analysis.locally_convex.strong_topology
β·
Mathlib.Analysis.LocallyConvex.StrongTopology
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
@@ -50,10 +50,10 @@ variable [NormedField πβ] [NormedField πβ] [Module πβ E] [Module
variable [Module R F] [ContinuousConstSMul R F] [LocallyConvexSpace R F] [SMulCommClass πβ R F]
-#print ContinuousLinearMap.strongTopology.locallyConvexSpace /-
-theorem strongTopology.locallyConvexSpace (π : Set (Set E)) (hπβ : π.Nonempty)
+#print UniformConvergenceCLM.locallyConvexSpace /-
+theorem UniformConvergenceCLM.locallyConvexSpace (π : Set (Set E)) (hπβ : π.Nonempty)
(hπβ : DirectedOn (Β· β Β·) π) :
- @LocallyConvexSpace R (E βSL[Ο] F) _ _ _ (strongTopology Ο F π) :=
+ @LocallyConvexSpace R (E βSL[Ο] F) _ _ _ (instTopologicalSpace Ο F π) :=
by
letI : TopologicalSpace (E βSL[Ο] F) := strong_topology Ο F π
haveI : TopologicalAddGroup (E βSL[Ο] F) := strong_topology.topological_add_group _ _ _
@@ -64,7 +64,7 @@ theorem strongTopology.locallyConvexSpace (π : Set (Set E)) (hπβ : π.
_
rintro β¨S, Vβ© β¨hS, hVmem, hVconvexβ© f hf g hg a b ha hb hab x hx
exact hVconvex (hf x hx) (hg x hx) ha hb hab
-#align continuous_linear_map.strong_topology.locally_convex_space ContinuousLinearMap.strongTopology.locallyConvexSpace
+#align continuous_linear_map.strong_topology.locally_convex_space UniformConvergenceCLM.locallyConvexSpace
-/
end General
@@ -78,7 +78,7 @@ variable [NormedField πβ] [NormedField πβ] [Module πβ E] [Module
variable [Module R F] [ContinuousConstSMul R F] [LocallyConvexSpace R F] [SMulCommClass πβ R F]
instance : LocallyConvexSpace R (E βSL[Ο] F) :=
- strongTopology.locallyConvexSpace R _ β¨β
, Bornology.isVonNBounded_empty πβ Eβ©
+ UniformConvergenceCLM.locallyConvexSpace R _ β¨β
, Bornology.isVonNBounded_empty πβ Eβ©
(directedOn_of_sup_mem fun _ _ => Bornology.IsVonNBounded.union)
end BoundedSets
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2022 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
-/
-import Mathbin.Topology.Algebra.Module.StrongTopology
-import Mathbin.Topology.Algebra.Module.LocallyConvex
+import Topology.Algebra.Module.StrongTopology
+import Topology.Algebra.Module.LocallyConvex
#align_import analysis.locally_convex.strong_topology from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2022 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
-
-! This file was ported from Lean 3 source module analysis.locally_convex.strong_topology
-! leanprover-community/mathlib commit 38df578a6450a8c5142b3727e3ae894c2300cae0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Topology.Algebra.Module.StrongTopology
import Mathbin.Topology.Algebra.Module.LocallyConvex
+#align_import analysis.locally_convex.strong_topology from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"
+
/-!
# Local convexity of the strong topology
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -53,6 +53,7 @@ variable [NormedField πβ] [NormedField πβ] [Module πβ E] [Module
variable [Module R F] [ContinuousConstSMul R F] [LocallyConvexSpace R F] [SMulCommClass πβ R F]
+#print ContinuousLinearMap.strongTopology.locallyConvexSpace /-
theorem strongTopology.locallyConvexSpace (π : Set (Set E)) (hπβ : π.Nonempty)
(hπβ : DirectedOn (Β· β Β·) π) :
@LocallyConvexSpace R (E βSL[Ο] F) _ _ _ (strongTopology Ο F π) :=
@@ -67,6 +68,7 @@ theorem strongTopology.locallyConvexSpace (π : Set (Set E)) (hπβ : π.
rintro β¨S, Vβ© β¨hS, hVmem, hVconvexβ© f hf g hg a b ha hb hab x hx
exact hVconvex (hf x hx) (hg x hx) ha hb hab
#align continuous_linear_map.strong_topology.locally_convex_space ContinuousLinearMap.strongTopology.locallyConvexSpace
+-/
end General
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -34,7 +34,7 @@ locally convex, bounded convergence
-/
-open Topology UniformConvergence
+open scoped Topology UniformConvergence
variable {R πβ πβ E F : Type _}
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -53,9 +53,6 @@ variable [NormedField πβ] [NormedField πβ] [Module πβ E] [Module
variable [Module R F] [ContinuousConstSMul R F] [LocallyConvexSpace R F] [SMulCommClass πβ R F]
-/- warning: continuous_linear_map.strong_topology.locally_convex_space -> ContinuousLinearMap.strongTopology.locallyConvexSpace is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.strong_topology.locally_convex_space ContinuousLinearMap.strongTopology.locallyConvexSpaceβ'. -/
theorem strongTopology.locallyConvexSpace (π : Set (Set E)) (hπβ : π.Nonempty)
(hπβ : DirectedOn (Β· β Β·) π) :
@LocallyConvexSpace R (E βSL[Ο] F) _ _ _ (strongTopology Ο F π) :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -54,10 +54,7 @@ variable [NormedField πβ] [NormedField πβ] [Module πβ E] [Module
variable [Module R F] [ContinuousConstSMul R F] [LocallyConvexSpace R F] [SMulCommClass πβ R F]
/- warning: continuous_linear_map.strong_topology.locally_convex_space -> ContinuousLinearMap.strongTopology.locallyConvexSpace is a dubious translation:
-lean 3 declaration is
- forall (R : Type.{u1}) {πβ : Type.{u2}} {πβ : Type.{u3}} {E : Type.{u4}} {F : Type.{u5}} [_inst_1 : AddCommGroup.{u4} E] [_inst_2 : TopologicalSpace.{u4} E] [_inst_3 : AddCommGroup.{u5} F] [_inst_4 : TopologicalSpace.{u5} F] [_inst_5 : TopologicalAddGroup.{u5} F _inst_4 (AddCommGroup.toAddGroup.{u5} F _inst_3)] [_inst_6 : OrderedSemiring.{u1} R] [_inst_7 : NormedField.{u2} πβ] [_inst_8 : NormedField.{u3} πβ] [_inst_9 : Module.{u2, u4} πβ E (Ring.toSemiring.{u2} πβ (NormedRing.toRing.{u2} πβ (NormedCommRing.toNormedRing.{u2} πβ (NormedField.toNormedCommRing.{u2} πβ _inst_7)))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_1)] [_inst_10 : Module.{u3, u5} πβ F (Ring.toSemiring.{u3} πβ (NormedRing.toRing.{u3} πβ (NormedCommRing.toNormedRing.{u3} πβ (NormedField.toNormedCommRing.{u3} πβ _inst_8)))) (AddCommGroup.toAddCommMonoid.{u5} F _inst_3)] {Ο : RingHom.{u2, u3} πβ πβ (NonAssocRing.toNonAssocSemiring.{u2} πβ (Ring.toNonAssocRing.{u2} πβ (NormedRing.toRing.{u2} πβ (NormedCommRing.toNormedRing.{u2} πβ (NormedField.toNormedCommRing.{u2} πβ _inst_7))))) (NonAssocRing.toNonAssocSemiring.{u3} πβ (Ring.toNonAssocRing.{u3} πβ (NormedRing.toRing.{u3} πβ (NormedCommRing.toNormedRing.{u3} πβ (NormedField.toNormedCommRing.{u3} πβ _inst_8)))))} [_inst_11 : Module.{u1, u5} R F (OrderedSemiring.toSemiring.{u1} R _inst_6) (AddCommGroup.toAddCommMonoid.{u5} F _inst_3)] [_inst_12 : ContinuousConstSMul.{u1, u5} R F _inst_4 (SMulZeroClass.toHasSmul.{u1, u5} R F (AddZeroClass.toHasZero.{u5} F (AddMonoid.toAddZeroClass.{u5} F (AddCommMonoid.toAddMonoid.{u5} F (AddCommGroup.toAddCommMonoid.{u5} F _inst_3)))) (SMulWithZero.toSmulZeroClass.{u1, u5} R F (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (OrderedSemiring.toSemiring.{u1} R _inst_6))))) (AddZeroClass.toHasZero.{u5} F (AddMonoid.toAddZeroClass.{u5} F (AddCommMonoid.toAddMonoid.{u5} F (AddCommGroup.toAddCommMonoid.{u5} F _inst_3)))) (MulActionWithZero.toSMulWithZero.{u1, u5} R F (Semiring.toMonoidWithZero.{u1} R (OrderedSemiring.toSemiring.{u1} R _inst_6)) (AddZeroClass.toHasZero.{u5} F (AddMonoid.toAddZeroClass.{u5} F (AddCommMonoid.toAddMonoid.{u5} F (AddCommGroup.toAddCommMonoid.{u5} F _inst_3)))) (Module.toMulActionWithZero.{u1, u5} R F (OrderedSemiring.toSemiring.{u1} R _inst_6) (AddCommGroup.toAddCommMonoid.{u5} F _inst_3) _inst_11))))] [_inst_13 : LocallyConvexSpace.{u1, u5} R F _inst_6 (AddCommGroup.toAddCommMonoid.{u5} F _inst_3) _inst_11 _inst_4] [_inst_14 : SMulCommClass.{u3, u1, u5} πβ R F (SMulZeroClass.toHasSmul.{u3, u5} πβ F (AddZeroClass.toHasZero.{u5} F (AddMonoid.toAddZeroClass.{u5} F (AddCommMonoid.toAddMonoid.{u5} F (AddCommGroup.toAddCommMonoid.{u5} F _inst_3)))) (SMulWithZero.toSmulZeroClass.{u3, u5} πβ F (MulZeroClass.toHasZero.{u3} πβ (MulZeroOneClass.toMulZeroClass.{u3} πβ (MonoidWithZero.toMulZeroOneClass.{u3} πβ (Semiring.toMonoidWithZero.{u3} πβ (Ring.toSemiring.{u3} πβ (NormedRing.toRing.{u3} πβ (NormedCommRing.toNormedRing.{u3} πβ (NormedField.toNormedCommRing.{u3} πβ _inst_8)))))))) (AddZeroClass.toHasZero.{u5} F (AddMonoid.toAddZeroClass.{u5} F (AddCommMonoid.toAddMonoid.{u5} F (AddCommGroup.toAddCommMonoid.{u5} F _inst_3)))) (MulActionWithZero.toSMulWithZero.{u3, u5} πβ F (Semiring.toMonoidWithZero.{u3} πβ (Ring.toSemiring.{u3} πβ (NormedRing.toRing.{u3} πβ (NormedCommRing.toNormedRing.{u3} πβ (NormedField.toNormedCommRing.{u3} πβ _inst_8))))) (AddZeroClass.toHasZero.{u5} F (AddMonoid.toAddZeroClass.{u5} F (AddCommMonoid.toAddMonoid.{u5} F (AddCommGroup.toAddCommMonoid.{u5} F _inst_3)))) (Module.toMulActionWithZero.{u3, u5} πβ F (Ring.toSemiring.{u3} πβ (NormedRing.toRing.{u3} πβ (NormedCommRing.toNormedRing.{u3} πβ (NormedField.toNormedCommRing.{u3} πβ _inst_8)))) (AddCommGroup.toAddCommMonoid.{u5} F _inst_3) _inst_10)))) (SMulZeroClass.toHasSmul.{u1, u5} R F (AddZeroClass.toHasZero.{u5} F (AddMonoid.toAddZeroClass.{u5} F (AddCommMonoid.toAddMonoid.{u5} F (AddCommGroup.toAddCommMonoid.{u5} F _inst_3)))) (SMulWithZero.toSmulZeroClass.{u1, u5} R F (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (OrderedSemiring.toSemiring.{u1} R _inst_6))))) (AddZeroClass.toHasZero.{u5} F (AddMonoid.toAddZeroClass.{u5} F (AddCommMonoid.toAddMonoid.{u5} F (AddCommGroup.toAddCommMonoid.{u5} F _inst_3)))) (MulActionWithZero.toSMulWithZero.{u1, u5} R F (Semiring.toMonoidWithZero.{u1} R (OrderedSemiring.toSemiring.{u1} R _inst_6)) (AddZeroClass.toHasZero.{u5} F (AddMonoid.toAddZeroClass.{u5} F (AddCommMonoid.toAddMonoid.{u5} F (AddCommGroup.toAddCommMonoid.{u5} F _inst_3)))) (Module.toMulActionWithZero.{u1, u5} R F (OrderedSemiring.toSemiring.{u1} R _inst_6) (AddCommGroup.toAddCommMonoid.{u5} F _inst_3) _inst_11))))] (π : Set.{u4} (Set.{u4} E)), (Set.Nonempty.{u4} (Set.{u4} E) π) -> (DirectedOn.{u4} (Set.{u4} E) (HasSubset.Subset.{u4} (Set.{u4} E) (Set.hasSubset.{u4} E)) π) -> (LocallyConvexSpace.{u1, max u4 u5} R (ContinuousLinearMap.{u2, u3, u4, u5} πβ πβ (Ring.toSemiring.{u2} πβ (NormedRing.toRing.{u2} πβ (NormedCommRing.toNormedRing.{u2} πβ (NormedField.toNormedCommRing.{u2} πβ _inst_7)))) (Ring.toSemiring.{u3} πβ (NormedRing.toRing.{u3} πβ (NormedCommRing.toNormedRing.{u3} πβ (NormedField.toNormedCommRing.{u3} πβ _inst_8)))) Ο E _inst_2 (AddCommGroup.toAddCommMonoid.{u4} E _inst_1) F _inst_4 (AddCommGroup.toAddCommMonoid.{u5} F _inst_3) _inst_9 _inst_10) _inst_6 (ContinuousLinearMap.addCommMonoid.{u2, u3, u4, u5} πβ πβ (Ring.toSemiring.{u2} πβ (NormedRing.toRing.{u2} πβ (NormedCommRing.toNormedRing.{u2} πβ (NormedField.toNormedCommRing.{u2} πβ _inst_7)))) (Ring.toSemiring.{u3} πβ (NormedRing.toRing.{u3} πβ (NormedCommRing.toNormedRing.{u3} πβ (NormedField.toNormedCommRing.{u3} πβ _inst_8)))) Ο E _inst_2 (AddCommGroup.toAddCommMonoid.{u4} E _inst_1) F _inst_4 (AddCommGroup.toAddCommMonoid.{u5} F _inst_3) _inst_9 _inst_10 (TopologicalAddGroup.to_continuousAdd.{u5} F _inst_4 (AddCommGroup.toAddGroup.{u5} F _inst_3) _inst_5)) (ContinuousLinearMap.module.{u2, u3, u1, u4, u5} πβ πβ R (Ring.toSemiring.{u2} πβ (NormedRing.toRing.{u2} πβ (NormedCommRing.toNormedRing.{u2} πβ (NormedField.toNormedCommRing.{u2} πβ _inst_7)))) (Ring.toSemiring.{u3} πβ (NormedRing.toRing.{u3} πβ (NormedCommRing.toNormedRing.{u3} πβ (NormedField.toNormedCommRing.{u3} πβ _inst_8)))) (OrderedSemiring.toSemiring.{u1} R _inst_6) E _inst_2 (AddCommGroup.toAddCommMonoid.{u4} E _inst_1) _inst_9 F _inst_4 (AddCommGroup.toAddCommMonoid.{u5} F _inst_3) _inst_10 _inst_11 _inst_14 _inst_12 Ο (TopologicalAddGroup.to_continuousAdd.{u5} F _inst_4 (AddCommGroup.toAddGroup.{u5} F _inst_3) _inst_5)) (ContinuousLinearMap.strongTopology.{u2, u3, u4, u5} πβ πβ _inst_7 _inst_8 Ο E F _inst_1 _inst_9 _inst_3 _inst_10 _inst_2 _inst_4 _inst_5 π))
-but is expected to have type
- forall (R : Type.{u4}) {πβ : Type.{u2}} {πβ : Type.{u1}} {E : Type.{u5}} {F : Type.{u3}} [_inst_1 : AddCommGroup.{u5} E] [_inst_2 : TopologicalSpace.{u5} E] [_inst_3 : AddCommGroup.{u3} F] [_inst_4 : TopologicalSpace.{u3} F] [_inst_5 : TopologicalAddGroup.{u3} F _inst_4 (AddCommGroup.toAddGroup.{u3} F _inst_3)] [_inst_6 : OrderedSemiring.{u4} R] [_inst_7 : NormedField.{u2} πβ] [_inst_8 : NormedField.{u1} πβ] [_inst_9 : Module.{u2, u5} πβ E (DivisionSemiring.toSemiring.{u2} πβ (Semifield.toDivisionSemiring.{u2} πβ (Field.toSemifield.{u2} πβ (NormedField.toField.{u2} πβ _inst_7)))) (AddCommGroup.toAddCommMonoid.{u5} E _inst_1)] [_inst_10 : Module.{u1, u3} πβ F (DivisionSemiring.toSemiring.{u1} πβ (Semifield.toDivisionSemiring.{u1} πβ (Field.toSemifield.{u1} πβ (NormedField.toField.{u1} πβ _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} F _inst_3)] {Ο : RingHom.{u2, u1} πβ πβ (Semiring.toNonAssocSemiring.{u2} πβ (DivisionSemiring.toSemiring.{u2} πβ (Semifield.toDivisionSemiring.{u2} πβ (Field.toSemifield.{u2} πβ (NormedField.toField.{u2} πβ _inst_7))))) (Semiring.toNonAssocSemiring.{u1} πβ (DivisionSemiring.toSemiring.{u1} πβ (Semifield.toDivisionSemiring.{u1} πβ (Field.toSemifield.{u1} πβ (NormedField.toField.{u1} πβ _inst_8)))))} [_inst_11 : Module.{u4, u3} R F (OrderedSemiring.toSemiring.{u4} R _inst_6) (AddCommGroup.toAddCommMonoid.{u3} F _inst_3)] [_inst_12 : ContinuousConstSMul.{u4, u3} R F _inst_4 (SMulZeroClass.toSMul.{u4, u3} R F (NegZeroClass.toZero.{u3} F (SubNegZeroMonoid.toNegZeroClass.{u3} F (SubtractionMonoid.toSubNegZeroMonoid.{u3} F (SubtractionCommMonoid.toSubtractionMonoid.{u3} F (AddCommGroup.toDivisionAddCommMonoid.{u3} F _inst_3))))) (SMulWithZero.toSMulZeroClass.{u4, u3} R F (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (OrderedSemiring.toSemiring.{u4} R _inst_6))) (NegZeroClass.toZero.{u3} F (SubNegZeroMonoid.toNegZeroClass.{u3} F (SubtractionMonoid.toSubNegZeroMonoid.{u3} F (SubtractionCommMonoid.toSubtractionMonoid.{u3} F (AddCommGroup.toDivisionAddCommMonoid.{u3} F _inst_3))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R (OrderedSemiring.toSemiring.{u4} R _inst_6)) (NegZeroClass.toZero.{u3} F (SubNegZeroMonoid.toNegZeroClass.{u3} F (SubtractionMonoid.toSubNegZeroMonoid.{u3} F (SubtractionCommMonoid.toSubtractionMonoid.{u3} F (AddCommGroup.toDivisionAddCommMonoid.{u3} F _inst_3))))) (Module.toMulActionWithZero.{u4, u3} R F (OrderedSemiring.toSemiring.{u4} R _inst_6) (AddCommGroup.toAddCommMonoid.{u3} F _inst_3) _inst_11))))] [_inst_13 : LocallyConvexSpace.{u4, u3} R F _inst_6 (AddCommGroup.toAddCommMonoid.{u3} F _inst_3) _inst_11 _inst_4] [_inst_14 : SMulCommClass.{u1, u4, u3} πβ R F (SMulZeroClass.toSMul.{u1, u3} πβ F (NegZeroClass.toZero.{u3} F (SubNegZeroMonoid.toNegZeroClass.{u3} F (SubtractionMonoid.toSubNegZeroMonoid.{u3} F (SubtractionCommMonoid.toSubtractionMonoid.{u3} F (AddCommGroup.toDivisionAddCommMonoid.{u3} F _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u3} πβ F (CommMonoidWithZero.toZero.{u1} πβ (CommGroupWithZero.toCommMonoidWithZero.{u1} πβ (Semifield.toCommGroupWithZero.{u1} πβ (Field.toSemifield.{u1} πβ (NormedField.toField.{u1} πβ _inst_8))))) (NegZeroClass.toZero.{u3} F (SubNegZeroMonoid.toNegZeroClass.{u3} F (SubtractionMonoid.toSubNegZeroMonoid.{u3} F (SubtractionCommMonoid.toSubtractionMonoid.{u3} F (AddCommGroup.toDivisionAddCommMonoid.{u3} F _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} πβ F (Semiring.toMonoidWithZero.{u1} πβ (DivisionSemiring.toSemiring.{u1} πβ (Semifield.toDivisionSemiring.{u1} πβ (Field.toSemifield.{u1} πβ (NormedField.toField.{u1} πβ _inst_8))))) (NegZeroClass.toZero.{u3} F (SubNegZeroMonoid.toNegZeroClass.{u3} F (SubtractionMonoid.toSubNegZeroMonoid.{u3} F (SubtractionCommMonoid.toSubtractionMonoid.{u3} F (AddCommGroup.toDivisionAddCommMonoid.{u3} F _inst_3))))) (Module.toMulActionWithZero.{u1, u3} πβ F (DivisionSemiring.toSemiring.{u1} πβ (Semifield.toDivisionSemiring.{u1} πβ (Field.toSemifield.{u1} πβ (NormedField.toField.{u1} πβ _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} F _inst_3) _inst_10)))) (SMulZeroClass.toSMul.{u4, u3} R F (NegZeroClass.toZero.{u3} F (SubNegZeroMonoid.toNegZeroClass.{u3} F (SubtractionMonoid.toSubNegZeroMonoid.{u3} F (SubtractionCommMonoid.toSubtractionMonoid.{u3} F (AddCommGroup.toDivisionAddCommMonoid.{u3} F _inst_3))))) (SMulWithZero.toSMulZeroClass.{u4, u3} R F (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (OrderedSemiring.toSemiring.{u4} R _inst_6))) (NegZeroClass.toZero.{u3} F (SubNegZeroMonoid.toNegZeroClass.{u3} F (SubtractionMonoid.toSubNegZeroMonoid.{u3} F (SubtractionCommMonoid.toSubtractionMonoid.{u3} F (AddCommGroup.toDivisionAddCommMonoid.{u3} F _inst_3))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R (OrderedSemiring.toSemiring.{u4} R _inst_6)) (NegZeroClass.toZero.{u3} F (SubNegZeroMonoid.toNegZeroClass.{u3} F (SubtractionMonoid.toSubNegZeroMonoid.{u3} F (SubtractionCommMonoid.toSubtractionMonoid.{u3} F (AddCommGroup.toDivisionAddCommMonoid.{u3} F _inst_3))))) (Module.toMulActionWithZero.{u4, u3} R F (OrderedSemiring.toSemiring.{u4} R _inst_6) (AddCommGroup.toAddCommMonoid.{u3} F _inst_3) _inst_11))))] (π : Set.{u5} (Set.{u5} E)), (Set.Nonempty.{u5} (Set.{u5} E) π) -> (DirectedOn.{u5} (Set.{u5} E) (fun (x._@.Mathlib.Analysis.LocallyConvex.StrongTopology._hyg.275 : Set.{u5} E) (x._@.Mathlib.Analysis.LocallyConvex.StrongTopology._hyg.277 : Set.{u5} E) => HasSubset.Subset.{u5} (Set.{u5} E) (Set.instHasSubsetSet.{u5} E) x._@.Mathlib.Analysis.LocallyConvex.StrongTopology._hyg.275 x._@.Mathlib.Analysis.LocallyConvex.StrongTopology._hyg.277) π) -> (LocallyConvexSpace.{u4, max u3 u5} R (ContinuousLinearMap.{u2, u1, u5, u3} πβ πβ (DivisionSemiring.toSemiring.{u2} πβ (Semifield.toDivisionSemiring.{u2} πβ (Field.toSemifield.{u2} πβ (NormedField.toField.{u2} πβ _inst_7)))) (DivisionSemiring.toSemiring.{u1} πβ (Semifield.toDivisionSemiring.{u1} πβ (Field.toSemifield.{u1} πβ (NormedField.toField.{u1} πβ _inst_8)))) Ο E _inst_2 (AddCommGroup.toAddCommMonoid.{u5} E _inst_1) F _inst_4 (AddCommGroup.toAddCommMonoid.{u3} F _inst_3) _inst_9 _inst_10) _inst_6 (ContinuousLinearMap.addCommMonoid.{u2, u1, u5, u3} πβ πβ (DivisionSemiring.toSemiring.{u2} πβ (Semifield.toDivisionSemiring.{u2} πβ (Field.toSemifield.{u2} πβ (NormedField.toField.{u2} πβ _inst_7)))) (DivisionSemiring.toSemiring.{u1} πβ (Semifield.toDivisionSemiring.{u1} πβ (Field.toSemifield.{u1} πβ (NormedField.toField.{u1} πβ _inst_8)))) Ο E _inst_2 (AddCommGroup.toAddCommMonoid.{u5} E _inst_1) F _inst_4 (AddCommGroup.toAddCommMonoid.{u3} F _inst_3) _inst_9 _inst_10 (TopologicalAddGroup.toContinuousAdd.{u3} F _inst_4 (AddCommGroup.toAddGroup.{u3} F _inst_3) _inst_5)) (ContinuousLinearMap.module.{u2, u1, u4, u5, u3} πβ πβ R (DivisionSemiring.toSemiring.{u2} πβ (Semifield.toDivisionSemiring.{u2} πβ (Field.toSemifield.{u2} πβ (NormedField.toField.{u2} πβ _inst_7)))) (DivisionSemiring.toSemiring.{u1} πβ (Semifield.toDivisionSemiring.{u1} πβ (Field.toSemifield.{u1} πβ (NormedField.toField.{u1} πβ _inst_8)))) (OrderedSemiring.toSemiring.{u4} R _inst_6) E _inst_2 (AddCommGroup.toAddCommMonoid.{u5} E _inst_1) _inst_9 F _inst_4 (AddCommGroup.toAddCommMonoid.{u3} F _inst_3) _inst_10 _inst_11 _inst_14 _inst_12 Ο (TopologicalAddGroup.toContinuousAdd.{u3} F _inst_4 (AddCommGroup.toAddGroup.{u3} F _inst_3) _inst_5)) (ContinuousLinearMap.strongTopology.{u2, u1, u5, u3} πβ πβ _inst_7 _inst_8 Ο E F _inst_1 _inst_9 _inst_3 _inst_10 _inst_2 _inst_4 _inst_5 π))
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.strong_topology.locally_convex_space ContinuousLinearMap.strongTopology.locallyConvexSpaceβ'. -/
theorem strongTopology.locallyConvexSpace (π : Set (Set E)) (hπβ : π.Nonempty)
(hπβ : DirectedOn (Β· β Β·) π) :
mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
! This file was ported from Lean 3 source module analysis.locally_convex.strong_topology
-! leanprover-community/mathlib commit 47b12e7f2502f14001f891ca87fbae2b4acaed3f
+! leanprover-community/mathlib commit 38df578a6450a8c5142b3727e3ae894c2300cae0
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -14,6 +14,9 @@ import Mathbin.Topology.Algebra.Module.LocallyConvex
/-!
# Local convexity of the strong topology
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
In this file we prove that the strong topology on `E βL[β] F` is locally convex provided that `F` is
locally convex.
mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828
@@ -50,6 +50,12 @@ variable [NormedField πβ] [NormedField πβ] [Module πβ E] [Module
variable [Module R F] [ContinuousConstSMul R F] [LocallyConvexSpace R F] [SMulCommClass πβ R F]
+/- warning: continuous_linear_map.strong_topology.locally_convex_space -> ContinuousLinearMap.strongTopology.locallyConvexSpace is a dubious translation:
+lean 3 declaration is
+ forall (R : Type.{u1}) {πβ : Type.{u2}} {πβ : Type.{u3}} {E : Type.{u4}} {F : Type.{u5}} [_inst_1 : AddCommGroup.{u4} E] [_inst_2 : TopologicalSpace.{u4} E] [_inst_3 : AddCommGroup.{u5} F] [_inst_4 : TopologicalSpace.{u5} F] [_inst_5 : TopologicalAddGroup.{u5} F _inst_4 (AddCommGroup.toAddGroup.{u5} F _inst_3)] [_inst_6 : OrderedSemiring.{u1} R] [_inst_7 : NormedField.{u2} πβ] [_inst_8 : NormedField.{u3} πβ] [_inst_9 : Module.{u2, u4} πβ E (Ring.toSemiring.{u2} πβ (NormedRing.toRing.{u2} πβ (NormedCommRing.toNormedRing.{u2} πβ (NormedField.toNormedCommRing.{u2} πβ _inst_7)))) (AddCommGroup.toAddCommMonoid.{u4} E _inst_1)] [_inst_10 : Module.{u3, u5} πβ F (Ring.toSemiring.{u3} πβ (NormedRing.toRing.{u3} πβ (NormedCommRing.toNormedRing.{u3} πβ (NormedField.toNormedCommRing.{u3} πβ _inst_8)))) (AddCommGroup.toAddCommMonoid.{u5} F _inst_3)] {Ο : RingHom.{u2, u3} πβ πβ (NonAssocRing.toNonAssocSemiring.{u2} πβ (Ring.toNonAssocRing.{u2} πβ (NormedRing.toRing.{u2} πβ (NormedCommRing.toNormedRing.{u2} πβ (NormedField.toNormedCommRing.{u2} πβ _inst_7))))) (NonAssocRing.toNonAssocSemiring.{u3} πβ (Ring.toNonAssocRing.{u3} πβ (NormedRing.toRing.{u3} πβ (NormedCommRing.toNormedRing.{u3} πβ (NormedField.toNormedCommRing.{u3} πβ _inst_8)))))} [_inst_11 : Module.{u1, u5} R F (OrderedSemiring.toSemiring.{u1} R _inst_6) (AddCommGroup.toAddCommMonoid.{u5} F _inst_3)] [_inst_12 : ContinuousConstSMul.{u1, u5} R F _inst_4 (SMulZeroClass.toHasSmul.{u1, u5} R F (AddZeroClass.toHasZero.{u5} F (AddMonoid.toAddZeroClass.{u5} F (AddCommMonoid.toAddMonoid.{u5} F (AddCommGroup.toAddCommMonoid.{u5} F _inst_3)))) (SMulWithZero.toSmulZeroClass.{u1, u5} R F (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (OrderedSemiring.toSemiring.{u1} R _inst_6))))) (AddZeroClass.toHasZero.{u5} F (AddMonoid.toAddZeroClass.{u5} F (AddCommMonoid.toAddMonoid.{u5} F (AddCommGroup.toAddCommMonoid.{u5} F _inst_3)))) (MulActionWithZero.toSMulWithZero.{u1, u5} R F (Semiring.toMonoidWithZero.{u1} R (OrderedSemiring.toSemiring.{u1} R _inst_6)) (AddZeroClass.toHasZero.{u5} F (AddMonoid.toAddZeroClass.{u5} F (AddCommMonoid.toAddMonoid.{u5} F (AddCommGroup.toAddCommMonoid.{u5} F _inst_3)))) (Module.toMulActionWithZero.{u1, u5} R F (OrderedSemiring.toSemiring.{u1} R _inst_6) (AddCommGroup.toAddCommMonoid.{u5} F _inst_3) _inst_11))))] [_inst_13 : LocallyConvexSpace.{u1, u5} R F _inst_6 (AddCommGroup.toAddCommMonoid.{u5} F _inst_3) _inst_11 _inst_4] [_inst_14 : SMulCommClass.{u3, u1, u5} πβ R F (SMulZeroClass.toHasSmul.{u3, u5} πβ F (AddZeroClass.toHasZero.{u5} F (AddMonoid.toAddZeroClass.{u5} F (AddCommMonoid.toAddMonoid.{u5} F (AddCommGroup.toAddCommMonoid.{u5} F _inst_3)))) (SMulWithZero.toSmulZeroClass.{u3, u5} πβ F (MulZeroClass.toHasZero.{u3} πβ (MulZeroOneClass.toMulZeroClass.{u3} πβ (MonoidWithZero.toMulZeroOneClass.{u3} πβ (Semiring.toMonoidWithZero.{u3} πβ (Ring.toSemiring.{u3} πβ (NormedRing.toRing.{u3} πβ (NormedCommRing.toNormedRing.{u3} πβ (NormedField.toNormedCommRing.{u3} πβ _inst_8)))))))) (AddZeroClass.toHasZero.{u5} F (AddMonoid.toAddZeroClass.{u5} F (AddCommMonoid.toAddMonoid.{u5} F (AddCommGroup.toAddCommMonoid.{u5} F _inst_3)))) (MulActionWithZero.toSMulWithZero.{u3, u5} πβ F (Semiring.toMonoidWithZero.{u3} πβ (Ring.toSemiring.{u3} πβ (NormedRing.toRing.{u3} πβ (NormedCommRing.toNormedRing.{u3} πβ (NormedField.toNormedCommRing.{u3} πβ _inst_8))))) (AddZeroClass.toHasZero.{u5} F (AddMonoid.toAddZeroClass.{u5} F (AddCommMonoid.toAddMonoid.{u5} F (AddCommGroup.toAddCommMonoid.{u5} F _inst_3)))) (Module.toMulActionWithZero.{u3, u5} πβ F (Ring.toSemiring.{u3} πβ (NormedRing.toRing.{u3} πβ (NormedCommRing.toNormedRing.{u3} πβ (NormedField.toNormedCommRing.{u3} πβ _inst_8)))) (AddCommGroup.toAddCommMonoid.{u5} F _inst_3) _inst_10)))) (SMulZeroClass.toHasSmul.{u1, u5} R F (AddZeroClass.toHasZero.{u5} F (AddMonoid.toAddZeroClass.{u5} F (AddCommMonoid.toAddMonoid.{u5} F (AddCommGroup.toAddCommMonoid.{u5} F _inst_3)))) (SMulWithZero.toSmulZeroClass.{u1, u5} R F (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (OrderedSemiring.toSemiring.{u1} R _inst_6))))) (AddZeroClass.toHasZero.{u5} F (AddMonoid.toAddZeroClass.{u5} F (AddCommMonoid.toAddMonoid.{u5} F (AddCommGroup.toAddCommMonoid.{u5} F _inst_3)))) (MulActionWithZero.toSMulWithZero.{u1, u5} R F (Semiring.toMonoidWithZero.{u1} R (OrderedSemiring.toSemiring.{u1} R _inst_6)) (AddZeroClass.toHasZero.{u5} F (AddMonoid.toAddZeroClass.{u5} F (AddCommMonoid.toAddMonoid.{u5} F (AddCommGroup.toAddCommMonoid.{u5} F _inst_3)))) (Module.toMulActionWithZero.{u1, u5} R F (OrderedSemiring.toSemiring.{u1} R _inst_6) (AddCommGroup.toAddCommMonoid.{u5} F _inst_3) _inst_11))))] (π : Set.{u4} (Set.{u4} E)), (Set.Nonempty.{u4} (Set.{u4} E) π) -> (DirectedOn.{u4} (Set.{u4} E) (HasSubset.Subset.{u4} (Set.{u4} E) (Set.hasSubset.{u4} E)) π) -> (LocallyConvexSpace.{u1, max u4 u5} R (ContinuousLinearMap.{u2, u3, u4, u5} πβ πβ (Ring.toSemiring.{u2} πβ (NormedRing.toRing.{u2} πβ (NormedCommRing.toNormedRing.{u2} πβ (NormedField.toNormedCommRing.{u2} πβ _inst_7)))) (Ring.toSemiring.{u3} πβ (NormedRing.toRing.{u3} πβ (NormedCommRing.toNormedRing.{u3} πβ (NormedField.toNormedCommRing.{u3} πβ _inst_8)))) Ο E _inst_2 (AddCommGroup.toAddCommMonoid.{u4} E _inst_1) F _inst_4 (AddCommGroup.toAddCommMonoid.{u5} F _inst_3) _inst_9 _inst_10) _inst_6 (ContinuousLinearMap.addCommMonoid.{u2, u3, u4, u5} πβ πβ (Ring.toSemiring.{u2} πβ (NormedRing.toRing.{u2} πβ (NormedCommRing.toNormedRing.{u2} πβ (NormedField.toNormedCommRing.{u2} πβ _inst_7)))) (Ring.toSemiring.{u3} πβ (NormedRing.toRing.{u3} πβ (NormedCommRing.toNormedRing.{u3} πβ (NormedField.toNormedCommRing.{u3} πβ _inst_8)))) Ο E _inst_2 (AddCommGroup.toAddCommMonoid.{u4} E _inst_1) F _inst_4 (AddCommGroup.toAddCommMonoid.{u5} F _inst_3) _inst_9 _inst_10 (TopologicalAddGroup.to_continuousAdd.{u5} F _inst_4 (AddCommGroup.toAddGroup.{u5} F _inst_3) _inst_5)) (ContinuousLinearMap.module.{u2, u3, u1, u4, u5} πβ πβ R (Ring.toSemiring.{u2} πβ (NormedRing.toRing.{u2} πβ (NormedCommRing.toNormedRing.{u2} πβ (NormedField.toNormedCommRing.{u2} πβ _inst_7)))) (Ring.toSemiring.{u3} πβ (NormedRing.toRing.{u3} πβ (NormedCommRing.toNormedRing.{u3} πβ (NormedField.toNormedCommRing.{u3} πβ _inst_8)))) (OrderedSemiring.toSemiring.{u1} R _inst_6) E _inst_2 (AddCommGroup.toAddCommMonoid.{u4} E _inst_1) _inst_9 F _inst_4 (AddCommGroup.toAddCommMonoid.{u5} F _inst_3) _inst_10 _inst_11 _inst_14 _inst_12 Ο (TopologicalAddGroup.to_continuousAdd.{u5} F _inst_4 (AddCommGroup.toAddGroup.{u5} F _inst_3) _inst_5)) (ContinuousLinearMap.strongTopology.{u2, u3, u4, u5} πβ πβ _inst_7 _inst_8 Ο E F _inst_1 _inst_9 _inst_3 _inst_10 _inst_2 _inst_4 _inst_5 π))
+but is expected to have type
+ forall (R : Type.{u4}) {πβ : Type.{u2}} {πβ : Type.{u1}} {E : Type.{u5}} {F : Type.{u3}} [_inst_1 : AddCommGroup.{u5} E] [_inst_2 : TopologicalSpace.{u5} E] [_inst_3 : AddCommGroup.{u3} F] [_inst_4 : TopologicalSpace.{u3} F] [_inst_5 : TopologicalAddGroup.{u3} F _inst_4 (AddCommGroup.toAddGroup.{u3} F _inst_3)] [_inst_6 : OrderedSemiring.{u4} R] [_inst_7 : NormedField.{u2} πβ] [_inst_8 : NormedField.{u1} πβ] [_inst_9 : Module.{u2, u5} πβ E (DivisionSemiring.toSemiring.{u2} πβ (Semifield.toDivisionSemiring.{u2} πβ (Field.toSemifield.{u2} πβ (NormedField.toField.{u2} πβ _inst_7)))) (AddCommGroup.toAddCommMonoid.{u5} E _inst_1)] [_inst_10 : Module.{u1, u3} πβ F (DivisionSemiring.toSemiring.{u1} πβ (Semifield.toDivisionSemiring.{u1} πβ (Field.toSemifield.{u1} πβ (NormedField.toField.{u1} πβ _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} F _inst_3)] {Ο : RingHom.{u2, u1} πβ πβ (Semiring.toNonAssocSemiring.{u2} πβ (DivisionSemiring.toSemiring.{u2} πβ (Semifield.toDivisionSemiring.{u2} πβ (Field.toSemifield.{u2} πβ (NormedField.toField.{u2} πβ _inst_7))))) (Semiring.toNonAssocSemiring.{u1} πβ (DivisionSemiring.toSemiring.{u1} πβ (Semifield.toDivisionSemiring.{u1} πβ (Field.toSemifield.{u1} πβ (NormedField.toField.{u1} πβ _inst_8)))))} [_inst_11 : Module.{u4, u3} R F (OrderedSemiring.toSemiring.{u4} R _inst_6) (AddCommGroup.toAddCommMonoid.{u3} F _inst_3)] [_inst_12 : ContinuousConstSMul.{u4, u3} R F _inst_4 (SMulZeroClass.toSMul.{u4, u3} R F (NegZeroClass.toZero.{u3} F (SubNegZeroMonoid.toNegZeroClass.{u3} F (SubtractionMonoid.toSubNegZeroMonoid.{u3} F (SubtractionCommMonoid.toSubtractionMonoid.{u3} F (AddCommGroup.toDivisionAddCommMonoid.{u3} F _inst_3))))) (SMulWithZero.toSMulZeroClass.{u4, u3} R F (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (OrderedSemiring.toSemiring.{u4} R _inst_6))) (NegZeroClass.toZero.{u3} F (SubNegZeroMonoid.toNegZeroClass.{u3} F (SubtractionMonoid.toSubNegZeroMonoid.{u3} F (SubtractionCommMonoid.toSubtractionMonoid.{u3} F (AddCommGroup.toDivisionAddCommMonoid.{u3} F _inst_3))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R (OrderedSemiring.toSemiring.{u4} R _inst_6)) (NegZeroClass.toZero.{u3} F (SubNegZeroMonoid.toNegZeroClass.{u3} F (SubtractionMonoid.toSubNegZeroMonoid.{u3} F (SubtractionCommMonoid.toSubtractionMonoid.{u3} F (AddCommGroup.toDivisionAddCommMonoid.{u3} F _inst_3))))) (Module.toMulActionWithZero.{u4, u3} R F (OrderedSemiring.toSemiring.{u4} R _inst_6) (AddCommGroup.toAddCommMonoid.{u3} F _inst_3) _inst_11))))] [_inst_13 : LocallyConvexSpace.{u4, u3} R F _inst_6 (AddCommGroup.toAddCommMonoid.{u3} F _inst_3) _inst_11 _inst_4] [_inst_14 : SMulCommClass.{u1, u4, u3} πβ R F (SMulZeroClass.toSMul.{u1, u3} πβ F (NegZeroClass.toZero.{u3} F (SubNegZeroMonoid.toNegZeroClass.{u3} F (SubtractionMonoid.toSubNegZeroMonoid.{u3} F (SubtractionCommMonoid.toSubtractionMonoid.{u3} F (AddCommGroup.toDivisionAddCommMonoid.{u3} F _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u3} πβ F (CommMonoidWithZero.toZero.{u1} πβ (CommGroupWithZero.toCommMonoidWithZero.{u1} πβ (Semifield.toCommGroupWithZero.{u1} πβ (Field.toSemifield.{u1} πβ (NormedField.toField.{u1} πβ _inst_8))))) (NegZeroClass.toZero.{u3} F (SubNegZeroMonoid.toNegZeroClass.{u3} F (SubtractionMonoid.toSubNegZeroMonoid.{u3} F (SubtractionCommMonoid.toSubtractionMonoid.{u3} F (AddCommGroup.toDivisionAddCommMonoid.{u3} F _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} πβ F (Semiring.toMonoidWithZero.{u1} πβ (DivisionSemiring.toSemiring.{u1} πβ (Semifield.toDivisionSemiring.{u1} πβ (Field.toSemifield.{u1} πβ (NormedField.toField.{u1} πβ _inst_8))))) (NegZeroClass.toZero.{u3} F (SubNegZeroMonoid.toNegZeroClass.{u3} F (SubtractionMonoid.toSubNegZeroMonoid.{u3} F (SubtractionCommMonoid.toSubtractionMonoid.{u3} F (AddCommGroup.toDivisionAddCommMonoid.{u3} F _inst_3))))) (Module.toMulActionWithZero.{u1, u3} πβ F (DivisionSemiring.toSemiring.{u1} πβ (Semifield.toDivisionSemiring.{u1} πβ (Field.toSemifield.{u1} πβ (NormedField.toField.{u1} πβ _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} F _inst_3) _inst_10)))) (SMulZeroClass.toSMul.{u4, u3} R F (NegZeroClass.toZero.{u3} F (SubNegZeroMonoid.toNegZeroClass.{u3} F (SubtractionMonoid.toSubNegZeroMonoid.{u3} F (SubtractionCommMonoid.toSubtractionMonoid.{u3} F (AddCommGroup.toDivisionAddCommMonoid.{u3} F _inst_3))))) (SMulWithZero.toSMulZeroClass.{u4, u3} R F (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (OrderedSemiring.toSemiring.{u4} R _inst_6))) (NegZeroClass.toZero.{u3} F (SubNegZeroMonoid.toNegZeroClass.{u3} F (SubtractionMonoid.toSubNegZeroMonoid.{u3} F (SubtractionCommMonoid.toSubtractionMonoid.{u3} F (AddCommGroup.toDivisionAddCommMonoid.{u3} F _inst_3))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R (OrderedSemiring.toSemiring.{u4} R _inst_6)) (NegZeroClass.toZero.{u3} F (SubNegZeroMonoid.toNegZeroClass.{u3} F (SubtractionMonoid.toSubNegZeroMonoid.{u3} F (SubtractionCommMonoid.toSubtractionMonoid.{u3} F (AddCommGroup.toDivisionAddCommMonoid.{u3} F _inst_3))))) (Module.toMulActionWithZero.{u4, u3} R F (OrderedSemiring.toSemiring.{u4} R _inst_6) (AddCommGroup.toAddCommMonoid.{u3} F _inst_3) _inst_11))))] (π : Set.{u5} (Set.{u5} E)), (Set.Nonempty.{u5} (Set.{u5} E) π) -> (DirectedOn.{u5} (Set.{u5} E) (fun (x._@.Mathlib.Analysis.LocallyConvex.StrongTopology._hyg.275 : Set.{u5} E) (x._@.Mathlib.Analysis.LocallyConvex.StrongTopology._hyg.277 : Set.{u5} E) => HasSubset.Subset.{u5} (Set.{u5} E) (Set.instHasSubsetSet.{u5} E) x._@.Mathlib.Analysis.LocallyConvex.StrongTopology._hyg.275 x._@.Mathlib.Analysis.LocallyConvex.StrongTopology._hyg.277) π) -> (LocallyConvexSpace.{u4, max u3 u5} R (ContinuousLinearMap.{u2, u1, u5, u3} πβ πβ (DivisionSemiring.toSemiring.{u2} πβ (Semifield.toDivisionSemiring.{u2} πβ (Field.toSemifield.{u2} πβ (NormedField.toField.{u2} πβ _inst_7)))) (DivisionSemiring.toSemiring.{u1} πβ (Semifield.toDivisionSemiring.{u1} πβ (Field.toSemifield.{u1} πβ (NormedField.toField.{u1} πβ _inst_8)))) Ο E _inst_2 (AddCommGroup.toAddCommMonoid.{u5} E _inst_1) F _inst_4 (AddCommGroup.toAddCommMonoid.{u3} F _inst_3) _inst_9 _inst_10) _inst_6 (ContinuousLinearMap.addCommMonoid.{u2, u1, u5, u3} πβ πβ (DivisionSemiring.toSemiring.{u2} πβ (Semifield.toDivisionSemiring.{u2} πβ (Field.toSemifield.{u2} πβ (NormedField.toField.{u2} πβ _inst_7)))) (DivisionSemiring.toSemiring.{u1} πβ (Semifield.toDivisionSemiring.{u1} πβ (Field.toSemifield.{u1} πβ (NormedField.toField.{u1} πβ _inst_8)))) Ο E _inst_2 (AddCommGroup.toAddCommMonoid.{u5} E _inst_1) F _inst_4 (AddCommGroup.toAddCommMonoid.{u3} F _inst_3) _inst_9 _inst_10 (TopologicalAddGroup.toContinuousAdd.{u3} F _inst_4 (AddCommGroup.toAddGroup.{u3} F _inst_3) _inst_5)) (ContinuousLinearMap.module.{u2, u1, u4, u5, u3} πβ πβ R (DivisionSemiring.toSemiring.{u2} πβ (Semifield.toDivisionSemiring.{u2} πβ (Field.toSemifield.{u2} πβ (NormedField.toField.{u2} πβ _inst_7)))) (DivisionSemiring.toSemiring.{u1} πβ (Semifield.toDivisionSemiring.{u1} πβ (Field.toSemifield.{u1} πβ (NormedField.toField.{u1} πβ _inst_8)))) (OrderedSemiring.toSemiring.{u4} R _inst_6) E _inst_2 (AddCommGroup.toAddCommMonoid.{u5} E _inst_1) _inst_9 F _inst_4 (AddCommGroup.toAddCommMonoid.{u3} F _inst_3) _inst_10 _inst_11 _inst_14 _inst_12 Ο (TopologicalAddGroup.toContinuousAdd.{u3} F _inst_4 (AddCommGroup.toAddGroup.{u3} F _inst_3) _inst_5)) (ContinuousLinearMap.strongTopology.{u2, u1, u5, u3} πβ πβ _inst_7 _inst_8 Ο E F _inst_1 _inst_9 _inst_3 _inst_10 _inst_2 _inst_4 _inst_5 π))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.strong_topology.locally_convex_space ContinuousLinearMap.strongTopology.locallyConvexSpaceβ'. -/
theorem strongTopology.locallyConvexSpace (π : Set (Set E)) (hπβ : π.Nonempty)
(hπβ : DirectedOn (Β· β Β·) π) :
@LocallyConvexSpace R (E βSL[Ο] F) _ _ _ (strongTopology Ο F π) :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/172bf2812857f5e56938cc148b7a539f52f84ca9
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
! This file was ported from Lean 3 source module analysis.locally_convex.strong_topology
-! leanprover-community/mathlib commit b8627dbac120a9ad6267a75575ae1e070d5bff5b
+! leanprover-community/mathlib commit 47b12e7f2502f14001f891ca87fbae2b4acaed3f
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -33,25 +33,33 @@ locally convex, bounded convergence
open Topology UniformConvergence
-variable {E F : Type _}
+variable {R πβ πβ E F : Type _}
namespace ContinuousLinearMap
+variable [AddCommGroup E] [TopologicalSpace E] [AddCommGroup F] [TopologicalSpace F]
+ [TopologicalAddGroup F]
+
section General
-variable [AddCommGroup E] [Module β E] [TopologicalSpace E] [AddCommGroup F] [Module β F]
- [TopologicalSpace F] [TopologicalAddGroup F] [ContinuousConstSMul β F] [LocallyConvexSpace β F]
+variable (R)
+
+variable [OrderedSemiring R]
+
+variable [NormedField πβ] [NormedField πβ] [Module πβ E] [Module πβ F] {Ο : πβ β+* πβ}
+
+variable [Module R F] [ContinuousConstSMul R F] [LocallyConvexSpace R F] [SMulCommClass πβ R F]
theorem strongTopology.locallyConvexSpace (π : Set (Set E)) (hπβ : π.Nonempty)
(hπβ : DirectedOn (Β· β Β·) π) :
- @LocallyConvexSpace β (E βL[β] F) _ _ _ (strongTopology (RingHom.id β) F π) :=
+ @LocallyConvexSpace R (E βSL[Ο] F) _ _ _ (strongTopology Ο F π) :=
by
- letI : TopologicalSpace (E βL[β] F) := strong_topology (RingHom.id β) F π
- haveI : TopologicalAddGroup (E βL[β] F) := strong_topology.topological_add_group _ _ _
+ letI : TopologicalSpace (E βSL[Ο] F) := strong_topology Ο F π
+ haveI : TopologicalAddGroup (E βSL[Ο] F) := strong_topology.topological_add_group _ _ _
refine'
LocallyConvexSpace.ofBasisZero _ _ _ _
(strong_topology.has_basis_nhds_zero_of_basis _ _ _ hπβ hπβ
- (LocallyConvexSpace.convex_basis_zero β F))
+ (LocallyConvexSpace.convex_basis_zero R F))
_
rintro β¨S, Vβ© β¨hS, hVmem, hVconvexβ© f hf g hg a b ha hb hab x hx
exact hVconvex (hf x hx) (hg x hx) ha hb hab
@@ -61,11 +69,14 @@ end General
section BoundedSets
-variable [AddCommGroup E] [Module β E] [TopologicalSpace E] [AddCommGroup F] [Module β F]
- [TopologicalSpace F] [TopologicalAddGroup F] [ContinuousConstSMul β F] [LocallyConvexSpace β F]
+variable [OrderedSemiring R]
+
+variable [NormedField πβ] [NormedField πβ] [Module πβ E] [Module πβ F] {Ο : πβ β+* πβ}
+
+variable [Module R F] [ContinuousConstSMul R F] [LocallyConvexSpace R F] [SMulCommClass πβ R F]
-instance : LocallyConvexSpace β (E βL[β] F) :=
- strongTopology.locallyConvexSpace _ β¨β
, Bornology.isVonNBounded_empty β Eβ©
+instance : LocallyConvexSpace R (E βSL[Ο] F) :=
+ strongTopology.locallyConvexSpace R _ β¨β
, Bornology.isVonNBounded_empty πβ Eβ©
(directedOn_of_sup_mem fun _ _ => Bornology.IsVonNBounded.union)
end BoundedSets
mathlib commit https://github.com/leanprover-community/mathlib/commit/728baa2f54e6062c5879a3e397ac6bac323e506f
@@ -32,42 +32,44 @@ open Topology UniformConvergence
variable {R πβ πβ E F : Type*}
-namespace ContinuousLinearMap
-
variable [AddCommGroup E] [TopologicalSpace E] [AddCommGroup F] [TopologicalSpace F]
[TopologicalAddGroup F]
section General
+namespace UniformConvergenceCLM
+
variable (R)
variable [OrderedSemiring R]
variable [NormedField πβ] [NormedField πβ] [Module πβ E] [Module πβ F] {Ο : πβ β+* πβ}
variable [Module R F] [ContinuousConstSMul R F] [LocallyConvexSpace R F] [SMulCommClass πβ R F]
-theorem strongTopology.locallyConvexSpace (π : Set (Set E)) (hπβ : π.Nonempty)
+theorem locallyConvexSpace (π : Set (Set E)) (hπβ : π.Nonempty)
(hπβ : DirectedOn (Β· β Β·) π) :
- @LocallyConvexSpace R (E βSL[Ο] F) _ _ _ (strongTopology Ο F π) := by
- letI : TopologicalSpace (E βSL[Ο] F) := strongTopology Ο F π
- haveI : TopologicalAddGroup (E βSL[Ο] F) := strongTopology.topologicalAddGroup _ _ _
+ LocallyConvexSpace R (UniformConvergenceCLM Ο F π) := by
apply LocallyConvexSpace.ofBasisZero _ _ _ _
- (strongTopology.hasBasis_nhds_zero_of_basis _ _ _ hπβ hπβ
+ (UniformConvergenceCLM.hasBasis_nhds_zero_of_basis _ _ _ hπβ hπβ
(LocallyConvexSpace.convex_basis_zero R F)) _
rintro β¨S, Vβ© β¨_, _, hVconvexβ© f hf g hg a b ha hb hab x hx
exact hVconvex (hf x hx) (hg x hx) ha hb hab
-#align continuous_linear_map.strong_topology.locally_convex_space ContinuousLinearMap.strongTopology.locallyConvexSpace
+#align continuous_linear_map.strong_topology.locally_convex_space UniformConvergenceCLM.locallyConvexSpace
+
+end UniformConvergenceCLM
end General
section BoundedSets
+namespace ContinuousLinearMap
+
variable [OrderedSemiring R]
variable [NormedField πβ] [NormedField πβ] [Module πβ E] [Module πβ F] {Ο : πβ β+* πβ}
variable [Module R F] [ContinuousConstSMul R F] [LocallyConvexSpace R F] [SMulCommClass πβ R F]
-instance : LocallyConvexSpace R (E βSL[Ο] F) :=
- strongTopology.locallyConvexSpace R _ β¨β
, Bornology.isVonNBounded_empty πβ Eβ©
+instance instLocallyConvexSpace : LocallyConvexSpace R (E βSL[Ο] F) :=
+ UniformConvergenceCLM.locallyConvexSpace R _ β¨β
, Bornology.isVonNBounded_empty πβ Eβ©
(directedOn_of_sup_mem fun _ _ => Bornology.IsVonNBounded.union)
-end BoundedSets
-
end ContinuousLinearMap
+
+end BoundedSets
Empty lines were removed by executing the following Python script twice
import os
import re
# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
for filename in files:
if filename.endswith('.lean'):
file_path = os.path.join(dir_path, filename)
# Open the file and read its contents
with open(file_path, 'r') as file:
content = file.read()
# Use a regular expression to replace sequences of "variable" lines separated by empty lines
# with sequences without empty lines
modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)
# Write the modified content back to the file
with open(file_path, 'w') as file:
file.write(modified_content)
@@ -40,11 +40,8 @@ variable [AddCommGroup E] [TopologicalSpace E] [AddCommGroup F] [TopologicalSpac
section General
variable (R)
-
variable [OrderedSemiring R]
-
variable [NormedField πβ] [NormedField πβ] [Module πβ E] [Module πβ F] {Ο : πβ β+* πβ}
-
variable [Module R F] [ContinuousConstSMul R F] [LocallyConvexSpace R F] [SMulCommClass πβ R F]
theorem strongTopology.locallyConvexSpace (π : Set (Set E)) (hπβ : π.Nonempty)
@@ -64,9 +61,7 @@ end General
section BoundedSets
variable [OrderedSemiring R]
-
variable [NormedField πβ] [NormedField πβ] [Module πβ E] [Module πβ F] {Ο : πβ β+* πβ}
-
variable [Module R F] [ContinuousConstSMul R F] [LocallyConvexSpace R F] [SMulCommClass πβ R F]
instance : LocallyConvexSpace R (E βSL[Ο] F) :=
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -30,7 +30,7 @@ locally convex, bounded convergence
open Topology UniformConvergence
-variable {R πβ πβ E F : Type _}
+variable {R πβ πβ E F : Type*}
namespace ContinuousLinearMap
@@ -2,15 +2,12 @@
Copyright (c) 2022 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
-
-! This file was ported from Lean 3 source module analysis.locally_convex.strong_topology
-! leanprover-community/mathlib commit 47b12e7f2502f14001f891ca87fbae2b4acaed3f
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Topology.Algebra.Module.StrongTopology
import Mathlib.Topology.Algebra.Module.LocallyConvex
+#align_import analysis.locally_convex.strong_topology from "leanprover-community/mathlib"@"47b12e7f2502f14001f891ca87fbae2b4acaed3f"
+
/-!
# Local convexity of the strong topology
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