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 γ (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 γ (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 γ (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (Module.toMulActionWithZero.{u4, u2} 𝕜 γ (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7))))) (NormedSpace.boundedSMul.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7)))) (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u4, max u1 u3, max u1 u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (RingHom.id.{u4} 𝕜 (Semiring.toNonAssocSemiring.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.compactOpen.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.instAddCommMonoidContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (TopologicalAddGroup.toContinuousAdd.{u3} β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (ContinuousMap.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))))) (ContinuousMap.compactOpen.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))))) (ContinuousMap.instAddCommMonoidContinuousMap.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (TopologicalAddGroup.toContinuousAdd.{u2} γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (NormedAddGroup.toAddGroup.{u2} γ (NormedAddCommGroup.toNormedAddGroup.{u2} γ _inst_6)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (ContinuousMap.module.{u1, u4, u3} X _inst_1 𝕜 β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (TopologicalAddGroup.toContinuousAdd.{u3} β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (ContinuousSMul.continuousConstSMul.{u4, u3} 𝕜 β (UniformSpace.toTopologicalSpace.{u4} 𝕜 (PseudoMetricSpace.toUniformSpace.{u4} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (SMulZeroClass.toSMul.{u4, u3} 𝕜 β (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 β (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (Module.toMulActionWithZero.{u4, u3} 𝕜 β (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (BoundedSMul.continuousSMul.{u4, u3} 𝕜 β (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)) (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (NegZeroClass.toZero.{u3} β (SubNegZeroMonoid.toNegZeroClass.{u3} β (SubtractionMonoid.toSubNegZeroMonoid.{u3} β (SubtractionCommMonoid.toSubtractionMonoid.{u3} β (AddCommGroup.toDivisionAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))))) (SMulZeroClass.toSMul.{u4, u3} 𝕜 β (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 β (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (Module.toMulActionWithZero.{u4, u3} 𝕜 β (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (NormedSpace.boundedSMul.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5)))) (ContinuousMap.module.{u1, u4, u2} X _inst_1 𝕜 γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (TopologicalAddGroup.toContinuousAdd.{u2} γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (NormedAddGroup.toAddGroup.{u2} γ (NormedAddCommGroup.toNormedAddGroup.{u2} γ _inst_6)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7) (ContinuousSMul.continuousConstSMul.{u4, u2} 𝕜 γ (UniformSpace.toTopologicalSpace.{u4} 𝕜 (PseudoMetricSpace.toUniformSpace.{u4} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 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(SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)) (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (NegZeroClass.toZero.{u2} γ (SubNegZeroMonoid.toNegZeroClass.{u2} γ (SubtractionMonoid.toSubNegZeroMonoid.{u2} γ (SubtractionCommMonoid.toSubtractionMonoid.{u2} γ (AddCommGroup.toDivisionAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 γ (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) 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(NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7)) 𝕜 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (RingHom.id.{u4} 𝕜 (Semiring.toNonAssocSemiring.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) γ 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(NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7)))) g (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) X (fun (_x : X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : X) => β) _x) (ContinuousMapClass.toFunLike.{max u1 u3, u1, u3} (ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β 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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_left_continuous_compact_apply ContinuousLinearMap.compLeftContinuousCompact_applyₓ'. -/
@[simp]
theorem ContinuousLinearMap.compLeftContinuousCompact_apply (g : β →L[𝕜] γ) (f : C(X, β)) (x : X) :
@@ -738,10 +705,7 @@ def compRightHomeomorph {X Y : Type _} (T : Type _) [TopologicalSpace X] [Compac
-/
/- warning: continuous_map.comp_right_alg_hom_continuous -> ContinuousMap.compRightAlgHom_continuous is a dubious translation:
-lean 3 declaration is
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(UniformSpace.toTopologicalSpace.{u4} A (PseudoMetricSpace.toUniformSpace.{u4} A (MetricSpace.toPseudoMetricSpace.{u4} A _inst_7))) _inst_6 _inst_8) (ContinuousMap.semiring.{u1, u4} X A _inst_1 (UniformSpace.toTopologicalSpace.{u4} A (PseudoMetricSpace.toUniformSpace.{u4} A (MetricSpace.toPseudoMetricSpace.{u4} A _inst_7))) _inst_6 _inst_8) (ContinuousMap.algebra.{u2, u3, u4} Y _inst_3 R _inst_5 A (UniformSpace.toTopologicalSpace.{u4} A (PseudoMetricSpace.toUniformSpace.{u4} A (MetricSpace.toPseudoMetricSpace.{u4} A _inst_7))) _inst_6 _inst_9 _inst_8) (ContinuousMap.algebra.{u1, u3, u4} X _inst_1 R _inst_5 A (UniformSpace.toTopologicalSpace.{u4} A (PseudoMetricSpace.toUniformSpace.{u4} A (MetricSpace.toPseudoMetricSpace.{u4} A _inst_7))) _inst_6 _inst_9 _inst_8)) (fun (_x : AlgHom.{u3, max u2 u4, max u1 u4} R (ContinuousMap.{u2, u4} Y A _inst_3 (UniformSpace.toTopologicalSpace.{u4} A (PseudoMetricSpace.toUniformSpace.{u4} A (MetricSpace.toPseudoMetricSpace.{u4} A _inst_7)))) 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(ContinuousMap.{u2, u4} Y A _inst_3 (UniformSpace.toTopologicalSpace.{u4} A (PseudoMetricSpace.toUniformSpace.{u4} A (MetricSpace.toPseudoMetricSpace.{u4} A _inst_7)))) -> (ContinuousMap.{u1, u4} X A _inst_1 (UniformSpace.toTopologicalSpace.{u4} A (PseudoMetricSpace.toUniformSpace.{u4} A (MetricSpace.toPseudoMetricSpace.{u4} A _inst_7))))) ([anonymous].{u3, max u2 u4, max u1 u4} R (ContinuousMap.{u2, u4} Y A _inst_3 (UniformSpace.toTopologicalSpace.{u4} A (PseudoMetricSpace.toUniformSpace.{u4} A (MetricSpace.toPseudoMetricSpace.{u4} A _inst_7)))) (ContinuousMap.{u1, u4} X A _inst_1 (UniformSpace.toTopologicalSpace.{u4} A (PseudoMetricSpace.toUniformSpace.{u4} A (MetricSpace.toPseudoMetricSpace.{u4} A _inst_7)))) _inst_5 (ContinuousMap.semiring.{u2, u4} Y A _inst_3 (UniformSpace.toTopologicalSpace.{u4} A (PseudoMetricSpace.toUniformSpace.{u4} A (MetricSpace.toPseudoMetricSpace.{u4} A _inst_7))) _inst_6 _inst_8) (ContinuousMap.semiring.{u1, u4} X A _inst_1 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- forall {X : Type.{u4}} {Y : Type.{u3}} (R : Type.{u2}) (A : Type.{u1}) [_inst_1 : TopologicalSpace.{u4} X] [_inst_2 : CompactSpace.{u4} X _inst_1] [_inst_3 : TopologicalSpace.{u3} Y] [_inst_4 : CompactSpace.{u3} Y _inst_3] [_inst_5 : CommSemiring.{u2} R] [_inst_6 : Semiring.{u1} A] [_inst_7 : MetricSpace.{u1} A] [_inst_8 : TopologicalSemiring.{u1} A (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_6))] [_inst_9 : Algebra.{u2, u1} R A _inst_5 _inst_6] (f : ContinuousMap.{u4, u3} X Y _inst_1 _inst_3), Continuous.{max u3 u1, max u4 u1} (ContinuousMap.{u3, u1} Y A _inst_3 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7)))) (ContinuousMap.{u4, u1} X A _inst_1 (UniformSpace.toTopologicalSpace.{u1} A 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(PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) _inst_6 _inst_8) (ContinuousMap.algebra.{u3, u2, u1} Y _inst_3 R _inst_5 A (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) _inst_6 _inst_9 _inst_8))) (Module.toDistribMulAction.{u2, max u4 u1} R (ContinuousMap.{u4, u1} X A _inst_1 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7)))) (CommSemiring.toSemiring.{u2} R _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (ContinuousMap.{u4, u1} X A _inst_1 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (ContinuousMap.{u4, u1} X A _inst_1 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7)))) (Semiring.toNonAssocSemiring.{max u4 u1} (ContinuousMap.{u4, u1} X A _inst_1 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7)))) (ContinuousMap.instSemiringContinuousMap.{u4, u1} X A _inst_1 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) _inst_6 _inst_8)))) (Algebra.toModule.{u2, max u4 u1} R (ContinuousMap.{u4, u1} X A _inst_1 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7)))) _inst_5 (ContinuousMap.instSemiringContinuousMap.{u4, u1} X A _inst_1 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) _inst_6 _inst_8) (ContinuousMap.algebra.{u4, u2, u1} X _inst_1 R _inst_5 A (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) _inst_6 _inst_9 _inst_8))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u1, max u4 u1, max (max u4 u3) u1} R (ContinuousMap.{u3, u1} Y A _inst_3 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7)))) (ContinuousMap.{u4, u1} X A _inst_1 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7)))) _inst_5 (ContinuousMap.instSemiringContinuousMap.{u3, u1} Y A _inst_3 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) _inst_6 _inst_8) (ContinuousMap.instSemiringContinuousMap.{u4, u1} X A _inst_1 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) _inst_6 _inst_8) (ContinuousMap.algebra.{u3, u2, u1} Y _inst_3 R _inst_5 A (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) _inst_6 _inst_9 _inst_8) (ContinuousMap.algebra.{u4, u2, u1} X _inst_1 R _inst_5 A (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) _inst_6 _inst_9 _inst_8) (AlgHom.{u2, max u1 u3, max u1 u4} R (ContinuousMap.{u3, u1} Y A _inst_3 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7)))) (ContinuousMap.{u4, u1} X A _inst_1 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7)))) _inst_5 (ContinuousMap.instSemiringContinuousMap.{u3, u1} Y A _inst_3 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) _inst_6 _inst_8) (ContinuousMap.instSemiringContinuousMap.{u4, u1} X A _inst_1 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) _inst_6 _inst_8) (ContinuousMap.algebra.{u3, u2, u1} Y _inst_3 R _inst_5 A (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) _inst_6 _inst_9 _inst_8) (ContinuousMap.algebra.{u4, u2, u1} X _inst_1 R _inst_5 A (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) _inst_6 _inst_9 _inst_8)) (AlgHom.algHomClass.{u2, max u3 u1, max u4 u1} R (ContinuousMap.{u3, u1} Y A _inst_3 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7)))) (ContinuousMap.{u4, u1} X A _inst_1 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7)))) _inst_5 (ContinuousMap.instSemiringContinuousMap.{u3, u1} Y A _inst_3 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) _inst_6 _inst_8) (ContinuousMap.instSemiringContinuousMap.{u4, u1} X A _inst_1 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) _inst_6 _inst_8) (ContinuousMap.algebra.{u3, u2, u1} Y _inst_3 R _inst_5 A (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) _inst_6 _inst_9 _inst_8) (ContinuousMap.algebra.{u4, u2, u1} X _inst_1 R _inst_5 A (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) _inst_6 _inst_9 _inst_8)))))) (ContinuousMap.compRightAlgHom.{u2, u1, u4, u3} R _inst_5 A (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) _inst_6 _inst_9 _inst_8 X Y _inst_1 _inst_3 f))
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_map.comp_right_alg_hom_continuous ContinuousMap.compRightAlgHom_continuousₓ'. -/
theorem compRightAlgHom_continuous {X Y : Type _} (R A : Type _) [TopologicalSpace X]
[CompactSpace X] [TopologicalSpace Y] [CompactSpace Y] [CommSemiring R] [Semiring A]
@@ -768,10 +732,7 @@ variable {X : Type _} [TopologicalSpace X] [T2Space X] [LocallyCompactSpace X]
variable {E : Type _} [NormedAddCommGroup E] [CompleteSpace E]
/- warning: continuous_map.summable_of_locally_summable_norm -> ContinuousMap.summable_of_locally_summable_norm is a dubious translation:
-lean 3 declaration is
- forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : T2Space.{u1} X _inst_1] [_inst_3 : LocallyCompactSpace.{u1} X _inst_1] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : CompleteSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))] {ι : Type.{u3}} {F : ι -> (ContinuousMap.{u1, u2} X E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))))}, (forall (K : TopologicalSpace.Compacts.{u1} X _inst_1), Summable.{0, u3} Real ι Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => Norm.norm.{max u1 u2} (ContinuousMap.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} X) Type.{u1} (Set.hasCoeToSort.{u1} X) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Compacts.{u1} X _inst_1) (Set.{u1} X) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} X _inst_1) (Set.{u1} X) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} X _inst_1) (Set.{u1} X) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Compacts.{u1} X _inst_1) X (TopologicalSpace.Compacts.setLike.{u1} X _inst_1)))) K)) E (Subtype.topologicalSpace.{u1} X (fun (x : X) => Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) x ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Compacts.{u1} X _inst_1) (Set.{u1} X) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} X _inst_1) (Set.{u1} X) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} X _inst_1) (Set.{u1} X) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Compacts.{u1} X _inst_1) X (TopologicalSpace.Compacts.setLike.{u1} X _inst_1)))) K)) _inst_1) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.hasNorm.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} X) Type.{u1} (Set.hasCoeToSort.{u1} X) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Compacts.{u1} X _inst_1) (Set.{u1} X) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} X _inst_1) (Set.{u1} X) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} X _inst_1) (Set.{u1} X) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Compacts.{u1} X _inst_1) X (TopologicalSpace.Compacts.setLike.{u1} X _inst_1)))) K)) E (Subtype.topologicalSpace.{u1} X (fun (x : X) => Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) x ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Compacts.{u1} X _inst_1) (Set.{u1} X) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} X _inst_1) (Set.{u1} X) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} X _inst_1) (Set.{u1} X) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Compacts.{u1} X _inst_1) X (TopologicalSpace.Compacts.setLike.{u1} X _inst_1)))) K)) _inst_1) (TopologicalSpace.Compacts.compactSpace.{u1} X _inst_1 K) _inst_4) (ContinuousMap.restrict.{u1, u2} X E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Compacts.{u1} X _inst_1) (Set.{u1} X) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} X _inst_1) (Set.{u1} X) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} X _inst_1) (Set.{u1} X) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Compacts.{u1} X _inst_1) X (TopologicalSpace.Compacts.setLike.{u1} X _inst_1)))) K) (F i)))) -> (Summable.{max u1 u2, u3} (ContinuousMap.{u1, u2} X E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) ι (ContinuousMap.addCommMonoid.{u1, u2} X E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (LipschitzAdd.continuousAdd.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (ContinuousMap.compactOpen.{u1, u2} X E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) F)
-but is expected to have type
- forall {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : T2Space.{u2} X _inst_1] [_inst_3 : LocallyCompactSpace.{u2} X _inst_1] {E : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} E] [_inst_5 : CompleteSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4)))] {ι : Type.{u3}} {F : ι -> (ContinuousMap.{u2, u1} X E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4)))))}, (forall (K : TopologicalSpace.Compacts.{u2} X _inst_1), Summable.{0, u3} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => Norm.norm.{max u2 u1} (ContinuousMap.{u2, u1} (Set.Elem.{u2} X (SetLike.coe.{u2, u2} (TopologicalSpace.Compacts.{u2} X _inst_1) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u2} X _inst_1) K)) E (instTopologicalSpaceSubtype.{u2} X (fun (x : X) => Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) x (SetLike.coe.{u2, u2} (TopologicalSpace.Compacts.{u2} X _inst_1) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u2} X _inst_1) K)) _inst_1) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) (ContinuousMap.instNormContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u2, u1} (Set.Elem.{u2} X (SetLike.coe.{u2, u2} (TopologicalSpace.Compacts.{u2} X _inst_1) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u2} X _inst_1) K)) E (instTopologicalSpaceSubtype.{u2} X (fun (x : X) => Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) x (SetLike.coe.{u2, u2} (TopologicalSpace.Compacts.{u2} X _inst_1) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u2} X _inst_1) K)) _inst_1) (TopologicalSpace.Compacts.instCompactSpaceSubtypeMemCompactsInstMembershipInstSetLikeCompactsInstTopologicalSpaceSubtype.{u2} X _inst_1 K) _inst_4) (ContinuousMap.restrict.{u2, u1} X E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4)))) (SetLike.coe.{u2, u2} (TopologicalSpace.Compacts.{u2} X _inst_1) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u2} X _inst_1) K) (F i)))) -> (Summable.{max u2 u1, u3} (ContinuousMap.{u2, u1} X E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) ι (ContinuousMap.instAddCommMonoidContinuousMap.{u2, u1} X E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_4)) (TopologicalAddGroup.toContinuousAdd.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4)))) (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4)))) (ContinuousMap.compactOpen.{u2, u1} X E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) F)
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_map.summable_of_locally_summable_norm ContinuousMap.summable_of_locally_summable_normₓ'. -/
theorem summable_of_locally_summable_norm {ι : Type _} {F : ι → C(X, E)}
(hF : ∀ K : Compacts X, Summable fun i => ‖(F i).restrict K‖) : Summable F :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/ef95945cd48c932c9e034872bd25c3c220d9c946
@@ -46,6 +46,7 @@ section
variable (α β)
+#print ContinuousMap.equivBoundedOfCompact /-
/-- When `α` is compact, the bounded continuous maps `α →ᵇ β` are
equivalent to `C(α, β)`.
-/
@@ -58,7 +59,14 @@ def equivBoundedOfCompact : C(α, β) ≃ (α →ᵇ β) :=
ext
rfl⟩
#align continuous_map.equiv_bounded_of_compact ContinuousMap.equivBoundedOfCompact
+-/
+/- warning: continuous_map.uniform_inducing_equiv_bounded_of_compact -> ContinuousMap.uniformInducing_equivBoundedOfCompact is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align continuous_map.uniform_inducing_equiv_bounded_of_compact ContinuousMap.uniformInducing_equivBoundedOfCompactₓ'. -/
theorem uniformInducing_equivBoundedOfCompact : UniformInducing (equivBoundedOfCompact α β) :=
UniformInducing.mk'
(by
@@ -72,10 +80,22 @@ theorem uniformInducing_equivBoundedOfCompact : UniformInducing (equivBoundedOfC
fun ⟨f, g⟩ h => hs _ _ (ht ((dist_le hε.le).mpr fun x => h x (mem_univ x)))⟩⟩)
#align continuous_map.uniform_inducing_equiv_bounded_of_compact ContinuousMap.uniformInducing_equivBoundedOfCompact
+/- warning: continuous_map.uniform_embedding_equiv_bounded_of_compact -> ContinuousMap.uniformEmbedding_equivBoundedOfCompact is a dubious translation:
+lean 3 declaration is
+ forall (α : Type.{u1}) (β : Type.{u2}) [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_3 : MetricSpace.{u2} β], UniformEmbedding.{max u1 u2, max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (BoundedContinuousFunction.{u1, u2} α β _inst_1 (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)) (ContinuousMap.compactConvergenceUniformSpace.{u1, u2} α β _inst_1 (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3))) (PseudoMetricSpace.toUniformSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)) (BoundedContinuousFunction.pseudoMetricSpace.{u1, u2} α β _inst_1 (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3))) (coeFn.{max 1 (max (max (succ u1) (succ u2)) (succ (max u1 u2))) (succ (max u1 u2)) (succ u1) (succ u2), max (max (succ u1) (succ u2)) (succ (max u1 u2))} (Equiv.{max (succ u1) (succ u2), succ (max u1 u2)} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (BoundedContinuousFunction.{u1, u2} α β _inst_1 (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3))) (fun (_x : Equiv.{max (succ u1) (succ u2), succ (max u1 u2)} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (BoundedContinuousFunction.{u1, u2} α β _inst_1 (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3))) => (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) -> (BoundedContinuousFunction.{u1, u2} α β _inst_1 (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3))) (Equiv.hasCoeToFun.{max (succ u1) (succ u2), succ (max u1 u2)} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (BoundedContinuousFunction.{u1, u2} α β _inst_1 (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3))) (ContinuousMap.equivBoundedOfCompact.{u1, u2} α β _inst_1 _inst_2 _inst_3))
+but is expected to have type
+ forall (α : Type.{u2}) (β : Type.{u1}) [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : CompactSpace.{u2} α _inst_1] [_inst_3 : MetricSpace.{u1} β], UniformEmbedding.{max u2 u1, max u2 u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) (BoundedContinuousFunction.{u2, u1} α β _inst_1 (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)) (ContinuousMap.compactConvergenceUniformSpace.{u2, u1} α β _inst_1 (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3))) (PseudoMetricSpace.toUniformSpace.{max u2 u1} (BoundedContinuousFunction.{u2, u1} α β _inst_1 (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)) (BoundedContinuousFunction.instPseudoMetricSpaceBoundedContinuousFunction.{u2, u1} α β _inst_1 (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3))) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (Equiv.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) (BoundedContinuousFunction.{u2, u1} α β _inst_1 (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3))) (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) (fun (_x : ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) => BoundedContinuousFunction.{u2, u1} α β _inst_1 (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)) _x) (Equiv.instFunLikeEquiv.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) (BoundedContinuousFunction.{u2, u1} α β _inst_1 (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3))) (ContinuousMap.equivBoundedOfCompact.{u2, u1} α β _inst_1 _inst_2 _inst_3))
+Case conversion may be inaccurate. Consider using '#align continuous_map.uniform_embedding_equiv_bounded_of_compact ContinuousMap.uniformEmbedding_equivBoundedOfCompactₓ'. -/
theorem uniformEmbedding_equivBoundedOfCompact : UniformEmbedding (equivBoundedOfCompact α β) :=
{ uniformInducing_equivBoundedOfCompact α β with inj := (equivBoundedOfCompact α β).Injective }
#align continuous_map.uniform_embedding_equiv_bounded_of_compact ContinuousMap.uniformEmbedding_equivBoundedOfCompact
+/- warning: continuous_map.add_equiv_bounded_of_compact -> ContinuousMap.addEquivBoundedOfCompact is a dubious translation:
+lean 3 declaration is
+ forall (α : Type.{u1}) (β : Type.{u2}) [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_3 : MetricSpace.{u2} β] [_inst_5 : AddMonoid.{u2} β] [_inst_6 : LipschitzAdd.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3) _inst_5], AddEquiv.{max u1 u2, max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (BoundedContinuousFunction.{u1, u2} α β _inst_1 (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)) (ContinuousMap.instAdd.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3))) (AddZeroClass.toHasAdd.{u2} β (AddMonoid.toAddZeroClass.{u2} β _inst_5)) (ContinuousMap.addEquivBoundedOfCompact._proof_1.{u2} β _inst_3 _inst_5 _inst_6)) (BoundedContinuousFunction.hasAdd.{u1, u2} α β _inst_1 (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3) _inst_5 _inst_6)
+but is expected to have type
+ forall (α : Type.{u1}) (β : Type.{u2}) [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_3 : MetricSpace.{u2} β] [_inst_5 : AddMonoid.{u2} β] [_inst_6 : LipschitzAdd.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3) _inst_5], AddEquiv.{max u2 u1, max u2 u1} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (BoundedContinuousFunction.{u1, u2} α β _inst_1 (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)) (ContinuousMap.instAdd.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3))) (AddZeroClass.toAdd.{u2} β (AddMonoid.toAddZeroClass.{u2} β _inst_5)) (LipschitzAdd.continuousAdd.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3) _inst_5 _inst_6)) (BoundedContinuousFunction.instAddBoundedContinuousFunction.{u1, u2} α β _inst_1 (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3) _inst_5 _inst_6)
+Case conversion may be inaccurate. Consider using '#align continuous_map.add_equiv_bounded_of_compact ContinuousMap.addEquivBoundedOfCompactₓ'. -/
/-- When `α` is compact, the bounded continuous maps `α →ᵇ 𝕜` are
additively equivalent to `C(α, 𝕜)`.
-/
@@ -87,6 +107,12 @@ def addEquivBoundedOfCompact [AddMonoid β] [LipschitzAdd β] : C(α, β) ≃+ (
instance : MetricSpace C(α, β) :=
(uniformEmbedding_equivBoundedOfCompact α β).comapMetricSpace _
+/- warning: continuous_map.isometry_equiv_bounded_of_compact -> ContinuousMap.isometryEquivBoundedOfCompact is a dubious translation:
+lean 3 declaration is
+ forall (α : Type.{u1}) (β : Type.{u2}) [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_3 : MetricSpace.{u2} β], IsometryEquiv.{max u1 u2, max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (BoundedContinuousFunction.{u1, u2} α β _inst_1 (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)) (PseudoMetricSpace.toPseudoEMetricSpace.{max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (MetricSpace.toPseudoMetricSpace.{max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (ContinuousMap.metricSpace.{u1, u2} α β _inst_1 _inst_2 _inst_3))) (PseudoMetricSpace.toPseudoEMetricSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)) (BoundedContinuousFunction.pseudoMetricSpace.{u1, u2} α β _inst_1 (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))
+but is expected to have type
+ forall (α : Type.{u1}) (β : Type.{u2}) [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_3 : MetricSpace.{u2} β], IsometryEquiv.{max u2 u1, max u2 u1} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (BoundedContinuousFunction.{u1, u2} α β _inst_1 (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)) (EMetricSpace.toPseudoEMetricSpace.{max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (MetricSpace.toEMetricSpace.{max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (ContinuousMap.metricSpace.{u1, u2} α β _inst_1 _inst_2 _inst_3))) (EMetricSpace.toPseudoEMetricSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)) (MetricSpace.toEMetricSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)) (BoundedContinuousFunction.instMetricSpaceBoundedContinuousFunctionToPseudoMetricSpace.{u1, u2} α β _inst_1 _inst_3)))
+Case conversion may be inaccurate. Consider using '#align continuous_map.isometry_equiv_bounded_of_compact ContinuousMap.isometryEquivBoundedOfCompactₓ'. -/
/-- When `α` is compact, and `β` is a metric space, the bounded continuous maps `α →ᵇ β` are
isometric to `C(α, β)`.
-/
@@ -99,12 +125,24 @@ def isometryEquivBoundedOfCompact : C(α, β) ≃ᵢ (α →ᵇ β)
end
+/- warning: bounded_continuous_function.dist_mk_of_compact -> BoundedContinuousFunction.dist_mkOfCompact is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : CompactSpace.{u2} α _inst_1] [_inst_3 : MetricSpace.{u1} β] (f : ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) (g : ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))), Eq.{1} Real (Dist.dist.{max u1 u2} (BoundedContinuousFunction.{u2, u1} α β _inst_1 (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)) (BoundedContinuousFunction.instDistBoundedContinuousFunction.{u2, u1} α β _inst_1 (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)) (BoundedContinuousFunction.mkOfCompact.{u2, u1} α β _inst_1 (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3) _inst_2 f) (BoundedContinuousFunction.mkOfCompact.{u2, u1} α β _inst_1 (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3) _inst_2 g)) (Dist.dist.{max u2 u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) (PseudoMetricSpace.toDist.{max u2 u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) (MetricSpace.toPseudoMetricSpace.{max u2 u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) (ContinuousMap.metricSpace.{u2, u1} α β _inst_1 _inst_2 _inst_3))) f g)
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.dist_mk_of_compact BoundedContinuousFunction.dist_mkOfCompactₓ'. -/
@[simp]
theorem BoundedContinuousFunction.dist_mkOfCompact (f g : C(α, β)) :
dist (mkOfCompact f) (mkOfCompact g) = dist f g :=
rfl
#align bounded_continuous_function.dist_mk_of_compact BoundedContinuousFunction.dist_mkOfCompact
+/- warning: bounded_continuous_function.dist_to_continuous_map -> BoundedContinuousFunction.dist_toContinuousMap is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_3 : MetricSpace.{u2} β] (f : BoundedContinuousFunction.{u1, u2} α β _inst_1 (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)) (g : BoundedContinuousFunction.{u1, u2} α β _inst_1 (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)), Eq.{1} Real (Dist.dist.{max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (PseudoMetricSpace.toHasDist.{max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (MetricSpace.toPseudoMetricSpace.{max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (ContinuousMap.metricSpace.{u1, u2} α β _inst_1 _inst_2 _inst_3))) (BoundedContinuousFunction.toContinuousMap.{u1, u2} α β _inst_1 (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3) f) (BoundedContinuousFunction.toContinuousMap.{u1, u2} α β _inst_1 (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3) g)) (Dist.dist.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)) (BoundedContinuousFunction.hasDist.{u1, u2} α β _inst_1 (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)) f g)
+but is expected to have type
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : CompactSpace.{u2} α _inst_1] [_inst_3 : MetricSpace.{u1} β] (f : BoundedContinuousFunction.{u2, u1} α β _inst_1 (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)) (g : BoundedContinuousFunction.{u2, u1} α β _inst_1 (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)), Eq.{1} Real (Dist.dist.{max u2 u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) (PseudoMetricSpace.toDist.{max u2 u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) (MetricSpace.toPseudoMetricSpace.{max u2 u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) (ContinuousMap.metricSpace.{u2, u1} α β _inst_1 _inst_2 _inst_3))) (BoundedContinuousFunction.toContinuousMap.{u2, u1} α β _inst_1 (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3) f) (BoundedContinuousFunction.toContinuousMap.{u2, u1} α β _inst_1 (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3) g)) (Dist.dist.{max u2 u1} (BoundedContinuousFunction.{u2, u1} α β _inst_1 (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)) (BoundedContinuousFunction.instDistBoundedContinuousFunction.{u2, u1} α β _inst_1 (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)) f g)
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.dist_to_continuous_map BoundedContinuousFunction.dist_toContinuousMapₓ'. -/
@[simp]
theorem BoundedContinuousFunction.dist_toContinuousMap (f g : α →ᵇ β) :
dist f.toContinuousMap g.toContinuousMap = dist f g :=
@@ -117,28 +155,64 @@ section
variable {α β} {f g : C(α, β)} {C : ℝ}
+/- warning: continuous_map.dist_apply_le_dist -> ContinuousMap.dist_apply_le_dist is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_3 : MetricSpace.{u2} β] {f : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))} {g : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))} (x : α), LE.le.{0} Real Real.hasLe (Dist.dist.{u2} β (PseudoMetricSpace.toHasDist.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (fun (_x : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) => α -> β) (ContinuousMap.hasCoeToFun.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (fun (_x : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) => α -> β) (ContinuousMap.hasCoeToFun.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) g x)) (Dist.dist.{max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (PseudoMetricSpace.toHasDist.{max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (MetricSpace.toPseudoMetricSpace.{max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (ContinuousMap.metricSpace.{u1, u2} α β _inst_1 _inst_2 _inst_3))) f g)
+but is expected to have type
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_3 : MetricSpace.{u2} β] {f : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))} {g : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))} (x : α), LE.le.{0} Real Real.instLEReal (Dist.dist.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) x) (PseudoMetricSpace.toDist.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) x) (MetricSpace.toPseudoMetricSpace.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) x) _inst_3)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) α (fun (_x : α) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3))) (ContinuousMap.instContinuousMapClassContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) α (fun (_x : α) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3))) (ContinuousMap.instContinuousMapClassContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3))))) g x)) (Dist.dist.{max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (PseudoMetricSpace.toDist.{max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (MetricSpace.toPseudoMetricSpace.{max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (ContinuousMap.metricSpace.{u1, u2} α β _inst_1 _inst_2 _inst_3))) f g)
+Case conversion may be inaccurate. Consider using '#align continuous_map.dist_apply_le_dist ContinuousMap.dist_apply_le_distₓ'. -/
/-- The pointwise distance is controlled by the distance between functions, by definition. -/
theorem dist_apply_le_dist (x : α) : dist (f x) (g x) ≤ dist f g := by
simp only [← dist_mk_of_compact, dist_coe_le_dist, ← mk_of_compact_apply]
#align continuous_map.dist_apply_le_dist ContinuousMap.dist_apply_le_dist
+/- warning: continuous_map.dist_le -> ContinuousMap.dist_le is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_3 : MetricSpace.{u2} β] {f : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))} {g : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))} {C : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) C) -> (Iff (LE.le.{0} Real Real.hasLe (Dist.dist.{max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (PseudoMetricSpace.toHasDist.{max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (MetricSpace.toPseudoMetricSpace.{max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (ContinuousMap.metricSpace.{u1, u2} α β _inst_1 _inst_2 _inst_3))) f g) C) (forall (x : α), LE.le.{0} Real Real.hasLe (Dist.dist.{u2} β (PseudoMetricSpace.toHasDist.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (fun (_x : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) => α -> β) (ContinuousMap.hasCoeToFun.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (fun (_x : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) => α -> β) (ContinuousMap.hasCoeToFun.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) g x)) C))
+but is expected to have type
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : CompactSpace.{u2} α _inst_1] [_inst_3 : MetricSpace.{u1} β] {f : ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))} {g : ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))} {C : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) C) -> (Iff (LE.le.{0} Real Real.instLEReal (Dist.dist.{max u2 u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) (PseudoMetricSpace.toDist.{max u2 u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) (MetricSpace.toPseudoMetricSpace.{max u2 u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) (ContinuousMap.metricSpace.{u2, u1} α β _inst_1 _inst_2 _inst_3))) f g) C) (forall (x : α), LE.le.{0} Real Real.instLEReal (Dist.dist.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) x) (PseudoMetricSpace.toDist.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) x) (MetricSpace.toPseudoMetricSpace.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) x) _inst_3)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) α (fun (_x : α) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3))) (ContinuousMap.instContinuousMapClassContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3))))) f x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) α (fun (_x : α) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3))) (ContinuousMap.instContinuousMapClassContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3))))) g x)) C))
+Case conversion may be inaccurate. Consider using '#align continuous_map.dist_le ContinuousMap.dist_leₓ'. -/
/-- The distance between two functions is controlled by the supremum of the pointwise distances -/
theorem dist_le (C0 : (0 : ℝ) ≤ C) : dist f g ≤ C ↔ ∀ x : α, dist (f x) (g x) ≤ C := by
simp only [← dist_mk_of_compact, dist_le C0, mk_of_compact_apply]
#align continuous_map.dist_le ContinuousMap.dist_le
+/- warning: continuous_map.dist_le_iff_of_nonempty -> ContinuousMap.dist_le_iff_of_nonempty is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_3 : MetricSpace.{u2} β] {f : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))} {g : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))} {C : Real} [_inst_5 : Nonempty.{succ u1} α], Iff (LE.le.{0} Real Real.hasLe (Dist.dist.{max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (PseudoMetricSpace.toHasDist.{max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (MetricSpace.toPseudoMetricSpace.{max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (ContinuousMap.metricSpace.{u1, u2} α β _inst_1 _inst_2 _inst_3))) f g) C) (forall (x : α), LE.le.{0} Real Real.hasLe (Dist.dist.{u2} β (PseudoMetricSpace.toHasDist.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (fun (_x : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) => α -> β) (ContinuousMap.hasCoeToFun.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (fun (_x : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) => α -> β) (ContinuousMap.hasCoeToFun.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) g x)) C)
+but is expected to have type
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : CompactSpace.{u2} α _inst_1] [_inst_3 : MetricSpace.{u1} β] {f : ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))} {g : ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))} {C : Real} [_inst_5 : Nonempty.{succ u2} α], Iff (LE.le.{0} Real Real.instLEReal (Dist.dist.{max u2 u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) (PseudoMetricSpace.toDist.{max u2 u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) (MetricSpace.toPseudoMetricSpace.{max u2 u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) (ContinuousMap.metricSpace.{u2, u1} α β _inst_1 _inst_2 _inst_3))) f g) C) (forall (x : α), LE.le.{0} Real Real.instLEReal (Dist.dist.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) x) (PseudoMetricSpace.toDist.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) x) (MetricSpace.toPseudoMetricSpace.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) x) _inst_3)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) α (fun (_x : α) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3))) (ContinuousMap.instContinuousMapClassContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3))))) f x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) α (fun (_x : α) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3))) (ContinuousMap.instContinuousMapClassContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3))))) g x)) C)
+Case conversion may be inaccurate. Consider using '#align continuous_map.dist_le_iff_of_nonempty ContinuousMap.dist_le_iff_of_nonemptyₓ'. -/
theorem dist_le_iff_of_nonempty [Nonempty α] : dist f g ≤ C ↔ ∀ x, dist (f x) (g x) ≤ C := by
simp only [← dist_mk_of_compact, dist_le_iff_of_nonempty, mk_of_compact_apply]
#align continuous_map.dist_le_iff_of_nonempty ContinuousMap.dist_le_iff_of_nonempty
+/- warning: continuous_map.dist_lt_iff_of_nonempty -> ContinuousMap.dist_lt_iff_of_nonempty is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_3 : MetricSpace.{u2} β] {f : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))} {g : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))} {C : Real} [_inst_5 : Nonempty.{succ u1} α], Iff (LT.lt.{0} Real Real.hasLt (Dist.dist.{max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (PseudoMetricSpace.toHasDist.{max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (MetricSpace.toPseudoMetricSpace.{max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (ContinuousMap.metricSpace.{u1, u2} α β _inst_1 _inst_2 _inst_3))) f g) C) (forall (x : α), LT.lt.{0} Real Real.hasLt (Dist.dist.{u2} β (PseudoMetricSpace.toHasDist.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (fun (_x : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) => α -> β) (ContinuousMap.hasCoeToFun.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (fun (_x : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) => α -> β) (ContinuousMap.hasCoeToFun.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) g x)) C)
+but is expected to have type
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : CompactSpace.{u2} α _inst_1] [_inst_3 : MetricSpace.{u1} β] {f : ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))} {g : ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))} {C : Real} [_inst_5 : Nonempty.{succ u2} α], Iff (LT.lt.{0} Real Real.instLTReal (Dist.dist.{max u2 u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) (PseudoMetricSpace.toDist.{max u2 u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) (MetricSpace.toPseudoMetricSpace.{max u2 u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) (ContinuousMap.metricSpace.{u2, u1} α β _inst_1 _inst_2 _inst_3))) f g) C) (forall (x : α), LT.lt.{0} Real Real.instLTReal (Dist.dist.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) x) (PseudoMetricSpace.toDist.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) x) (MetricSpace.toPseudoMetricSpace.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) x) _inst_3)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) α (fun (_x : α) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3))) (ContinuousMap.instContinuousMapClassContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3))))) f x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) α (fun (_x : α) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3))) (ContinuousMap.instContinuousMapClassContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3))))) g x)) C)
+Case conversion may be inaccurate. Consider using '#align continuous_map.dist_lt_iff_of_nonempty ContinuousMap.dist_lt_iff_of_nonemptyₓ'. -/
theorem dist_lt_iff_of_nonempty [Nonempty α] : dist f g < C ↔ ∀ x : α, dist (f x) (g x) < C := by
simp only [← dist_mk_of_compact, dist_lt_iff_of_nonempty_compact, mk_of_compact_apply]
#align continuous_map.dist_lt_iff_of_nonempty ContinuousMap.dist_lt_iff_of_nonempty
+/- warning: continuous_map.dist_lt_of_nonempty -> ContinuousMap.dist_lt_of_nonempty is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_3 : MetricSpace.{u2} β] {f : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))} {g : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))} {C : Real} [_inst_5 : Nonempty.{succ u1} α], (forall (x : α), LT.lt.{0} Real Real.hasLt (Dist.dist.{u2} β (PseudoMetricSpace.toHasDist.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (fun (_x : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) => α -> β) (ContinuousMap.hasCoeToFun.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (fun (_x : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) => α -> β) (ContinuousMap.hasCoeToFun.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) g x)) C) -> (LT.lt.{0} Real Real.hasLt (Dist.dist.{max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (PseudoMetricSpace.toHasDist.{max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (MetricSpace.toPseudoMetricSpace.{max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (ContinuousMap.metricSpace.{u1, u2} α β _inst_1 _inst_2 _inst_3))) f g) C)
+but is expected to have type
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : CompactSpace.{u2} α _inst_1] [_inst_3 : MetricSpace.{u1} β] {f : ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))} {g : ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))} {C : Real} [_inst_5 : Nonempty.{succ u2} α], (forall (x : α), LT.lt.{0} Real Real.instLTReal (Dist.dist.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) x) (PseudoMetricSpace.toDist.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) x) (MetricSpace.toPseudoMetricSpace.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) x) _inst_3)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) α (fun (_x : α) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3))) (ContinuousMap.instContinuousMapClassContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3))))) f x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) α (fun (_x : α) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3))) (ContinuousMap.instContinuousMapClassContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3))))) g x)) C) -> (LT.lt.{0} Real Real.instLTReal (Dist.dist.{max u2 u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) (PseudoMetricSpace.toDist.{max u2 u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) (MetricSpace.toPseudoMetricSpace.{max u2 u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) (ContinuousMap.metricSpace.{u2, u1} α β _inst_1 _inst_2 _inst_3))) f g) C)
+Case conversion may be inaccurate. Consider using '#align continuous_map.dist_lt_of_nonempty ContinuousMap.dist_lt_of_nonemptyₓ'. -/
theorem dist_lt_of_nonempty [Nonempty α] (w : ∀ x : α, dist (f x) (g x) < C) : dist f g < C :=
dist_lt_iff_of_nonempty.2 w
#align continuous_map.dist_lt_of_nonempty ContinuousMap.dist_lt_of_nonempty
+/- warning: continuous_map.dist_lt_iff -> ContinuousMap.dist_lt_iff is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_3 : MetricSpace.{u2} β] {f : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))} {g : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))} {C : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) C) -> (Iff (LT.lt.{0} Real Real.hasLt (Dist.dist.{max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (PseudoMetricSpace.toHasDist.{max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (MetricSpace.toPseudoMetricSpace.{max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (ContinuousMap.metricSpace.{u1, u2} α β _inst_1 _inst_2 _inst_3))) f g) C) (forall (x : α), LT.lt.{0} Real Real.hasLt (Dist.dist.{u2} β (PseudoMetricSpace.toHasDist.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (fun (_x : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) => α -> β) (ContinuousMap.hasCoeToFun.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (fun (_x : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) => α -> β) (ContinuousMap.hasCoeToFun.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) g x)) C))
+but is expected to have type
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : CompactSpace.{u2} α _inst_1] [_inst_3 : MetricSpace.{u1} β] {f : ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))} {g : ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))} {C : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) C) -> (Iff (LT.lt.{0} Real Real.instLTReal (Dist.dist.{max u2 u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) (PseudoMetricSpace.toDist.{max u2 u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) (MetricSpace.toPseudoMetricSpace.{max u2 u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) (ContinuousMap.metricSpace.{u2, u1} α β _inst_1 _inst_2 _inst_3))) f g) C) (forall (x : α), LT.lt.{0} Real Real.instLTReal (Dist.dist.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) x) (PseudoMetricSpace.toDist.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) x) (MetricSpace.toPseudoMetricSpace.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) x) _inst_3)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) α (fun (_x : α) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3))) (ContinuousMap.instContinuousMapClassContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3))))) f x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) α (fun (_x : α) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3))) (ContinuousMap.instContinuousMapClassContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3))))) g x)) C))
+Case conversion may be inaccurate. Consider using '#align continuous_map.dist_lt_iff ContinuousMap.dist_lt_iffₓ'. -/
theorem dist_lt_iff (C0 : (0 : ℝ) < C) : dist f g < C ↔ ∀ x : α, dist (f x) (g x) < C := by
simp only [← dist_mk_of_compact, dist_lt_iff_of_compact C0, mk_of_compact_apply]
#align continuous_map.dist_lt_iff ContinuousMap.dist_lt_iff
@@ -148,18 +222,36 @@ end
instance [CompleteSpace β] : CompleteSpace C(α, β) :=
(isometryEquivBoundedOfCompact α β).CompleteSpace
+/- warning: continuous_map.continuous_eval -> ContinuousMap.continuous_eval is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_3 : MetricSpace.{u2} β], Continuous.{max u1 u2, u2} (Prod.{max u1 u2, u1} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) α) β (Prod.topologicalSpace.{max u1 u2, u1} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) α (ContinuousMap.compactOpen.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) _inst_1) (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3))) (fun (p : Prod.{max u1 u2, u1} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) α) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (fun (_x : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) => α -> β) (ContinuousMap.hasCoeToFun.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (Prod.fst.{max u1 u2, u1} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) α p) (Prod.snd.{max u1 u2, u1} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) α p))
+but is expected to have type
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : CompactSpace.{u2} α _inst_1] [_inst_3 : MetricSpace.{u1} β], Continuous.{max u2 u1, u1} (Prod.{max u1 u2, u2} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) α) β (instTopologicalSpaceProd.{max u2 u1, u2} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) α (ContinuousMap.compactOpen.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) _inst_1) (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3))) (fun (p : Prod.{max u1 u2, u2} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) α) => FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) α (fun (_x : α) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3))) (ContinuousMap.instContinuousMapClassContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3))))) (Prod.fst.{max u2 u1, u2} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) α p) (Prod.snd.{max u2 u1, u2} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) α p))
+Case conversion may be inaccurate. Consider using '#align continuous_map.continuous_eval ContinuousMap.continuous_evalₓ'. -/
/-- See also `continuous_map.continuous_eval'` -/
@[continuity]
theorem continuous_eval : Continuous fun p : C(α, β) × α => p.1 p.2 :=
continuous_eval.comp ((isometryEquivBoundedOfCompact α β).Continuous.Prod_map continuous_id)
#align continuous_map.continuous_eval ContinuousMap.continuous_eval
+/- warning: continuous_map.continuous_eval_const -> ContinuousMap.continuous_eval_const is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_3 : MetricSpace.{u2} β] (x : α), Continuous.{max u1 u2, u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) β (ContinuousMap.compactOpen.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3))) (fun (f : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (fun (_x : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) => α -> β) (ContinuousMap.hasCoeToFun.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) f x)
+but is expected to have type
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : CompactSpace.{u2} α _inst_1] [_inst_3 : MetricSpace.{u1} β] (x : α), Continuous.{max u2 u1, u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) x) (ContinuousMap.compactOpen.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) (UniformSpace.toTopologicalSpace.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) x) (PseudoMetricSpace.toUniformSpace.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) x) (MetricSpace.toPseudoMetricSpace.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) x) _inst_3))) (fun (f : ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) => FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) α (fun (_x : α) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3))) (ContinuousMap.instContinuousMapClassContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3))))) f x)
+Case conversion may be inaccurate. Consider using '#align continuous_map.continuous_eval_const ContinuousMap.continuous_eval_constₓ'. -/
/-- See also `continuous_map.continuous_eval_const` -/
@[continuity]
theorem continuous_eval_const (x : α) : Continuous fun f : C(α, β) => f x :=
continuous_eval.comp (continuous_id.prod_mk continuous_const)
#align continuous_map.continuous_eval_const ContinuousMap.continuous_eval_const
+/- warning: continuous_map.continuous_coe -> ContinuousMap.continuous_coe is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_3 : MetricSpace.{u2} β], Continuous.{max u1 u2, max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (α -> β) (ContinuousMap.compactOpen.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (Pi.topologicalSpace.{u1, u2} α (fun (ᾰ : α) => β) (fun (a : α) => UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (fun (ᾰ : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) => α -> β) (ContinuousMap.hasCoeToFun.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))))
+but is expected to have type
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_3 : MetricSpace.{u2} β], Continuous.{max u2 u1, max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (α -> β) (ContinuousMap.compactOpen.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (Pi.topologicalSpace.{u1, u2} α (fun (ᾰ : α) => β) (fun (a : α) => UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) α (fun (ᾰ : α) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) ᾰ) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3))) (ContinuousMap.instContinuousMapClassContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3))))))
+Case conversion may be inaccurate. Consider using '#align continuous_map.continuous_coe ContinuousMap.continuous_coeₓ'. -/
/-- See also `continuous_map.continuous_coe'` -/
theorem continuous_coe : @Continuous C(α, β) (α → β) _ _ coeFn :=
continuous_pi continuous_eval_const
@@ -169,11 +261,23 @@ theorem continuous_coe : @Continuous C(α, β) (α → β) _ _ coeFn :=
-- At the moment the only way to reason about it is to transfer `f : C(α,E)` back to `α →ᵇ E`.
instance : Norm C(α, E) where norm x := dist x 0
+/- warning: bounded_continuous_function.norm_mk_of_compact -> BoundedContinuousFunction.norm_mkOfCompact is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {E : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_4 : NormedAddCommGroup.{u2} E] (f : ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))), Eq.{1} Real (Norm.norm.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (BoundedContinuousFunction.hasNorm.{u1, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (BoundedContinuousFunction.mkOfCompact.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) _inst_2 f)) (Norm.norm.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.hasNorm.{u1, u2} α E _inst_1 _inst_2 _inst_4) f)
+but is expected to have type
+ forall {α : Type.{u2}} {E : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : CompactSpace.{u2} α _inst_1] [_inst_4 : NormedAddCommGroup.{u1} E] (f : ContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))), Eq.{1} Real (Norm.norm.{max u1 u2} (BoundedContinuousFunction.{u2, u1} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))) (BoundedContinuousFunction.instNormBoundedContinuousFunctionToPseudoMetricSpace.{u2, u1} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4)) (BoundedContinuousFunction.mkOfCompact.{u2, u1} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4)) _inst_2 f)) (Norm.norm.{max u2 u1} (ContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) (ContinuousMap.instNormContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u2, u1} α E _inst_1 _inst_2 _inst_4) f)
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.norm_mk_of_compact BoundedContinuousFunction.norm_mkOfCompactₓ'. -/
@[simp]
theorem BoundedContinuousFunction.norm_mkOfCompact (f : C(α, E)) : ‖mkOfCompact f‖ = ‖f‖ :=
rfl
#align bounded_continuous_function.norm_mk_of_compact BoundedContinuousFunction.norm_mkOfCompact
+/- warning: bounded_continuous_function.norm_to_continuous_map_eq -> BoundedContinuousFunction.norm_toContinuousMap_eq is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {E : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_4 : NormedAddCommGroup.{u2} E] (f : BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))), Eq.{1} Real (Norm.norm.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.hasNorm.{u1, u2} α E _inst_1 _inst_2 _inst_4) (BoundedContinuousFunction.toContinuousMap.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) f)) (Norm.norm.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (BoundedContinuousFunction.hasNorm.{u1, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) f)
+but is expected to have type
+ forall {α : Type.{u2}} {E : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : CompactSpace.{u2} α _inst_1] [_inst_4 : NormedAddCommGroup.{u1} E] (f : BoundedContinuousFunction.{u2, u1} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))), Eq.{1} Real (Norm.norm.{max u2 u1} (ContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) (ContinuousMap.instNormContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u2, u1} α E _inst_1 _inst_2 _inst_4) (BoundedContinuousFunction.toContinuousMap.{u2, u1} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4)) f)) (Norm.norm.{max u2 u1} (BoundedContinuousFunction.{u2, u1} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))) (BoundedContinuousFunction.instNormBoundedContinuousFunctionToPseudoMetricSpace.{u2, u1} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4)) f)
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.norm_to_continuous_map_eq BoundedContinuousFunction.norm_toContinuousMap_eqₓ'. -/
@[simp]
theorem BoundedContinuousFunction.norm_toContinuousMap_eq (f : α →ᵇ E) :
‖f.toContinuousMap‖ = ‖f‖ :=
@@ -197,54 +301,126 @@ section
variable (f : C(α, E))
+/- warning: continuous_map.norm_coe_le_norm -> ContinuousMap.norm_coe_le_norm is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {E : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_4 : NormedAddCommGroup.{u2} E] (f : ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (x : α), LE.le.{0} Real Real.hasLe (Norm.norm.{u2} E (NormedAddCommGroup.toHasNorm.{u2} E _inst_4) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (fun (_x : ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) => α -> E) (ContinuousMap.hasCoeToFun.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) f x)) (Norm.norm.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.hasNorm.{u1, u2} α E _inst_1 _inst_2 _inst_4) f)
+but is expected to have type
+ forall {α : Type.{u1}} {E : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_4 : NormedAddCommGroup.{u2} E] (f : ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (x : α), LE.le.{0} Real Real.instLEReal (Norm.norm.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => E) x) (NormedAddCommGroup.toNorm.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => E) x) _inst_4) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) α (fun (_x : α) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => E) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (ContinuousMap.instContinuousMapClassContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))))) f x)) (Norm.norm.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u1, u2} α E _inst_1 _inst_2 _inst_4) f)
+Case conversion may be inaccurate. Consider using '#align continuous_map.norm_coe_le_norm ContinuousMap.norm_coe_le_normₓ'. -/
-- The corresponding lemmas for `bounded_continuous_function` are stated with `{f}`,
-- and so can not be used in dot notation.
theorem norm_coe_le_norm (x : α) : ‖f x‖ ≤ ‖f‖ :=
(mkOfCompact f).norm_coe_le_norm x
#align continuous_map.norm_coe_le_norm ContinuousMap.norm_coe_le_norm
+/- warning: continuous_map.dist_le_two_norm -> ContinuousMap.dist_le_two_norm is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {E : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_4 : NormedAddCommGroup.{u2} E] (f : ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (x : α) (y : α), LE.le.{0} Real Real.hasLe (Dist.dist.{u2} E (PseudoMetricSpace.toHasDist.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (fun (_x : ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) => α -> E) (ContinuousMap.hasCoeToFun.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (fun (_x : ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) => α -> E) (ContinuousMap.hasCoeToFun.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) f y)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) (Norm.norm.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.hasNorm.{u1, u2} α E _inst_1 _inst_2 _inst_4) f))
+but is expected to have type
+ forall {α : Type.{u1}} {E : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_4 : NormedAddCommGroup.{u2} E] (f : ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (x : α) (y : α), LE.le.{0} Real Real.instLEReal (Dist.dist.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => E) x) (PseudoMetricSpace.toDist.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => E) x) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => E) x) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => E) x) _inst_4))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) α (fun (_x : α) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => E) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (ContinuousMap.instContinuousMapClassContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) α (fun (_x : α) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => E) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (ContinuousMap.instContinuousMapClassContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))))) f y)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Norm.norm.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u1, u2} α E _inst_1 _inst_2 _inst_4) f))
+Case conversion may be inaccurate. Consider using '#align continuous_map.dist_le_two_norm ContinuousMap.dist_le_two_normₓ'. -/
/-- Distance between the images of any two points is at most twice the norm of the function. -/
theorem dist_le_two_norm (x y : α) : dist (f x) (f y) ≤ 2 * ‖f‖ :=
(mkOfCompact f).dist_le_two_norm x y
#align continuous_map.dist_le_two_norm ContinuousMap.dist_le_two_norm
+/- warning: continuous_map.norm_le -> ContinuousMap.norm_le is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {E : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_4 : NormedAddCommGroup.{u2} E] (f : ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) {C : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) C) -> (Iff (LE.le.{0} Real Real.hasLe (Norm.norm.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.hasNorm.{u1, u2} α E _inst_1 _inst_2 _inst_4) f) C) (forall (x : α), LE.le.{0} Real Real.hasLe (Norm.norm.{u2} E (NormedAddCommGroup.toHasNorm.{u2} E _inst_4) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (fun (_x : ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) => α -> E) (ContinuousMap.hasCoeToFun.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) f x)) C))
+but is expected to have type
+ forall {α : Type.{u2}} {E : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : CompactSpace.{u2} α _inst_1] [_inst_4 : NormedAddCommGroup.{u1} E] (f : ContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) {C : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) C) -> (Iff (LE.le.{0} Real Real.instLEReal (Norm.norm.{max u2 u1} (ContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) (ContinuousMap.instNormContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u2, u1} α E _inst_1 _inst_2 _inst_4) f) C) (forall (x : α), LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => E) x) (NormedAddCommGroup.toNorm.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => E) x) _inst_4) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) α (fun (_x : α) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => E) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4)))) (ContinuousMap.instContinuousMapClassContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4)))))) f x)) C))
+Case conversion may be inaccurate. Consider using '#align continuous_map.norm_le ContinuousMap.norm_leₓ'. -/
/-- The norm of a function is controlled by the supremum of the pointwise norms -/
theorem norm_le {C : ℝ} (C0 : (0 : ℝ) ≤ C) : ‖f‖ ≤ C ↔ ∀ x : α, ‖f x‖ ≤ C :=
@BoundedContinuousFunction.norm_le _ _ _ _ (mkOfCompact f) _ C0
#align continuous_map.norm_le ContinuousMap.norm_le
+/- warning: continuous_map.norm_le_of_nonempty -> ContinuousMap.norm_le_of_nonempty is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {E : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_4 : NormedAddCommGroup.{u2} E] (f : ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) [_inst_5 : Nonempty.{succ u1} α] {M : Real}, Iff (LE.le.{0} Real Real.hasLe (Norm.norm.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.hasNorm.{u1, u2} α E _inst_1 _inst_2 _inst_4) f) M) (forall (x : α), LE.le.{0} Real Real.hasLe (Norm.norm.{u2} E (NormedAddCommGroup.toHasNorm.{u2} E _inst_4) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (fun (_x : ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) => α -> E) (ContinuousMap.hasCoeToFun.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) f x)) M)
+but is expected to have type
+ forall {α : Type.{u2}} {E : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : CompactSpace.{u2} α _inst_1] [_inst_4 : NormedAddCommGroup.{u1} E] (f : ContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) [_inst_5 : Nonempty.{succ u2} α] {M : Real}, Iff (LE.le.{0} Real Real.instLEReal (Norm.norm.{max u2 u1} (ContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) (ContinuousMap.instNormContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u2, u1} α E _inst_1 _inst_2 _inst_4) f) M) (forall (x : α), LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => E) x) (NormedAddCommGroup.toNorm.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => E) x) _inst_4) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) α (fun (_x : α) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => E) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4)))) (ContinuousMap.instContinuousMapClassContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4)))))) f x)) M)
+Case conversion may be inaccurate. Consider using '#align continuous_map.norm_le_of_nonempty ContinuousMap.norm_le_of_nonemptyₓ'. -/
theorem norm_le_of_nonempty [Nonempty α] {M : ℝ} : ‖f‖ ≤ M ↔ ∀ x, ‖f x‖ ≤ M :=
@BoundedContinuousFunction.norm_le_of_nonempty _ _ _ _ _ (mkOfCompact f) _
#align continuous_map.norm_le_of_nonempty ContinuousMap.norm_le_of_nonempty
+/- warning: continuous_map.norm_lt_iff -> ContinuousMap.norm_lt_iff is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {E : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_4 : NormedAddCommGroup.{u2} E] (f : ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) {M : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) M) -> (Iff (LT.lt.{0} Real Real.hasLt (Norm.norm.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.hasNorm.{u1, u2} α E _inst_1 _inst_2 _inst_4) f) M) (forall (x : α), LT.lt.{0} Real Real.hasLt (Norm.norm.{u2} E (NormedAddCommGroup.toHasNorm.{u2} E _inst_4) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (fun (_x : ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) => α -> E) (ContinuousMap.hasCoeToFun.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) f x)) M))
+but is expected to have type
+ forall {α : Type.{u2}} {E : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : CompactSpace.{u2} α _inst_1] [_inst_4 : NormedAddCommGroup.{u1} E] (f : ContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) {M : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) M) -> (Iff (LT.lt.{0} Real Real.instLTReal (Norm.norm.{max u2 u1} (ContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) (ContinuousMap.instNormContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u2, u1} α E _inst_1 _inst_2 _inst_4) f) M) (forall (x : α), LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => E) x) (NormedAddCommGroup.toNorm.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => E) x) _inst_4) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) α (fun (_x : α) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => E) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4)))) (ContinuousMap.instContinuousMapClassContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4)))))) f x)) M))
+Case conversion may be inaccurate. Consider using '#align continuous_map.norm_lt_iff ContinuousMap.norm_lt_iffₓ'. -/
theorem norm_lt_iff {M : ℝ} (M0 : 0 < M) : ‖f‖ < M ↔ ∀ x, ‖f x‖ < M :=
@BoundedContinuousFunction.norm_lt_iff_of_compact _ _ _ _ _ (mkOfCompact f) _ M0
#align continuous_map.norm_lt_iff ContinuousMap.norm_lt_iff
+/- warning: continuous_map.nnnorm_lt_iff -> ContinuousMap.nnnorm_lt_iff is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {E : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_4 : NormedAddCommGroup.{u2} E] (f : ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) {M : NNReal}, (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) M) -> (Iff (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (NNNorm.nnnorm.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (SeminormedAddGroup.toNNNorm.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (SeminormedAddCommGroup.toSeminormedAddGroup.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.normedAddCommGroup.{u1, u2} α E _inst_1 _inst_2 _inst_4)))) f) M) (forall (x : α), LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (NNNorm.nnnorm.{u2} E (SeminormedAddGroup.toNNNorm.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (fun (_x : ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) => α -> E) (ContinuousMap.hasCoeToFun.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) f x)) M))
+but is expected to have type
+ forall {α : Type.{u2}} {E : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : CompactSpace.{u2} α _inst_1] [_inst_4 : NormedAddCommGroup.{u1} E] (f : ContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) {M : NNReal}, (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) M) -> (Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (NNNorm.nnnorm.{max u2 u1} (ContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) (SeminormedAddGroup.toNNNorm.{max u2 u1} (ContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) (SeminormedAddCommGroup.toSeminormedAddGroup.{max u2 u1} (ContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u2 u1} (ContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u2, u1} α E _inst_1 _inst_2 _inst_4)))) f) M) (forall (x : α), LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (NNNorm.nnnorm.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => E) x) (SeminormedAddGroup.toNNNorm.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => E) x) (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => E) x) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => E) x) _inst_4))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) α (fun (_x : α) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => E) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4)))) (ContinuousMap.instContinuousMapClassContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4)))))) f x)) M))
+Case conversion may be inaccurate. Consider using '#align continuous_map.nnnorm_lt_iff ContinuousMap.nnnorm_lt_iffₓ'. -/
theorem nnnorm_lt_iff {M : ℝ≥0} (M0 : 0 < M) : ‖f‖₊ < M ↔ ∀ x : α, ‖f x‖₊ < M :=
f.norm_lt_iff M0
#align continuous_map.nnnorm_lt_iff ContinuousMap.nnnorm_lt_iff
+/- warning: continuous_map.norm_lt_iff_of_nonempty -> ContinuousMap.norm_lt_iff_of_nonempty is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {E : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_4 : NormedAddCommGroup.{u2} E] (f : ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) [_inst_5 : Nonempty.{succ u1} α] {M : Real}, Iff (LT.lt.{0} Real Real.hasLt (Norm.norm.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.hasNorm.{u1, u2} α E _inst_1 _inst_2 _inst_4) f) M) (forall (x : α), LT.lt.{0} Real Real.hasLt (Norm.norm.{u2} E (NormedAddCommGroup.toHasNorm.{u2} E _inst_4) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (fun (_x : ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) => α -> E) (ContinuousMap.hasCoeToFun.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) f x)) M)
+but is expected to have type
+ forall {α : Type.{u2}} {E : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : CompactSpace.{u2} α _inst_1] [_inst_4 : NormedAddCommGroup.{u1} E] (f : ContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) [_inst_5 : Nonempty.{succ u2} α] {M : Real}, Iff (LT.lt.{0} Real Real.instLTReal (Norm.norm.{max u2 u1} (ContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) (ContinuousMap.instNormContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u2, u1} α E _inst_1 _inst_2 _inst_4) f) M) (forall (x : α), LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => E) x) (NormedAddCommGroup.toNorm.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => E) x) _inst_4) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) α (fun (_x : α) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => E) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4)))) (ContinuousMap.instContinuousMapClassContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4)))))) f x)) M)
+Case conversion may be inaccurate. Consider using '#align continuous_map.norm_lt_iff_of_nonempty ContinuousMap.norm_lt_iff_of_nonemptyₓ'. -/
theorem norm_lt_iff_of_nonempty [Nonempty α] {M : ℝ} : ‖f‖ < M ↔ ∀ x, ‖f x‖ < M :=
@BoundedContinuousFunction.norm_lt_iff_of_nonempty_compact _ _ _ _ _ _ (mkOfCompact f) _
#align continuous_map.norm_lt_iff_of_nonempty ContinuousMap.norm_lt_iff_of_nonempty
+/- warning: continuous_map.nnnorm_lt_iff_of_nonempty -> ContinuousMap.nnnorm_lt_iff_of_nonempty is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {E : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_4 : NormedAddCommGroup.{u2} E] (f : ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) [_inst_5 : Nonempty.{succ u1} α] {M : NNReal}, Iff (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (NNNorm.nnnorm.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (SeminormedAddGroup.toNNNorm.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (SeminormedAddCommGroup.toSeminormedAddGroup.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.normedAddCommGroup.{u1, u2} α E _inst_1 _inst_2 _inst_4)))) f) M) (forall (x : α), LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (NNNorm.nnnorm.{u2} E (SeminormedAddGroup.toNNNorm.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (fun (_x : ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) => α -> E) (ContinuousMap.hasCoeToFun.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) f x)) M)
+but is expected to have type
+ forall {α : Type.{u2}} {E : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : CompactSpace.{u2} α _inst_1] [_inst_4 : NormedAddCommGroup.{u1} E] (f : ContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) [_inst_5 : Nonempty.{succ u2} α] {M : NNReal}, Iff (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (NNNorm.nnnorm.{max u2 u1} (ContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) (SeminormedAddGroup.toNNNorm.{max u2 u1} (ContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) (SeminormedAddCommGroup.toSeminormedAddGroup.{max u2 u1} (ContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u2 u1} (ContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u2, u1} α E _inst_1 _inst_2 _inst_4)))) f) M) (forall (x : α), LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (NNNorm.nnnorm.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => E) x) (SeminormedAddGroup.toNNNorm.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => E) x) (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => E) x) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => E) x) _inst_4))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) α (fun (_x : α) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => E) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4)))) (ContinuousMap.instContinuousMapClassContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4)))))) f x)) M)
+Case conversion may be inaccurate. Consider using '#align continuous_map.nnnorm_lt_iff_of_nonempty ContinuousMap.nnnorm_lt_iff_of_nonemptyₓ'. -/
theorem nnnorm_lt_iff_of_nonempty [Nonempty α] {M : ℝ≥0} : ‖f‖₊ < M ↔ ∀ x, ‖f x‖₊ < M :=
f.norm_lt_iff_of_nonempty
#align continuous_map.nnnorm_lt_iff_of_nonempty ContinuousMap.nnnorm_lt_iff_of_nonempty
+/- warning: continuous_map.apply_le_norm -> ContinuousMap.apply_le_norm is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] (f : ContinuousMap.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (x : α), LE.le.{0} Real Real.hasLe (coeFn.{succ u1, succ u1} (ContinuousMap.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (fun (_x : ContinuousMap.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) => α -> Real) (ContinuousMap.hasCoeToFun.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) f x) (Norm.norm.{u1} (ContinuousMap.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (ContinuousMap.hasNorm.{u1, 0} α Real _inst_1 _inst_2 Real.normedAddCommGroup) f)
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] (f : ContinuousMap.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (x : α), LE.le.{0} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => Real) x) Real.instLEReal (FunLike.coe.{succ u1, succ u1, 1} (ContinuousMap.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) α (fun (_x : α) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousMap.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousMap.instContinuousMapClassContinuousMap.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)))) f x) (Norm.norm.{u1} (ContinuousMap.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (ContinuousMap.instNormContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u1, 0} α Real _inst_1 _inst_2 Real.normedAddCommGroup) f)
+Case conversion may be inaccurate. Consider using '#align continuous_map.apply_le_norm ContinuousMap.apply_le_normₓ'. -/
theorem apply_le_norm (f : C(α, ℝ)) (x : α) : f x ≤ ‖f‖ :=
le_trans (le_abs.mpr (Or.inl (le_refl (f x)))) (f.norm_coe_le_norm x)
#align continuous_map.apply_le_norm ContinuousMap.apply_le_norm
+/- warning: continuous_map.neg_norm_le_apply -> ContinuousMap.neg_norm_le_apply is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] (f : ContinuousMap.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (x : α), LE.le.{0} Real Real.hasLe (Neg.neg.{0} Real Real.hasNeg (Norm.norm.{u1} (ContinuousMap.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (ContinuousMap.hasNorm.{u1, 0} α Real _inst_1 _inst_2 Real.normedAddCommGroup) f)) (coeFn.{succ u1, succ u1} (ContinuousMap.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (fun (_x : ContinuousMap.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) => α -> Real) (ContinuousMap.hasCoeToFun.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) f x)
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] (f : ContinuousMap.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (x : α), LE.le.{0} Real Real.instLEReal (Neg.neg.{0} Real Real.instNegReal (Norm.norm.{u1} (ContinuousMap.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (ContinuousMap.instNormContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u1, 0} α Real _inst_1 _inst_2 Real.normedAddCommGroup) f)) (FunLike.coe.{succ u1, succ u1, 1} (ContinuousMap.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) α (fun (_x : α) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousMap.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousMap.instContinuousMapClassContinuousMap.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)))) f x)
+Case conversion may be inaccurate. Consider using '#align continuous_map.neg_norm_le_apply ContinuousMap.neg_norm_le_applyₓ'. -/
theorem neg_norm_le_apply (f : C(α, ℝ)) (x : α) : -‖f‖ ≤ f x :=
le_trans (neg_le_neg (f.norm_coe_le_norm x)) (neg_le.mp (neg_le_abs_self (f x)))
#align continuous_map.neg_norm_le_apply ContinuousMap.neg_norm_le_apply
+/- warning: continuous_map.norm_eq_supr_norm -> ContinuousMap.norm_eq_iSup_norm is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {E : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_4 : NormedAddCommGroup.{u2} E] (f : ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))), Eq.{1} Real (Norm.norm.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.hasNorm.{u1, u2} α E _inst_1 _inst_2 _inst_4) f) (iSup.{0, succ u1} Real Real.hasSup α (fun (x : α) => Norm.norm.{u2} E (NormedAddCommGroup.toHasNorm.{u2} E _inst_4) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (fun (_x : ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) => α -> E) (ContinuousMap.hasCoeToFun.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) f x)))
+but is expected to have type
+ forall {α : Type.{u2}} {E : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : CompactSpace.{u2} α _inst_1] [_inst_4 : NormedAddCommGroup.{u1} E] (f : ContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))), Eq.{1} Real (Norm.norm.{max u2 u1} (ContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) (ContinuousMap.instNormContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u2, u1} α E _inst_1 _inst_2 _inst_4) f) (iSup.{0, succ u2} Real Real.instSupSetReal α (fun (x : α) => Norm.norm.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => E) x) (NormedAddCommGroup.toNorm.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => E) x) _inst_4) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) α (fun (_x : α) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => E) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4)))) (ContinuousMap.instContinuousMapClassContinuousMap.{u2, u1} α E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4)))))) f x)))
+Case conversion may be inaccurate. Consider using '#align continuous_map.norm_eq_supr_norm ContinuousMap.norm_eq_iSup_normₓ'. -/
theorem norm_eq_iSup_norm : ‖f‖ = ⨆ x : α, ‖f x‖ :=
(mkOfCompact f).norm_eq_iSup_norm
#align continuous_map.norm_eq_supr_norm ContinuousMap.norm_eq_iSup_norm
+/- warning: continuous_map.norm_restrict_mono_set -> ContinuousMap.norm_restrict_mono_set is a dubious translation:
+lean 3 declaration is
+ forall {E : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} E] {X : Type.{u2}} [_inst_5 : TopologicalSpace.{u2} X] (f : ContinuousMap.{u2, u1} X E _inst_5 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) {K : TopologicalSpace.Compacts.{u2} X _inst_5} {L : TopologicalSpace.Compacts.{u2} X _inst_5}, (LE.le.{u2} (TopologicalSpace.Compacts.{u2} X _inst_5) (Preorder.toHasLe.{u2} (TopologicalSpace.Compacts.{u2} X _inst_5) (PartialOrder.toPreorder.{u2} (TopologicalSpace.Compacts.{u2} X _inst_5) (SetLike.partialOrder.{u2, u2} (TopologicalSpace.Compacts.{u2} X _inst_5) X (TopologicalSpace.Compacts.setLike.{u2} X _inst_5)))) K L) -> (LE.le.{0} Real Real.hasLe (Norm.norm.{max u2 u1} (ContinuousMap.{u2, u1} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} X) Type.{u2} (Set.hasCoeToSort.{u2} X) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ 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(UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) (ContinuousMap.hasNorm.{u2, u1} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} X) Type.{u2} (Set.hasCoeToSort.{u2} X) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (TopologicalSpace.Compacts.{u2} X _inst_5) (Set.{u2} X) (HasLiftT.mk.{succ u2, succ u2} (TopologicalSpace.Compacts.{u2} X _inst_5) (Set.{u2} X) (CoeTCₓ.coe.{succ u2, succ u2} (TopologicalSpace.Compacts.{u2} X _inst_5) (Set.{u2} X) (SetLike.Set.hasCoeT.{u2, u2} (TopologicalSpace.Compacts.{u2} X _inst_5) X (TopologicalSpace.Compacts.setLike.{u2} X _inst_5)))) K)) E (Subtype.topologicalSpace.{u2} X (fun (x : X) => Membership.Mem.{u2, u2} X (Set.{u2} X) (Set.hasMem.{u2} X) x ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (TopologicalSpace.Compacts.{u2} X _inst_5) (Set.{u2} X) (HasLiftT.mk.{succ u2, succ u2} (TopologicalSpace.Compacts.{u2} X _inst_5) (Set.{u2} X) (CoeTCₓ.coe.{succ u2, succ u2} (TopologicalSpace.Compacts.{u2} X _inst_5) (Set.{u2} X) (SetLike.Set.hasCoeT.{u2, u2} (TopologicalSpace.Compacts.{u2} X _inst_5) X (TopologicalSpace.Compacts.setLike.{u2} X _inst_5)))) K)) _inst_5) (TopologicalSpace.Compacts.compactSpace.{u2} X _inst_5 K) _inst_4) (ContinuousMap.restrict.{u2, u1} X E _inst_5 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (TopologicalSpace.Compacts.{u2} X _inst_5) (Set.{u2} X) (HasLiftT.mk.{succ u2, succ u2} (TopologicalSpace.Compacts.{u2} X _inst_5) (Set.{u2} X) (CoeTCₓ.coe.{succ u2, succ u2} (TopologicalSpace.Compacts.{u2} X _inst_5) (Set.{u2} X) (SetLike.Set.hasCoeT.{u2, u2} (TopologicalSpace.Compacts.{u2} X _inst_5) X (TopologicalSpace.Compacts.setLike.{u2} X _inst_5)))) K) f)) (Norm.norm.{max u2 u1} (ContinuousMap.{u2, u1} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} X) Type.{u2} (Set.hasCoeToSort.{u2} X) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (TopologicalSpace.Compacts.{u2} X _inst_5) (Set.{u2} X) (HasLiftT.mk.{succ u2, succ u2} (TopologicalSpace.Compacts.{u2} X _inst_5) (Set.{u2} X) (CoeTCₓ.coe.{succ u2, succ u2} (TopologicalSpace.Compacts.{u2} X _inst_5) (Set.{u2} X) (SetLike.Set.hasCoeT.{u2, u2} (TopologicalSpace.Compacts.{u2} X _inst_5) X (TopologicalSpace.Compacts.setLike.{u2} X _inst_5)))) L)) E (Subtype.topologicalSpace.{u2} X (fun (x : X) => Membership.Mem.{u2, u2} X (Set.{u2} X) (Set.hasMem.{u2} X) x ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (TopologicalSpace.Compacts.{u2} X _inst_5) (Set.{u2} X) (HasLiftT.mk.{succ u2, succ u2} 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(TopologicalSpace.Compacts.setLike.{u2} X _inst_5)))) L)) E (Subtype.topologicalSpace.{u2} X (fun (x : X) => Membership.Mem.{u2, u2} X (Set.{u2} X) (Set.hasMem.{u2} X) x ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (TopologicalSpace.Compacts.{u2} X _inst_5) (Set.{u2} X) (HasLiftT.mk.{succ u2, succ u2} (TopologicalSpace.Compacts.{u2} X _inst_5) (Set.{u2} X) (CoeTCₓ.coe.{succ u2, succ u2} (TopologicalSpace.Compacts.{u2} X _inst_5) (Set.{u2} X) (SetLike.Set.hasCoeT.{u2, u2} (TopologicalSpace.Compacts.{u2} X _inst_5) X (TopologicalSpace.Compacts.setLike.{u2} X _inst_5)))) L)) _inst_5) (TopologicalSpace.Compacts.compactSpace.{u2} X _inst_5 L) _inst_4) (ContinuousMap.restrict.{u2, u1} X E _inst_5 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (TopologicalSpace.Compacts.{u2} X _inst_5) (Set.{u2} X) (HasLiftT.mk.{succ u2, succ u2} (TopologicalSpace.Compacts.{u2} X _inst_5) (Set.{u2} X) (CoeTCₓ.coe.{succ u2, succ u2} (TopologicalSpace.Compacts.{u2} X _inst_5) (Set.{u2} X) (SetLike.Set.hasCoeT.{u2, u2} (TopologicalSpace.Compacts.{u2} X _inst_5) X (TopologicalSpace.Compacts.setLike.{u2} X _inst_5)))) L) f)))
+but is expected to have type
+ forall {E : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} E] {X : Type.{u2}} [_inst_5 : TopologicalSpace.{u2} X] (f : ContinuousMap.{u2, u1} X E _inst_5 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) {K : TopologicalSpace.Compacts.{u2} X _inst_5} {L : TopologicalSpace.Compacts.{u2} X _inst_5}, (LE.le.{u2} (TopologicalSpace.Compacts.{u2} X _inst_5) (Preorder.toLE.{u2} (TopologicalSpace.Compacts.{u2} X _inst_5) (PartialOrder.toPreorder.{u2} (TopologicalSpace.Compacts.{u2} X _inst_5) (SemilatticeSup.toPartialOrder.{u2} (TopologicalSpace.Compacts.{u2} X _inst_5) (TopologicalSpace.Compacts.instSemilatticeSupCompacts.{u2} X _inst_5)))) K L) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{max u1 u2} (ContinuousMap.{u2, u1} (Set.Elem.{u2} X (SetLike.coe.{u2, u2} (TopologicalSpace.Compacts.{u2} X _inst_5) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u2} X _inst_5) K)) E (instTopologicalSpaceSubtype.{u2} X (fun (x : X) => Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) x (SetLike.coe.{u2, u2} (TopologicalSpace.Compacts.{u2} X _inst_5) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u2} X _inst_5) K)) _inst_5) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) (ContinuousMap.instNormContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u2, u1} (Set.Elem.{u2} X (SetLike.coe.{u2, u2} (TopologicalSpace.Compacts.{u2} X _inst_5) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u2} X _inst_5) K)) E (instTopologicalSpaceSubtype.{u2} X (fun (x : X) => Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) x (SetLike.coe.{u2, u2} (TopologicalSpace.Compacts.{u2} X _inst_5) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u2} X _inst_5) K)) _inst_5) (TopologicalSpace.Compacts.instCompactSpaceSubtypeMemCompactsInstMembershipInstSetLikeCompactsInstTopologicalSpaceSubtype.{u2} X _inst_5 K) _inst_4) (ContinuousMap.restrict.{u2, u1} X E _inst_5 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4)))) (SetLike.coe.{u2, u2} (TopologicalSpace.Compacts.{u2} X _inst_5) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u2} X _inst_5) K) f)) (Norm.norm.{max u1 u2} (ContinuousMap.{u2, u1} (Set.Elem.{u2} X (SetLike.coe.{u2, u2} (TopologicalSpace.Compacts.{u2} X _inst_5) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u2} X _inst_5) L)) E (instTopologicalSpaceSubtype.{u2} X (fun (x : X) => Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) x (SetLike.coe.{u2, u2} (TopologicalSpace.Compacts.{u2} X _inst_5) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u2} X _inst_5) L)) _inst_5) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) (ContinuousMap.instNormContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u2, u1} (Set.Elem.{u2} X (SetLike.coe.{u2, u2} (TopologicalSpace.Compacts.{u2} X _inst_5) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u2} X _inst_5) L)) E (instTopologicalSpaceSubtype.{u2} X (fun (x : X) => Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) x (SetLike.coe.{u2, u2} (TopologicalSpace.Compacts.{u2} X _inst_5) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u2} X _inst_5) L)) _inst_5) (TopologicalSpace.Compacts.instCompactSpaceSubtypeMemCompactsInstMembershipInstSetLikeCompactsInstTopologicalSpaceSubtype.{u2} X _inst_5 L) _inst_4) (ContinuousMap.restrict.{u2, u1} X E _inst_5 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4)))) (SetLike.coe.{u2, u2} (TopologicalSpace.Compacts.{u2} X _inst_5) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u2} X _inst_5) L) f)))
+Case conversion may be inaccurate. Consider using '#align continuous_map.norm_restrict_mono_set ContinuousMap.norm_restrict_mono_setₓ'. -/
theorem norm_restrict_mono_set {X : Type _} [TopologicalSpace X] (f : C(X, E))
{K L : TopologicalSpace.Compacts X} (hKL : K ≤ L) : ‖f.restrict K‖ ≤ ‖f.restrict L‖ :=
(norm_le _ (norm_nonneg _)).mpr fun x => norm_coe_le_norm (f.restrict L) <| Set.inclusion hKL x
@@ -272,6 +448,12 @@ section
variable (α 𝕜 E)
+/- warning: continuous_map.linear_isometry_bounded_of_compact -> ContinuousMap.linearIsometryBoundedOfCompact is a dubious translation:
+lean 3 declaration is
+ forall (α : Type.{u1}) (E : Type.{u2}) [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_4 : NormedAddCommGroup.{u2} E] (𝕜 : Type.{u3}) [_inst_5 : NormedField.{u3} 𝕜] [_inst_6 : NormedSpace.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)], LinearIsometryEquiv.{u3, u3, max u1 u2, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))))) (ContinuousMap.linearIsometryBoundedOfCompact._proof_1.{u3} 𝕜 _inst_5) (ContinuousMap.linearIsometryBoundedOfCompact._proof_2.{u3} 𝕜 _inst_5) (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.normedAddCommGroup.{u1, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.seminormedAddCommGroup.{u1, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (ContinuousMap.module.{u1, u3, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.linearIsometryBoundedOfCompact._proof_3.{u2} E _inst_4) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_4.{u2, u3} E _inst_4 𝕜 _inst_5 _inst_6)) (BoundedContinuousFunction.module.{u1, u2, u3} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u3} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_5.{u2, u3} E _inst_4 𝕜 _inst_5 _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_6.{u2} E _inst_4))
+but is expected to have type
+ forall (α : Type.{u1}) (E : Type.{u2}) [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_4 : NormedAddCommGroup.{u2} E] (𝕜 : Type.{u3}) [_inst_5 : NormedField.{u3} 𝕜] [_inst_6 : NormedSpace.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)], LinearIsometryEquiv.{u3, u3, max u2 u1, max u2 u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5)))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5)))))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5))))) (RingHomInvPair.ids.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5))))) (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u1, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.seminormedAddCommGroup.{u1, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (ContinuousMap.module.{u1, u3, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u3, u2} 𝕜 E (UniformSpace.toTopologicalSpace.{u3} 𝕜 (PseudoMetricSpace.toUniformSpace.{u3} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u3} 𝕜 (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (MonoidWithZero.toZero.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u3, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u3} 𝕜 (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (MonoidWithZero.toZero.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (BoundedContinuousFunction.module.{u1, u2, u3} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u3} 𝕜 (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))
+Case conversion may be inaccurate. Consider using '#align continuous_map.linear_isometry_bounded_of_compact ContinuousMap.linearIsometryBoundedOfCompactₓ'. -/
/-- When `α` is compact and `𝕜` is a normed field,
the `𝕜`-algebra of bounded continuous maps `α →ᵇ β` is
`𝕜`-linearly isometric to `C(α, β)`.
@@ -288,6 +470,12 @@ def linearIsometryBoundedOfCompact : C(α, E) ≃ₗᵢ[𝕜] α →ᵇ E :=
variable {α E}
+/- warning: continuous_map.eval_clm -> ContinuousMap.evalClm is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {E : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_4 : NormedAddCommGroup.{u2} E] (𝕜 : Type.{u3}) [_inst_5 : NormedField.{u3} 𝕜] [_inst_6 : NormedSpace.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)], α -> (ContinuousLinearMap.{u3, u3, max u1 u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))))) (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.compactOpen.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.addCommMonoid.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.evalClm._proof_1.{u2} E _inst_4)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.module.{u1, u3, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.evalClm._proof_2.{u2} E _inst_4) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousMap.evalClm._proof_3.{u2, u3} E _inst_4 𝕜 _inst_5 _inst_6)) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))
+but is expected to have type
+ forall {α : Type.{u1}} {E : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_4 : NormedAddCommGroup.{u2} E] (𝕜 : Type.{u3}) [_inst_5 : NormedField.{u3} 𝕜] [_inst_6 : NormedSpace.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)], α -> (ContinuousLinearMap.{u3, u3, max u2 u1, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5)))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5)))))) (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.compactOpen.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instAddCommMonoidContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (TopologicalAddGroup.toContinuousAdd.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.module.{u1, u3, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (TopologicalAddGroup.toContinuousAdd.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u3, u2} 𝕜 E (UniformSpace.toTopologicalSpace.{u3} 𝕜 (PseudoMetricSpace.toUniformSpace.{u3} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u3} 𝕜 (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (MonoidWithZero.toZero.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u3, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u3} 𝕜 (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (MonoidWithZero.toZero.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))
+Case conversion may be inaccurate. Consider using '#align continuous_map.eval_clm ContinuousMap.evalClmₓ'. -/
-- to match bounded_continuous_function.eval_clm
/-- The evaluation at a point, as a continuous linear map from `C(α, 𝕜)` to `𝕜`. -/
def evalClm (x : α) : C(α, E) →L[𝕜] E :=
@@ -296,6 +484,12 @@ def evalClm (x : α) : C(α, E) →L[𝕜] E :=
end
+/- warning: continuous_map.linear_isometry_bounded_of_compact_symm_apply -> ContinuousMap.linearIsometryBoundedOfCompact_symm_apply is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {E : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_4 : NormedAddCommGroup.{u2} E] {𝕜 : Type.{u3}} [_inst_5 : NormedField.{u3} 𝕜] [_inst_6 : NormedSpace.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] (f : BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))), Eq.{max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearIsometryEquiv.{u3, u3, max u1 u2, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))))) (ContinuousMap.linearIsometryBoundedOfCompact._proof_2.{u3} 𝕜 _inst_5) (ContinuousMap.linearIsometryBoundedOfCompact._proof_1.{u3} 𝕜 _inst_5) (BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.seminormedAddCommGroup.{u1, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.normedAddCommGroup.{u1, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.module.{u1, u2, u3} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u3} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 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(NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_4.{u2, u3} E _inst_4 𝕜 _inst_5 _inst_6))) (fun (_x : LinearIsometryEquiv.{u3, u3, max u1 u2, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))))) (ContinuousMap.linearIsometryBoundedOfCompact._proof_2.{u3} 𝕜 _inst_5) 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_inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_5.{u2, u3} E _inst_4 𝕜 _inst_5 _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_6.{u2} E _inst_4)) (ContinuousMap.module.{u1, u3, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.linearIsometryBoundedOfCompact._proof_3.{u2} E _inst_4) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_4.{u2, u3} E _inst_4 𝕜 _inst_5 _inst_6))) (LinearIsometryEquiv.symm.{u3, u3, max u1 u2, max u1 u2} 𝕜 𝕜 (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))))) (ContinuousMap.linearIsometryBoundedOfCompact._proof_1.{u3} 𝕜 _inst_5) (ContinuousMap.linearIsometryBoundedOfCompact._proof_2.{u3} 𝕜 _inst_5) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.normedAddCommGroup.{u1, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.seminormedAddCommGroup.{u1, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (ContinuousMap.module.{u1, u3, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.linearIsometryBoundedOfCompact._proof_3.{u2} E _inst_4) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_4.{u2, u3} E _inst_4 𝕜 _inst_5 _inst_6)) (BoundedContinuousFunction.module.{u1, u2, u3} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u3} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_5.{u2, u3} E _inst_4 𝕜 _inst_5 _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_6.{u2} E _inst_4)) (ContinuousMap.linearIsometryBoundedOfCompact.{u1, u2, u3} α E _inst_1 _inst_2 _inst_4 𝕜 _inst_5 _inst_6)) f) (BoundedContinuousFunction.toContinuousMap.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) f)
+but is expected to have type
+ forall {α : Type.{u3}} {E : Type.{u2}} [_inst_1 : TopologicalSpace.{u3} α] [_inst_2 : CompactSpace.{u3} α _inst_1] [_inst_4 : NormedAddCommGroup.{u2} E] {𝕜 : Type.{u1}} [_inst_5 : NormedField.{u1} 𝕜] [_inst_6 : NormedSpace.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] (f : BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) => ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) f) (FunLike.coe.{max (succ u3) 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(ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (fun (_x : BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) => ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) _x) (ContinuousMapClass.toFunLike.{max u3 u2, max u3 u2, max u3 u2} (LinearIsometryEquiv.{u1, u1, max u3 u2, max u3 u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (UniformSpace.toTopologicalSpace.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E 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_inst_4))) (UniformSpace.toTopologicalSpace.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (PseudoMetricSpace.toUniformSpace.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (SeminormedAddCommGroup.toPseudoMetricSpace.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (AddCommGroup.toAddCommMonoid.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (SeminormedAddCommGroup.toAddCommGroup.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (UniformSpace.toTopologicalSpace.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (PseudoMetricSpace.toUniformSpace.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E 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(SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{u1, u1, max u3 u2, max u3 u2, max u3 u2} 𝕜 𝕜 (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (LinearIsometryEquiv.{u1, u1, max u3 u2, max u3 u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (SemilinearIsometryEquivClass.instSemilinearIsometryClass.{u1, u1, max u3 u2, max u3 u2, max u3 u2} 𝕜 𝕜 (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (LinearIsometryEquiv.{u1, u1, max u3 u2, max u3 u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (LinearIsometryEquiv.instSemilinearIsometryEquivClassLinearIsometryEquiv.{u1, u1, max u3 u2, max u3 u2} 𝕜 𝕜 (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) 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(UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.linearIsometryBoundedOfCompact.{u3, u2, u1} α E _inst_1 _inst_2 _inst_4 𝕜 _inst_5 _inst_6)) f) (BoundedContinuousFunction.toContinuousMap.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) f)
+Case conversion may be inaccurate. Consider using '#align continuous_map.linear_isometry_bounded_of_compact_symm_apply ContinuousMap.linearIsometryBoundedOfCompact_symm_applyₓ'. -/
-- this lemma and the next are the analogues of those autogenerated by `@[simps]` for
-- `equiv_bounded_of_compact`, `add_equiv_bounded_of_compact`
@[simp]
@@ -304,18 +498,36 @@ theorem linearIsometryBoundedOfCompact_symm_apply (f : α →ᵇ E) :
rfl
#align continuous_map.linear_isometry_bounded_of_compact_symm_apply ContinuousMap.linearIsometryBoundedOfCompact_symm_apply
+/- warning: continuous_map.linear_isometry_bounded_of_compact_apply_apply -> ContinuousMap.linearIsometryBoundedOfCompact_apply_apply is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {E : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_4 : NormedAddCommGroup.{u2} E] {𝕜 : Type.{u3}} [_inst_5 : NormedField.{u3} 𝕜] [_inst_6 : NormedSpace.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] (f : ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (a : α), Eq.{succ u2} E (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (fun (_x : BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) => α -> E) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearIsometryEquiv.{u3, u3, max u1 u2, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))))) (ContinuousMap.linearIsometryBoundedOfCompact._proof_1.{u3} 𝕜 _inst_5) (ContinuousMap.linearIsometryBoundedOfCompact._proof_2.{u3} 𝕜 _inst_5) (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.normedAddCommGroup.{u1, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.seminormedAddCommGroup.{u1, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (ContinuousMap.module.{u1, u3, u2} α 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E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_5.{u2, u3} E _inst_4 𝕜 _inst_5 _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_6.{u2} E _inst_4))) (fun (_x : LinearIsometryEquiv.{u3, u3, max u1 u2, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 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+but is expected to have type
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(ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (fun (_x : ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) => BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) _x) (ContinuousMapClass.toFunLike.{max u3 u2, max u3 u2, max u3 u2} (LinearIsometryEquiv.{u1, u1, max u2 u3, max u2 u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (UniformSpace.toTopologicalSpace.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (PseudoMetricSpace.toUniformSpace.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4))))) (UniformSpace.toTopologicalSpace.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (PseudoMetricSpace.toUniformSpace.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (SeminormedAddCommGroup.toPseudoMetricSpace.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u2, u1, u1, max u3 u2, max u3 u2} (LinearIsometryEquiv.{u1, u1, max u2 u3, max u2 u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E 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(AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (UniformSpace.toTopologicalSpace.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (PseudoMetricSpace.toUniformSpace.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4))))) (AddCommGroup.toAddCommMonoid.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (SeminormedAddCommGroup.toAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (UniformSpace.toTopologicalSpace.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (PseudoMetricSpace.toUniformSpace.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 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(NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{u1, u1, max u3 u2, max u3 u2, max u3 u2} 𝕜 𝕜 (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (LinearIsometryEquiv.{u1, u1, max u2 u3, max u2 u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (SemilinearIsometryEquivClass.instSemilinearIsometryClass.{u1, u1, max u3 u2, max u3 u2, max u3 u2} 𝕜 𝕜 (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (LinearIsometryEquiv.{u1, u1, max u2 u3, max u2 u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 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(NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (LinearIsometryEquiv.instSemilinearIsometryEquivClassLinearIsometryEquiv.{u1, u1, max u3 u2, max u3 u2} 𝕜 𝕜 (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))))))) (ContinuousMap.linearIsometryBoundedOfCompact.{u3, u2, u1} α E _inst_1 _inst_2 _inst_4 𝕜 _inst_5 _inst_6) f) a) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) α (fun (_x : α) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => E) _x) (ContinuousMapClass.toFunLike.{max u3 u2, u3, u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (ContinuousMap.instContinuousMapClassContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))))) f a)
+Case conversion may be inaccurate. Consider using '#align continuous_map.linear_isometry_bounded_of_compact_apply_apply ContinuousMap.linearIsometryBoundedOfCompact_apply_applyₓ'. -/
@[simp]
theorem linearIsometryBoundedOfCompact_apply_apply (f : C(α, E)) (a : α) :
(linearIsometryBoundedOfCompact α E 𝕜 f) a = f a :=
rfl
#align continuous_map.linear_isometry_bounded_of_compact_apply_apply ContinuousMap.linearIsometryBoundedOfCompact_apply_apply
+/- warning: continuous_map.linear_isometry_bounded_of_compact_to_isometry_equiv -> ContinuousMap.linearIsometryBoundedOfCompact_toIsometryEquiv is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {E : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_4 : NormedAddCommGroup.{u2} E] {𝕜 : Type.{u3}} [_inst_5 : NormedField.{u3} 𝕜] [_inst_6 : NormedSpace.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)], Eq.{succ (max u1 u2)} (IsometryEquiv.{max u1 u2, max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (PseudoMetricSpace.toPseudoEMetricSpace.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.normedAddCommGroup.{u1, u2} α E _inst_1 _inst_2 _inst_4)))) (PseudoMetricSpace.toPseudoEMetricSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (SeminormedAddCommGroup.toPseudoMetricSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (BoundedContinuousFunction.seminormedAddCommGroup.{u1, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (LinearIsometryEquiv.toIsometryEquiv.{u3, u3, max u1 u2, max u1 u2} 𝕜 𝕜 (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))))) (ContinuousMap.linearIsometryBoundedOfCompact._proof_1.{u3} 𝕜 _inst_5) (ContinuousMap.linearIsometryBoundedOfCompact._proof_2.{u3} 𝕜 _inst_5) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.normedAddCommGroup.{u1, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.seminormedAddCommGroup.{u1, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (ContinuousMap.module.{u1, u3, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.linearIsometryBoundedOfCompact._proof_3.{u2} E _inst_4) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_4.{u2, u3} E _inst_4 𝕜 _inst_5 _inst_6)) (BoundedContinuousFunction.module.{u1, u2, u3} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u3} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_5.{u2, u3} E _inst_4 𝕜 _inst_5 _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_6.{u2} E _inst_4)) (ContinuousMap.linearIsometryBoundedOfCompact.{u1, u2, u3} α E _inst_1 _inst_2 _inst_4 𝕜 _inst_5 _inst_6)) (ContinuousMap.isometryEquivBoundedOfCompact.{u1, u2} α E _inst_1 _inst_2 (NormedAddCommGroup.toMetricSpace.{u2} E _inst_4))
+but is expected to have type
+ forall {α : Type.{u3}} {E : Type.{u2}} [_inst_1 : TopologicalSpace.{u3} α] [_inst_2 : CompactSpace.{u3} α _inst_1] [_inst_4 : NormedAddCommGroup.{u2} E] {𝕜 : Type.{u1}} [_inst_5 : NormedField.{u1} 𝕜] [_inst_6 : NormedSpace.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)], Eq.{max (succ u3) (succ u2)} (IsometryEquiv.{max u3 u2, max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (PseudoMetricSpace.toPseudoEMetricSpace.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)))) (PseudoMetricSpace.toPseudoEMetricSpace.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E 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(NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 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(AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.linearIsometryBoundedOfCompact.{u3, u2, u1} α E _inst_1 _inst_2 _inst_4 𝕜 _inst_5 _inst_6)) (ContinuousMap.isometryEquivBoundedOfCompact.{u3, u2} α E _inst_1 _inst_2 (NormedAddCommGroup.toMetricSpace.{u2} E _inst_4))
+Case conversion may be inaccurate. Consider using '#align continuous_map.linear_isometry_bounded_of_compact_to_isometry_equiv ContinuousMap.linearIsometryBoundedOfCompact_toIsometryEquivₓ'. -/
@[simp]
theorem linearIsometryBoundedOfCompact_toIsometryEquiv :
(linearIsometryBoundedOfCompact α E 𝕜).toIsometryEquiv = isometryEquivBoundedOfCompact α E :=
rfl
#align continuous_map.linear_isometry_bounded_of_compact_to_isometry_equiv ContinuousMap.linearIsometryBoundedOfCompact_toIsometryEquiv
+/- warning: continuous_map.linear_isometry_bounded_of_compact_to_add_equiv -> ContinuousMap.linearIsometryBoundedOfCompact_toAddEquiv is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {E : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_4 : NormedAddCommGroup.{u2} E] {𝕜 : Type.{u3}} [_inst_5 : NormedField.{u3} 𝕜] [_inst_6 : NormedSpace.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)], Eq.{succ (max u1 u2)} (AddEquiv.{max u1 u2, max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (AddZeroClass.toHasAdd.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (AddMonoid.toAddZeroClass.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (AddCommGroup.toAddCommMonoid.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (SeminormedAddCommGroup.toAddCommGroup.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.normedAddCommGroup.{u1, u2} α E _inst_1 _inst_2 _inst_4))))))) (AddZeroClass.toHasAdd.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (AddMonoid.toAddZeroClass.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (AddCommMonoid.toAddMonoid.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (AddCommGroup.toAddCommMonoid.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (SeminormedAddCommGroup.toAddCommGroup.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (BoundedContinuousFunction.seminormedAddCommGroup.{u1, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))))))) (LinearEquiv.toAddEquiv.{u3, u3, max u1 u2, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))))) (ContinuousMap.linearIsometryBoundedOfCompact._proof_1.{u3} 𝕜 _inst_5) (ContinuousMap.linearIsometryBoundedOfCompact._proof_2.{u3} 𝕜 _inst_5) (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (AddCommGroup.toAddCommMonoid.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (SeminormedAddCommGroup.toAddCommGroup.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.normedAddCommGroup.{u1, u2} α E _inst_1 _inst_2 _inst_4)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (SeminormedAddCommGroup.toAddCommGroup.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (BoundedContinuousFunction.seminormedAddCommGroup.{u1, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (ContinuousMap.module.{u1, u3, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.linearIsometryBoundedOfCompact._proof_3.{u2} E _inst_4) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_4.{u2, u3} E _inst_4 𝕜 _inst_5 _inst_6)) (BoundedContinuousFunction.module.{u1, u2, u3} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u3} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_5.{u2, u3} E _inst_4 𝕜 _inst_5 _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_6.{u2} E _inst_4)) (LinearIsometryEquiv.toLinearEquiv.{u3, u3, max u1 u2, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))))) (ContinuousMap.linearIsometryBoundedOfCompact._proof_1.{u3} 𝕜 _inst_5) (ContinuousMap.linearIsometryBoundedOfCompact._proof_2.{u3} 𝕜 _inst_5) (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.normedAddCommGroup.{u1, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.seminormedAddCommGroup.{u1, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (ContinuousMap.module.{u1, u3, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.linearIsometryBoundedOfCompact._proof_3.{u2} E _inst_4) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_4.{u2, u3} E _inst_4 𝕜 _inst_5 _inst_6)) (BoundedContinuousFunction.module.{u1, u2, u3} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u3} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_5.{u2, u3} E _inst_4 𝕜 _inst_5 _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_6.{u2} E _inst_4)) (ContinuousMap.linearIsometryBoundedOfCompact.{u1, u2, u3} α E _inst_1 _inst_2 _inst_4 𝕜 _inst_5 _inst_6))) (ContinuousMap.addEquivBoundedOfCompact.{u1, u2} α E _inst_1 _inst_2 (NormedAddCommGroup.toMetricSpace.{u2} E _inst_4) (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))
+but is expected to have type
+ forall {α : Type.{u3}} {E : Type.{u2}} [_inst_1 : TopologicalSpace.{u3} α] [_inst_2 : CompactSpace.{u3} α _inst_1] [_inst_4 : NormedAddCommGroup.{u2} E] {𝕜 : Type.{u1}} [_inst_5 : NormedField.{u1} 𝕜] [_inst_6 : NormedSpace.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)], Eq.{max (succ u3) (succ u2)} (AddEquiv.{max u3 u2, max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.instAdd.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_4)))))) (TopologicalAddGroup.toContinuousAdd.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (BoundedContinuousFunction.instAddBoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (AddEquivClass.toAddEquiv.{max u3 u2, max u3 u2, max u3 u2} (LinearEquiv.{u1, u1, max u3 u2, max u3 u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (AddCommGroup.toAddCommMonoid.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (SeminormedAddCommGroup.toAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)))) (AddCommGroup.toAddCommMonoid.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (SeminormedAddCommGroup.toAddCommGroup.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.instAdd.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_4)))))) (TopologicalAddGroup.toContinuousAdd.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (BoundedContinuousFunction.instAddBoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (SemilinearEquivClass.toAddEquivClass.{max u3 u2, u1, u1, max u3 u2, max u3 u2} (LinearEquiv.{u1, u1, max u3 u2, max u3 u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (AddCommGroup.toAddCommMonoid.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (SeminormedAddCommGroup.toAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)))) (AddCommGroup.toAddCommMonoid.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (SeminormedAddCommGroup.toAddCommGroup.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.instAddCommMonoidContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (TopologicalAddGroup.toContinuousAdd.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max u3 u2, max u3 u2} 𝕜 𝕜 (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (SeminormedAddCommGroup.toAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)))) (AddCommGroup.toAddCommMonoid.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (SeminormedAddCommGroup.toAddCommGroup.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))))) (LinearIsometryEquiv.toLinearEquiv.{u1, u1, max u3 u2, max u3 u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.linearIsometryBoundedOfCompact.{u3, u2, u1} α E _inst_1 _inst_2 _inst_4 𝕜 _inst_5 _inst_6))) (ContinuousMap.addEquivBoundedOfCompact.{u3, u2} α E _inst_1 _inst_2 (NormedAddCommGroup.toMetricSpace.{u2} E _inst_4) (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))
+Case conversion may be inaccurate. Consider using '#align continuous_map.linear_isometry_bounded_of_compact_to_add_equiv ContinuousMap.linearIsometryBoundedOfCompact_toAddEquivₓ'. -/
@[simp]
theorem linearIsometryBoundedOfCompact_toAddEquiv :
(linearIsometryBoundedOfCompact α E 𝕜).toLinearEquiv.toAddEquiv =
@@ -323,6 +535,12 @@ theorem linearIsometryBoundedOfCompact_toAddEquiv :
rfl
#align continuous_map.linear_isometry_bounded_of_compact_to_add_equiv ContinuousMap.linearIsometryBoundedOfCompact_toAddEquiv
+/- warning: continuous_map.linear_isometry_bounded_of_compact_of_compact_to_equiv -> ContinuousMap.linearIsometryBoundedOfCompact_of_compact_toEquiv is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {E : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_4 : NormedAddCommGroup.{u2} E] {𝕜 : Type.{u3}} [_inst_5 : NormedField.{u3} 𝕜] [_inst_6 : NormedSpace.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)], Eq.{succ (max u1 u2)} (Equiv.{succ (max u1 u2), succ (max u1 u2)} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (LinearEquiv.toEquiv.{u3, u3, max u1 u2, max u1 u2} 𝕜 𝕜 (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (SeminormedAddCommGroup.toAddCommGroup.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.normedAddCommGroup.{u1, u2} α E _inst_1 _inst_2 _inst_4)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (SeminormedAddCommGroup.toAddCommGroup.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (BoundedContinuousFunction.seminormedAddCommGroup.{u1, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (ContinuousMap.module.{u1, u3, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.linearIsometryBoundedOfCompact._proof_3.{u2} E _inst_4) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_4.{u2, u3} E _inst_4 𝕜 _inst_5 _inst_6)) (BoundedContinuousFunction.module.{u1, u2, u3} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u3} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_5.{u2, u3} E _inst_4 𝕜 _inst_5 _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_6.{u2} E _inst_4)) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))))) (ContinuousMap.linearIsometryBoundedOfCompact._proof_1.{u3} 𝕜 _inst_5) (ContinuousMap.linearIsometryBoundedOfCompact._proof_2.{u3} 𝕜 _inst_5) (LinearIsometryEquiv.toLinearEquiv.{u3, u3, max u1 u2, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))))) (ContinuousMap.linearIsometryBoundedOfCompact._proof_1.{u3} 𝕜 _inst_5) (ContinuousMap.linearIsometryBoundedOfCompact._proof_2.{u3} 𝕜 _inst_5) (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u1, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u1 u2} (ContinuousMap.{u1, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.normedAddCommGroup.{u1, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.seminormedAddCommGroup.{u1, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (ContinuousMap.module.{u1, u3, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.linearIsometryBoundedOfCompact._proof_3.{u2} E _inst_4) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_4.{u2, u3} E _inst_4 𝕜 _inst_5 _inst_6)) (BoundedContinuousFunction.module.{u1, u2, u3} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u3} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u3, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_5.{u2, u3} E _inst_4 𝕜 _inst_5 _inst_6) (ContinuousMap.linearIsometryBoundedOfCompact._proof_6.{u2} E _inst_4)) (ContinuousMap.linearIsometryBoundedOfCompact.{u1, u2, u3} α E _inst_1 _inst_2 _inst_4 𝕜 _inst_5 _inst_6))) (ContinuousMap.equivBoundedOfCompact.{u1, u2} α E _inst_1 _inst_2 (NormedAddCommGroup.toMetricSpace.{u2} E _inst_4))
+but is expected to have type
+ forall {α : Type.{u3}} {E : Type.{u2}} [_inst_1 : TopologicalSpace.{u3} α] [_inst_2 : CompactSpace.{u3} α _inst_1] [_inst_4 : NormedAddCommGroup.{u2} E] {𝕜 : Type.{u1}} [_inst_5 : NormedField.{u1} 𝕜] [_inst_6 : NormedSpace.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)], Eq.{max (succ u3) (succ u2)} (Equiv.{succ (max u3 u2), succ (max u3 u2)} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (LinearEquiv.toEquiv.{u1, u1, max u3 u2, max u3 u2} 𝕜 𝕜 (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (SeminormedAddCommGroup.toAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)))) (AddCommGroup.toAddCommMonoid.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (SeminormedAddCommGroup.toAddCommGroup.{max u3 u2} (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (LinearIsometryEquiv.toLinearEquiv.{u1, u1, max u3 u2, max u3 u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (BoundedContinuousFunction.{u3, u2} α E _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (NormedAddCommGroup.toSeminormedAddCommGroup.{max u3 u2} (ContinuousMap.{u3, u2} α E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u3, u2} α E _inst_1 _inst_2 _inst_4)) (BoundedContinuousFunction.seminormedAddCommGroup.{u3, u2} α E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (ContinuousMap.module.{u3, u1, u2} α _inst_1 𝕜 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (ContinuousMap.instAddCommGroupContinuousMap.proof_1.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4) (ContinuousMap.instNormedAddCommGroupContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.proof_1.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (ContinuousSMul.continuousConstSMul.{u1, u2} 𝕜 E (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_5)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6)))) (BoundedContinuousFunction.module.{u3, u2, u1} α E 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_5)))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E _inst_5 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))) (ContinuousMap.linearIsometryBoundedOfCompact.{u3, u2, u1} α E _inst_1 _inst_2 _inst_4 𝕜 _inst_5 _inst_6))) (ContinuousMap.equivBoundedOfCompact.{u3, u2} α E _inst_1 _inst_2 (NormedAddCommGroup.toMetricSpace.{u2} E _inst_4))
+Case conversion may be inaccurate. Consider using '#align continuous_map.linear_isometry_bounded_of_compact_of_compact_to_equiv ContinuousMap.linearIsometryBoundedOfCompact_of_compact_toEquivₓ'. -/
@[simp]
theorem linearIsometryBoundedOfCompact_of_compact_toEquiv :
(linearIsometryBoundedOfCompact α E 𝕜).toLinearEquiv.toEquiv = equivBoundedOfCompact α E :=
@@ -355,11 +573,23 @@ We now set up some declarations making it convenient to use uniform continuity.
-/
+/- warning: continuous_map.uniform_continuity -> ContinuousMap.uniform_continuity is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : MetricSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)))] [_inst_3 : MetricSpace.{u2} β] (f : ContinuousMap.{u1, u2} α β (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))) (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (ε : Real), (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε) -> (Exists.{1} Real (fun (δ : Real) => Exists.{0} (GT.gt.{0} Real Real.hasLt δ (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (fun (H : GT.gt.{0} Real Real.hasLt δ (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) => forall {x : α} {y : α}, (LT.lt.{0} Real Real.hasLt (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) x y) δ) -> (LT.lt.{0} Real Real.hasLt (Dist.dist.{u2} β (PseudoMetricSpace.toHasDist.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} α β (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))) (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (fun (_x : ContinuousMap.{u1, u2} α β (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))) (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) => α -> β) (ContinuousMap.hasCoeToFun.{u1, u2} α β (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))) (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} α β (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))) (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (fun (_x : ContinuousMap.{u1, u2} α β (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))) (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) => α -> β) (ContinuousMap.hasCoeToFun.{u1, u2} α β (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))) (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) f y)) ε))))
+but is expected to have type
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : MetricSpace.{u2} α] [_inst_2 : CompactSpace.{u2} α (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1)))] [_inst_3 : MetricSpace.{u1} β] (f : ContinuousMap.{u2, u1} α β (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1))) (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) (ε : Real), (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) -> (Exists.{1} Real (fun (δ : Real) => And (GT.gt.{0} Real Real.instLTReal δ (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (forall {x : α} {y : α}, (LT.lt.{0} Real Real.instLTReal (Dist.dist.{u2} α (PseudoMetricSpace.toDist.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1)) x y) δ) -> (LT.lt.{0} Real Real.instLTReal (Dist.dist.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) x) (PseudoMetricSpace.toDist.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) x) (MetricSpace.toPseudoMetricSpace.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) x) _inst_3)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousMap.{u2, u1} α β (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1))) (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) α (fun (a : α) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) a) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousMap.{u2, u1} α β (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1))) (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) α β (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1))) (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3))) (ContinuousMap.instContinuousMapClassContinuousMap.{u2, u1} α β (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1))) (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3))))) f x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousMap.{u2, u1} α β (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1))) (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) α (fun (a : α) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) a) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousMap.{u2, u1} α β (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1))) (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) α β (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1))) (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3))) (ContinuousMap.instContinuousMapClassContinuousMap.{u2, u1} α β (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1))) (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3))))) f y)) ε))))
+Case conversion may be inaccurate. Consider using '#align continuous_map.uniform_continuity ContinuousMap.uniform_continuityₓ'. -/
theorem uniform_continuity (f : C(α, β)) (ε : ℝ) (h : 0 < ε) :
∃ δ > 0, ∀ {x y}, dist x y < δ → dist (f x) (f y) < ε :=
Metric.uniformContinuous_iff.mp (CompactSpace.uniformContinuous_of_continuous f.Continuous) ε h
#align continuous_map.uniform_continuity ContinuousMap.uniform_continuity
+/- warning: continuous_map.modulus -> ContinuousMap.modulus is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : MetricSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)))] [_inst_3 : MetricSpace.{u2} β], (ContinuousMap.{u1, u2} α β (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))) (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) -> (forall (ε : Real), (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε) -> Real)
+but is expected to have type
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : MetricSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)))] [_inst_3 : MetricSpace.{u2} β], (ContinuousMap.{u1, u2} α β (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))) (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) -> (forall (ε : Real), (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) -> Real)
+Case conversion may be inaccurate. Consider using '#align continuous_map.modulus ContinuousMap.modulusₓ'. -/
-- This definition allows us to separate the choice of some `δ`,
-- and the corresponding use of `dist a b < δ → dist (f a) (f b) < ε`,
-- even across different declarations.
@@ -369,10 +599,22 @@ def modulus (f : C(α, β)) (ε : ℝ) (h : 0 < ε) : ℝ :=
Classical.choose (uniform_continuity f ε h)
#align continuous_map.modulus ContinuousMap.modulus
+/- warning: continuous_map.modulus_pos -> ContinuousMap.modulus_pos is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : MetricSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)))] [_inst_3 : MetricSpace.{u2} β] (f : ContinuousMap.{u1, u2} α β (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))) (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) {ε : Real} {h : LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε}, LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (ContinuousMap.modulus.{u1, u2} α β _inst_1 _inst_2 _inst_3 f ε h)
+but is expected to have type
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : MetricSpace.{u2} α] [_inst_2 : CompactSpace.{u2} α (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1)))] [_inst_3 : MetricSpace.{u1} β] (f : ContinuousMap.{u2, u1} α β (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1))) (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) {ε : Real} {h : LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε}, LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (ContinuousMap.modulus.{u2, u1} α β _inst_1 _inst_2 _inst_3 f ε h)
+Case conversion may be inaccurate. Consider using '#align continuous_map.modulus_pos ContinuousMap.modulus_posₓ'. -/
theorem modulus_pos (f : C(α, β)) {ε : ℝ} {h : 0 < ε} : 0 < f.modulus ε h :=
(Classical.choose_spec (uniform_continuity f ε h)).fst
#align continuous_map.modulus_pos ContinuousMap.modulus_pos
+/- warning: continuous_map.dist_lt_of_dist_lt_modulus -> ContinuousMap.dist_lt_of_dist_lt_modulus is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : MetricSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)))] [_inst_3 : MetricSpace.{u2} β] (f : ContinuousMap.{u1, u2} α β (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))) (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (ε : Real) (h : LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε) {a : α} {b : α}, (LT.lt.{0} Real Real.hasLt (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) a b) (ContinuousMap.modulus.{u1, u2} α β _inst_1 _inst_2 _inst_3 f ε h)) -> (LT.lt.{0} Real Real.hasLt (Dist.dist.{u2} β (PseudoMetricSpace.toHasDist.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} α β (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))) (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (fun (_x : ContinuousMap.{u1, u2} α β (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))) (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) => α -> β) (ContinuousMap.hasCoeToFun.{u1, u2} α β (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))) (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) f a) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} α β (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))) (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) (fun (_x : ContinuousMap.{u1, u2} α β (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))) (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) => α -> β) (ContinuousMap.hasCoeToFun.{u1, u2} α β (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))) (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (MetricSpace.toPseudoMetricSpace.{u2} β _inst_3)))) f b)) ε)
+but is expected to have type
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : MetricSpace.{u2} α] [_inst_2 : CompactSpace.{u2} α (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1)))] [_inst_3 : MetricSpace.{u1} β] (f : ContinuousMap.{u2, u1} α β (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1))) (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) (ε : Real) (h : LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) {a : α} {b : α}, (LT.lt.{0} Real Real.instLTReal (Dist.dist.{u2} α (PseudoMetricSpace.toDist.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1)) a b) (ContinuousMap.modulus.{u2, u1} α β _inst_1 _inst_2 _inst_3 f ε h)) -> (LT.lt.{0} Real Real.instLTReal (Dist.dist.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) a) (PseudoMetricSpace.toDist.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) a) (MetricSpace.toPseudoMetricSpace.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) a) _inst_3)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousMap.{u2, u1} α β (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1))) (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) α (fun (_x : α) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousMap.{u2, u1} α β (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1))) (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) α β (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1))) (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3))) (ContinuousMap.instContinuousMapClassContinuousMap.{u2, u1} α β (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1))) (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3))))) f a) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousMap.{u2, u1} α β (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1))) (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) α (fun (_x : α) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousMap.{u2, u1} α β (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1))) (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3)))) α β (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1))) (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3))) (ContinuousMap.instContinuousMapClassContinuousMap.{u2, u1} α β (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1))) (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (MetricSpace.toPseudoMetricSpace.{u1} β _inst_3))))) f b)) ε)
+Case conversion may be inaccurate. Consider using '#align continuous_map.dist_lt_of_dist_lt_modulus ContinuousMap.dist_lt_of_dist_lt_modulusₓ'. -/
theorem dist_lt_of_dist_lt_modulus (f : C(α, β)) (ε : ℝ) (h : 0 < ε) {a b : α}
(w : dist a b < f.modulus ε h) : dist (f a) (f b) < ε :=
(Classical.choose_spec (uniform_continuity f ε h)).snd w
@@ -391,6 +633,12 @@ variable [NormedAddCommGroup β] [NormedSpace 𝕜 β] [NormedAddCommGroup γ] [
open ContinuousMap
+/- warning: continuous_linear_map.comp_left_continuous_compact -> ContinuousLinearMap.compLeftContinuousCompact is a dubious translation:
+lean 3 declaration is
+ forall (X : Type.{u1}) {𝕜 : Type.{u2}} {β : Type.{u3}} {γ : Type.{u4}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : CompactSpace.{u1} X _inst_1] [_inst_3 : NontriviallyNormedField.{u2} 𝕜] [_inst_4 : NormedAddCommGroup.{u3} β] [_inst_5 : NormedSpace.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)] [_inst_6 : NormedAddCommGroup.{u4} γ] [_inst_7 : NormedSpace.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)], (ContinuousLinearMap.{u2, u2, u3, u4} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) γ (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7)) -> (ContinuousLinearMap.{u2, u2, max u1 u3, max u1 u4} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.compactOpen.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.addCommMonoid.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (ContinuousLinearMap.compLeftContinuousCompact._proof_1.{u3} β _inst_4)) (ContinuousMap.{u1, u4} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))))) (ContinuousMap.compactOpen.{u1, u4} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))))) (ContinuousMap.addCommMonoid.{u1, u4} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (ContinuousLinearMap.compLeftContinuousCompact._proof_2.{u4} γ _inst_6)) (ContinuousMap.module.{u1, u2, u3} X _inst_1 𝕜 β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (ContinuousLinearMap.compLeftContinuousCompact._proof_3.{u3} β _inst_4) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (ContinuousLinearMap.compLeftContinuousCompact._proof_4.{u2, u3} 𝕜 β _inst_3 _inst_4 _inst_5)) (ContinuousMap.module.{u1, u2, u4} X _inst_1 𝕜 γ (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (ContinuousLinearMap.compLeftContinuousCompact._proof_5.{u4} γ _inst_6) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7) (ContinuousLinearMap.compLeftContinuousCompact._proof_6.{u2, u4} 𝕜 γ _inst_3 _inst_6 _inst_7)))
+but is expected to have type
+ forall (X : Type.{u1}) {𝕜 : Type.{u2}} {β : Type.{u3}} {γ : Type.{u4}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : CompactSpace.{u1} X _inst_1] [_inst_3 : NontriviallyNormedField.{u2} 𝕜] [_inst_4 : NormedAddCommGroup.{u3} β] [_inst_5 : NormedSpace.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)] [_inst_6 : NormedAddCommGroup.{u4} γ] [_inst_7 : NormedSpace.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)], (ContinuousLinearMap.{u2, u2, u3, u4} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) γ (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7)) -> (ContinuousLinearMap.{u2, u2, max u3 u1, max u4 u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.compactOpen.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.instAddCommMonoidContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (TopologicalAddGroup.toContinuousAdd.{u3} β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (ContinuousMap.{u1, u4} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))))) (ContinuousMap.compactOpen.{u1, u4} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))))) (ContinuousMap.instAddCommMonoidContinuousMap.{u1, u4} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (TopologicalAddGroup.toContinuousAdd.{u4} γ (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (NormedAddGroup.toAddGroup.{u4} γ (NormedAddCommGroup.toNormedAddGroup.{u4} γ _inst_6)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (ContinuousMap.module.{u1, u2, u3} X _inst_1 𝕜 β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (TopologicalAddGroup.toContinuousAdd.{u3} β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (ContinuousSMul.continuousConstSMul.{u2, u3} 𝕜 β (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (SMulZeroClass.toSMul.{u2, u3} 𝕜 β (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕜 β (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 β (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (Module.toMulActionWithZero.{u2, u3} 𝕜 β (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (BoundedSMul.continuousSMul.{u2, u3} 𝕜 β (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (NegZeroClass.toZero.{u3} β (SubNegZeroMonoid.toNegZeroClass.{u3} β (SubtractionMonoid.toSubNegZeroMonoid.{u3} β (SubtractionCommMonoid.toSubtractionMonoid.{u3} β (AddCommGroup.toDivisionAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))))) (SMulZeroClass.toSMul.{u2, u3} 𝕜 β (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕜 β (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 β (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (Module.toMulActionWithZero.{u2, u3} 𝕜 β (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (NormedSpace.boundedSMul.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5)))) (ContinuousMap.module.{u1, u2, u4} X _inst_1 𝕜 γ (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (TopologicalAddGroup.toContinuousAdd.{u4} γ (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (NormedAddGroup.toAddGroup.{u4} γ (NormedAddCommGroup.toNormedAddGroup.{u4} γ _inst_6)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7) (ContinuousSMul.continuousConstSMul.{u2, u4} 𝕜 γ (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (SMulZeroClass.toSMul.{u2, u4} 𝕜 γ (AddMonoid.toZero.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)))) (SMulWithZero.toSMulZeroClass.{u2, u4} 𝕜 γ (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)))) (MulActionWithZero.toSMulWithZero.{u2, u4} 𝕜 γ (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)))) (Module.toMulActionWithZero.{u2, u4} 𝕜 γ (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7))))) (BoundedSMul.continuousSMul.{u2, u4} 𝕜 γ (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (NegZeroClass.toZero.{u4} γ (SubNegZeroMonoid.toNegZeroClass.{u4} γ (SubtractionMonoid.toSubNegZeroMonoid.{u4} γ (SubtractionCommMonoid.toSubtractionMonoid.{u4} γ (AddCommGroup.toDivisionAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)))))) (SMulZeroClass.toSMul.{u2, u4} 𝕜 γ (AddMonoid.toZero.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)))) (SMulWithZero.toSMulZeroClass.{u2, u4} 𝕜 γ (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)))) (MulActionWithZero.toSMulWithZero.{u2, u4} 𝕜 γ (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)))) (Module.toMulActionWithZero.{u2, u4} 𝕜 γ (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7))))) (NormedSpace.boundedSMul.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7)))))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_left_continuous_compact ContinuousLinearMap.compLeftContinuousCompactₓ'. -/
/-- Postcomposition of continuous functions into a normed module by a continuous linear map is a
continuous linear map.
Transferred version of `continuous_linear_map.comp_left_continuous_bounded`,
@@ -403,14 +651,26 @@ protected def ContinuousLinearMap.compLeftContinuousCompact (g : β →L[𝕜]
(linearIsometryBoundedOfCompact X β 𝕜).toLinearIsometry.toContinuousLinearMap
#align continuous_linear_map.comp_left_continuous_compact ContinuousLinearMap.compLeftContinuousCompact
+/- warning: continuous_linear_map.to_linear_comp_left_continuous_compact -> ContinuousLinearMap.toLinear_compLeftContinuousCompact is a dubious translation:
+lean 3 declaration is
+ forall (X : Type.{u1}) {𝕜 : Type.{u2}} {β : Type.{u3}} {γ : Type.{u4}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : CompactSpace.{u1} X _inst_1] [_inst_3 : NontriviallyNormedField.{u2} 𝕜] [_inst_4 : NormedAddCommGroup.{u3} β] [_inst_5 : NormedSpace.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)] [_inst_6 : NormedAddCommGroup.{u4} γ] [_inst_7 : NormedSpace.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)] (g : ContinuousLinearMap.{u2, u2, u3, u4} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) γ (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7)), Eq.{max (succ (max u1 u3)) (succ (max u1 u4))} (LinearMap.{u2, u2, max u1 u3, max u1 u4} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.{u1, u4} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))))) (ContinuousMap.addCommMonoid.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (LipschitzAdd.continuousAdd.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)) (SubNegMonoid.toAddMonoid.{u3} β (AddGroup.toSubNegMonoid.{u3} β (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (ContinuousMap.addCommMonoid.{u1, u4} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (LipschitzAdd.continuousAdd.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)) (SubNegMonoid.toAddMonoid.{u4} γ (AddGroup.toSubNegMonoid.{u4} γ (NormedAddGroup.toAddGroup.{u4} γ (NormedAddCommGroup.toNormedAddGroup.{u4} γ _inst_6)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (ContinuousMap.module.{u1, u2, u3} X _inst_1 𝕜 β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (LipschitzAdd.continuousAdd.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)) (SubNegMonoid.toAddMonoid.{u3} β (AddGroup.toSubNegMonoid.{u3} β (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (ContinuousSMul.continuousConstSMul.{u2, u3} 𝕜 β (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (SMulZeroClass.toHasSmul.{u2, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (SMulWithZero.toSmulZeroClass.{u2, u3} 𝕜 β (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 β (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 β (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (BoundedSMul.continuousSMul.{u2, u3} 𝕜 β (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)) (MulZeroClass.toHasZero.{u2} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (SubNegMonoid.toAddMonoid.{u3} β (AddGroup.toSubNegMonoid.{u3} β (SeminormedAddGroup.toAddGroup.{u3} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))))) (SMulZeroClass.toHasSmul.{u2, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (SMulWithZero.toSmulZeroClass.{u2, u3} 𝕜 β (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 β (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 β (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (NormedSpace.boundedSMul.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5)))) (ContinuousMap.module.{u1, u2, u4} X _inst_1 𝕜 γ (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (LipschitzAdd.continuousAdd.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)) (SubNegMonoid.toAddMonoid.{u4} γ (AddGroup.toSubNegMonoid.{u4} γ (NormedAddGroup.toAddGroup.{u4} γ (NormedAddCommGroup.toNormedAddGroup.{u4} γ _inst_6)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7) (ContinuousSMul.continuousConstSMul.{u2, u4} 𝕜 γ (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (SMulZeroClass.toHasSmul.{u2, u4} 𝕜 γ (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (SMulWithZero.toSmulZeroClass.{u2, u4} 𝕜 γ (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (MulActionWithZero.toSMulWithZero.{u2, u4} 𝕜 γ (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (Module.toMulActionWithZero.{u2, u4} 𝕜 γ (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7))))) (BoundedSMul.continuousSMul.{u2, u4} 𝕜 γ (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)) (MulZeroClass.toHasZero.{u2} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (SubNegMonoid.toAddMonoid.{u4} γ (AddGroup.toSubNegMonoid.{u4} γ (SeminormedAddGroup.toAddGroup.{u4} γ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))))))) (SMulZeroClass.toHasSmul.{u2, u4} 𝕜 γ (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (SMulWithZero.toSmulZeroClass.{u2, u4} 𝕜 γ (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (MulActionWithZero.toSMulWithZero.{u2, u4} 𝕜 γ (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (Module.toMulActionWithZero.{u2, u4} 𝕜 γ (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7))))) (NormedSpace.boundedSMul.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7))))) ((fun (a : Sort.{max (succ (max u1 u3)) (succ (max u1 u4))}) (b : Sort.{max (succ (max u1 u3)) (succ (max u1 u4))}) [self : HasLiftT.{max (succ (max u1 u3)) (succ (max u1 u4)), max (succ (max u1 u3)) (succ (max u1 u4))} a b] => self.0) (ContinuousLinearMap.{u2, u2, max u1 u3, max u1 u4} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.compactOpen.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.addCommMonoid.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (ContinuousLinearMap.compLeftContinuousCompact._proof_1.{u3} β _inst_4)) (ContinuousMap.{u1, u4} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))))) (ContinuousMap.compactOpen.{u1, u4} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))))) (ContinuousMap.addCommMonoid.{u1, u4} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ 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_inst_7))) (LinearMap.{u2, u2, max u1 u3, max u1 u4} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.{u1, u4} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u4} γ 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(NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (LipschitzAdd.continuousAdd.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)) (SubNegMonoid.toAddMonoid.{u3} β (AddGroup.toSubNegMonoid.{u3} β (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (ContinuousSMul.continuousConstSMul.{u2, u3} 𝕜 β (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (SMulZeroClass.toHasSmul.{u2, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (SMulWithZero.toSmulZeroClass.{u2, u3} 𝕜 β (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 β (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 β (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (BoundedSMul.continuousSMul.{u2, u3} 𝕜 β (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)) (MulZeroClass.toHasZero.{u2} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (SubNegMonoid.toAddMonoid.{u3} β (AddGroup.toSubNegMonoid.{u3} β (SeminormedAddGroup.toAddGroup.{u3} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))))) (SMulZeroClass.toHasSmul.{u2, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (SMulWithZero.toSmulZeroClass.{u2, u3} 𝕜 β (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 β (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 β (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (NormedSpace.boundedSMul.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5)))) (ContinuousMap.module.{u1, u2, u4} X _inst_1 𝕜 γ (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (LipschitzAdd.continuousAdd.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)) (SubNegMonoid.toAddMonoid.{u4} γ (AddGroup.toSubNegMonoid.{u4} γ (NormedAddGroup.toAddGroup.{u4} γ (NormedAddCommGroup.toNormedAddGroup.{u4} γ _inst_6)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7) (ContinuousSMul.continuousConstSMul.{u2, u4} 𝕜 γ (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (SMulZeroClass.toHasSmul.{u2, u4} 𝕜 γ (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (SMulWithZero.toSmulZeroClass.{u2, u4} 𝕜 γ (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (MulActionWithZero.toSMulWithZero.{u2, u4} 𝕜 γ (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (Module.toMulActionWithZero.{u2, u4} 𝕜 γ (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7))))) (BoundedSMul.continuousSMul.{u2, u4} 𝕜 γ (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)) (MulZeroClass.toHasZero.{u2} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (SubNegMonoid.toAddMonoid.{u4} γ (AddGroup.toSubNegMonoid.{u4} γ (SeminormedAddGroup.toAddGroup.{u4} γ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))))))) (SMulZeroClass.toHasSmul.{u2, u4} 𝕜 γ (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (SMulWithZero.toSmulZeroClass.{u2, u4} 𝕜 γ (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 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(NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7))))) (NormedSpace.boundedSMul.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7))))) (HasLiftT.mk.{max (succ (max u1 u3)) (succ (max u1 u4)), max (succ (max u1 u3)) (succ (max u1 u4))} (ContinuousLinearMap.{u2, u2, max u1 u3, max u1 u4} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) 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(NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (SMulZeroClass.toHasSmul.{u2, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (SMulWithZero.toSmulZeroClass.{u2, u3} 𝕜 β (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 β (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 β (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (BoundedSMul.continuousSMul.{u2, u3} 𝕜 β (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)) (MulZeroClass.toHasZero.{u2} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (SubNegMonoid.toAddMonoid.{u3} β (AddGroup.toSubNegMonoid.{u3} β (SeminormedAddGroup.toAddGroup.{u3} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))))) (SMulZeroClass.toHasSmul.{u2, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (SMulWithZero.toSmulZeroClass.{u2, u3} 𝕜 β (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 β (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 β (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (NormedSpace.boundedSMul.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5)))) (ContinuousMap.module.{u1, u2, u4} X _inst_1 𝕜 γ (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (LipschitzAdd.continuousAdd.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)) (SubNegMonoid.toAddMonoid.{u4} γ (AddGroup.toSubNegMonoid.{u4} γ (NormedAddGroup.toAddGroup.{u4} γ (NormedAddCommGroup.toNormedAddGroup.{u4} γ _inst_6)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7) (ContinuousSMul.continuousConstSMul.{u2, u4} 𝕜 γ (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (SMulZeroClass.toHasSmul.{u2, u4} 𝕜 γ (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (SMulWithZero.toSmulZeroClass.{u2, u4} 𝕜 γ (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (MulActionWithZero.toSMulWithZero.{u2, u4} 𝕜 γ (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (Module.toMulActionWithZero.{u2, u4} 𝕜 γ (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7))))) (BoundedSMul.continuousSMul.{u2, u4} 𝕜 γ (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)) (MulZeroClass.toHasZero.{u2} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (SubNegMonoid.toAddMonoid.{u4} γ (AddGroup.toSubNegMonoid.{u4} γ (SeminormedAddGroup.toAddGroup.{u4} γ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))))))) (SMulZeroClass.toHasSmul.{u2, u4} 𝕜 γ (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (SMulWithZero.toSmulZeroClass.{u2, u4} 𝕜 γ (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} 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γ _inst_6) _inst_7))))) (NormedSpace.boundedSMul.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7))))) (CoeTCₓ.coe.{max (succ (max u1 u3)) (succ (max u1 u4)), max (succ (max u1 u3)) (succ (max u1 u4))} (ContinuousLinearMap.{u2, u2, max u1 u3, max u1 u4} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (ContinuousMap.{u1, u3} X β _inst_1 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(NormedAddCommGroup.toNormedAddGroup.{u4} γ _inst_6)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (ContinuousMap.module.{u1, u2, u3} X _inst_1 𝕜 β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (LipschitzAdd.continuousAdd.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)) (SubNegMonoid.toAddMonoid.{u3} β (AddGroup.toSubNegMonoid.{u3} β (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)))) 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(NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (SMulWithZero.toSmulZeroClass.{u2, u3} 𝕜 β (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 β (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β 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(AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (LipschitzAdd.continuousAdd.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)) (SubNegMonoid.toAddMonoid.{u4} γ (AddGroup.toSubNegMonoid.{u4} γ (NormedAddGroup.toAddGroup.{u4} γ (NormedAddCommGroup.toNormedAddGroup.{u4} γ _inst_6)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7) (ContinuousSMul.continuousConstSMul.{u2, u4} 𝕜 γ (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (SMulZeroClass.toHasSmul.{u2, u4} 𝕜 γ (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (SMulWithZero.toSmulZeroClass.{u2, u4} 𝕜 γ (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ 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γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7) (ContinuousLinearMap.compLeftContinuousCompact._proof_6.{u2, u4} 𝕜 γ _inst_3 _inst_6 _inst_7))) (LinearMap.{u2, u2, max u1 u3, max u1 u4} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.{u1, u4} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))))) (ContinuousMap.addCommMonoid.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (LipschitzAdd.continuousAdd.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)) (SubNegMonoid.toAddMonoid.{u3} β (AddGroup.toSubNegMonoid.{u3} β (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (ContinuousMap.addCommMonoid.{u1, u4} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (LipschitzAdd.continuousAdd.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)) (SubNegMonoid.toAddMonoid.{u4} γ (AddGroup.toSubNegMonoid.{u4} γ (NormedAddGroup.toAddGroup.{u4} γ (NormedAddCommGroup.toNormedAddGroup.{u4} γ _inst_6)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (ContinuousMap.module.{u1, u2, u3} X _inst_1 𝕜 β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (LipschitzAdd.continuousAdd.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)) (SubNegMonoid.toAddMonoid.{u3} β (AddGroup.toSubNegMonoid.{u3} β (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (ContinuousSMul.continuousConstSMul.{u2, u3} 𝕜 β (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (SMulZeroClass.toHasSmul.{u2, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (SMulWithZero.toSmulZeroClass.{u2, u3} 𝕜 β (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 β (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 β (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (BoundedSMul.continuousSMul.{u2, u3} 𝕜 β (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)) (MulZeroClass.toHasZero.{u2} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (SubNegMonoid.toAddMonoid.{u3} β (AddGroup.toSubNegMonoid.{u3} β (SeminormedAddGroup.toAddGroup.{u3} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))))) (SMulZeroClass.toHasSmul.{u2, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (SMulWithZero.toSmulZeroClass.{u2, u3} 𝕜 β (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 β (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 β (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (NormedSpace.boundedSMul.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5)))) (ContinuousMap.module.{u1, u2, u4} X _inst_1 𝕜 γ (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (LipschitzAdd.continuousAdd.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)) (SubNegMonoid.toAddMonoid.{u4} γ (AddGroup.toSubNegMonoid.{u4} γ (NormedAddGroup.toAddGroup.{u4} γ (NormedAddCommGroup.toNormedAddGroup.{u4} γ _inst_6)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7) (ContinuousSMul.continuousConstSMul.{u2, u4} 𝕜 γ (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (SMulZeroClass.toHasSmul.{u2, u4} 𝕜 γ (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (SMulWithZero.toSmulZeroClass.{u2, u4} 𝕜 γ (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (MulActionWithZero.toSMulWithZero.{u2, u4} 𝕜 γ (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (Module.toMulActionWithZero.{u2, u4} 𝕜 γ (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7))))) (BoundedSMul.continuousSMul.{u2, u4} 𝕜 γ (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)) (MulZeroClass.toHasZero.{u2} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (SubNegMonoid.toAddMonoid.{u4} γ (AddGroup.toSubNegMonoid.{u4} γ (SeminormedAddGroup.toAddGroup.{u4} γ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))))))) (SMulZeroClass.toHasSmul.{u2, u4} 𝕜 γ (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (SMulWithZero.toSmulZeroClass.{u2, u4} 𝕜 γ (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (MulActionWithZero.toSMulWithZero.{u2, u4} 𝕜 γ (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (Module.toMulActionWithZero.{u2, u4} 𝕜 γ (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7))))) (NormedSpace.boundedSMul.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7))))) (ContinuousLinearMap.LinearMap.coe.{u2, u2, max u1 u3, max u1 u4} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.compactOpen.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.addCommMonoid.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (ContinuousLinearMap.compLeftContinuousCompact._proof_1.{u3} β _inst_4)) (ContinuousMap.{u1, u4} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))))) (ContinuousMap.compactOpen.{u1, u4} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))))) (ContinuousMap.addCommMonoid.{u1, u4} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (ContinuousLinearMap.compLeftContinuousCompact._proof_2.{u4} γ _inst_6)) (ContinuousMap.module.{u1, u2, u3} X _inst_1 𝕜 β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (ContinuousLinearMap.compLeftContinuousCompact._proof_3.{u3} β _inst_4) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (ContinuousLinearMap.compLeftContinuousCompact._proof_4.{u2, u3} 𝕜 β _inst_3 _inst_4 _inst_5)) (ContinuousMap.module.{u1, u2, u4} X _inst_1 𝕜 γ (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (ContinuousLinearMap.compLeftContinuousCompact._proof_5.{u4} γ _inst_6) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7) (ContinuousLinearMap.compLeftContinuousCompact._proof_6.{u2, u4} 𝕜 γ _inst_3 _inst_6 _inst_7)))))) (ContinuousLinearMap.compLeftContinuousCompact.{u1, u2, u3, u4} X 𝕜 β γ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 g)) (ContinuousLinearMap.compLeftContinuous.{u2, u3, u4, u1} 𝕜 β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) γ (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (LipschitzAdd.continuousAdd.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)) (SubNegMonoid.toAddMonoid.{u3} β (AddGroup.toSubNegMonoid.{u3} β (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (ContinuousSMul.continuousConstSMul.{u2, u3} 𝕜 β (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (SMulZeroClass.toHasSmul.{u2, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (SMulWithZero.toSmulZeroClass.{u2, u3} 𝕜 β (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 β (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 β (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (BoundedSMul.continuousSMul.{u2, u3} 𝕜 β (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)) (MulZeroClass.toHasZero.{u2} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (SubNegMonoid.toAddMonoid.{u3} β (AddGroup.toSubNegMonoid.{u3} β (SeminormedAddGroup.toAddGroup.{u3} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))))) (SMulZeroClass.toHasSmul.{u2, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (SMulWithZero.toSmulZeroClass.{u2, u3} 𝕜 β (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 β (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 β (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (NormedSpace.boundedSMul.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))) (LipschitzAdd.continuousAdd.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)) (SubNegMonoid.toAddMonoid.{u4} γ (AddGroup.toSubNegMonoid.{u4} γ (NormedAddGroup.toAddGroup.{u4} γ (NormedAddCommGroup.toNormedAddGroup.{u4} γ _inst_6)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7) (ContinuousSMul.continuousConstSMul.{u2, u4} 𝕜 γ (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (SMulZeroClass.toHasSmul.{u2, u4} 𝕜 γ (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (SMulWithZero.toSmulZeroClass.{u2, u4} 𝕜 γ (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (MulActionWithZero.toSMulWithZero.{u2, u4} 𝕜 γ (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (Module.toMulActionWithZero.{u2, u4} 𝕜 γ (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7))))) (BoundedSMul.continuousSMul.{u2, u4} 𝕜 γ (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)) (MulZeroClass.toHasZero.{u2} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (SubNegMonoid.toAddMonoid.{u4} γ (AddGroup.toSubNegMonoid.{u4} γ (SeminormedAddGroup.toAddGroup.{u4} γ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))))))) (SMulZeroClass.toHasSmul.{u2, u4} 𝕜 γ (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (SMulWithZero.toSmulZeroClass.{u2, u4} 𝕜 γ (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (MulActionWithZero.toSMulWithZero.{u2, u4} 𝕜 γ (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3)))))) (AddZeroClass.toHasZero.{u4} γ (AddMonoid.toAddZeroClass.{u4} γ (AddCommMonoid.toAddMonoid.{u4} γ (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6))))) (Module.toMulActionWithZero.{u2, u4} 𝕜 γ (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7))))) (NormedSpace.boundedSMul.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7))) X _inst_1 g)
+but is expected to have type
+ forall (X : Type.{u1}) {𝕜 : Type.{u4}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : CompactSpace.{u1} X _inst_1] [_inst_3 : NontriviallyNormedField.{u4} 𝕜] [_inst_4 : NormedAddCommGroup.{u3} β] [_inst_5 : NormedSpace.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)] [_inst_6 : NormedAddCommGroup.{u2} γ] [_inst_7 : NormedSpace.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)] (g : ContinuousLinearMap.{u4, u4, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (RingHom.id.{u4} 𝕜 (Semiring.toNonAssocSemiring.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7)), Eq.{max (max (succ u1) (succ u3)) (succ u2)} (LinearMap.{u4, u4, max u1 u3, max u1 u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (RingHom.id.{u4} 𝕜 (Semiring.toNonAssocSemiring.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))))) (ContinuousMap.instAddCommMonoidContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (TopologicalAddGroup.toContinuousAdd.{u3} β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (ContinuousMap.instAddCommMonoidContinuousMap.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (TopologicalAddGroup.toContinuousAdd.{u2} γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (NormedAddGroup.toAddGroup.{u2} γ (NormedAddCommGroup.toNormedAddGroup.{u2} γ _inst_6)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (ContinuousMap.module.{u1, u4, u3} X _inst_1 𝕜 β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (TopologicalAddGroup.toContinuousAdd.{u3} β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (ContinuousSMul.continuousConstSMul.{u4, u3} 𝕜 β (UniformSpace.toTopologicalSpace.{u4} 𝕜 (PseudoMetricSpace.toUniformSpace.{u4} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (SMulZeroClass.toSMul.{u4, u3} 𝕜 β (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 β (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (Module.toMulActionWithZero.{u4, u3} 𝕜 β (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (BoundedSMul.continuousSMul.{u4, u3} 𝕜 β (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)) (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (NegZeroClass.toZero.{u3} β (SubNegZeroMonoid.toNegZeroClass.{u3} β (SubtractionMonoid.toSubNegZeroMonoid.{u3} β (SubtractionCommMonoid.toSubtractionMonoid.{u3} β (AddCommGroup.toDivisionAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))))) (SMulZeroClass.toSMul.{u4, u3} 𝕜 β (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 β (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (Module.toMulActionWithZero.{u4, u3} 𝕜 β (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (NormedSpace.boundedSMul.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5)))) (ContinuousMap.module.{u1, u4, u2} X _inst_1 𝕜 γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (TopologicalAddGroup.toContinuousAdd.{u2} γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (NormedAddGroup.toAddGroup.{u2} γ (NormedAddCommGroup.toNormedAddGroup.{u2} γ _inst_6)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7) (ContinuousSMul.continuousConstSMul.{u4, u2} 𝕜 γ (UniformSpace.toTopologicalSpace.{u4} 𝕜 (PseudoMetricSpace.toUniformSpace.{u4} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 γ (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 γ (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 γ (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (Module.toMulActionWithZero.{u4, u2} 𝕜 γ (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7))))) (BoundedSMul.continuousSMul.{u4, u2} 𝕜 γ (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)) (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (NegZeroClass.toZero.{u2} γ (SubNegZeroMonoid.toNegZeroClass.{u2} γ (SubtractionMonoid.toSubNegZeroMonoid.{u2} γ (SubtractionCommMonoid.toSubtractionMonoid.{u2} γ (AddCommGroup.toDivisionAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 γ (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 γ (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 γ (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (Module.toMulActionWithZero.{u4, u2} 𝕜 γ (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7))))) (NormedSpace.boundedSMul.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7))))) (ContinuousLinearMap.toLinearMap.{u4, u4, max u1 u3, max u1 u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (RingHom.id.{u4} 𝕜 (Semiring.toNonAssocSemiring.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.compactOpen.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.instAddCommMonoidContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (TopologicalAddGroup.toContinuousAdd.{u3} β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (ContinuousMap.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))))) (ContinuousMap.compactOpen.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))))) (ContinuousMap.instAddCommMonoidContinuousMap.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (TopologicalAddGroup.toContinuousAdd.{u2} γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (NormedAddGroup.toAddGroup.{u2} γ (NormedAddCommGroup.toNormedAddGroup.{u2} γ _inst_6)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (ContinuousMap.module.{u1, u4, u3} X _inst_1 𝕜 β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (TopologicalAddGroup.toContinuousAdd.{u3} β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (ContinuousSMul.continuousConstSMul.{u4, u3} 𝕜 β (UniformSpace.toTopologicalSpace.{u4} 𝕜 (PseudoMetricSpace.toUniformSpace.{u4} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (SMulZeroClass.toSMul.{u4, u3} 𝕜 β (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 β (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (Module.toMulActionWithZero.{u4, u3} 𝕜 β (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (BoundedSMul.continuousSMul.{u4, u3} 𝕜 β (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)) (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (NegZeroClass.toZero.{u3} β (SubNegZeroMonoid.toNegZeroClass.{u3} β (SubtractionMonoid.toSubNegZeroMonoid.{u3} β (SubtractionCommMonoid.toSubtractionMonoid.{u3} β (AddCommGroup.toDivisionAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))))) (SMulZeroClass.toSMul.{u4, u3} 𝕜 β (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 β (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (Module.toMulActionWithZero.{u4, u3} 𝕜 β (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (NormedSpace.boundedSMul.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5)))) (ContinuousMap.module.{u1, u4, u2} X _inst_1 𝕜 γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (TopologicalAddGroup.toContinuousAdd.{u2} γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (NormedAddGroup.toAddGroup.{u2} γ (NormedAddCommGroup.toNormedAddGroup.{u2} γ _inst_6)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7) (ContinuousSMul.continuousConstSMul.{u4, u2} 𝕜 γ (UniformSpace.toTopologicalSpace.{u4} 𝕜 (PseudoMetricSpace.toUniformSpace.{u4} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 γ (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 γ (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 γ (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (Module.toMulActionWithZero.{u4, u2} 𝕜 γ (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7))))) (BoundedSMul.continuousSMul.{u4, u2} 𝕜 γ (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)) (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (NegZeroClass.toZero.{u2} γ (SubNegZeroMonoid.toNegZeroClass.{u2} γ (SubtractionMonoid.toSubNegZeroMonoid.{u2} γ (SubtractionCommMonoid.toSubtractionMonoid.{u2} γ (AddCommGroup.toDivisionAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 γ (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 γ (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 γ (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (Module.toMulActionWithZero.{u4, u2} 𝕜 γ (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7))))) (NormedSpace.boundedSMul.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7)))) (ContinuousLinearMap.compLeftContinuousCompact.{u1, u4, u3, u2} X 𝕜 β γ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 g)) (ContinuousLinearMap.compLeftContinuous.{u4, u3, u2, u1} 𝕜 β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (TopologicalAddGroup.toContinuousAdd.{u3} β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (ContinuousSMul.continuousConstSMul.{u4, u3} 𝕜 β (UniformSpace.toTopologicalSpace.{u4} 𝕜 (PseudoMetricSpace.toUniformSpace.{u4} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (SMulZeroClass.toSMul.{u4, u3} 𝕜 β (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 β (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (Module.toMulActionWithZero.{u4, u3} 𝕜 β (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (BoundedSMul.continuousSMul.{u4, u3} 𝕜 β (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)) (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (NegZeroClass.toZero.{u3} β (SubNegZeroMonoid.toNegZeroClass.{u3} β (SubtractionMonoid.toSubNegZeroMonoid.{u3} β (SubtractionCommMonoid.toSubtractionMonoid.{u3} β (AddCommGroup.toDivisionAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))))) (SMulZeroClass.toSMul.{u4, u3} 𝕜 β (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 β (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (Module.toMulActionWithZero.{u4, u3} 𝕜 β (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (NormedSpace.boundedSMul.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))) (TopologicalAddGroup.toContinuousAdd.{u2} γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (NormedAddGroup.toAddGroup.{u2} γ (NormedAddCommGroup.toNormedAddGroup.{u2} γ _inst_6)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7) (ContinuousSMul.continuousConstSMul.{u4, u2} 𝕜 γ (UniformSpace.toTopologicalSpace.{u4} 𝕜 (PseudoMetricSpace.toUniformSpace.{u4} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 γ (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 γ (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 γ (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (Module.toMulActionWithZero.{u4, u2} 𝕜 γ (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7))))) (BoundedSMul.continuousSMul.{u4, u2} 𝕜 γ (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)) (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (NegZeroClass.toZero.{u2} γ (SubNegZeroMonoid.toNegZeroClass.{u2} γ (SubtractionMonoid.toSubNegZeroMonoid.{u2} γ (SubtractionCommMonoid.toSubtractionMonoid.{u2} γ (AddCommGroup.toDivisionAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 γ (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 γ (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 γ (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (Module.toMulActionWithZero.{u4, u2} 𝕜 γ (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7))))) (NormedSpace.boundedSMul.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7))) X _inst_1 g)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.to_linear_comp_left_continuous_compact ContinuousLinearMap.toLinear_compLeftContinuousCompactₓ'. -/
@[simp]
-theorem ContinuousLinearMap.to_linear_compLeftContinuousCompact (g : β →L[𝕜] γ) :
+theorem ContinuousLinearMap.toLinear_compLeftContinuousCompact (g : β →L[𝕜] γ) :
(g.compLeftContinuousCompact X : C(X, β) →ₗ[𝕜] C(X, γ)) = g.compLeftContinuous 𝕜 X :=
by
ext f
rfl
-#align continuous_linear_map.to_linear_comp_left_continuous_compact ContinuousLinearMap.to_linear_compLeftContinuousCompact
-
+#align continuous_linear_map.to_linear_comp_left_continuous_compact ContinuousLinearMap.toLinear_compLeftContinuousCompact
+
+/- warning: continuous_linear_map.comp_left_continuous_compact_apply -> ContinuousLinearMap.compLeftContinuousCompact_apply is a dubious translation:
+lean 3 declaration is
+ forall (X : Type.{u1}) {𝕜 : Type.{u2}} {β : Type.{u3}} {γ : Type.{u4}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : CompactSpace.{u1} X _inst_1] [_inst_3 : NontriviallyNormedField.{u2} 𝕜] [_inst_4 : NormedAddCommGroup.{u3} β] [_inst_5 : NormedSpace.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)] [_inst_6 : NormedAddCommGroup.{u4} γ] [_inst_7 : NormedSpace.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)] (g : ContinuousLinearMap.{u2, u2, u3, u4} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3))))))) β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) γ (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u4} γ (NormedAddCommGroup.toAddCommGroup.{u4} γ _inst_6)) (NormedSpace.toModule.{u2, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (NormedSpace.toModule.{u2, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6) _inst_7)) (f : ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (x : X), Eq.{succ u4} γ (coeFn.{max (succ u1) (succ u4), max (succ u1) (succ u4)} (ContinuousMap.{u1, u4} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))))) (fun (_x : ContinuousMap.{u1, u4} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} γ _inst_6))))) => X -> γ) (ContinuousMap.hasCoeToFun.{u1, u4} X γ _inst_1 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+but is expected to have type
+ forall (X : Type.{u1}) {𝕜 : Type.{u4}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : CompactSpace.{u1} X _inst_1] [_inst_3 : NontriviallyNormedField.{u4} 𝕜] [_inst_4 : NormedAddCommGroup.{u3} β] [_inst_5 : NormedSpace.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)] [_inst_6 : NormedAddCommGroup.{u2} γ] [_inst_7 : NormedSpace.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)] (g : ContinuousLinearMap.{u4, u4, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) 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(NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (TopologicalAddGroup.toContinuousAdd.{u3} β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (ContinuousSMul.continuousConstSMul.{u4, u3} 𝕜 β (UniformSpace.toTopologicalSpace.{u4} 𝕜 (PseudoMetricSpace.toUniformSpace.{u4} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (SMulZeroClass.toSMul.{u4, u3} 𝕜 β (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 β (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (Module.toMulActionWithZero.{u4, u3} 𝕜 β (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (BoundedSMul.continuousSMul.{u4, u3} 𝕜 β (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)) (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (NegZeroClass.toZero.{u3} β (SubNegZeroMonoid.toNegZeroClass.{u3} β (SubtractionMonoid.toSubNegZeroMonoid.{u3} β (SubtractionCommMonoid.toSubtractionMonoid.{u3} β (AddCommGroup.toDivisionAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))))) (SMulZeroClass.toSMul.{u4, u3} 𝕜 β (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 β (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (Module.toMulActionWithZero.{u4, u3} 𝕜 β (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (NormedSpace.boundedSMul.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5)))) (ContinuousMap.module.{u1, u4, u2} X _inst_1 𝕜 γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (TopologicalAddGroup.toContinuousAdd.{u2} γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (NormedAddGroup.toAddGroup.{u2} γ (NormedAddCommGroup.toNormedAddGroup.{u2} γ _inst_6)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7) (ContinuousSMul.continuousConstSMul.{u4, u2} 𝕜 γ (UniformSpace.toTopologicalSpace.{u4} 𝕜 (PseudoMetricSpace.toUniformSpace.{u4} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 γ (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 γ (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 γ (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (Module.toMulActionWithZero.{u4, u2} 𝕜 γ (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7))))) (BoundedSMul.continuousSMul.{u4, u2} 𝕜 γ (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)) (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (NegZeroClass.toZero.{u2} γ (SubNegZeroMonoid.toNegZeroClass.{u2} γ (SubtractionMonoid.toSubNegZeroMonoid.{u2} γ (SubtractionCommMonoid.toSubtractionMonoid.{u2} γ (AddCommGroup.toDivisionAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 γ (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 γ (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 γ (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (Module.toMulActionWithZero.{u4, u2} 𝕜 γ (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7))))) (NormedSpace.boundedSMul.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7))))) (ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (fun (_x : ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) => ContinuousMap.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))))) _x) (ContinuousMapClass.toFunLike.{max (max u1 u3) u2, max u1 u3, max u1 u2} (ContinuousLinearMap.{u4, u4, max u3 u1, max u2 u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (RingHom.id.{u4} 𝕜 (Semiring.toNonAssocSemiring.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.compactOpen.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.instAddCommMonoidContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (TopologicalAddGroup.toContinuousAdd.{u3} β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (ContinuousMap.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))))) (ContinuousMap.compactOpen.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))))) (ContinuousMap.instAddCommMonoidContinuousMap.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (TopologicalAddGroup.toContinuousAdd.{u2} γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (NormedAddGroup.toAddGroup.{u2} γ (NormedAddCommGroup.toNormedAddGroup.{u2} γ _inst_6)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (ContinuousMap.module.{u1, u4, u3} X _inst_1 𝕜 β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (TopologicalAddGroup.toContinuousAdd.{u3} β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (ContinuousSMul.continuousConstSMul.{u4, u3} 𝕜 β (UniformSpace.toTopologicalSpace.{u4} 𝕜 (PseudoMetricSpace.toUniformSpace.{u4} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (SMulZeroClass.toSMul.{u4, u3} 𝕜 β (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 β (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (Module.toMulActionWithZero.{u4, u3} 𝕜 β (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (BoundedSMul.continuousSMul.{u4, u3} 𝕜 β (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)) (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (NegZeroClass.toZero.{u3} β (SubNegZeroMonoid.toNegZeroClass.{u3} β (SubtractionMonoid.toSubNegZeroMonoid.{u3} β (SubtractionCommMonoid.toSubtractionMonoid.{u3} β (AddCommGroup.toDivisionAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))))) (SMulZeroClass.toSMul.{u4, u3} 𝕜 β (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 β (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (Module.toMulActionWithZero.{u4, u3} 𝕜 β (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (NormedSpace.boundedSMul.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5)))) (ContinuousMap.module.{u1, u4, u2} X _inst_1 𝕜 γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (TopologicalAddGroup.toContinuousAdd.{u2} γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (NormedAddGroup.toAddGroup.{u2} γ (NormedAddCommGroup.toNormedAddGroup.{u2} γ _inst_6)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7) (ContinuousSMul.continuousConstSMul.{u4, u2} 𝕜 γ (UniformSpace.toTopologicalSpace.{u4} 𝕜 (PseudoMetricSpace.toUniformSpace.{u4} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 γ (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 γ (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 γ (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (Module.toMulActionWithZero.{u4, u2} 𝕜 γ (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7))))) (BoundedSMul.continuousSMul.{u4, u2} 𝕜 γ (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)) (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (NegZeroClass.toZero.{u2} γ (SubNegZeroMonoid.toNegZeroClass.{u2} γ (SubtractionMonoid.toSubNegZeroMonoid.{u2} γ (SubtractionCommMonoid.toSubtractionMonoid.{u2} γ (AddCommGroup.toDivisionAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 γ (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 γ (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 γ (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (Module.toMulActionWithZero.{u4, u2} 𝕜 γ (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7))))) (NormedSpace.boundedSMul.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7))))) (ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))))) (ContinuousMap.compactOpen.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.compactOpen.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max (max u1 u3) u2, u4, u4, max u1 u3, max u1 u2} (ContinuousLinearMap.{u4, u4, max u3 u1, max u2 u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (RingHom.id.{u4} 𝕜 (Semiring.toNonAssocSemiring.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.compactOpen.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.instAddCommMonoidContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (TopologicalAddGroup.toContinuousAdd.{u3} β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (ContinuousMap.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))))) (ContinuousMap.compactOpen.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))))) (ContinuousMap.instAddCommMonoidContinuousMap.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (TopologicalAddGroup.toContinuousAdd.{u2} γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (NormedAddGroup.toAddGroup.{u2} γ (NormedAddCommGroup.toNormedAddGroup.{u2} γ _inst_6)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (ContinuousMap.module.{u1, u4, u3} X _inst_1 𝕜 β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (TopologicalAddGroup.toContinuousAdd.{u3} β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (ContinuousSMul.continuousConstSMul.{u4, u3} 𝕜 β (UniformSpace.toTopologicalSpace.{u4} 𝕜 (PseudoMetricSpace.toUniformSpace.{u4} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (SMulZeroClass.toSMul.{u4, u3} 𝕜 β (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 β (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (Module.toMulActionWithZero.{u4, u3} 𝕜 β (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (BoundedSMul.continuousSMul.{u4, u3} 𝕜 β (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)) (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (NegZeroClass.toZero.{u3} β (SubNegZeroMonoid.toNegZeroClass.{u3} β (SubtractionMonoid.toSubNegZeroMonoid.{u3} β (SubtractionCommMonoid.toSubtractionMonoid.{u3} β (AddCommGroup.toDivisionAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))))) (SMulZeroClass.toSMul.{u4, u3} 𝕜 β (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 β (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (Module.toMulActionWithZero.{u4, u3} 𝕜 β (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (NormedSpace.boundedSMul.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5)))) (ContinuousMap.module.{u1, u4, u2} X _inst_1 𝕜 γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (TopologicalAddGroup.toContinuousAdd.{u2} γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (NormedAddGroup.toAddGroup.{u2} γ (NormedAddCommGroup.toNormedAddGroup.{u2} γ _inst_6)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7) (ContinuousSMul.continuousConstSMul.{u4, u2} 𝕜 γ (UniformSpace.toTopologicalSpace.{u4} 𝕜 (PseudoMetricSpace.toUniformSpace.{u4} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 γ (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 γ (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 γ (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (Module.toMulActionWithZero.{u4, u2} 𝕜 γ (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7))))) (BoundedSMul.continuousSMul.{u4, u2} 𝕜 γ (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)) (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (NegZeroClass.toZero.{u2} γ (SubNegZeroMonoid.toNegZeroClass.{u2} γ (SubtractionMonoid.toSubNegZeroMonoid.{u2} γ (SubtractionCommMonoid.toSubtractionMonoid.{u2} γ (AddCommGroup.toDivisionAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 γ (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 γ (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 γ (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (Module.toMulActionWithZero.{u4, u2} 𝕜 γ (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7))))) (NormedSpace.boundedSMul.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7))))) 𝕜 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (RingHom.id.{u4} 𝕜 (Semiring.toNonAssocSemiring.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.compactOpen.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.instAddCommMonoidContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (TopologicalAddGroup.toContinuousAdd.{u3} β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (ContinuousMap.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))))) (ContinuousMap.compactOpen.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))))) (ContinuousMap.instAddCommMonoidContinuousMap.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (TopologicalAddGroup.toContinuousAdd.{u2} γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (NormedAddGroup.toAddGroup.{u2} γ (NormedAddCommGroup.toNormedAddGroup.{u2} γ _inst_6)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (ContinuousMap.module.{u1, u4, u3} X _inst_1 𝕜 β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (TopologicalAddGroup.toContinuousAdd.{u3} β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (ContinuousSMul.continuousConstSMul.{u4, u3} 𝕜 β (UniformSpace.toTopologicalSpace.{u4} 𝕜 (PseudoMetricSpace.toUniformSpace.{u4} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (SMulZeroClass.toSMul.{u4, u3} 𝕜 β (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 β (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (Module.toMulActionWithZero.{u4, u3} 𝕜 β (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (BoundedSMul.continuousSMul.{u4, u3} 𝕜 β (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)) (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (NegZeroClass.toZero.{u3} β (SubNegZeroMonoid.toNegZeroClass.{u3} β (SubtractionMonoid.toSubNegZeroMonoid.{u3} β (SubtractionCommMonoid.toSubtractionMonoid.{u3} β (AddCommGroup.toDivisionAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))))) (SMulZeroClass.toSMul.{u4, u3} 𝕜 β (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 β (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (Module.toMulActionWithZero.{u4, u3} 𝕜 β (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (NormedSpace.boundedSMul.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5)))) (ContinuousMap.module.{u1, u4, u2} X _inst_1 𝕜 γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (TopologicalAddGroup.toContinuousAdd.{u2} γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (NormedAddGroup.toAddGroup.{u2} γ (NormedAddCommGroup.toNormedAddGroup.{u2} γ _inst_6)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7) (ContinuousSMul.continuousConstSMul.{u4, u2} 𝕜 γ (UniformSpace.toTopologicalSpace.{u4} 𝕜 (PseudoMetricSpace.toUniformSpace.{u4} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 γ (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 γ (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 γ (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (Module.toMulActionWithZero.{u4, u2} 𝕜 γ (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7))))) (BoundedSMul.continuousSMul.{u4, u2} 𝕜 γ (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)) (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (NegZeroClass.toZero.{u2} γ (SubNegZeroMonoid.toNegZeroClass.{u2} γ (SubtractionMonoid.toSubNegZeroMonoid.{u2} γ (SubtractionCommMonoid.toSubtractionMonoid.{u2} γ (AddCommGroup.toDivisionAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 γ (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 γ (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 γ (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (Module.toMulActionWithZero.{u4, u2} 𝕜 γ (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7))))) (NormedSpace.boundedSMul.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7)))) (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u4, max u1 u3, max u1 u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (RingHom.id.{u4} 𝕜 (Semiring.toNonAssocSemiring.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.compactOpen.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) (ContinuousMap.instAddCommMonoidContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (TopologicalAddGroup.toContinuousAdd.{u3} β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (ContinuousMap.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))))) (ContinuousMap.compactOpen.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))))) (ContinuousMap.instAddCommMonoidContinuousMap.{u1, u2} X γ _inst_1 (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (TopologicalAddGroup.toContinuousAdd.{u2} γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (NormedAddGroup.toAddGroup.{u2} γ (NormedAddCommGroup.toNormedAddGroup.{u2} γ _inst_6)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (ContinuousMap.module.{u1, u4, u3} X _inst_1 𝕜 β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (TopologicalAddGroup.toContinuousAdd.{u3} β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (NormedAddGroup.toAddGroup.{u3} β (NormedAddCommGroup.toNormedAddGroup.{u3} β _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (ContinuousSMul.continuousConstSMul.{u4, u3} 𝕜 β 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(AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (Module.toMulActionWithZero.{u4, u3} 𝕜 β (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (BoundedSMul.continuousSMul.{u4, u3} 𝕜 β (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)) (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (NegZeroClass.toZero.{u3} β (SubNegZeroMonoid.toNegZeroClass.{u3} β (SubtractionMonoid.toSubNegZeroMonoid.{u3} β (SubtractionCommMonoid.toSubtractionMonoid.{u3} β (AddCommGroup.toDivisionAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))))) (SMulZeroClass.toSMul.{u4, u3} 𝕜 β (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 β (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)))) (Module.toMulActionWithZero.{u4, u3} 𝕜 β (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5))))) (NormedSpace.boundedSMul.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5)))) (ContinuousMap.module.{u1, u4, u2} X _inst_1 𝕜 γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (TopologicalAddGroup.toContinuousAdd.{u2} γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (NormedAddGroup.toAddGroup.{u2} γ (NormedAddCommGroup.toNormedAddGroup.{u2} γ _inst_6)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6))) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7) (ContinuousSMul.continuousConstSMul.{u4, u2} 𝕜 γ (UniformSpace.toTopologicalSpace.{u4} 𝕜 (PseudoMetricSpace.toUniformSpace.{u4} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 γ (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 γ (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 γ (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (Module.toMulActionWithZero.{u4, u2} 𝕜 γ (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7))))) (BoundedSMul.continuousSMul.{u4, u2} 𝕜 γ (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)) (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (NegZeroClass.toZero.{u2} γ (SubNegZeroMonoid.toNegZeroClass.{u2} γ (SubtractionMonoid.toSubNegZeroMonoid.{u2} γ (SubtractionCommMonoid.toSubtractionMonoid.{u2} γ (AddCommGroup.toDivisionAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 γ (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 γ (MonoidWithZero.toZero.{u4} 𝕜 (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 γ (Semiring.toMonoidWithZero.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3)))))) (AddMonoid.toZero.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)))) (Module.toMulActionWithZero.{u4, u2} 𝕜 γ (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7))))) (NormedSpace.boundedSMul.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7))))))) (ContinuousLinearMap.compLeftContinuousCompact.{u1, u4, u3, u2} X 𝕜 β γ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 g) f) x) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (ContinuousLinearMap.{u4, u4, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (RingHom.id.{u4} 𝕜 (Semiring.toNonAssocSemiring.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7)) β (fun (_x : β) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : β) => γ) _x) (ContinuousMapClass.toFunLike.{max u3 u2, u3, u2} (ContinuousLinearMap.{u4, u4, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (RingHom.id.{u4} 𝕜 (Semiring.toNonAssocSemiring.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7)) β γ (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u2, u4, u4, u3, u2} (ContinuousLinearMap.{u4, u4, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (RingHom.id.{u4} 𝕜 (Semiring.toNonAssocSemiring.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7)) 𝕜 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (RingHom.id.{u4} 𝕜 (Semiring.toNonAssocSemiring.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7) (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u4, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (RingHom.id.{u4} 𝕜 (Semiring.toNonAssocSemiring.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} β (NormedAddCommGroup.toAddCommGroup.{u3} β _inst_4)) γ (UniformSpace.toTopologicalSpace.{u2} γ (PseudoMetricSpace.toUniformSpace.{u2} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} γ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} γ (NormedAddCommGroup.toAddCommGroup.{u2} γ _inst_6)) (NormedSpace.toModule.{u4, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4) _inst_5) (NormedSpace.toModule.{u4, u2} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} γ _inst_6) _inst_7)))) g (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) X (fun (_x : X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : X) => β) _x) (ContinuousMapClass.toFunLike.{max u1 u3, u1, u3} (ContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4))))) X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))) (ContinuousMap.instContinuousMapClassContinuousMap.{u1, u3} X β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} β _inst_4)))))) f x))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_left_continuous_compact_apply ContinuousLinearMap.compLeftContinuousCompact_applyₓ'. -/
@[simp]
theorem ContinuousLinearMap.compLeftContinuousCompact_apply (g : β →L[𝕜] γ) (f : C(X, β)) (x : X) :
g.compLeftContinuousCompact X f x = g (f x) :=
@@ -435,6 +695,7 @@ In particular:
section CompRight
+#print ContinuousMap.compRightContinuousMap /-
/-- Precomposition by a continuous map is itself a continuous map between spaces of continuous maps.
-/
def compRightContinuousMap {X Y : Type _} (T : Type _) [TopologicalSpace X] [CompactSpace X]
@@ -448,7 +709,14 @@ def compRightContinuousMap {X Y : Type _} (T : Type _) [TopologicalSpace X] [Com
rw [ContinuousMap.dist_lt_iff ε_pos] at h⊢
· exact fun x => h (f x)
#align continuous_map.comp_right_continuous_map ContinuousMap.compRightContinuousMap
+-/
+/- warning: continuous_map.comp_right_continuous_map_apply -> ContinuousMap.compRightContinuousMap_apply is a dubious translation:
+lean 3 declaration is
+ forall {X : Type.{u1}} {Y : Type.{u2}} (T : Type.{u3}) [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : CompactSpace.{u1} X _inst_1] [_inst_3 : TopologicalSpace.{u2} Y] [_inst_4 : CompactSpace.{u2} Y _inst_3] [_inst_5 : MetricSpace.{u3} T] (f : ContinuousMap.{u1, u2} X Y _inst_1 _inst_3) (g : ContinuousMap.{u2, u3} Y T _inst_3 (UniformSpace.toTopologicalSpace.{u3} T (PseudoMetricSpace.toUniformSpace.{u3} T (MetricSpace.toPseudoMetricSpace.{u3} T _inst_5)))), Eq.{max (succ u1) (succ u3)} (ContinuousMap.{u1, u3} X T _inst_1 (UniformSpace.toTopologicalSpace.{u3} T (PseudoMetricSpace.toUniformSpace.{u3} T (MetricSpace.toPseudoMetricSpace.{u3} T _inst_5)))) (coeFn.{max (succ (max u2 u3)) (succ (max u1 u3)), max (succ (max u2 u3)) (succ (max u1 u3))} (ContinuousMap.{max u2 u3, max u1 u3} (ContinuousMap.{u2, u3} Y T _inst_3 (UniformSpace.toTopologicalSpace.{u3} T (PseudoMetricSpace.toUniformSpace.{u3} T (MetricSpace.toPseudoMetricSpace.{u3} T _inst_5)))) (ContinuousMap.{u1, u3} X T _inst_1 (UniformSpace.toTopologicalSpace.{u3} T (PseudoMetricSpace.toUniformSpace.{u3} T (MetricSpace.toPseudoMetricSpace.{u3} T _inst_5)))) (ContinuousMap.compactOpen.{u2, u3} Y T _inst_3 (UniformSpace.toTopologicalSpace.{u3} T (PseudoMetricSpace.toUniformSpace.{u3} T (MetricSpace.toPseudoMetricSpace.{u3} T _inst_5)))) (ContinuousMap.compactOpen.{u1, u3} X T _inst_1 (UniformSpace.toTopologicalSpace.{u3} T (PseudoMetricSpace.toUniformSpace.{u3} T (MetricSpace.toPseudoMetricSpace.{u3} T _inst_5))))) (fun (_x : ContinuousMap.{max u2 u3, max u1 u3} (ContinuousMap.{u2, u3} Y T _inst_3 (UniformSpace.toTopologicalSpace.{u3} T (PseudoMetricSpace.toUniformSpace.{u3} T (MetricSpace.toPseudoMetricSpace.{u3} T _inst_5)))) (ContinuousMap.{u1, u3} X T _inst_1 (UniformSpace.toTopologicalSpace.{u3} T (PseudoMetricSpace.toUniformSpace.{u3} T (MetricSpace.toPseudoMetricSpace.{u3} T _inst_5)))) (ContinuousMap.compactOpen.{u2, u3} Y T _inst_3 (UniformSpace.toTopologicalSpace.{u3} T (PseudoMetricSpace.toUniformSpace.{u3} T (MetricSpace.toPseudoMetricSpace.{u3} T _inst_5)))) (ContinuousMap.compactOpen.{u1, u3} X T _inst_1 (UniformSpace.toTopologicalSpace.{u3} T (PseudoMetricSpace.toUniformSpace.{u3} T (MetricSpace.toPseudoMetricSpace.{u3} T _inst_5))))) => (ContinuousMap.{u2, u3} Y T _inst_3 (UniformSpace.toTopologicalSpace.{u3} T (PseudoMetricSpace.toUniformSpace.{u3} T (MetricSpace.toPseudoMetricSpace.{u3} T _inst_5)))) -> (ContinuousMap.{u1, u3} X T _inst_1 (UniformSpace.toTopologicalSpace.{u3} T (PseudoMetricSpace.toUniformSpace.{u3} T (MetricSpace.toPseudoMetricSpace.{u3} T _inst_5))))) (ContinuousMap.hasCoeToFun.{max u2 u3, max u1 u3} (ContinuousMap.{u2, u3} Y T _inst_3 (UniformSpace.toTopologicalSpace.{u3} T (PseudoMetricSpace.toUniformSpace.{u3} T (MetricSpace.toPseudoMetricSpace.{u3} T _inst_5)))) (ContinuousMap.{u1, u3} X T _inst_1 (UniformSpace.toTopologicalSpace.{u3} T (PseudoMetricSpace.toUniformSpace.{u3} T (MetricSpace.toPseudoMetricSpace.{u3} T _inst_5)))) (ContinuousMap.compactOpen.{u2, u3} Y T _inst_3 (UniformSpace.toTopologicalSpace.{u3} T (PseudoMetricSpace.toUniformSpace.{u3} T (MetricSpace.toPseudoMetricSpace.{u3} T _inst_5)))) (ContinuousMap.compactOpen.{u1, u3} X T _inst_1 (UniformSpace.toTopologicalSpace.{u3} T (PseudoMetricSpace.toUniformSpace.{u3} T (MetricSpace.toPseudoMetricSpace.{u3} T _inst_5))))) (ContinuousMap.compRightContinuousMap.{u1, u2, u3} X Y T _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f) g) (ContinuousMap.comp.{u1, u2, u3} X Y T _inst_1 _inst_3 (UniformSpace.toTopologicalSpace.{u3} T (PseudoMetricSpace.toUniformSpace.{u3} T (MetricSpace.toPseudoMetricSpace.{u3} T _inst_5))) g f)
+but is expected to have type
+ forall {X : Type.{u3}} {Y : Type.{u2}} (T : Type.{u1}) [_inst_1 : TopologicalSpace.{u3} X] [_inst_2 : CompactSpace.{u3} X _inst_1] [_inst_3 : TopologicalSpace.{u2} Y] [_inst_4 : CompactSpace.{u2} Y _inst_3] [_inst_5 : MetricSpace.{u1} T] (f : ContinuousMap.{u3, u2} X Y _inst_1 _inst_3) (g : ContinuousMap.{u2, u1} Y T _inst_3 (UniformSpace.toTopologicalSpace.{u1} T (PseudoMetricSpace.toUniformSpace.{u1} T (MetricSpace.toPseudoMetricSpace.{u1} T _inst_5)))), Eq.{max (succ u3) (succ u1)} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : ContinuousMap.{u2, u1} Y T _inst_3 (UniformSpace.toTopologicalSpace.{u1} T (PseudoMetricSpace.toUniformSpace.{u1} T (MetricSpace.toPseudoMetricSpace.{u1} T _inst_5)))) => ContinuousMap.{u3, u1} X T _inst_1 (UniformSpace.toTopologicalSpace.{u1} T (PseudoMetricSpace.toUniformSpace.{u1} T (MetricSpace.toPseudoMetricSpace.{u1} T _inst_5)))) g) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u2) (succ u1), max (succ u3) (succ u1)} (ContinuousMap.{max u1 u2, max u1 u3} (ContinuousMap.{u2, u1} Y T _inst_3 (UniformSpace.toTopologicalSpace.{u1} T (PseudoMetricSpace.toUniformSpace.{u1} T (MetricSpace.toPseudoMetricSpace.{u1} T _inst_5)))) (ContinuousMap.{u3, u1} X T _inst_1 (UniformSpace.toTopologicalSpace.{u1} T (PseudoMetricSpace.toUniformSpace.{u1} T (MetricSpace.toPseudoMetricSpace.{u1} T _inst_5)))) (ContinuousMap.compactOpen.{u2, u1} Y T _inst_3 (UniformSpace.toTopologicalSpace.{u1} T (PseudoMetricSpace.toUniformSpace.{u1} T (MetricSpace.toPseudoMetricSpace.{u1} T _inst_5)))) (ContinuousMap.compactOpen.{u3, u1} X T _inst_1 (UniformSpace.toTopologicalSpace.{u1} T (PseudoMetricSpace.toUniformSpace.{u1} T (MetricSpace.toPseudoMetricSpace.{u1} T _inst_5))))) (ContinuousMap.{u2, u1} Y T _inst_3 (UniformSpace.toTopologicalSpace.{u1} T (PseudoMetricSpace.toUniformSpace.{u1} T (MetricSpace.toPseudoMetricSpace.{u1} T _inst_5)))) (fun (_x : ContinuousMap.{u2, u1} Y T _inst_3 (UniformSpace.toTopologicalSpace.{u1} T (PseudoMetricSpace.toUniformSpace.{u1} T (MetricSpace.toPseudoMetricSpace.{u1} T _inst_5)))) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : ContinuousMap.{u2, u1} Y T _inst_3 (UniformSpace.toTopologicalSpace.{u1} T (PseudoMetricSpace.toUniformSpace.{u1} T (MetricSpace.toPseudoMetricSpace.{u1} T _inst_5)))) => ContinuousMap.{u3, u1} X T _inst_1 (UniformSpace.toTopologicalSpace.{u1} T (PseudoMetricSpace.toUniformSpace.{u1} T (MetricSpace.toPseudoMetricSpace.{u1} T _inst_5)))) _x) (ContinuousMapClass.toFunLike.{max (max u3 u2) u1, max u2 u1, max u3 u1} (ContinuousMap.{max u1 u2, max u1 u3} (ContinuousMap.{u2, u1} Y T _inst_3 (UniformSpace.toTopologicalSpace.{u1} T (PseudoMetricSpace.toUniformSpace.{u1} T (MetricSpace.toPseudoMetricSpace.{u1} T _inst_5)))) (ContinuousMap.{u3, u1} X T _inst_1 (UniformSpace.toTopologicalSpace.{u1} T (PseudoMetricSpace.toUniformSpace.{u1} T (MetricSpace.toPseudoMetricSpace.{u1} T _inst_5)))) (ContinuousMap.compactOpen.{u2, u1} Y T _inst_3 (UniformSpace.toTopologicalSpace.{u1} T (PseudoMetricSpace.toUniformSpace.{u1} T (MetricSpace.toPseudoMetricSpace.{u1} T _inst_5)))) (ContinuousMap.compactOpen.{u3, u1} X T _inst_1 (UniformSpace.toTopologicalSpace.{u1} T (PseudoMetricSpace.toUniformSpace.{u1} T (MetricSpace.toPseudoMetricSpace.{u1} T _inst_5))))) (ContinuousMap.{u2, u1} Y T _inst_3 (UniformSpace.toTopologicalSpace.{u1} T (PseudoMetricSpace.toUniformSpace.{u1} T (MetricSpace.toPseudoMetricSpace.{u1} T _inst_5)))) (ContinuousMap.{u3, u1} X T _inst_1 (UniformSpace.toTopologicalSpace.{u1} T (PseudoMetricSpace.toUniformSpace.{u1} T (MetricSpace.toPseudoMetricSpace.{u1} T _inst_5)))) (ContinuousMap.compactOpen.{u2, u1} Y T _inst_3 (UniformSpace.toTopologicalSpace.{u1} T (PseudoMetricSpace.toUniformSpace.{u1} T (MetricSpace.toPseudoMetricSpace.{u1} T _inst_5)))) (ContinuousMap.compactOpen.{u3, u1} X T _inst_1 (UniformSpace.toTopologicalSpace.{u1} T (PseudoMetricSpace.toUniformSpace.{u1} T (MetricSpace.toPseudoMetricSpace.{u1} T _inst_5)))) (ContinuousMap.instContinuousMapClassContinuousMap.{max u2 u1, max u3 u1} (ContinuousMap.{u2, u1} Y T _inst_3 (UniformSpace.toTopologicalSpace.{u1} T (PseudoMetricSpace.toUniformSpace.{u1} T (MetricSpace.toPseudoMetricSpace.{u1} T _inst_5)))) (ContinuousMap.{u3, u1} X T _inst_1 (UniformSpace.toTopologicalSpace.{u1} T (PseudoMetricSpace.toUniformSpace.{u1} T (MetricSpace.toPseudoMetricSpace.{u1} T _inst_5)))) (ContinuousMap.compactOpen.{u2, u1} Y T _inst_3 (UniformSpace.toTopologicalSpace.{u1} T (PseudoMetricSpace.toUniformSpace.{u1} T (MetricSpace.toPseudoMetricSpace.{u1} T _inst_5)))) (ContinuousMap.compactOpen.{u3, u1} X T _inst_1 (UniformSpace.toTopologicalSpace.{u1} T (PseudoMetricSpace.toUniformSpace.{u1} T (MetricSpace.toPseudoMetricSpace.{u1} T _inst_5)))))) (ContinuousMap.compRightContinuousMap.{u3, u2, u1} X Y T _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f) g) (ContinuousMap.comp.{u3, u2, u1} X Y T _inst_1 _inst_3 (UniformSpace.toTopologicalSpace.{u1} T (PseudoMetricSpace.toUniformSpace.{u1} T (MetricSpace.toPseudoMetricSpace.{u1} T _inst_5))) g f)
+Case conversion may be inaccurate. Consider using '#align continuous_map.comp_right_continuous_map_apply ContinuousMap.compRightContinuousMap_applyₓ'. -/
@[simp]
theorem compRightContinuousMap_apply {X Y : Type _} (T : Type _) [TopologicalSpace X]
[CompactSpace X] [TopologicalSpace Y] [CompactSpace Y] [MetricSpace T] (f : C(X, Y))
@@ -456,6 +724,7 @@ theorem compRightContinuousMap_apply {X Y : Type _} (T : Type _) [TopologicalSpa
rfl
#align continuous_map.comp_right_continuous_map_apply ContinuousMap.compRightContinuousMap_apply
+#print ContinuousMap.compRightHomeomorph /-
/-- Precomposition by a homeomorphism is itself a homeomorphism between spaces of continuous maps.
-/
def compRightHomeomorph {X Y : Type _} (T : Type _) [TopologicalSpace X] [CompactSpace X]
@@ -466,7 +735,14 @@ def compRightHomeomorph {X Y : Type _} (T : Type _) [TopologicalSpace X] [Compac
left_inv g := ext fun _ => congr_arg g (f.apply_symm_apply _)
right_inv g := ext fun _ => congr_arg g (f.symm_apply_apply _)
#align continuous_map.comp_right_homeomorph ContinuousMap.compRightHomeomorph
+-/
+/- warning: continuous_map.comp_right_alg_hom_continuous -> ContinuousMap.compRightAlgHom_continuous is a dubious translation:
+lean 3 declaration is
+ forall {X : Type.{u1}} {Y : Type.{u2}} (R : Type.{u3}) (A : Type.{u4}) [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : CompactSpace.{u1} X _inst_1] [_inst_3 : TopologicalSpace.{u2} Y] [_inst_4 : CompactSpace.{u2} Y _inst_3] [_inst_5 : CommSemiring.{u3} R] [_inst_6 : Semiring.{u4} A] [_inst_7 : MetricSpace.{u4} A] [_inst_8 : TopologicalSemiring.{u4} A (UniformSpace.toTopologicalSpace.{u4} A (PseudoMetricSpace.toUniformSpace.{u4} A (MetricSpace.toPseudoMetricSpace.{u4} A _inst_7))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_6))] [_inst_9 : Algebra.{u3, u4} R A _inst_5 _inst_6] (f : ContinuousMap.{u1, u2} X Y _inst_1 _inst_3), Continuous.{max u2 u4, max u1 u4} (ContinuousMap.{u2, u4} Y A _inst_3 (UniformSpace.toTopologicalSpace.{u4} A (PseudoMetricSpace.toUniformSpace.{u4} A (MetricSpace.toPseudoMetricSpace.{u4} A _inst_7)))) (ContinuousMap.{u1, u4} X A _inst_1 (UniformSpace.toTopologicalSpace.{u4} A (PseudoMetricSpace.toUniformSpace.{u4} A (MetricSpace.toPseudoMetricSpace.{u4} A _inst_7)))) (ContinuousMap.compactOpen.{u2, u4} Y A _inst_3 (UniformSpace.toTopologicalSpace.{u4} A (PseudoMetricSpace.toUniformSpace.{u4} A (MetricSpace.toPseudoMetricSpace.{u4} A _inst_7)))) (ContinuousMap.compactOpen.{u1, u4} X A _inst_1 (UniformSpace.toTopologicalSpace.{u4} A (PseudoMetricSpace.toUniformSpace.{u4} A (MetricSpace.toPseudoMetricSpace.{u4} A _inst_7)))) (coeFn.{max (succ (max u2 u4)) (succ (max u1 u4)), max (succ (max u2 u4)) (succ (max u1 u4))} (AlgHom.{u3, max u2 u4, max u1 u4} R (ContinuousMap.{u2, u4} Y A _inst_3 (UniformSpace.toTopologicalSpace.{u4} A (PseudoMetricSpace.toUniformSpace.{u4} A (MetricSpace.toPseudoMetricSpace.{u4} A _inst_7)))) (ContinuousMap.{u1, u4} X A _inst_1 (UniformSpace.toTopologicalSpace.{u4} A (PseudoMetricSpace.toUniformSpace.{u4} A (MetricSpace.toPseudoMetricSpace.{u4} A _inst_7)))) _inst_5 (ContinuousMap.semiring.{u2, u4} Y A _inst_3 (UniformSpace.toTopologicalSpace.{u4} A (PseudoMetricSpace.toUniformSpace.{u4} A (MetricSpace.toPseudoMetricSpace.{u4} A _inst_7))) _inst_6 _inst_8) (ContinuousMap.semiring.{u1, u4} X A _inst_1 (UniformSpace.toTopologicalSpace.{u4} A (PseudoMetricSpace.toUniformSpace.{u4} A (MetricSpace.toPseudoMetricSpace.{u4} A _inst_7))) _inst_6 _inst_8) (ContinuousMap.algebra.{u2, u3, u4} Y _inst_3 R _inst_5 A (UniformSpace.toTopologicalSpace.{u4} A (PseudoMetricSpace.toUniformSpace.{u4} A (MetricSpace.toPseudoMetricSpace.{u4} A _inst_7))) _inst_6 _inst_9 _inst_8) (ContinuousMap.algebra.{u1, u3, u4} X _inst_1 R _inst_5 A (UniformSpace.toTopologicalSpace.{u4} A (PseudoMetricSpace.toUniformSpace.{u4} A (MetricSpace.toPseudoMetricSpace.{u4} A _inst_7))) _inst_6 _inst_9 _inst_8)) (fun (_x : AlgHom.{u3, max u2 u4, max u1 u4} R (ContinuousMap.{u2, u4} Y A _inst_3 (UniformSpace.toTopologicalSpace.{u4} A (PseudoMetricSpace.toUniformSpace.{u4} A (MetricSpace.toPseudoMetricSpace.{u4} A _inst_7)))) (ContinuousMap.{u1, u4} X A _inst_1 (UniformSpace.toTopologicalSpace.{u4} A (PseudoMetricSpace.toUniformSpace.{u4} A (MetricSpace.toPseudoMetricSpace.{u4} A _inst_7)))) _inst_5 (ContinuousMap.semiring.{u2, u4} Y A _inst_3 (UniformSpace.toTopologicalSpace.{u4} A (PseudoMetricSpace.toUniformSpace.{u4} A (MetricSpace.toPseudoMetricSpace.{u4} A _inst_7))) _inst_6 _inst_8) (ContinuousMap.semiring.{u1, u4} X A _inst_1 (UniformSpace.toTopologicalSpace.{u4} A (PseudoMetricSpace.toUniformSpace.{u4} A (MetricSpace.toPseudoMetricSpace.{u4} A _inst_7))) _inst_6 _inst_8) (ContinuousMap.algebra.{u2, u3, u4} Y _inst_3 R _inst_5 A (UniformSpace.toTopologicalSpace.{u4} A (PseudoMetricSpace.toUniformSpace.{u4} A (MetricSpace.toPseudoMetricSpace.{u4} A _inst_7))) _inst_6 _inst_9 _inst_8) (ContinuousMap.algebra.{u1, u3, u4} X _inst_1 R _inst_5 A (UniformSpace.toTopologicalSpace.{u4} A (PseudoMetricSpace.toUniformSpace.{u4} A (MetricSpace.toPseudoMetricSpace.{u4} A _inst_7))) _inst_6 _inst_9 _inst_8)) => (ContinuousMap.{u2, u4} Y A _inst_3 (UniformSpace.toTopologicalSpace.{u4} A (PseudoMetricSpace.toUniformSpace.{u4} A (MetricSpace.toPseudoMetricSpace.{u4} A _inst_7)))) -> (ContinuousMap.{u1, u4} X A _inst_1 (UniformSpace.toTopologicalSpace.{u4} A (PseudoMetricSpace.toUniformSpace.{u4} A (MetricSpace.toPseudoMetricSpace.{u4} A _inst_7))))) ([anonymous].{u3, max u2 u4, max u1 u4} R (ContinuousMap.{u2, u4} Y A _inst_3 (UniformSpace.toTopologicalSpace.{u4} A (PseudoMetricSpace.toUniformSpace.{u4} A (MetricSpace.toPseudoMetricSpace.{u4} A _inst_7)))) (ContinuousMap.{u1, u4} X A _inst_1 (UniformSpace.toTopologicalSpace.{u4} A (PseudoMetricSpace.toUniformSpace.{u4} A (MetricSpace.toPseudoMetricSpace.{u4} A _inst_7)))) _inst_5 (ContinuousMap.semiring.{u2, u4} Y A _inst_3 (UniformSpace.toTopologicalSpace.{u4} A (PseudoMetricSpace.toUniformSpace.{u4} A (MetricSpace.toPseudoMetricSpace.{u4} A _inst_7))) _inst_6 _inst_8) (ContinuousMap.semiring.{u1, u4} X A _inst_1 (UniformSpace.toTopologicalSpace.{u4} A (PseudoMetricSpace.toUniformSpace.{u4} A (MetricSpace.toPseudoMetricSpace.{u4} A _inst_7))) _inst_6 _inst_8) (ContinuousMap.algebra.{u2, u3, u4} Y _inst_3 R _inst_5 A (UniformSpace.toTopologicalSpace.{u4} A (PseudoMetricSpace.toUniformSpace.{u4} A (MetricSpace.toPseudoMetricSpace.{u4} A _inst_7))) _inst_6 _inst_9 _inst_8) (ContinuousMap.algebra.{u1, u3, u4} X _inst_1 R _inst_5 A (UniformSpace.toTopologicalSpace.{u4} A (PseudoMetricSpace.toUniformSpace.{u4} A (MetricSpace.toPseudoMetricSpace.{u4} A _inst_7))) _inst_6 _inst_9 _inst_8)) (ContinuousMap.compRightAlgHom.{u3, u4, u1, u2} R _inst_5 A (UniformSpace.toTopologicalSpace.{u4} A (PseudoMetricSpace.toUniformSpace.{u4} A (MetricSpace.toPseudoMetricSpace.{u4} A _inst_7))) _inst_6 _inst_9 _inst_8 X Y _inst_1 _inst_3 f))
+but is expected to have type
+ forall {X : Type.{u4}} {Y : Type.{u3}} (R : Type.{u2}) (A : Type.{u1}) [_inst_1 : TopologicalSpace.{u4} X] [_inst_2 : CompactSpace.{u4} X _inst_1] [_inst_3 : TopologicalSpace.{u3} Y] [_inst_4 : CompactSpace.{u3} Y _inst_3] [_inst_5 : CommSemiring.{u2} R] [_inst_6 : Semiring.{u1} A] [_inst_7 : MetricSpace.{u1} A] [_inst_8 : TopologicalSemiring.{u1} A (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_6))] [_inst_9 : Algebra.{u2, u1} R A _inst_5 _inst_6] (f : ContinuousMap.{u4, u3} X Y _inst_1 _inst_3), Continuous.{max u3 u1, max u4 u1} (ContinuousMap.{u3, u1} Y A _inst_3 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7)))) (ContinuousMap.{u4, u1} X A _inst_1 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7)))) (ContinuousMap.compactOpen.{u3, u1} Y A _inst_3 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7)))) (ContinuousMap.compactOpen.{u4, u1} X A _inst_1 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7)))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u1), max (succ u3) (succ u1), max (succ u4) (succ u1)} (AlgHom.{u2, max u1 u3, max u1 u4} R (ContinuousMap.{u3, u1} Y A _inst_3 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7)))) (ContinuousMap.{u4, u1} X A _inst_1 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7)))) _inst_5 (ContinuousMap.instSemiringContinuousMap.{u3, u1} Y A _inst_3 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) _inst_6 _inst_8) (ContinuousMap.instSemiringContinuousMap.{u4, u1} X A _inst_1 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) _inst_6 _inst_8) (ContinuousMap.algebra.{u3, u2, u1} Y _inst_3 R _inst_5 A (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) _inst_6 _inst_9 _inst_8) (ContinuousMap.algebra.{u4, u2, u1} X _inst_1 R _inst_5 A (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) _inst_6 _inst_9 _inst_8)) (ContinuousMap.{u3, u1} Y A _inst_3 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7)))) (fun (_x : ContinuousMap.{u3, 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(PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) _inst_6 _inst_8) (ContinuousMap.algebra.{u3, u2, u1} Y _inst_3 R _inst_5 A (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) _inst_6 _inst_9 _inst_8))) (Module.toDistribMulAction.{u2, max u4 u1} R (ContinuousMap.{u4, u1} X A _inst_1 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7)))) (CommSemiring.toSemiring.{u2} R _inst_5) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (ContinuousMap.{u4, u1} X A _inst_1 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (ContinuousMap.{u4, u1} X A _inst_1 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7)))) (Semiring.toNonAssocSemiring.{max u4 u1} (ContinuousMap.{u4, u1} X A _inst_1 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7)))) (ContinuousMap.instSemiringContinuousMap.{u4, u1} X A _inst_1 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) _inst_6 _inst_8)))) (Algebra.toModule.{u2, max u4 u1} R (ContinuousMap.{u4, u1} X A _inst_1 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7)))) _inst_5 (ContinuousMap.instSemiringContinuousMap.{u4, u1} X A _inst_1 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) _inst_6 _inst_8) (ContinuousMap.algebra.{u4, u2, u1} X _inst_1 R _inst_5 A (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) _inst_6 _inst_9 _inst_8))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u1, max u4 u1, max (max u4 u3) u1} R (ContinuousMap.{u3, u1} Y A _inst_3 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7)))) (ContinuousMap.{u4, u1} X A _inst_1 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7)))) _inst_5 (ContinuousMap.instSemiringContinuousMap.{u3, u1} Y A _inst_3 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) _inst_6 _inst_8) (ContinuousMap.instSemiringContinuousMap.{u4, u1} X A _inst_1 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) _inst_6 _inst_8) (ContinuousMap.algebra.{u3, u2, u1} Y _inst_3 R _inst_5 A (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) _inst_6 _inst_9 _inst_8) (ContinuousMap.algebra.{u4, u2, u1} X _inst_1 R _inst_5 A (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) _inst_6 _inst_9 _inst_8) (AlgHom.{u2, max u1 u3, max u1 u4} R (ContinuousMap.{u3, u1} Y A _inst_3 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7)))) (ContinuousMap.{u4, u1} X A _inst_1 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7)))) _inst_5 (ContinuousMap.instSemiringContinuousMap.{u3, u1} Y A _inst_3 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) _inst_6 _inst_8) (ContinuousMap.instSemiringContinuousMap.{u4, u1} X A _inst_1 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) _inst_6 _inst_8) (ContinuousMap.algebra.{u3, u2, u1} Y _inst_3 R _inst_5 A (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) _inst_6 _inst_9 _inst_8) (ContinuousMap.algebra.{u4, u2, u1} X _inst_1 R _inst_5 A (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) _inst_6 _inst_9 _inst_8)) (AlgHom.algHomClass.{u2, max u3 u1, max u4 u1} R (ContinuousMap.{u3, u1} Y A _inst_3 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7)))) (ContinuousMap.{u4, u1} X A _inst_1 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7)))) _inst_5 (ContinuousMap.instSemiringContinuousMap.{u3, u1} Y A _inst_3 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) _inst_6 _inst_8) (ContinuousMap.instSemiringContinuousMap.{u4, u1} X A _inst_1 (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) _inst_6 _inst_8) (ContinuousMap.algebra.{u3, u2, u1} Y _inst_3 R _inst_5 A (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) _inst_6 _inst_9 _inst_8) (ContinuousMap.algebra.{u4, u2, u1} X _inst_1 R _inst_5 A (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) _inst_6 _inst_9 _inst_8)))))) (ContinuousMap.compRightAlgHom.{u2, u1, u4, u3} R _inst_5 A (UniformSpace.toTopologicalSpace.{u1} A (PseudoMetricSpace.toUniformSpace.{u1} A (MetricSpace.toPseudoMetricSpace.{u1} A _inst_7))) _inst_6 _inst_9 _inst_8 X Y _inst_1 _inst_3 f))
+Case conversion may be inaccurate. Consider using '#align continuous_map.comp_right_alg_hom_continuous ContinuousMap.compRightAlgHom_continuousₓ'. -/
theorem compRightAlgHom_continuous {X Y : Type _} (R A : Type _) [TopologicalSpace X]
[CompactSpace X] [TopologicalSpace Y] [CompactSpace Y] [CommSemiring R] [Semiring A]
[MetricSpace A] [TopologicalSemiring A] [Algebra R A] (f : C(X, Y)) :
@@ -491,6 +767,12 @@ variable {X : Type _} [TopologicalSpace X] [T2Space X] [LocallyCompactSpace X]
variable {E : Type _} [NormedAddCommGroup E] [CompleteSpace E]
+/- warning: continuous_map.summable_of_locally_summable_norm -> ContinuousMap.summable_of_locally_summable_norm is a dubious translation:
+lean 3 declaration is
+ forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : T2Space.{u1} X _inst_1] [_inst_3 : LocallyCompactSpace.{u1} X _inst_1] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : CompleteSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))] {ι : Type.{u3}} {F : ι -> (ContinuousMap.{u1, u2} X E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))))}, (forall (K : TopologicalSpace.Compacts.{u1} X _inst_1), Summable.{0, u3} Real ι Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => Norm.norm.{max u1 u2} (ContinuousMap.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} X) Type.{u1} (Set.hasCoeToSort.{u1} X) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Compacts.{u1} X _inst_1) (Set.{u1} X) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} X _inst_1) (Set.{u1} X) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} X _inst_1) (Set.{u1} X) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Compacts.{u1} X _inst_1) X (TopologicalSpace.Compacts.setLike.{u1} X _inst_1)))) K)) E (Subtype.topologicalSpace.{u1} X (fun (x : X) => Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) x ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Compacts.{u1} X _inst_1) (Set.{u1} X) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} X _inst_1) (Set.{u1} X) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} X _inst_1) (Set.{u1} X) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Compacts.{u1} X _inst_1) X (TopologicalSpace.Compacts.setLike.{u1} X _inst_1)))) K)) _inst_1) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) (ContinuousMap.hasNorm.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} X) Type.{u1} (Set.hasCoeToSort.{u1} X) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Compacts.{u1} X _inst_1) (Set.{u1} X) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} X _inst_1) (Set.{u1} X) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} X _inst_1) (Set.{u1} X) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Compacts.{u1} X _inst_1) X (TopologicalSpace.Compacts.setLike.{u1} X _inst_1)))) K)) E (Subtype.topologicalSpace.{u1} X (fun (x : X) => Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) x ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Compacts.{u1} X _inst_1) (Set.{u1} X) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} X _inst_1) (Set.{u1} X) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} X _inst_1) (Set.{u1} X) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Compacts.{u1} X _inst_1) X (TopologicalSpace.Compacts.setLike.{u1} X _inst_1)))) K)) _inst_1) (TopologicalSpace.Compacts.compactSpace.{u1} X _inst_1 K) _inst_4) (ContinuousMap.restrict.{u1, u2} X E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Compacts.{u1} X _inst_1) (Set.{u1} X) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} X _inst_1) (Set.{u1} X) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} X _inst_1) (Set.{u1} X) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Compacts.{u1} X _inst_1) X (TopologicalSpace.Compacts.setLike.{u1} X _inst_1)))) K) (F i)))) -> (Summable.{max u1 u2, u3} (ContinuousMap.{u1, u2} X E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) ι (ContinuousMap.addCommMonoid.{u1, u2} X E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (LipschitzAdd.continuousAdd.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)) (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) (ContinuousMap.compactOpen.{u1, u2} X E _inst_1 (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4))))) F)
+but is expected to have type
+ forall {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : T2Space.{u2} X _inst_1] [_inst_3 : LocallyCompactSpace.{u2} X _inst_1] {E : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} E] [_inst_5 : CompleteSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4)))] {ι : Type.{u3}} {F : ι -> (ContinuousMap.{u2, u1} X E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4)))))}, (forall (K : TopologicalSpace.Compacts.{u2} X _inst_1), Summable.{0, u3} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => Norm.norm.{max u2 u1} (ContinuousMap.{u2, u1} (Set.Elem.{u2} X (SetLike.coe.{u2, u2} (TopologicalSpace.Compacts.{u2} X _inst_1) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u2} X _inst_1) K)) E (instTopologicalSpaceSubtype.{u2} X (fun (x : X) => Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) x (SetLike.coe.{u2, u2} (TopologicalSpace.Compacts.{u2} X _inst_1) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u2} X _inst_1) K)) _inst_1) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) (ContinuousMap.instNormContinuousMapToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroup.{u2, u1} (Set.Elem.{u2} X (SetLike.coe.{u2, u2} (TopologicalSpace.Compacts.{u2} X _inst_1) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u2} X _inst_1) K)) E (instTopologicalSpaceSubtype.{u2} X (fun (x : X) => Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) x (SetLike.coe.{u2, u2} (TopologicalSpace.Compacts.{u2} X _inst_1) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u2} X _inst_1) K)) _inst_1) (TopologicalSpace.Compacts.instCompactSpaceSubtypeMemCompactsInstMembershipInstSetLikeCompactsInstTopologicalSpaceSubtype.{u2} X _inst_1 K) _inst_4) (ContinuousMap.restrict.{u2, u1} X E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4)))) (SetLike.coe.{u2, u2} (TopologicalSpace.Compacts.{u2} X _inst_1) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u2} X _inst_1) K) (F i)))) -> (Summable.{max u2 u1, u3} (ContinuousMap.{u2, u1} X E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) ι (ContinuousMap.instAddCommMonoidContinuousMap.{u2, u1} X E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_4)) (TopologicalAddGroup.toContinuousAdd.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4)))) (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4)))) (ContinuousMap.compactOpen.{u2, u1} X E _inst_1 (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_4))))) F)
+Case conversion may be inaccurate. Consider using '#align continuous_map.summable_of_locally_summable_norm ContinuousMap.summable_of_locally_summable_normₓ'. -/
theorem summable_of_locally_summable_norm {ι : Type _} {F : ι → C(X, E)}
(hF : ∀ K : Compacts X, Summable fun i => ‖(F i).restrict K‖) : Summable F :=
by
@@ -521,6 +803,12 @@ variable {α : Type _} {β : Type _}
variable [TopologicalSpace α] [NormedAddCommGroup β] [StarAddMonoid β] [NormedStarGroup β]
+/- warning: bounded_continuous_function.mk_of_compact_star -> BoundedContinuousFunction.mkOfCompact_star is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : NormedAddCommGroup.{u2} β] [_inst_3 : StarAddMonoid.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (NormedAddGroup.toAddGroup.{u2} β (NormedAddCommGroup.toNormedAddGroup.{u2} β _inst_2))))] [_inst_4 : NormedStarGroup.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β _inst_2) _inst_3] [_inst_5 : CompactSpace.{u1} α _inst_1] (f : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β _inst_2))))), Eq.{succ (max u1 u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β _inst_2))) (BoundedContinuousFunction.mkOfCompact.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β _inst_2)) _inst_5 (Star.star.{max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β _inst_2))))) (ContinuousMap.hasStar.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β _inst_2)))) (InvolutiveStar.toHasStar.{u2} β (StarAddMonoid.toHasInvolutiveStar.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β _inst_2))))) _inst_3)) (NormedStarGroup.to_continuousStar.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β _inst_2) _inst_3 _inst_4)) f)) (Star.star.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β _inst_2))) (InvolutiveStar.toHasStar.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β _inst_2))) (StarAddMonoid.toHasInvolutiveStar.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β _inst_2))) (BoundedContinuousFunction.addMonoid.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β _inst_2)) (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β _inst_2))))) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β _inst_2))) (BoundedContinuousFunction.starAddMonoid.{u1, u2} α β _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β _inst_2) _inst_3 _inst_4))) (BoundedContinuousFunction.mkOfCompact.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β _inst_2)) _inst_5 f))
+but is expected to have type
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : NormedAddCommGroup.{u1} β] [_inst_3 : StarAddMonoid.{u1} β (SubNegMonoid.toAddMonoid.{u1} β (AddGroup.toSubNegMonoid.{u1} β (NormedAddGroup.toAddGroup.{u1} β (NormedAddCommGroup.toNormedAddGroup.{u1} β _inst_2))))] [_inst_4 : NormedStarGroup.{u1} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} β _inst_2) _inst_3] [_inst_5 : CompactSpace.{u2} α _inst_1] (f : ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} β _inst_2))))), Eq.{max (succ u2) (succ u1)} (BoundedContinuousFunction.{u2, u1} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} β _inst_2))) (BoundedContinuousFunction.mkOfCompact.{u2, u1} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} β _inst_2)) _inst_5 (Star.star.{max u1 u2} (ContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} β _inst_2))))) (ContinuousMap.instStarContinuousMap.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} β _inst_2)))) (InvolutiveStar.toStar.{u1} β (StarAddMonoid.toInvolutiveStar.{u1} β (SubNegMonoid.toAddMonoid.{u1} β (AddGroup.toSubNegMonoid.{u1} β (NormedAddGroup.toAddGroup.{u1} β (NormedAddCommGroup.toNormedAddGroup.{u1} β _inst_2)))) _inst_3)) (NormedStarGroup.to_continuousStar.{u1} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} β _inst_2) _inst_3 _inst_4)) f)) (Star.star.{max u1 u2} (BoundedContinuousFunction.{u2, u1} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} β _inst_2))) (InvolutiveStar.toStar.{max u2 u1} (BoundedContinuousFunction.{u2, u1} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} β _inst_2))) (StarAddMonoid.toInvolutiveStar.{max u2 u1} (BoundedContinuousFunction.{u2, u1} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} β _inst_2))) (BoundedContinuousFunction.addMonoid.{u2, u1} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} β _inst_2)) (SubNegMonoid.toAddMonoid.{u1} β (AddGroup.toSubNegMonoid.{u1} β (NormedAddGroup.toAddGroup.{u1} β (NormedAddCommGroup.toNormedAddGroup.{u1} β _inst_2)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u1} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} β _inst_2))) (BoundedContinuousFunction.starAddMonoid.{u2, u1} α β _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} β _inst_2) _inst_3 _inst_4))) (BoundedContinuousFunction.mkOfCompact.{u2, u1} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} β _inst_2)) _inst_5 f))
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.mk_of_compact_star BoundedContinuousFunction.mkOfCompact_starₓ'. -/
theorem BoundedContinuousFunction.mkOfCompact_star [CompactSpace α] (f : C(α, β)) :
mkOfCompact (star f) = star (mkOfCompact f) :=
rfl
mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee
@@ -241,9 +241,9 @@ theorem neg_norm_le_apply (f : C(α, ℝ)) (x : α) : -‖f‖ ≤ f x :=
le_trans (neg_le_neg (f.norm_coe_le_norm x)) (neg_le.mp (neg_le_abs_self (f x)))
#align continuous_map.neg_norm_le_apply ContinuousMap.neg_norm_le_apply
-theorem norm_eq_supᵢ_norm : ‖f‖ = ⨆ x : α, ‖f x‖ :=
- (mkOfCompact f).norm_eq_supᵢ_norm
-#align continuous_map.norm_eq_supr_norm ContinuousMap.norm_eq_supᵢ_norm
+theorem norm_eq_iSup_norm : ‖f‖ = ⨆ x : α, ‖f x‖ :=
+ (mkOfCompact f).norm_eq_iSup_norm
+#align continuous_map.norm_eq_supr_norm ContinuousMap.norm_eq_iSup_norm
theorem norm_restrict_mono_set {X : Type _} [TopologicalSpace X] (f : C(X, E))
{K L : TopologicalSpace.Compacts X} (hKL : K ≤ L) : ‖f.restrict K‖ ≤ ‖f.restrict L‖ :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/55d771df074d0dd020139ee1cd4b95521422df9f
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
! This file was ported from Lean 3 source module topology.continuous_function.compact
-! leanprover-community/mathlib commit 6efec6bb9fcaed3cf1baaddb2eaadd8a2a06679c
+! leanprover-community/mathlib commit d3af0609f6db8691dffdc3e1fb7feb7da72698f2
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -266,7 +266,7 @@ section
variable {𝕜 : Type _} [NormedField 𝕜] [NormedSpace 𝕜 E]
-instance : NormedSpace 𝕜 C(α, E) where norm_smul_le c f := le_of_eq (norm_smul c (mkOfCompact f))
+instance : NormedSpace 𝕜 C(α, E) where norm_smul_le c f := (norm_smul_le c (mkOfCompact f) : _)
section
mathlib commit https://github.com/leanprover-community/mathlib/commit/21e3562c5e12d846c7def5eff8cdbc520d7d4936
@@ -167,7 +167,7 @@ theorem continuous_coe : @Continuous C(α, β) (α → β) _ _ coeFn :=
-- TODO at some point we will need lemmas characterising this norm!
-- At the moment the only way to reason about it is to transfer `f : C(α,E)` back to `α →ᵇ E`.
-instance : HasNorm C(α, E) where norm x := dist x 0
+instance : Norm C(α, E) where norm x := dist x 0
@[simp]
theorem BoundedContinuousFunction.norm_mkOfCompact (f : C(α, E)) : ‖mkOfCompact f‖ = ‖f‖ :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/3b267e70a936eebb21ab546f49a8df34dd300b25
@@ -80,7 +80,7 @@ theorem uniformEmbedding_equivBoundedOfCompact : UniformEmbedding (equivBoundedO
additively equivalent to `C(α, 𝕜)`.
-/
@[simps (config := { fullyApplied := false }) apply symm_apply]
-def addEquivBoundedOfCompact [AddMonoid β] [HasLipschitzAdd β] : C(α, β) ≃+ (α →ᵇ β) :=
+def addEquivBoundedOfCompact [AddMonoid β] [LipschitzAdd β] : C(α, β) ≃+ (α →ᵇ β) :=
({ toContinuousMapAddHom α β, (equivBoundedOfCompact α β).symm with } : (α →ᵇ β) ≃+ C(α, β)).symm
#align continuous_map.add_equiv_bounded_of_compact ContinuousMap.addEquivBoundedOfCompact
mathlib commit https://github.com/leanprover-community/mathlib/commit/22131150f88a2d125713ffa0f4693e3355b1eb49
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
! This file was ported from Lean 3 source module topology.continuous_function.compact
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 6efec6bb9fcaed3cf1baaddb2eaadd8a2a06679c
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -245,6 +245,11 @@ theorem norm_eq_supᵢ_norm : ‖f‖ = ⨆ x : α, ‖f x‖ :=
(mkOfCompact f).norm_eq_supᵢ_norm
#align continuous_map.norm_eq_supr_norm ContinuousMap.norm_eq_supᵢ_norm
+theorem norm_restrict_mono_set {X : Type _} [TopologicalSpace X] (f : C(X, E))
+ {K L : TopologicalSpace.Compacts X} (hKL : K ≤ L) : ‖f.restrict K‖ ≤ ‖f.restrict L‖ :=
+ (norm_le _ (norm_nonneg _)).mpr fun x => norm_coe_le_norm (f.restrict L) <| Set.inclusion hKL x
+#align continuous_map.norm_restrict_mono_set ContinuousMap.norm_restrict_mono_set
+
end
section
@@ -471,7 +476,14 @@ theorem compRightAlgHom_continuous {X Y : Type _} (R A : Type _) [TopologicalSpa
end CompRight
-section Weierstrass
+section LocalNormalConvergence
+
+/-! ### Local normal convergence
+
+A sum of continuous functions (on a locally compact space) is "locally normally convergent" if the
+sum of its sup-norms on any compact subset is summable. This implies convergence in the topology
+of `C(X, E)` (i.e. locally uniform convergence). -/
+
open TopologicalSpace
@@ -492,7 +504,7 @@ theorem summable_of_locally_summable_norm {ι : Type _} {F : ι → C(X, E)}
simpa only [HasSum, A] using summable_of_summable_norm (hF K)
#align continuous_map.summable_of_locally_summable_norm ContinuousMap.summable_of_locally_summable_norm
-end Weierstrass
+end LocalNormalConvergence
/-!
### Star structures
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
Empty lines were removed by executing the following Python script twice
import os
import re
# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
for filename in files:
if filename.endswith('.lean'):
file_path = os.path.join(dir_path, filename)
# Open the file and read its contents
with open(file_path, 'r') as file:
content = file.read()
# Use a regular expression to replace sequences of "variable" lines separated by empty lines
# with sequences without empty lines
modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)
# Write the modified content back to the file
with open(file_path, 'w') as file:
file.write(modified_content)
@@ -344,7 +344,6 @@ namespace ContinuousMap
section UniformContinuity
variable {α β : Type*}
-
variable [MetricSpace α] [CompactSpace α] [MetricSpace β]
/-!
@@ -481,7 +480,6 @@ of `C(X, E)` (i.e. locally uniform convergence). -/
open TopologicalSpace
variable {X : Type*} [TopologicalSpace X] [T2Space X] [LocallyCompactSpace X]
-
variable {E : Type*} [NormedAddCommGroup E] [CompleteSpace E]
theorem summable_of_locally_summable_norm {ι : Type*} {F : ι → C(X, E)}
@@ -513,7 +511,6 @@ Furthermore, if `α` is compact and `β` is a C⋆-ring, then `C(α, β)` is a C
section NormedSpace
variable {α : Type*} {β : Type*}
-
variable [TopologicalSpace α] [NormedAddCommGroup β] [StarAddMonoid β] [NormedStarGroup β]
theorem _root_.BoundedContinuousFunction.mkOfCompact_star [CompactSpace α] (f : C(α, β)) :
@@ -531,7 +528,6 @@ end NormedSpace
section CstarRing
variable {α : Type*} {β : Type*}
-
variable [TopologicalSpace α] [NormedRing β] [StarRing β]
instance [CompactSpace α] [CstarRing β] : CstarRing C(α, β) where
open Classical
(#11199)
We remove all but one open Classical
s, instead preferring to use open scoped Classical
. The only real side-effect this led to is moving a couple declarations to use Exists.choose
instead of Classical.choose
.
The first few commits are explicitly labelled regex replaces for ease of review.
@@ -29,7 +29,8 @@ you should restate it here. You can also use
noncomputable section
-open Topology Classical NNReal BoundedContinuousFunction BigOperators
+open scoped Classical
+open Topology NNReal BoundedContinuousFunction BigOperators
open Set Filter Metric
Homogenises porting notes via capitalisation and addition of whitespace.
It makes the following changes:
@@ -76,19 +76,19 @@ theorem uniformEmbedding_equivBoundedOfCompact : UniformEmbedding (equivBoundedO
/-- When `α` is compact, the bounded continuous maps `α →ᵇ 𝕜` are
additively equivalent to `C(α, 𝕜)`.
-/
--- porting note: the following `simps` received a "maximum recursion depth" error
+-- Porting note: the following `simps` received a "maximum recursion depth" error
-- @[simps! (config := .asFn) apply symm_apply]
def addEquivBoundedOfCompact [AddMonoid β] [LipschitzAdd β] : C(α, β) ≃+ (α →ᵇ β) :=
({ toContinuousMapAddHom α β, (equivBoundedOfCompact α β).symm with } : (α →ᵇ β) ≃+ C(α, β)).symm
#align continuous_map.add_equiv_bounded_of_compact ContinuousMap.addEquivBoundedOfCompact
--- porting note: added this `simp` lemma manually because of the `simps` error above
+-- Porting note: added this `simp` lemma manually because of the `simps` error above
@[simp]
theorem addEquivBoundedOfCompact_symm_apply [AddMonoid β] [LipschitzAdd β] :
⇑((addEquivBoundedOfCompact α β).symm) = toContinuousMapAddHom α β :=
rfl
--- porting note: added this `simp` lemma manually because of the `simps` error above
+-- Porting note: added this `simp` lemma manually because of the `simps` error above
@[simp]
theorem addEquivBoundedOfCompact_apply [AddMonoid β] [LipschitzAdd β] :
⇑(addEquivBoundedOfCompact α β) = mkOfCompact :=
@@ -312,7 +312,7 @@ theorem linearIsometryBoundedOfCompact_toIsometryEquiv :
rfl
#align continuous_map.linear_isometry_bounded_of_compact_to_isometry_equiv ContinuousMap.linearIsometryBoundedOfCompact_toIsometryEquiv
-@[simp] -- porting note: adjusted LHS because `simpNF` complained it simplified.
+@[simp] -- Porting note: adjusted LHS because `simpNF` complained it simplified.
theorem linearIsometryBoundedOfCompact_toAddEquiv :
((linearIsometryBoundedOfCompact α E 𝕜).toLinearEquiv : C(α, E) ≃+ (α →ᵇ E)) =
addEquivBoundedOfCompact α E :=
Split the 2300-line behemoth OperatorNorm.lean
into 8 smaller files, of which the largest is 600 lines.
@@ -7,6 +7,7 @@ import Mathlib.Topology.ContinuousFunction.Bounded
import Mathlib.Topology.UniformSpace.Compact
import Mathlib.Topology.CompactOpen
import Mathlib.Topology.Sets.Compacts
+import Mathlib.Analysis.Normed.Group.InfiniteSum
#align_import topology.continuous_function.compact from "leanprover-community/mathlib"@"d3af0609f6db8691dffdc3e1fb7feb7da72698f2"
Clm
-> CLM
, Cle
-> CLE
(#10018)
Rename
Complex.equivRealProdClm
→ Complex.equivRealProdCLM
;
CLE
?Complex.reClm
→ Complex.reCLM
;Complex.imClm
→ Complex.imCLM
;Complex.conjLie
→ Complex.conjLIE
;Complex.conjCle
→ Complex.conjCLE
;Complex.ofRealLi
→ Complex.ofRealLI
;Complex.ofRealClm
→ Complex.ofRealCLM
;fderivInnerClm
→ fderivInnerCLM
;LinearPMap.adjointDomainMkClm
→ LinearPMap.adjointDomainMkCLM
;LinearPMap.adjointDomainMkClmExtend
→ LinearPMap.adjointDomainMkCLMExtend
;IsROrC.reClm
→ IsROrC.reCLM
;IsROrC.imClm
→ IsROrC.imCLM
;IsROrC.conjLie
→ IsROrC.conjLIE
;IsROrC.conjCle
→ IsROrC.conjCLE
;IsROrC.ofRealLi
→ IsROrC.ofRealLI
;IsROrC.ofRealClm
→ IsROrC.ofRealCLM
;MeasureTheory.condexpL1Clm
→ MeasureTheory.condexpL1CLM
;algebraMapClm
→ algebraMapCLM
;WeakDual.CharacterSpace.toClm
→ WeakDual.CharacterSpace.toCLM
;BoundedContinuousFunction.evalClm
→ BoundedContinuousFunction.evalCLM
;ContinuousMap.evalClm
→ ContinuousMap.evalCLM
;TrivSqZeroExt.fstClm
→ TrivSqZeroExt.fstClm
;TrivSqZeroExt.sndClm
→ TrivSqZeroExt.sndCLM
;TrivSqZeroExt.inlClm
→ TrivSqZeroExt.inlCLM
;TrivSqZeroExt.inrClm
→ TrivSqZeroExt.inrCLM
and related theorems.
@@ -282,12 +282,12 @@ def linearIsometryBoundedOfCompact : C(α, E) ≃ₗᵢ[𝕜] α →ᵇ E :=
variable {α E}
--- to match `BoundedContinuousFunction.evalClm`
+-- to match `BoundedContinuousFunction.evalCLM`
/-- The evaluation at a point, as a continuous linear map from `C(α, 𝕜)` to `𝕜`. -/
-def evalClm (x : α) : C(α, E) →L[𝕜] E :=
- (BoundedContinuousFunction.evalClm 𝕜 x).comp
+def evalCLM (x : α) : C(α, E) →L[𝕜] E :=
+ (BoundedContinuousFunction.evalCLM 𝕜 x).comp
(linearIsometryBoundedOfCompact α E 𝕜).toLinearIsometry.toContinuousLinearMap
-#align continuous_map.eval_clm ContinuousMap.evalClm
+#align continuous_map.eval_clm ContinuousMap.evalCLM
end
abs
(#9553)
The current design for abs
is flawed:
Abs
notation typeclass has exactly two instances: one for [Neg α] [Sup α]
, one for [Inv α] [Sup α]
. This means that:
Abs.abs
Abs
instances!Algebra.Order.Group.Abs
are about the additive version.Algebra.Order.Group.PosPart
, and they get additivised to duplicates of the lemmas in Algebra.Order.Group.Abs
!This PR changes the notation typeclass with two new definitions (related through to_additive
): mabs
and abs
. abs
inherits the |a|
notation and mabs
gets |a|ₘ
instead.
The first half of Algebra.Order.Group.Abs
gets multiplicativised. A later PR will multiplicativise the second half, and another one will deduplicate the lemmas in Algebra.Order.Group.PosPart
.
Part of #9411.
Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com>
@@ -232,7 +232,7 @@ theorem apply_le_norm (f : C(α, ℝ)) (x : α) : f x ≤ ‖f‖ :=
#align continuous_map.apply_le_norm ContinuousMap.apply_le_norm
theorem neg_norm_le_apply (f : C(α, ℝ)) (x : α) : -‖f‖ ≤ f x :=
- le_trans (neg_le_neg (f.norm_coe_le_norm x)) (neg_le.mp (neg_le_abs_self (f x)))
+ le_trans (neg_le_neg (f.norm_coe_le_norm x)) (neg_le.mp (neg_le_abs (f x)))
#align continuous_map.neg_norm_le_apply ContinuousMap.neg_norm_le_apply
theorem norm_eq_iSup_norm : ‖f‖ = ⨆ x : α, ‖f x‖ :=
continuous_eval
lemmas (#9264)
Introduce a typeclass LocallyCompactPair
that allows us to unify different versions of ContinuousMap.continuous_eval
and similar lemmas.
@@ -159,12 +159,6 @@ end
instance [CompleteSpace β] : CompleteSpace C(α, β) :=
(isometryEquivBoundedOfCompact α β).completeSpace
-/-- See also `ContinuousMap.continuous_eval'`. -/
-@[continuity]
-theorem continuous_eval : Continuous fun p : C(α, β) × α => p.1 p.2 :=
- continuous_eval.comp ((isometryEquivBoundedOfCompact α β).continuous.prod_map continuous_id)
-#align continuous_map.continuous_eval ContinuousMap.continuous_eval
-
-- TODO at some point we will need lemmas characterising this norm!
-- At the moment the only way to reason about it is to transfer `f : C(α,E)` back to `α →ᵇ E`.
instance : Norm C(α, E) where norm x := dist x 0
@@ -498,7 +498,7 @@ theorem summable_of_locally_summable_norm {ι : Type*} {F : ι → C(X, E)}
simp
-- This used to be the end of the proof before leanprover/lean4#2644
erw [restrict_apply, restrict_apply, restrict_apply, restrict_apply]
- simp
+ simp? says simp only [coe_sum, Finset.sum_apply]
congr!
simpa only [HasSum, A] using (hF K).of_norm
#align continuous_map.summable_of_locally_summable_norm ContinuousMap.summable_of_locally_summable_norm
summable_of_norm_bounded
-> Summable.of_norm_bounded
;summable_of_norm_bounded_eventually
-> Summable.of_norm_bounded_eventually
;summable_of_nnnorm_bounded
-> Summable.of_nnnorm_bounded
;summable_of_summable_norm
-> Summable.of_norm
;summable_of_summable_nnnorm
-> Summable.of_nnnorm
;Summable.of_norm_bounded_eventually_nat
Summable.norm
@@ -500,7 +500,7 @@ theorem summable_of_locally_summable_norm {ι : Type*} {F : ι → C(X, E)}
erw [restrict_apply, restrict_apply, restrict_apply, restrict_apply]
simp
congr!
- simpa only [HasSum, A] using summable_of_summable_norm (hF K)
+ simpa only [HasSum, A] using (hF K).of_norm
#align continuous_map.summable_of_locally_summable_norm ContinuousMap.summable_of_locally_summable_norm
end LocalNormalConvergence
Use .asFn
and .lemmasOnly
as simps
configuration options.
For reference, these are defined here:
@@ -46,7 +46,7 @@ variable (α β)
/-- When `α` is compact, the bounded continuous maps `α →ᵇ β` are
equivalent to `C(α, β)`.
-/
-@[simps (config := { fullyApplied := false })]
+@[simps (config := .asFn)]
def equivBoundedOfCompact : C(α, β) ≃ (α →ᵇ β) :=
⟨mkOfCompact, BoundedContinuousFunction.toContinuousMap, fun f => by
ext
@@ -76,7 +76,7 @@ theorem uniformEmbedding_equivBoundedOfCompact : UniformEmbedding (equivBoundedO
additively equivalent to `C(α, 𝕜)`.
-/
-- porting note: the following `simps` received a "maximum recursion depth" error
--- @[simps! (config := { fullyApplied := false }) apply symm_apply]
+-- @[simps! (config := .asFn) apply symm_apply]
def addEquivBoundedOfCompact [AddMonoid β] [LipschitzAdd β] : C(α, β) ≃+ (α →ᵇ β) :=
({ toContinuousMapAddHom α β, (equivBoundedOfCompact α β).symm with } : (α →ᵇ β) ≃+ C(α, β)).symm
#align continuous_map.add_equiv_bounded_of_compact ContinuousMap.addEquivBoundedOfCompact
@@ -100,7 +100,7 @@ instance metricSpace : MetricSpace C(α, β) :=
/-- When `α` is compact, and `β` is a metric space, the bounded continuous maps `α →ᵇ β` are
isometric to `C(α, β)`.
-/
-@[simps! (config := { fullyApplied := false }) toEquiv apply symm_apply]
+@[simps! (config := .asFn) toEquiv apply symm_apply]
def isometryEquivBoundedOfCompact : C(α, β) ≃ᵢ (α →ᵇ β) where
isometry_toFun _ _ := rfl
toEquiv := equivBoundedOfCompact α β
@@ -496,6 +496,10 @@ theorem summable_of_locally_summable_norm {ι : Type*} {F : ι → C(X, E)}
intro s
ext1 x
simp
+ -- This used to be the end of the proof before leanprover/lean4#2644
+ erw [restrict_apply, restrict_apply, restrict_apply, restrict_apply]
+ simp
+ congr!
simpa only [HasSum, A] using summable_of_summable_norm (hF K)
#align continuous_map.summable_of_locally_summable_norm ContinuousMap.summable_of_locally_summable_norm
@@ -496,10 +496,6 @@ theorem summable_of_locally_summable_norm {ι : Type*} {F : ι → C(X, E)}
intro s
ext1 x
simp
- -- This used to be the end of the proof before leanprover/lean4#2644
- erw [restrict_apply, restrict_apply, restrict_apply, restrict_apply]
- simp
- congr!
simpa only [HasSum, A] using summable_of_summable_norm (hF K)
#align continuous_map.summable_of_locally_summable_norm ContinuousMap.summable_of_locally_summable_norm
@@ -496,6 +496,10 @@ theorem summable_of_locally_summable_norm {ι : Type*} {F : ι → C(X, E)}
intro s
ext1 x
simp
+ -- This used to be the end of the proof before leanprover/lean4#2644
+ erw [restrict_apply, restrict_apply, restrict_apply, restrict_apply]
+ simp
+ congr!
simpa only [HasSum, A] using summable_of_summable_norm (hF K)
#align continuous_map.summable_of_locally_summable_norm ContinuousMap.summable_of_locally_summable_norm
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -36,7 +36,7 @@ open BoundedContinuousFunction
namespace ContinuousMap
-variable {α β E : Type _} [TopologicalSpace α] [CompactSpace α] [MetricSpace β]
+variable {α β E : Type*} [TopologicalSpace α] [CompactSpace α] [MetricSpace β]
[NormedAddCommGroup E]
section
@@ -245,7 +245,7 @@ theorem norm_eq_iSup_norm : ‖f‖ = ⨆ x : α, ‖f x‖ :=
(mkOfCompact f).norm_eq_iSup_norm
#align continuous_map.norm_eq_supr_norm ContinuousMap.norm_eq_iSup_norm
-theorem norm_restrict_mono_set {X : Type _} [TopologicalSpace X] (f : C(X, E))
+theorem norm_restrict_mono_set {X : Type*} [TopologicalSpace X] (f : C(X, E))
{K L : TopologicalSpace.Compacts X} (hKL : K ≤ L) : ‖f.restrict K‖ ≤ ‖f.restrict L‖ :=
(norm_le _ (norm_nonneg _)).mpr fun x => norm_coe_le_norm (f.restrict L) <| Set.inclusion hKL x
#align continuous_map.norm_restrict_mono_set ContinuousMap.norm_restrict_mono_set
@@ -254,7 +254,7 @@ end
section
-variable {R : Type _} [NormedRing R]
+variable {R : Type*} [NormedRing R]
instance : NormedRing C(α, R) :=
{ (inferInstance : NormedAddCommGroup C(α, R)), ContinuousMap.instRingContinuousMap with
@@ -264,7 +264,7 @@ end
section
-variable {𝕜 : Type _} [NormedField 𝕜] [NormedSpace 𝕜 E]
+variable {𝕜 : Type*} [NormedField 𝕜] [NormedSpace 𝕜 E]
instance normedSpace : NormedSpace 𝕜 C(α, E) where
norm_smul_le c f := (norm_smul_le c (mkOfCompact f) : _)
@@ -334,7 +334,7 @@ end
section
-variable {𝕜 : Type _} {γ : Type _} [NormedField 𝕜] [NormedRing γ] [NormedAlgebra 𝕜 γ]
+variable {𝕜 : Type*} {γ : Type*} [NormedField 𝕜] [NormedRing γ] [NormedAlgebra 𝕜 γ]
instance : NormedAlgebra 𝕜 C(α, γ) :=
{ ContinuousMap.normedSpace, ContinuousMap.algebra with }
@@ -347,7 +347,7 @@ namespace ContinuousMap
section UniformContinuity
-variable {α β : Type _}
+variable {α β : Type*}
variable [MetricSpace α] [CompactSpace α] [MetricSpace β]
@@ -384,7 +384,7 @@ end ContinuousMap
section CompLeft
-variable (X : Type _) {𝕜 β γ : Type _} [TopologicalSpace X] [CompactSpace X]
+variable (X : Type*) {𝕜 β γ : Type*} [TopologicalSpace X] [CompactSpace X]
[NontriviallyNormedField 𝕜]
variable [NormedAddCommGroup β] [NormedSpace 𝕜 β] [NormedAddCommGroup γ] [NormedSpace 𝕜 γ]
@@ -436,7 +436,7 @@ section CompRight
/-- Precomposition by a continuous map is itself a continuous map between spaces of continuous maps.
-/
-def compRightContinuousMap {X Y : Type _} (T : Type _) [TopologicalSpace X] [CompactSpace X]
+def compRightContinuousMap {X Y : Type*} (T : Type*) [TopologicalSpace X] [CompactSpace X]
[TopologicalSpace Y] [CompactSpace Y] [MetricSpace T] (f : C(X, Y)) : C(C(Y, T), C(X, T)) where
toFun g := g.comp f
continuous_toFun := by
@@ -448,7 +448,7 @@ def compRightContinuousMap {X Y : Type _} (T : Type _) [TopologicalSpace X] [Com
#align continuous_map.comp_right_continuous_map ContinuousMap.compRightContinuousMap
@[simp]
-theorem compRightContinuousMap_apply {X Y : Type _} (T : Type _) [TopologicalSpace X]
+theorem compRightContinuousMap_apply {X Y : Type*} (T : Type*) [TopologicalSpace X]
[CompactSpace X] [TopologicalSpace Y] [CompactSpace Y] [MetricSpace T] (f : C(X, Y))
(g : C(Y, T)) : (compRightContinuousMap T f) g = g.comp f :=
rfl
@@ -456,7 +456,7 @@ theorem compRightContinuousMap_apply {X Y : Type _} (T : Type _) [TopologicalSpa
/-- Precomposition by a homeomorphism is itself a homeomorphism between spaces of continuous maps.
-/
-def compRightHomeomorph {X Y : Type _} (T : Type _) [TopologicalSpace X] [CompactSpace X]
+def compRightHomeomorph {X Y : Type*} (T : Type*) [TopologicalSpace X] [CompactSpace X]
[TopologicalSpace Y] [CompactSpace Y] [MetricSpace T] (f : X ≃ₜ Y) : C(Y, T) ≃ₜ C(X, T) where
toFun := compRightContinuousMap T f.toContinuousMap
invFun := compRightContinuousMap T f.symm.toContinuousMap
@@ -464,7 +464,7 @@ def compRightHomeomorph {X Y : Type _} (T : Type _) [TopologicalSpace X] [Compac
right_inv g := ext fun _ => congr_arg g (f.symm_apply_apply _)
#align continuous_map.comp_right_homeomorph ContinuousMap.compRightHomeomorph
-theorem compRightAlgHom_continuous {X Y : Type _} (R A : Type _) [TopologicalSpace X]
+theorem compRightAlgHom_continuous {X Y : Type*} (R A : Type*) [TopologicalSpace X]
[CompactSpace X] [TopologicalSpace Y] [CompactSpace Y] [CommSemiring R] [Semiring A]
[MetricSpace A] [TopologicalSemiring A] [Algebra R A] (f : C(X, Y)) :
Continuous (compRightAlgHom R A f) :=
@@ -484,11 +484,11 @@ of `C(X, E)` (i.e. locally uniform convergence). -/
open TopologicalSpace
-variable {X : Type _} [TopologicalSpace X] [T2Space X] [LocallyCompactSpace X]
+variable {X : Type*} [TopologicalSpace X] [T2Space X] [LocallyCompactSpace X]
-variable {E : Type _} [NormedAddCommGroup E] [CompleteSpace E]
+variable {E : Type*} [NormedAddCommGroup E] [CompleteSpace E]
-theorem summable_of_locally_summable_norm {ι : Type _} {F : ι → C(X, E)}
+theorem summable_of_locally_summable_norm {ι : Type*} {F : ι → C(X, E)}
(hF : ∀ K : Compacts X, Summable fun i => ‖(F i).restrict K‖) : Summable F := by
refine' (ContinuousMap.exists_tendsto_compactOpen_iff_forall _).2 fun K hK => _
lift K to Compacts X using hK
@@ -512,7 +512,7 @@ Furthermore, if `α` is compact and `β` is a C⋆-ring, then `C(α, β)` is a C
section NormedSpace
-variable {α : Type _} {β : Type _}
+variable {α : Type*} {β : Type*}
variable [TopologicalSpace α] [NormedAddCommGroup β] [StarAddMonoid β] [NormedStarGroup β]
@@ -530,7 +530,7 @@ end NormedSpace
section CstarRing
-variable {α : Type _} {β : Type _}
+variable {α : Type*} {β : Type*}
variable [TopologicalSpace α] [NormedRing β] [StarRing β]
@@ -2,17 +2,14 @@
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module topology.continuous_function.compact
-! leanprover-community/mathlib commit d3af0609f6db8691dffdc3e1fb7feb7da72698f2
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Topology.ContinuousFunction.Bounded
import Mathlib.Topology.UniformSpace.Compact
import Mathlib.Topology.CompactOpen
import Mathlib.Topology.Sets.Compacts
+#align_import topology.continuous_function.compact from "leanprover-community/mathlib"@"d3af0609f6db8691dffdc3e1fb7feb7da72698f2"
+
/-!
# Continuous functions on a compact space
ContinuousMap.continuous_eval_const{,'}
(#5649)
We had continuity of fun f : C(X, Y) ↦ f a
in two cases:
X
is a locally compact space;X
is a compact space and Y
is a metric space.In fact, it is true in general topological spaces.
@@ -168,17 +168,6 @@ theorem continuous_eval : Continuous fun p : C(α, β) × α => p.1 p.2 :=
continuous_eval.comp ((isometryEquivBoundedOfCompact α β).continuous.prod_map continuous_id)
#align continuous_map.continuous_eval ContinuousMap.continuous_eval
-/-- See also `ContinuousMap.continuous_eval_const'`. -/
-@[continuity]
-theorem continuous_eval_const (x : α) : Continuous fun f : C(α, β) => f x :=
- continuous_eval.comp (continuous_id.prod_mk continuous_const)
-#align continuous_map.continuous_eval_const ContinuousMap.continuous_eval_const
-
-/-- See also `ContinuousMap.continuous_coe'`. -/
-theorem continuous_coe : @Continuous C(α, β) (α → β) _ _ (↑) :=
- continuous_pi continuous_eval_const
-#align continuous_map.continuous_coe ContinuousMap.continuous_coe
-
-- TODO at some point we will need lemmas characterising this norm!
-- At the moment the only way to reason about it is to transfer `f : C(α,E)` back to `α →ᵇ E`.
instance : Norm C(α, E) where norm x := dist x 0
at
and goals (#5387)
Changes are of the form
some_tactic at h⊢
-> some_tactic at h ⊢
some_tactic at h
-> some_tactic at h
@@ -457,7 +457,7 @@ def compRightContinuousMap {X Y : Type _} (T : Type _) [TopologicalSpace X] [Com
refine' Metric.continuous_iff.mpr _
intro g ε ε_pos
refine' ⟨ε, ε_pos, fun g' h => _⟩
- rw [ContinuousMap.dist_lt_iff ε_pos] at h⊢
+ rw [ContinuousMap.dist_lt_iff ε_pos] at h ⊢
exact fun x => h (f x)
#align continuous_map.comp_right_continuous_map ContinuousMap.compRightContinuousMap
The unported dependencies are
algebra.order.module
init.core
algebra.order.monoid.cancel.defs
algebra.abs
algebra.group_power.lemmas
init.data.list.basic
algebra.order.monoid.cancel.basic
init.data.list.default
topology.subset_properties
init.logic
The following 1 dependencies have changed in mathlib3 since they were ported, which may complicate porting this file