analysis.normed_space.completion
β·
Mathlib.Analysis.NormedSpace.Completion
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
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import Analysis.Normed.Group.Completion
-import Analysis.NormedSpace.OperatorNorm
+import Analysis.NormedSpace.OperatorNorm.Basic
import Topology.Algebra.UniformRing
#align_import analysis.normed_space.completion from "leanprover-community/mathlib"@"33c67ae661dd8988516ff7f247b0be3018cdd952"
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,9 +3,9 @@ Copyright (c) 2022 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
-import Mathbin.Analysis.Normed.Group.Completion
-import Mathbin.Analysis.NormedSpace.OperatorNorm
-import Mathbin.Topology.Algebra.UniformRing
+import Analysis.Normed.Group.Completion
+import Analysis.NormedSpace.OperatorNorm
+import Topology.Algebra.UniformRing
#align_import analysis.normed_space.completion from "leanprover-community/mathlib"@"33c67ae661dd8988516ff7f247b0be3018cdd952"
mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504
@@ -102,7 +102,8 @@ instance [SeminormedRing A] : NormedRing (Completion A) :=
exact Continuous.comp completion.continuous_extension continuous_sub
Β· intro x y
rw [β completion.coe_sub, norm_coe, completion.dist_eq, dist_eq_norm]
- norm_mul := fun x y => by
+ norm_hMul := fun x y =>
+ by
apply completion.induction_onβ x y <;> clear x y
Β·
exact
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,16 +2,13 @@
Copyright (c) 2022 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-
-! This file was ported from Lean 3 source module analysis.normed_space.completion
-! leanprover-community/mathlib commit 33c67ae661dd8988516ff7f247b0be3018cdd952
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Analysis.Normed.Group.Completion
import Mathbin.Analysis.NormedSpace.OperatorNorm
import Mathbin.Topology.Algebra.UniformRing
+#align_import analysis.normed_space.completion from "leanprover-community/mathlib"@"33c67ae661dd8988516ff7f247b0be3018cdd952"
+
/-!
# Normed space structure on the completion of a normed space
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -53,6 +53,7 @@ instance : NormedSpace π (Completion E) :=
variable {π E}
+#print UniformSpace.Completion.toComplβα΅’ /-
/-- Embedding of a normed space to its completion as a linear isometry. -/
def toComplβα΅’ : E ββα΅’[π] Completion E :=
{ toCompl with
@@ -60,27 +61,36 @@ def toComplβα΅’ : E ββα΅’[π] Completion E :=
map_smul' := coe_smul
norm_map' := norm_coe }
#align uniform_space.completion.to_complβα΅’ UniformSpace.Completion.toComplβα΅’
+-/
+#print UniformSpace.Completion.coe_toComplβα΅’ /-
@[simp]
theorem coe_toComplβα΅’ : β(toComplβα΅’ : E ββα΅’[π] Completion E) = coe :=
rfl
#align uniform_space.completion.coe_to_complβα΅’ UniformSpace.Completion.coe_toComplβα΅’
+-/
+#print UniformSpace.Completion.toComplL /-
/-- Embedding of a normed space to its completion as a continuous linear map. -/
def toComplL : E βL[π] Completion E :=
toComplβα΅’.toContinuousLinearMap
#align uniform_space.completion.to_complL UniformSpace.Completion.toComplL
+-/
+#print UniformSpace.Completion.coe_toComplL /-
@[simp]
theorem coe_toComplL : β(toComplL : E βL[π] Completion E) = coe :=
rfl
#align uniform_space.completion.coe_to_complL UniformSpace.Completion.coe_toComplL
+-/
+#print UniformSpace.Completion.norm_toComplL /-
@[simp]
theorem norm_toComplL {π E : Type _} [NontriviallyNormedField π] [NormedAddCommGroup E]
[NormedSpace π E] [Nontrivial E] : β(toComplL : E βL[π] Completion E)β = 1 :=
(toComplβα΅’ : E ββα΅’[π] Completion E).norm_toContinuousLinearMap
#align uniform_space.completion.norm_to_complL UniformSpace.Completion.norm_toComplL
+-/
section Algebra
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -53,12 +53,6 @@ instance : NormedSpace π (Completion E) :=
variable {π E}
-/- warning: uniform_space.completion.to_complβα΅’ -> UniformSpace.Completion.toComplβα΅’ is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)], LinearIsometry.{u1, u1, u2, u2} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))) E (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.normedAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.instModule.{u1, u2} π E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (UniformSpace.Completion.toComplβα΅’._proof_1.{u2} E _inst_2) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul.{u1, u2} π E _inst_1 _inst_2 _inst_3))
-but is expected to have type
- forall {π : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)], LinearIsometry.{u1, u1, u2, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))))) E (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.instModule.{u1, u2} π E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (SeminormedAddCommGroup.to_uniformAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul.{u1, u2} π E _inst_1 _inst_2 _inst_3))
-Case conversion may be inaccurate. Consider using '#align uniform_space.completion.to_complβα΅’ UniformSpace.Completion.toComplβα΅’β'. -/
/-- Embedding of a normed space to its completion as a linear isometry. -/
def toComplβα΅’ : E ββα΅’[π] Completion E :=
{ toCompl with
@@ -67,36 +61,21 @@ def toComplβα΅’ : E ββα΅’[π] Completion E :=
norm_map' := norm_coe }
#align uniform_space.completion.to_complβα΅’ UniformSpace.Completion.toComplβα΅’
-/- warning: uniform_space.completion.coe_to_complβα΅’ -> UniformSpace.Completion.coe_toComplβα΅’ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align uniform_space.completion.coe_to_complβα΅’ UniformSpace.Completion.coe_toComplβα΅’β'. -/
@[simp]
theorem coe_toComplβα΅’ : β(toComplβα΅’ : E ββα΅’[π] Completion E) = coe :=
rfl
#align uniform_space.completion.coe_to_complβα΅’ UniformSpace.Completion.coe_toComplβα΅’
-/- warning: uniform_space.completion.to_complL -> UniformSpace.Completion.toComplL is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align uniform_space.completion.to_complL UniformSpace.Completion.toComplLβ'. -/
/-- Embedding of a normed space to its completion as a continuous linear map. -/
def toComplL : E βL[π] Completion E :=
toComplβα΅’.toContinuousLinearMap
#align uniform_space.completion.to_complL UniformSpace.Completion.toComplL
-/- warning: uniform_space.completion.coe_to_complL -> UniformSpace.Completion.coe_toComplL is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align uniform_space.completion.coe_to_complL UniformSpace.Completion.coe_toComplLβ'. -/
@[simp]
theorem coe_toComplL : β(toComplL : E βL[π] Completion E) = coe :=
rfl
#align uniform_space.completion.coe_to_complL UniformSpace.Completion.coe_toComplL
-/- warning: uniform_space.completion.norm_to_complL -> UniformSpace.Completion.norm_toComplL is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align uniform_space.completion.norm_to_complL UniformSpace.Completion.norm_toComplLβ'. -/
@[simp]
theorem norm_toComplL {π E : Type _} [NontriviallyNormedField π] [NormedAddCommGroup E]
[NormedSpace π E] [Nontrivial E] : β(toComplL : E βL[π] Completion E)β = 1 :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -124,8 +124,7 @@ instance [SeminormedRing A] : NormedRing (Completion A) :=
(Continuous.comp Real.continuous_mul
(Continuous.prod_map continuous_norm continuous_norm))
Β· intro x y
- simp only [β coe_mul, norm_coe]
- exact norm_mul_le x y }
+ simp only [β coe_mul, norm_coe]; exact norm_mul_le x y }
instance [SeminormedCommRing A] [NormedAlgebra π A] [UniformContinuousConstSMul π A] :
NormedAlgebra π (Completion A) :=
@@ -138,8 +137,7 @@ instance [SeminormedCommRing A] [NormedAlgebra π A] [UniformContinuousConstSM
isClosed_le (Continuous.comp continuous_norm (continuous_const_smul r))
(Continuous.comp (continuous_mul_left _) continuous_norm)
Β· intro x
- simp only [β coe_smul, norm_coe]
- exact norm_smul_le r x }
+ simp only [β coe_smul, norm_coe]; exact norm_smul_le r x }
end Algebra
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -68,10 +68,7 @@ def toComplβα΅’ : E ββα΅’[π] Completion E :=
#align uniform_space.completion.to_complβα΅’ UniformSpace.Completion.toComplβα΅’
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(Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))))) E (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.instModule.{u1, u2} π E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (SeminormedAddCommGroup.to_uniformAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul.{u1, u2} π E _inst_1 _inst_2 _inst_3))) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) _x) (ContinuousMapClass.toFunLike.{u2, u2, u2} (LinearIsometry.{u1, u1, u2, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))))) E (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.instModule.{u1, u2} π E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (SeminormedAddCommGroup.to_uniformAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul.{u1, u2} π E _inst_1 _inst_2 _inst_3))) E (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (PseudoMetricSpace.toUniformSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (ContinuousSemilinearMapClass.toContinuousMapClass.{u2, u1, u1, u2, u2} (LinearIsometry.{u1, u1, u2, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))))) E (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.instModule.{u1, u2} π E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (SeminormedAddCommGroup.to_uniformAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul.{u1, u2} π E _inst_1 _inst_2 _inst_3))) π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (PseudoMetricSpace.toUniformSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (AddCommGroup.toAddCommMonoid.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.instModule.{u1, u2} π E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (SeminormedAddCommGroup.to_uniformAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul.{u1, u2} π E _inst_1 _inst_2 _inst_3)) (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{u1, u1, u2, u2, u2} π π E (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (LinearIsometry.{u1, u1, u2, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))))) E (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.instModule.{u1, u2} π E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (SeminormedAddCommGroup.to_uniformAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul.{u1, u2} π E _inst_1 _inst_2 _inst_3))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.instModule.{u1, u2} π E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (SeminormedAddCommGroup.to_uniformAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul.{u1, u2} π E _inst_1 _inst_2 _inst_3)) (LinearIsometry.instSemilinearIsometryClassLinearIsometry.{u1, u1, u2, u2} π π E (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.instModule.{u1, u2} π E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (SeminormedAddCommGroup.to_uniformAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul.{u1, u2} π E _inst_1 _inst_2 _inst_3)))))) (UniformSpace.Completion.toComplβα΅’.{u1, u2} π E _inst_1 _inst_2 _inst_3)) (UniformSpace.Completion.coe'.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))))
+<too large>
Case conversion may be inaccurate. Consider using '#align uniform_space.completion.coe_to_complβα΅’ UniformSpace.Completion.coe_toComplβα΅’β'. -/
@[simp]
theorem coe_toComplβα΅’ : β(toComplβα΅’ : E ββα΅’[π] Completion E) = coe :=
@@ -90,10 +87,7 @@ def toComplL : E βL[π] Completion E :=
#align uniform_space.completion.to_complL UniformSpace.Completion.toComplL
/- warning: uniform_space.completion.coe_to_complL -> UniformSpace.Completion.coe_toComplL is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)], Eq.{succ u2} (E -> (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))))) (coeFn.{succ u2, succ u2} (ContinuousLinearMap.{u1, u1, u2, u2} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (PseudoMetricSpace.toUniformSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (UniformSpace.Completion.{u2} E 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(UniformSpace.Completion.toComplL._proof_1.{u2} E _inst_2))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.instModule.{u1, u2} π E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (UniformSpace.Completion.toComplL._proof_2.{u2} E _inst_2) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul.{u1, u2} π E _inst_1 _inst_2 _inst_3))) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u2} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π 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(SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (PseudoMetricSpace.toUniformSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.normedAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (AddCommGroup.toAddCommMonoid.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.addCommGroup.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (UniformSpace.Completion.toComplL._proof_1.{u2} E _inst_2))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.instModule.{u1, u2} π E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (UniformSpace.Completion.toComplL._proof_2.{u2} E _inst_2) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul.{u1, u2} π E _inst_1 _inst_2 _inst_3))) => E -> (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))))) (ContinuousLinearMap.toFun.{u1, u1, u2, u2} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (PseudoMetricSpace.toUniformSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.normedAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (AddCommGroup.toAddCommMonoid.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.addCommGroup.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) 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Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) E (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (HasLiftT.mk.{succ u2, succ u2} E (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (CoeTCβ.coe.{succ u2, succ u2} E (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.hasCoeT.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))))
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- forall {π : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)], Eq.{succ u2} (forall (αΎ° : E), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) αΎ°) (FunLike.coe.{succ u2, succ u2, succ u2} (ContinuousLinearMap.{u1, u1, u2, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (PseudoMetricSpace.toUniformSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) 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(SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (SeminormedAddCommGroup.to_uniformAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.instModule.{u1, u2} π E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (SeminormedAddCommGroup.to_uniformAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E 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(UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (PseudoMetricSpace.toUniformSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (AddCommGroup.toAddCommMonoid.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instAddCommGroupCompletion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (SeminormedAddCommGroup.to_uniformAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.instModule.{u1, u2} π E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (SeminormedAddCommGroup.to_uniformAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul.{u1, u2} π E _inst_1 _inst_2 _inst_3))) E (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (PseudoMetricSpace.toUniformSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (ContinuousSemilinearMapClass.toContinuousMapClass.{u2, u1, u1, u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (PseudoMetricSpace.toUniformSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (AddCommGroup.toAddCommMonoid.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instAddCommGroupCompletion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (SeminormedAddCommGroup.to_uniformAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.instModule.{u1, u2} π E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (SeminormedAddCommGroup.to_uniformAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul.{u1, u2} π E _inst_1 _inst_2 _inst_3))) π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (PseudoMetricSpace.toUniformSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (AddCommGroup.toAddCommMonoid.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instAddCommGroupCompletion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (SeminormedAddCommGroup.to_uniformAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.instModule.{u1, u2} π E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (SeminormedAddCommGroup.to_uniformAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul.{u1, u2} π E _inst_1 _inst_2 _inst_3)) (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u2, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (PseudoMetricSpace.toUniformSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (AddCommGroup.toAddCommMonoid.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instAddCommGroupCompletion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (SeminormedAddCommGroup.to_uniformAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.instModule.{u1, u2} π E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (SeminormedAddCommGroup.to_uniformAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul.{u1, u2} π E _inst_1 _inst_2 _inst_3))))) (UniformSpace.Completion.toComplL.{u1, u2} π E _inst_1 _inst_2 _inst_3)) (UniformSpace.Completion.coe'.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))))
+<too large>
Case conversion may be inaccurate. Consider using '#align uniform_space.completion.coe_to_complL UniformSpace.Completion.coe_toComplLβ'. -/
@[simp]
theorem coe_toComplL : β(toComplL : E βL[π] Completion E) = coe :=
@@ -101,10 +95,7 @@ theorem coe_toComplL : β(toComplL : E βL[π] Completion E) = coe :=
#align uniform_space.completion.coe_to_complL UniformSpace.Completion.coe_toComplL
/- warning: uniform_space.completion.norm_to_complL -> UniformSpace.Completion.norm_toComplL is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} {E : Type.{u2}} [_inst_4 : NontriviallyNormedField.{u1} π] [_inst_5 : NormedAddCommGroup.{u2} E] [_inst_6 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_4) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_5)] [_inst_7 : Nontrivial.{u2} E], Eq.{1} Real (Norm.norm.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_4))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_4))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_4))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_5)) (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_5)))) (UniformSpace.toTopologicalSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_5)))) (PseudoMetricSpace.toUniformSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_5)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_5)))) (UniformSpace.Completion.normedAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_5)))))) (AddCommGroup.toAddCommMonoid.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_5)))) (UniformSpace.Completion.addCommGroup.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_5))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_5) (UniformSpace.Completion.toComplL._proof_1.{u2} E _inst_5))) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_4) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_5) _inst_6) (UniformSpace.Completion.instModule.{u1, u2} π E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_5))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_5) (UniformSpace.Completion.toComplL._proof_2.{u2} E _inst_5) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_4))))) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_4) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_5) _inst_6) (UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_4) _inst_5 _inst_6))) (ContinuousLinearMap.hasOpNorm.{u1, u1, u2, u2} π π E (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_5)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_5) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_5)))) (UniformSpace.Completion.normedAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_5))) _inst_4 _inst_4 _inst_6 (UniformSpace.Completion.normedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_4) _inst_5 _inst_6) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_4)))))))) (UniformSpace.Completion.toComplL.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_4) _inst_5 _inst_6)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
-but is expected to have type
- forall {π : Type.{u2}} {E : Type.{u1}} [_inst_4 : NontriviallyNormedField.{u2} π] [_inst_5 : NormedAddCommGroup.{u1} E] [_inst_6 : NormedSpace.{u2, u1} π E (NontriviallyNormedField.toNormedField.{u2} π _inst_4) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_5)] [_inst_7 : Nontrivial.{u1} E], Eq.{1} Real (Norm.norm.{u1} (ContinuousLinearMap.{u2, u2, u1, u1} π π (DivisionSemiring.toSemiring.{u2} π (Semifield.toDivisionSemiring.{u2} π (Field.toSemifield.{u2} π (NormedField.toField.{u2} π (NontriviallyNormedField.toNormedField.{u2} π _inst_4))))) (DivisionSemiring.toSemiring.{u2} π (Semifield.toDivisionSemiring.{u2} π (Field.toSemifield.{u2} π (NormedField.toField.{u2} π (NontriviallyNormedField.toNormedField.{u2} π _inst_4))))) (RingHom.id.{u2} π (Semiring.toNonAssocSemiring.{u2} π (DivisionSemiring.toSemiring.{u2} π (Semifield.toDivisionSemiring.{u2} π (Field.toSemifield.{u2} π (NormedField.toField.{u2} π (NontriviallyNormedField.toNormedField.{u2} π _inst_4))))))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_5)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_5)) (UniformSpace.Completion.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_5)))) (UniformSpace.toTopologicalSpace.{u1} (UniformSpace.Completion.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_5)))) (PseudoMetricSpace.toUniformSpace.{u1} (UniformSpace.Completion.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} (UniformSpace.Completion.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_5)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_5)))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_5)))))) (AddCommGroup.toAddCommMonoid.{u1} (UniformSpace.Completion.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_5)))) (UniformSpace.Completion.instAddCommGroupCompletion.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_5))) (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_5) (SeminormedAddCommGroup.to_uniformAddGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_5)))) (NormedSpace.toModule.{u2, u1} π E (NontriviallyNormedField.toNormedField.{u2} π _inst_4) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_5) _inst_6) (UniformSpace.Completion.instModule.{u2, u1} π E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_5))) (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_5) (SeminormedAddCommGroup.to_uniformAddGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_5)) (DivisionSemiring.toSemiring.{u2} π (Semifield.toDivisionSemiring.{u2} π (Field.toSemifield.{u2} π (NormedField.toField.{u2} π (NontriviallyNormedField.toNormedField.{u2} π _inst_4))))) (NormedSpace.toModule.{u2, u1} π E (NontriviallyNormedField.toNormedField.{u2} π _inst_4) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_5) _inst_6) (UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul.{u2, u1} π E (NontriviallyNormedField.toNormedField.{u2} π _inst_4) _inst_5 _inst_6))) (ContinuousLinearMap.hasOpNorm.{u2, u2, u1, u1} π π E (UniformSpace.Completion.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_5)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_5) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_5)))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_5))) _inst_4 _inst_4 _inst_6 (UniformSpace.Completion.instNormedSpaceCompletionToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroupInstNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2, u1} π E (NontriviallyNormedField.toNormedField.{u2} π _inst_4) _inst_5 _inst_6) (RingHom.id.{u2} π (Semiring.toNonAssocSemiring.{u2} π (DivisionSemiring.toSemiring.{u2} π (Semifield.toDivisionSemiring.{u2} π (Field.toSemifield.{u2} π (NormedField.toField.{u2} π (NontriviallyNormedField.toNormedField.{u2} π _inst_4)))))))) (UniformSpace.Completion.toComplL.{u2, u1} π E (NontriviallyNormedField.toNormedField.{u2} π _inst_4) _inst_5 _inst_6)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))
+<too large>
Case conversion may be inaccurate. Consider using '#align uniform_space.completion.norm_to_complL UniformSpace.Completion.norm_toComplLβ'. -/
@[simp]
theorem norm_toComplL {π E : Type _} [NontriviallyNormedField π] [NormedAddCommGroup E]
mathlib commit https://github.com/leanprover-community/mathlib/commit/33c67ae661dd8988516ff7f247b0be3018cdd952
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
! This file was ported from Lean 3 source module analysis.normed_space.completion
-! leanprover-community/mathlib commit d3af0609f6db8691dffdc3e1fb7feb7da72698f2
+! leanprover-community/mathlib commit 33c67ae661dd8988516ff7f247b0be3018cdd952
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -15,6 +15,9 @@ import Mathbin.Topology.Algebra.UniformRing
/-!
# Normed space structure on the completion of a normed space
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
If `E` is a normed space over `π`, then so is `uniform_space.completion E`. In this file we provide
necessary instances and define `uniform_space.completion.to_complβα΅’` - coercion
`E β uniform_space.completion E` as a bundled linear isometry.
mathlib commit https://github.com/leanprover-community/mathlib/commit/c89fe2d59ae06402c3f55f978016d1ada444f57e
@@ -33,13 +33,15 @@ namespace Completion
variable (π E : Type _) [NormedField π] [NormedAddCommGroup E] [NormedSpace π E]
+#print UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul /-
instance (priority := 100) NormedSpace.to_uniformContinuousConstSMul :
UniformContinuousConstSMul π E :=
β¨fun c => (lipschitzWith_smul c).UniformContinuousβ©
#align uniform_space.completion.normed_space.to_has_uniform_continuous_const_smul UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul
+-/
instance : NormedSpace π (Completion E) :=
- { Completion.module with
+ { Completion.instModule with
smul := (Β· β’ Β·)
norm_smul_le := fun c x =>
induction_on x
@@ -48,6 +50,12 @@ instance : NormedSpace π (Completion E) :=
variable {π E}
+/- warning: uniform_space.completion.to_complβα΅’ -> UniformSpace.Completion.toComplβα΅’ is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)], LinearIsometry.{u1, u1, u2, u2} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))) E (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.normedAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.instModule.{u1, u2} π E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (UniformSpace.Completion.toComplβα΅’._proof_1.{u2} E _inst_2) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul.{u1, u2} π E _inst_1 _inst_2 _inst_3))
+but is expected to have type
+ forall {π : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)], LinearIsometry.{u1, u1, u2, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))))) E (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.instModule.{u1, u2} π E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (SeminormedAddCommGroup.to_uniformAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul.{u1, u2} π E _inst_1 _inst_2 _inst_3))
+Case conversion may be inaccurate. Consider using '#align uniform_space.completion.to_complβα΅’ UniformSpace.Completion.toComplβα΅’β'. -/
/-- Embedding of a normed space to its completion as a linear isometry. -/
def toComplβα΅’ : E ββα΅’[π] Completion E :=
{ toCompl with
@@ -56,21 +64,45 @@ def toComplβα΅’ : E ββα΅’[π] Completion E :=
norm_map' := norm_coe }
#align uniform_space.completion.to_complβα΅’ UniformSpace.Completion.toComplβα΅’
+/- warning: uniform_space.completion.coe_to_complβα΅’ -> UniformSpace.Completion.coe_toComplβα΅’ is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)], Eq.{succ u2} (E -> (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))))) (coeFn.{succ u2, succ u2} (LinearIsometry.{u1, u1, u2, u2} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))) E (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.normedAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.instModule.{u1, u2} π E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (UniformSpace.Completion.toComplβα΅’._proof_1.{u2} E _inst_2) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul.{u1, u2} π E _inst_1 _inst_2 _inst_3))) (fun (_x : LinearIsometry.{u1, u1, u2, u2} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))) E (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.normedAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.instModule.{u1, u2} π E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (UniformSpace.Completion.toComplβα΅’._proof_1.{u2} E _inst_2) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul.{u1, u2} π E _inst_1 _inst_2 _inst_3))) => E -> (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))))) (LinearIsometry.hasCoeToFun.{u1, u1, u2, u2} π π E (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.normedAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.instModule.{u1, u2} π E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (UniformSpace.Completion.toComplβα΅’._proof_1.{u2} E _inst_2) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul.{u1, u2} π E _inst_1 _inst_2 _inst_3))) (UniformSpace.Completion.toComplβα΅’.{u1, u2} π E _inst_1 _inst_2 _inst_3)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) E (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (HasLiftT.mk.{succ u2, succ u2} E (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (CoeTCβ.coe.{succ u2, succ u2} E (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.hasCoeT.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))))
+but is expected to have type
+ forall {π : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)], Eq.{succ u2} (forall (αΎ° : E), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) αΎ°) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearIsometry.{u1, u1, u2, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))))) E (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.instModule.{u1, u2} π E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (SeminormedAddCommGroup.to_uniformAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul.{u1, u2} π E _inst_1 _inst_2 _inst_3))) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) _x) (ContinuousMapClass.toFunLike.{u2, u2, u2} (LinearIsometry.{u1, u1, u2, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))))) E (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.instModule.{u1, u2} π E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (SeminormedAddCommGroup.to_uniformAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul.{u1, u2} π E _inst_1 _inst_2 _inst_3))) E (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (PseudoMetricSpace.toUniformSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (ContinuousSemilinearMapClass.toContinuousMapClass.{u2, u1, u1, u2, u2} (LinearIsometry.{u1, u1, u2, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))))) E (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.instModule.{u1, u2} π E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (SeminormedAddCommGroup.to_uniformAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul.{u1, u2} π E _inst_1 _inst_2 _inst_3))) π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (PseudoMetricSpace.toUniformSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (AddCommGroup.toAddCommMonoid.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.instModule.{u1, u2} π E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (SeminormedAddCommGroup.to_uniformAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul.{u1, u2} π E _inst_1 _inst_2 _inst_3)) (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{u1, u1, u2, u2, u2} π π E (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (LinearIsometry.{u1, u1, u2, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))))) E (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.instModule.{u1, u2} π E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (SeminormedAddCommGroup.to_uniformAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul.{u1, u2} π E _inst_1 _inst_2 _inst_3))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.instModule.{u1, u2} π E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (SeminormedAddCommGroup.to_uniformAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul.{u1, u2} π E _inst_1 _inst_2 _inst_3)) (LinearIsometry.instSemilinearIsometryClassLinearIsometry.{u1, u1, u2, u2} π π E (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.instModule.{u1, u2} π E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (SeminormedAddCommGroup.to_uniformAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul.{u1, u2} π E _inst_1 _inst_2 _inst_3)))))) (UniformSpace.Completion.toComplβα΅’.{u1, u2} π E _inst_1 _inst_2 _inst_3)) (UniformSpace.Completion.coe'.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))))
+Case conversion may be inaccurate. Consider using '#align uniform_space.completion.coe_to_complβα΅’ UniformSpace.Completion.coe_toComplβα΅’β'. -/
@[simp]
theorem coe_toComplβα΅’ : β(toComplβα΅’ : E ββα΅’[π] Completion E) = coe :=
rfl
#align uniform_space.completion.coe_to_complβα΅’ UniformSpace.Completion.coe_toComplβα΅’
+/- warning: uniform_space.completion.to_complL -> UniformSpace.Completion.toComplL is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)], ContinuousLinearMap.{u1, u1, u2, u2} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (PseudoMetricSpace.toUniformSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.normedAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (AddCommGroup.toAddCommMonoid.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.addCommGroup.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (UniformSpace.Completion.toComplL._proof_1.{u2} E _inst_2))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.instModule.{u1, u2} π E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (UniformSpace.Completion.toComplL._proof_2.{u2} E _inst_2) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul.{u1, u2} π E _inst_1 _inst_2 _inst_3))
+but is expected to have type
+ forall {π : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)], ContinuousLinearMap.{u1, u1, u2, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (PseudoMetricSpace.toUniformSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (AddCommGroup.toAddCommMonoid.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instAddCommGroupCompletion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (SeminormedAddCommGroup.to_uniformAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.instModule.{u1, u2} π E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (SeminormedAddCommGroup.to_uniformAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul.{u1, u2} π E _inst_1 _inst_2 _inst_3))
+Case conversion may be inaccurate. Consider using '#align uniform_space.completion.to_complL UniformSpace.Completion.toComplLβ'. -/
/-- Embedding of a normed space to its completion as a continuous linear map. -/
def toComplL : E βL[π] Completion E :=
toComplβα΅’.toContinuousLinearMap
#align uniform_space.completion.to_complL UniformSpace.Completion.toComplL
+/- warning: uniform_space.completion.coe_to_complL -> UniformSpace.Completion.coe_toComplL is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)], Eq.{succ u2} (E -> (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))))) (coeFn.{succ u2, succ u2} (ContinuousLinearMap.{u1, u1, u2, u2} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (PseudoMetricSpace.toUniformSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.normedAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (AddCommGroup.toAddCommMonoid.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.addCommGroup.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (UniformSpace.Completion.toComplL._proof_1.{u2} E _inst_2))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.instModule.{u1, u2} π E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (UniformSpace.Completion.toComplL._proof_2.{u2} E _inst_2) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul.{u1, u2} π E _inst_1 _inst_2 _inst_3))) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u2} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (PseudoMetricSpace.toUniformSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.normedAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (AddCommGroup.toAddCommMonoid.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.addCommGroup.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (UniformSpace.Completion.toComplL._proof_1.{u2} E _inst_2))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.instModule.{u1, u2} π E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (UniformSpace.Completion.toComplL._proof_2.{u2} E _inst_2) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul.{u1, u2} π E _inst_1 _inst_2 _inst_3))) => E -> (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))))) (ContinuousLinearMap.toFun.{u1, u1, u2, u2} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (PseudoMetricSpace.toUniformSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.normedAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (AddCommGroup.toAddCommMonoid.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.addCommGroup.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (UniformSpace.Completion.toComplL._proof_1.{u2} E _inst_2))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.instModule.{u1, u2} π E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (UniformSpace.Completion.toComplL._proof_2.{u2} E _inst_2) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul.{u1, u2} π E _inst_1 _inst_2 _inst_3))) (UniformSpace.Completion.toComplL.{u1, u2} π E _inst_1 _inst_2 _inst_3)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) E (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (HasLiftT.mk.{succ u2, succ u2} E (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (CoeTCβ.coe.{succ u2, succ u2} E (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.hasCoeT.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))))
+but is expected to have type
+ forall {π : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} π] [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)], Eq.{succ u2} (forall (αΎ° : E), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) αΎ°) (FunLike.coe.{succ u2, succ u2, succ u2} (ContinuousLinearMap.{u1, u1, u2, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (PseudoMetricSpace.toUniformSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (AddCommGroup.toAddCommMonoid.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instAddCommGroupCompletion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (SeminormedAddCommGroup.to_uniformAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.instModule.{u1, u2} π E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (SeminormedAddCommGroup.to_uniformAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul.{u1, u2} π E _inst_1 _inst_2 _inst_3))) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) _x) (ContinuousMapClass.toFunLike.{u2, u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (PseudoMetricSpace.toUniformSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (AddCommGroup.toAddCommMonoid.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instAddCommGroupCompletion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (SeminormedAddCommGroup.to_uniformAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.instModule.{u1, u2} π E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (SeminormedAddCommGroup.to_uniformAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul.{u1, u2} π E _inst_1 _inst_2 _inst_3))) E (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (PseudoMetricSpace.toUniformSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (ContinuousSemilinearMapClass.toContinuousMapClass.{u2, u1, u1, u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (PseudoMetricSpace.toUniformSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (AddCommGroup.toAddCommMonoid.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instAddCommGroupCompletion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (SeminormedAddCommGroup.to_uniformAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.instModule.{u1, u2} π E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (SeminormedAddCommGroup.to_uniformAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul.{u1, u2} π E _inst_1 _inst_2 _inst_3))) π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (PseudoMetricSpace.toUniformSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (AddCommGroup.toAddCommMonoid.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instAddCommGroupCompletion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (SeminormedAddCommGroup.to_uniformAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.instModule.{u1, u2} π E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (SeminormedAddCommGroup.to_uniformAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul.{u1, u2} π E _inst_1 _inst_2 _inst_3)) (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u2, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (PseudoMetricSpace.toUniformSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (AddCommGroup.toAddCommMonoid.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.Completion.instAddCommGroupCompletion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (SeminormedAddCommGroup.to_uniformAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.instModule.{u1, u2} π E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (SeminormedAddCommGroup.to_uniformAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u2} π E _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul.{u1, u2} π E _inst_1 _inst_2 _inst_3))))) (UniformSpace.Completion.toComplL.{u1, u2} π E _inst_1 _inst_2 _inst_3)) (UniformSpace.Completion.coe'.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))))
+Case conversion may be inaccurate. Consider using '#align uniform_space.completion.coe_to_complL UniformSpace.Completion.coe_toComplLβ'. -/
@[simp]
theorem coe_toComplL : β(toComplL : E βL[π] Completion E) = coe :=
rfl
#align uniform_space.completion.coe_to_complL UniformSpace.Completion.coe_toComplL
+/- warning: uniform_space.completion.norm_to_complL -> UniformSpace.Completion.norm_toComplL is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} {E : Type.{u2}} [_inst_4 : NontriviallyNormedField.{u1} π] [_inst_5 : NormedAddCommGroup.{u2} E] [_inst_6 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_4) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_5)] [_inst_7 : Nontrivial.{u2} E], Eq.{1} Real (Norm.norm.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_4))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_4))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_4))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_5)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_5)) (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_5)))) (UniformSpace.toTopologicalSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_5)))) (PseudoMetricSpace.toUniformSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_5)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_5)))) (UniformSpace.Completion.normedAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_5)))))) (AddCommGroup.toAddCommMonoid.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_5)))) (UniformSpace.Completion.addCommGroup.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_5))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_5) (UniformSpace.Completion.toComplL._proof_1.{u2} E _inst_5))) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_4) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_5) _inst_6) (UniformSpace.Completion.instModule.{u1, u2} π E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_5))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_5) (UniformSpace.Completion.toComplL._proof_2.{u2} E _inst_5) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_4))))) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_4) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_5) _inst_6) (UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_4) _inst_5 _inst_6))) (ContinuousLinearMap.hasOpNorm.{u1, u1, u2, u2} π π E (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_5)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_5) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} (UniformSpace.Completion.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_5)))) (UniformSpace.Completion.normedAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_5))) _inst_4 _inst_4 _inst_6 (UniformSpace.Completion.normedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_4) _inst_5 _inst_6) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_4)))))))) (UniformSpace.Completion.toComplL.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_4) _inst_5 _inst_6)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
+but is expected to have type
+ forall {π : Type.{u2}} {E : Type.{u1}} [_inst_4 : NontriviallyNormedField.{u2} π] [_inst_5 : NormedAddCommGroup.{u1} E] [_inst_6 : NormedSpace.{u2, u1} π E (NontriviallyNormedField.toNormedField.{u2} π _inst_4) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_5)] [_inst_7 : Nontrivial.{u1} E], Eq.{1} Real (Norm.norm.{u1} (ContinuousLinearMap.{u2, u2, u1, u1} π π (DivisionSemiring.toSemiring.{u2} π (Semifield.toDivisionSemiring.{u2} π (Field.toSemifield.{u2} π (NormedField.toField.{u2} π (NontriviallyNormedField.toNormedField.{u2} π _inst_4))))) (DivisionSemiring.toSemiring.{u2} π (Semifield.toDivisionSemiring.{u2} π (Field.toSemifield.{u2} π (NormedField.toField.{u2} π (NontriviallyNormedField.toNormedField.{u2} π _inst_4))))) (RingHom.id.{u2} π (Semiring.toNonAssocSemiring.{u2} π (DivisionSemiring.toSemiring.{u2} π (Semifield.toDivisionSemiring.{u2} π (Field.toSemifield.{u2} π (NormedField.toField.{u2} π (NontriviallyNormedField.toNormedField.{u2} π _inst_4))))))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_5)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_5)) (UniformSpace.Completion.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_5)))) (UniformSpace.toTopologicalSpace.{u1} (UniformSpace.Completion.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_5)))) (PseudoMetricSpace.toUniformSpace.{u1} (UniformSpace.Completion.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_5)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} (UniformSpace.Completion.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_5)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_5)))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_5)))))) (AddCommGroup.toAddCommMonoid.{u1} (UniformSpace.Completion.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_5)))) (UniformSpace.Completion.instAddCommGroupCompletion.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_5))) (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_5) (SeminormedAddCommGroup.to_uniformAddGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_5)))) (NormedSpace.toModule.{u2, u1} π E (NontriviallyNormedField.toNormedField.{u2} π _inst_4) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_5) _inst_6) (UniformSpace.Completion.instModule.{u2, u1} π E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_5))) (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_5) (SeminormedAddCommGroup.to_uniformAddGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_5)) (DivisionSemiring.toSemiring.{u2} π (Semifield.toDivisionSemiring.{u2} π (Field.toSemifield.{u2} π (NormedField.toField.{u2} π (NontriviallyNormedField.toNormedField.{u2} π _inst_4))))) (NormedSpace.toModule.{u2, u1} π E (NontriviallyNormedField.toNormedField.{u2} π _inst_4) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_5) _inst_6) (UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul.{u2, u1} π E (NontriviallyNormedField.toNormedField.{u2} π _inst_4) _inst_5 _inst_6))) (ContinuousLinearMap.hasOpNorm.{u2, u2, u1, u1} π π E (UniformSpace.Completion.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_5)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_5) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} (UniformSpace.Completion.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_5)))) (UniformSpace.Completion.instNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_5))) _inst_4 _inst_4 _inst_6 (UniformSpace.Completion.instNormedSpaceCompletionToUniformSpaceToPseudoMetricSpaceToSeminormedAddCommGroupInstNormedAddCommGroupCompletionToUniformSpaceToPseudoMetricSpace.{u2, u1} π E (NontriviallyNormedField.toNormedField.{u2} π _inst_4) _inst_5 _inst_6) (RingHom.id.{u2} π (Semiring.toNonAssocSemiring.{u2} π (DivisionSemiring.toSemiring.{u2} π (Semifield.toDivisionSemiring.{u2} π (Field.toSemifield.{u2} π (NormedField.toField.{u2} π (NontriviallyNormedField.toNormedField.{u2} π _inst_4)))))))) (UniformSpace.Completion.toComplL.{u2, u1} π E (NontriviallyNormedField.toNormedField.{u2} π _inst_4) _inst_5 _inst_6)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))
+Case conversion may be inaccurate. Consider using '#align uniform_space.completion.norm_to_complL UniformSpace.Completion.norm_toComplLβ'. -/
@[simp]
theorem norm_toComplL {π E : Type _} [NontriviallyNormedField π] [NormedAddCommGroup E]
[NormedSpace π E] [Nontrivial E] : β(toComplL : E βL[π] Completion E)β = 1 :=
@@ -83,7 +115,7 @@ variable (π) (A : Type _)
instance [SeminormedRing A] : NormedRing (Completion A) :=
{ Completion.ring,
- Completion.metricSpace with
+ Completion.instMetricSpace with
dist_eq := fun x y => by
apply completion.induction_onβ x y <;> clear x y
Β· refine' isClosed_eq (completion.uniform_continuous_extensionβ _).Continuous _
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: Yury G. Kudryashov
! This file was ported from Lean 3 source module analysis.normed_space.completion
-! leanprover-community/mathlib commit 17ef379e997badd73e5eabb4d38f11919ab3c4b3
+! leanprover-community/mathlib commit d3af0609f6db8691dffdc3e1fb7feb7da72698f2
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -113,7 +113,7 @@ instance [SeminormedCommRing A] [NormedAlgebra π A] [UniformContinuousConstSM
(Continuous.comp (continuous_mul_left _) continuous_norm)
Β· intro x
simp only [β coe_smul, norm_coe]
- exact NormedSpace.norm_smul_le r x }
+ exact norm_smul_le r x }
end Algebra
mathlib commit https://github.com/leanprover-community/mathlib/commit/2af0836443b4cfb5feda0df0051acdb398304931
@@ -81,7 +81,7 @@ section Algebra
variable (π) (A : Type _)
-instance [SemiNormedRing A] : NormedRing (Completion A) :=
+instance [SeminormedRing A] : NormedRing (Completion A) :=
{ Completion.ring,
Completion.metricSpace with
dist_eq := fun x y => by
@@ -101,7 +101,7 @@ instance [SemiNormedRing A] : NormedRing (Completion A) :=
simp only [β coe_mul, norm_coe]
exact norm_mul_le x y }
-instance [SemiNormedCommRing A] [NormedAlgebra π A] [UniformContinuousConstSMul π A] :
+instance [SeminormedCommRing A] [NormedAlgebra π A] [UniformContinuousConstSMul π A] :
NormedAlgebra π (Completion A) :=
{ Completion.algebra A π with
norm_smul_le := fun r x =>
mathlib commit https://github.com/leanprover-community/mathlib/commit/195fcd60ff2bfe392543bceb0ec2adcdb472db4c
@@ -33,10 +33,10 @@ namespace Completion
variable (π E : Type _) [NormedField π] [NormedAddCommGroup E] [NormedSpace π E]
-instance (priority := 100) NormedSpace.to_hasUniformContinuousConstSmul :
- HasUniformContinuousConstSmul π E :=
+instance (priority := 100) NormedSpace.to_uniformContinuousConstSMul :
+ UniformContinuousConstSMul π E :=
β¨fun c => (lipschitzWith_smul c).UniformContinuousβ©
-#align uniform_space.completion.normed_space.to_has_uniform_continuous_const_smul UniformSpace.Completion.NormedSpace.to_hasUniformContinuousConstSmul
+#align uniform_space.completion.normed_space.to_has_uniform_continuous_const_smul UniformSpace.Completion.NormedSpace.to_uniformContinuousConstSMul
instance : NormedSpace π (Completion E) :=
{ Completion.module with
@@ -101,7 +101,7 @@ instance [SemiNormedRing A] : NormedRing (Completion A) :=
simp only [β coe_mul, norm_coe]
exact norm_mul_le x y }
-instance [SemiNormedCommRing A] [NormedAlgebra π A] [HasUniformContinuousConstSmul π A] :
+instance [SemiNormedCommRing A] [NormedAlgebra π A] [UniformContinuousConstSMul π A] :
NormedAlgebra π (Completion A) :=
{ Completion.algebra A π with
norm_smul_le := fun r x =>
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
Split the 2300-line behemoth OperatorNorm.lean
into 8 smaller files, of which the largest is 600 lines.
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import Mathlib.Analysis.Normed.Group.Completion
-import Mathlib.Analysis.NormedSpace.OperatorNorm
+import Mathlib.Analysis.NormedSpace.OperatorNorm.NormedSpace
import Mathlib.Topology.Algebra.UniformRing
#align_import analysis.normed_space.completion from "leanprover-community/mathlib"@"d3af0609f6db8691dffdc3e1fb7feb7da72698f2"
This removes redundant field values of the form add := add
for smaller terms and less unfolding during unification.
A list of all files containing a structure instance of the form { a1, ... with x1 := val, ... }
where some xi
is a field of some aj
was generated by modifying the structure instance elaboration algorithm to print such overlaps to stdout in a custom toolchain.
Using that toolchain, I went through each file on the list and attempted to remove algebraic fields that overlapped and were redundant, eg add := add
and not toFun
(though some other ones did creep in). If things broke (which was the case in a couple of cases), I did not push further and reverted.
It is possible that pushing harder and trying to remove all redundant overlaps will yield further improvements.
@@ -37,7 +37,6 @@ instance (priority := 100) NormedSpace.to_uniformContinuousConstSMul :
instance : NormedSpace π (Completion E) :=
{ Completion.instModule with
- smul := (Β· β’ Β·)
norm_smul_le := fun c x =>
induction_on x
(isClosed_le (continuous_const_smul _).norm (continuous_const.mul continuous_norm)) fun y =>
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -28,7 +28,7 @@ namespace UniformSpace
namespace Completion
-variable (π E : Type _) [NormedField π] [NormedAddCommGroup E] [NormedSpace π E]
+variable (π E : Type*) [NormedField π] [NormedAddCommGroup E] [NormedSpace π E]
instance (priority := 100) NormedSpace.to_uniformContinuousConstSMul :
UniformContinuousConstSMul π E :=
@@ -71,7 +71,7 @@ set_option linter.uppercaseLean3 false in
#align uniform_space.completion.coe_to_complL UniformSpace.Completion.coe_toComplL
@[simp]
-theorem norm_toComplL {π E : Type _} [NontriviallyNormedField π] [NormedAddCommGroup E]
+theorem norm_toComplL {π E : Type*} [NontriviallyNormedField π] [NormedAddCommGroup E]
[NormedSpace π E] [Nontrivial E] : β(toComplL : E βL[π] Completion E)β = 1 :=
(toComplβα΅’ : E ββα΅’[π] Completion E).norm_toContinuousLinearMap
set_option linter.uppercaseLean3 false in
@@ -79,7 +79,7 @@ set_option linter.uppercaseLean3 false in
section Algebra
-variable (π) (A : Type _)
+variable (π) (A : Type*)
instance [SeminormedRing A] : NormedRing (Completion A) :=
{ Completion.ring,
@@ -2,16 +2,13 @@
Copyright (c) 2022 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-
-! This file was ported from Lean 3 source module analysis.normed_space.completion
-! 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.Analysis.Normed.Group.Completion
import Mathlib.Analysis.NormedSpace.OperatorNorm
import Mathlib.Topology.Algebra.UniformRing
+#align_import analysis.normed_space.completion from "leanprover-community/mathlib"@"d3af0609f6db8691dffdc3e1fb7feb7da72698f2"
+
/-!
# Normed space structure on the completion of a normed space
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