topology.algebra.uniform_filter_basis
⟷
Mathlib.Topology.Algebra.UniformFilterBasis
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
@@ -46,8 +46,8 @@ protected theorem uniformAddGroup : @UniformAddGroup G B.UniformSpace _ :=
#align add_group_filter_basis.uniform_add_group AddGroupFilterBasis.uniformAddGroup
-/
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » M) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » M) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x y «expr ∈ » M) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x y «expr ∈ » M) -/
#print AddGroupFilterBasis.cauchy_iff /-
theorem cauchy_iff {F : Filter G} :
@Cauchy G B.UniformSpace F ↔
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2021 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
-import Mathbin.Topology.Algebra.FilterBasis
-import Mathbin.Topology.Algebra.UniformGroup
+import Topology.Algebra.FilterBasis
+import Topology.Algebra.UniformGroup
#align_import topology.algebra.uniform_filter_basis from "leanprover-community/mathlib"@"19cb3751e5e9b3d97adb51023949c50c13b5fdfd"
@@ -46,8 +46,8 @@ protected theorem uniformAddGroup : @UniformAddGroup G B.UniformSpace _ :=
#align add_group_filter_basis.uniform_add_group AddGroupFilterBasis.uniformAddGroup
-/
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » M) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » M) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » M) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » M) -/
#print AddGroupFilterBasis.cauchy_iff /-
theorem cauchy_iff {F : Filter G} :
@Cauchy G B.UniformSpace F ↔
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2021 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-
-! This file was ported from Lean 3 source module topology.algebra.uniform_filter_basis
-! leanprover-community/mathlib commit 19cb3751e5e9b3d97adb51023949c50c13b5fdfd
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Topology.Algebra.FilterBasis
import Mathbin.Topology.Algebra.UniformGroup
+#align_import topology.algebra.uniform_filter_basis from "leanprover-community/mathlib"@"19cb3751e5e9b3d97adb51023949c50c13b5fdfd"
+
/-!
# Uniform properties of neighborhood bases in topological algebra
@@ -49,8 +46,8 @@ protected theorem uniformAddGroup : @UniformAddGroup G B.UniformSpace _ :=
#align add_group_filter_basis.uniform_add_group AddGroupFilterBasis.uniformAddGroup
-/
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » M) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » M) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » M) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » M) -/
#print AddGroupFilterBasis.cauchy_iff /-
theorem cauchy_iff {F : Filter G} :
@Cauchy G B.UniformSpace F ↔
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -51,6 +51,7 @@ protected theorem uniformAddGroup : @UniformAddGroup G B.UniformSpace _ :=
/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » M) -/
/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » M) -/
+#print AddGroupFilterBasis.cauchy_iff /-
theorem cauchy_iff {F : Filter G} :
@Cauchy G B.UniformSpace F ↔
F.ne_bot ∧ ∀ U ∈ B, ∃ M ∈ F, ∀ (x) (_ : x ∈ M) (y) (_ : y ∈ M), y - x ∈ U :=
@@ -63,6 +64,7 @@ theorem cauchy_iff {F : Filter G} :
change tendsto _ _ _ ↔ _
simp [(basis_sets F).prod_self.tendsto_iffₓ B.nhds_zero_has_basis, @forall_swap (_ ∈ _) G]
#align add_group_filter_basis.cauchy_iff AddGroupFilterBasis.cauchy_iff
+-/
end AddGroupFilterBasis
mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004
@@ -49,8 +49,8 @@ protected theorem uniformAddGroup : @UniformAddGroup G B.UniformSpace _ :=
#align add_group_filter_basis.uniform_add_group AddGroupFilterBasis.uniformAddGroup
-/
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » M) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » M) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » M) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » M) -/
theorem cauchy_iff {F : Filter G} :
@Cauchy G B.UniformSpace F ↔
F.ne_bot ∧ ∀ U ∈ B, ∃ M ∈ F, ∀ (x) (_ : x ∈ M) (y) (_ : y ∈ M), y - x ∈ U :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -58,7 +58,7 @@ theorem cauchy_iff {F : Filter G} :
letI := B.uniform_space
haveI := B.uniform_add_group
suffices F ×ᶠ F ≤ 𝓤 G ↔ ∀ U ∈ B, ∃ M ∈ F, ∀ (x) (_ : x ∈ M) (y) (_ : y ∈ M), y - x ∈ U by
- constructor <;> rintro ⟨h', h⟩ <;> refine' ⟨h', _⟩ <;> [rwa [← this];rwa [this]]
+ constructor <;> rintro ⟨h', h⟩ <;> refine' ⟨h', _⟩ <;> [rwa [← this]; rwa [this]]
rw [uniformity_eq_comap_nhds_zero G, ← map_le_iff_le_comap]
change tendsto _ _ _ ↔ _
simp [(basis_sets F).prod_self.tendsto_iffₓ B.nhds_zero_has_basis, @forall_swap (_ ∈ _) G]
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -25,7 +25,7 @@ The only result so far is a characterization of Cauchy filters in topological gr
-/
-open uniformity Filter
+open scoped uniformity Filter
open Filter
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -49,12 +49,6 @@ protected theorem uniformAddGroup : @UniformAddGroup G B.UniformSpace _ :=
#align add_group_filter_basis.uniform_add_group AddGroupFilterBasis.uniformAddGroup
-/
-/- warning: add_group_filter_basis.cauchy_iff -> AddGroupFilterBasis.cauchy_iff is a dubious translation:
-lean 3 declaration is
- forall {G : Type.{u1}} [_inst_1 : AddCommGroup.{u1} G] (B : AddGroupFilterBasis.{u1} G (AddCommGroup.toAddGroup.{u1} G _inst_1)) {F : Filter.{u1} G}, Iff (Cauchy.{u1} G (AddGroupFilterBasis.uniformSpace.{u1} G _inst_1 B) F) (And (Filter.NeBot.{u1} G F) (forall (U : Set.{u1} G), (Membership.Mem.{u1, u1} (Set.{u1} G) (AddGroupFilterBasis.{u1} G (AddCommGroup.toAddGroup.{u1} G _inst_1)) (AddGroupFilterBasis.hasMem.{u1} G (AddCommGroup.toAddGroup.{u1} G _inst_1)) U B) -> (Exists.{succ u1} (Set.{u1} G) (fun (M : Set.{u1} G) => Exists.{0} (Membership.Mem.{u1, u1} (Set.{u1} G) (Filter.{u1} G) (Filter.hasMem.{u1} G) M F) (fun (H : Membership.Mem.{u1, u1} (Set.{u1} G) (Filter.{u1} G) (Filter.hasMem.{u1} G) M F) => forall (x : G), (Membership.Mem.{u1, u1} G (Set.{u1} G) (Set.hasMem.{u1} G) x M) -> (forall (y : G), (Membership.Mem.{u1, u1} G (Set.{u1} G) (Set.hasMem.{u1} G) y M) -> (Membership.Mem.{u1, u1} G (Set.{u1} G) (Set.hasMem.{u1} G) (HSub.hSub.{u1, u1, u1} G G G (instHSub.{u1} G (SubNegMonoid.toHasSub.{u1} G (AddGroup.toSubNegMonoid.{u1} G (AddCommGroup.toAddGroup.{u1} G _inst_1)))) y x) U)))))))
-but is expected to have type
- forall {G : Type.{u1}} [_inst_1 : AddCommGroup.{u1} G] (B : AddGroupFilterBasis.{u1} G (AddCommGroup.toAddGroup.{u1} G _inst_1)) {F : Filter.{u1} G}, Iff (Cauchy.{u1} G (AddGroupFilterBasis.uniformSpace.{u1} G _inst_1 B) F) (And (Filter.NeBot.{u1} G F) (forall (U : Set.{u1} G), (Membership.mem.{u1, u1} (Set.{u1} G) (AddGroupFilterBasis.{u1} G (AddCommGroup.toAddGroup.{u1} G _inst_1)) (AddGroupFilterBasis.instMembershipSetAddGroupFilterBasis.{u1} G (AddCommGroup.toAddGroup.{u1} G _inst_1)) U B) -> (Exists.{succ u1} (Set.{u1} G) (fun (M : Set.{u1} G) => And (Membership.mem.{u1, u1} (Set.{u1} G) (Filter.{u1} G) (instMembershipSetFilter.{u1} G) M F) (forall (x : G), (Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x M) -> (forall (y : G), (Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) y M) -> (Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) (HSub.hSub.{u1, u1, u1} G G G (instHSub.{u1} G (SubNegMonoid.toSub.{u1} G (AddGroup.toSubNegMonoid.{u1} G (AddCommGroup.toAddGroup.{u1} G _inst_1)))) y x) U)))))))
-Case conversion may be inaccurate. Consider using '#align add_group_filter_basis.cauchy_iff AddGroupFilterBasis.cauchy_iffₓ'. -/
/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » M) -/
/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » M) -/
theorem cauchy_iff {F : Filter G} :
mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b
@@ -64,7 +64,7 @@ theorem cauchy_iff {F : Filter G} :
letI := B.uniform_space
haveI := B.uniform_add_group
suffices F ×ᶠ F ≤ 𝓤 G ↔ ∀ U ∈ B, ∃ M ∈ F, ∀ (x) (_ : x ∈ M) (y) (_ : y ∈ M), y - x ∈ U by
- constructor <;> rintro ⟨h', h⟩ <;> refine' ⟨h', _⟩ <;> [rwa [← this], rwa [this]]
+ constructor <;> rintro ⟨h', h⟩ <;> refine' ⟨h', _⟩ <;> [rwa [← this];rwa [this]]
rw [uniformity_eq_comap_nhds_zero G, ← map_le_iff_le_comap]
change tendsto _ _ _ ↔ _
simp [(basis_sets F).prod_self.tendsto_iffₓ B.nhds_zero_has_basis, @forall_swap (_ ∈ _) G]
mathlib commit https://github.com/leanprover-community/mathlib/commit/284fdd2962e67d2932fa3a79ce19fcf92d38e228
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
! This file was ported from Lean 3 source module topology.algebra.uniform_filter_basis
-! leanprover-community/mathlib commit 531db2ef0fdddf8b3c8dcdcd87138fe969e1a81a
+! leanprover-community/mathlib commit 19cb3751e5e9b3d97adb51023949c50c13b5fdfd
! 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.UniformGroup
/-!
# Uniform properties of neighborhood bases in topological algebra
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
This files contains properties of filter bases on algebraic structures that also require the theory
of uniform spaces.
mathlib commit https://github.com/leanprover-community/mathlib/commit/06a655b5fcfbda03502f9158bbf6c0f1400886f9
@@ -30,18 +30,28 @@ namespace AddGroupFilterBasis
variable {G : Type _} [AddCommGroup G] (B : AddGroupFilterBasis G)
+#print AddGroupFilterBasis.uniformSpace /-
/-- The uniform space structure associated to an abelian group filter basis via the associated
topological abelian group structure. -/
protected def uniformSpace : UniformSpace G :=
@TopologicalAddGroup.toUniformSpace G _ B.topology B.isTopologicalAddGroup
#align add_group_filter_basis.uniform_space AddGroupFilterBasis.uniformSpace
+-/
+#print AddGroupFilterBasis.uniformAddGroup /-
/-- The uniform space structure associated to an abelian group filter basis via the associated
topological abelian group structure is compatible with its group structure. -/
protected theorem uniformAddGroup : @UniformAddGroup G B.UniformSpace _ :=
@comm_topologicalAddGroup_is_uniform G _ B.topology B.isTopologicalAddGroup
#align add_group_filter_basis.uniform_add_group AddGroupFilterBasis.uniformAddGroup
+-/
+/- warning: add_group_filter_basis.cauchy_iff -> AddGroupFilterBasis.cauchy_iff is a dubious translation:
+lean 3 declaration is
+ forall {G : Type.{u1}} [_inst_1 : AddCommGroup.{u1} G] (B : AddGroupFilterBasis.{u1} G (AddCommGroup.toAddGroup.{u1} G _inst_1)) {F : Filter.{u1} G}, Iff (Cauchy.{u1} G (AddGroupFilterBasis.uniformSpace.{u1} G _inst_1 B) F) (And (Filter.NeBot.{u1} G F) (forall (U : Set.{u1} G), (Membership.Mem.{u1, u1} (Set.{u1} G) (AddGroupFilterBasis.{u1} G (AddCommGroup.toAddGroup.{u1} G _inst_1)) (AddGroupFilterBasis.hasMem.{u1} G (AddCommGroup.toAddGroup.{u1} G _inst_1)) U B) -> (Exists.{succ u1} (Set.{u1} G) (fun (M : Set.{u1} G) => Exists.{0} (Membership.Mem.{u1, u1} (Set.{u1} G) (Filter.{u1} G) (Filter.hasMem.{u1} G) M F) (fun (H : Membership.Mem.{u1, u1} (Set.{u1} G) (Filter.{u1} G) (Filter.hasMem.{u1} G) M F) => forall (x : G), (Membership.Mem.{u1, u1} G (Set.{u1} G) (Set.hasMem.{u1} G) x M) -> (forall (y : G), (Membership.Mem.{u1, u1} G (Set.{u1} G) (Set.hasMem.{u1} G) y M) -> (Membership.Mem.{u1, u1} G (Set.{u1} G) (Set.hasMem.{u1} G) (HSub.hSub.{u1, u1, u1} G G G (instHSub.{u1} G (SubNegMonoid.toHasSub.{u1} G (AddGroup.toSubNegMonoid.{u1} G (AddCommGroup.toAddGroup.{u1} G _inst_1)))) y x) U)))))))
+but is expected to have type
+ forall {G : Type.{u1}} [_inst_1 : AddCommGroup.{u1} G] (B : AddGroupFilterBasis.{u1} G (AddCommGroup.toAddGroup.{u1} G _inst_1)) {F : Filter.{u1} G}, Iff (Cauchy.{u1} G (AddGroupFilterBasis.uniformSpace.{u1} G _inst_1 B) F) (And (Filter.NeBot.{u1} G F) (forall (U : Set.{u1} G), (Membership.mem.{u1, u1} (Set.{u1} G) (AddGroupFilterBasis.{u1} G (AddCommGroup.toAddGroup.{u1} G _inst_1)) (AddGroupFilterBasis.instMembershipSetAddGroupFilterBasis.{u1} G (AddCommGroup.toAddGroup.{u1} G _inst_1)) U B) -> (Exists.{succ u1} (Set.{u1} G) (fun (M : Set.{u1} G) => And (Membership.mem.{u1, u1} (Set.{u1} G) (Filter.{u1} G) (instMembershipSetFilter.{u1} G) M F) (forall (x : G), (Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x M) -> (forall (y : G), (Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) y M) -> (Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) (HSub.hSub.{u1, u1, u1} G G G (instHSub.{u1} G (SubNegMonoid.toSub.{u1} G (AddGroup.toSubNegMonoid.{u1} G (AddCommGroup.toAddGroup.{u1} G _inst_1)))) y x) U)))))))
+Case conversion may be inaccurate. Consider using '#align add_group_filter_basis.cauchy_iff AddGroupFilterBasis.cauchy_iffₓ'. -/
/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » M) -/
/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » M) -/
theorem cauchy_iff {F : Filter G} :
mathlib commit https://github.com/leanprover-community/mathlib/commit/06a655b5fcfbda03502f9158bbf6c0f1400886f9
@@ -33,13 +33,13 @@ variable {G : Type _} [AddCommGroup G] (B : AddGroupFilterBasis G)
/-- The uniform space structure associated to an abelian group filter basis via the associated
topological abelian group structure. -/
protected def uniformSpace : UniformSpace G :=
- @TopologicalAddGroup.toUniformSpace G _ B.topology B.is_topological_add_group
+ @TopologicalAddGroup.toUniformSpace G _ B.topology B.isTopologicalAddGroup
#align add_group_filter_basis.uniform_space AddGroupFilterBasis.uniformSpace
/-- The uniform space structure associated to an abelian group filter basis via the associated
topological abelian group structure is compatible with its group structure. -/
protected theorem uniformAddGroup : @UniformAddGroup G B.UniformSpace _ :=
- @comm_topologicalAddGroup_is_uniform G _ B.topology B.is_topological_add_group
+ @comm_topologicalAddGroup_is_uniform G _ B.topology B.isTopologicalAddGroup
#align add_group_filter_basis.uniform_add_group AddGroupFilterBasis.uniformAddGroup
/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » M) -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442
@@ -42,8 +42,8 @@ protected theorem uniformAddGroup : @UniformAddGroup G B.UniformSpace _ :=
@comm_topologicalAddGroup_is_uniform G _ B.topology B.is_topological_add_group
#align add_group_filter_basis.uniform_add_group AddGroupFilterBasis.uniformAddGroup
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x y «expr ∈ » M) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x y «expr ∈ » M) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » M) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » M) -/
theorem cauchy_iff {F : Filter G} :
@Cauchy G B.UniformSpace F ↔
F.ne_bot ∧ ∀ U ∈ B, ∃ M ∈ F, ∀ (x) (_ : x ∈ M) (y) (_ : y ∈ M), y - x ∈ U :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/eb0cb4511aaef0da2462207b67358a0e1fe1e2ee
@@ -39,7 +39,7 @@ protected def uniformSpace : UniformSpace G :=
/-- The uniform space structure associated to an abelian group filter basis via the associated
topological abelian group structure is compatible with its group structure. -/
protected theorem uniformAddGroup : @UniformAddGroup G B.UniformSpace _ :=
- @topological_add_commGroup_is_uniform G _ B.topology B.is_topological_add_group
+ @comm_topologicalAddGroup_is_uniform G _ B.topology B.is_topological_add_group
#align add_group_filter_basis.uniform_add_group AddGroupFilterBasis.uniformAddGroup
/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x y «expr ∈ » M) -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
∃ x ∈ s, _
instead of ∃ (x) (_ : x ∈ s), _
(#9184)
Search for [∀∃].*(_
and manually replace some occurrences with more readable versions.
In case of ∀
, the new expressions are defeq to the old ones.
In case of ∃
, they differ by exists_prop
.
In some rare cases, golf proofs that needed fixing.
@@ -41,10 +41,10 @@ protected theorem uniformAddGroup : @UniformAddGroup G B.uniformSpace _ :=
theorem cauchy_iff {F : Filter G} :
@Cauchy G B.uniformSpace F ↔
- F.NeBot ∧ ∀ U ∈ B, ∃ M ∈ F, ∀ (x) (_ : x ∈ M) (y) (_ : y ∈ M), y - x ∈ U := by
+ F.NeBot ∧ ∀ U ∈ B, ∃ M ∈ F, ∀ᵉ (x ∈ M) (y ∈ M), y - x ∈ U := by
letI := B.uniformSpace
haveI := B.uniformAddGroup
- suffices F ×ˢ F ≤ uniformity G ↔ ∀ U ∈ B, ∃ M ∈ F, ∀ (x) (_ : x ∈ M) (y) (_ : y ∈ M), y - x ∈ U by
+ suffices F ×ˢ F ≤ uniformity G ↔ ∀ U ∈ B, ∃ M ∈ F, ∀ᵉ (x ∈ M) (y ∈ M), y - x ∈ U by
constructor <;> rintro ⟨h', h⟩ <;> refine' ⟨h', _⟩ <;> [rwa [← this]; rwa [this]]
rw [uniformity_eq_comap_nhds_zero G, ← map_le_iff_le_comap]
change Tendsto _ _ _ ↔ _
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -25,7 +25,7 @@ open Filter
namespace AddGroupFilterBasis
-variable {G : Type _} [AddCommGroup G] (B : AddGroupFilterBasis G)
+variable {G : Type*} [AddCommGroup G] (B : AddGroupFilterBasis G)
/-- The uniform space structure associated to an abelian group filter basis via the associated
topological abelian group structure. -/
@@ -2,15 +2,12 @@
Copyright (c) 2021 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-
-! This file was ported from Lean 3 source module topology.algebra.uniform_filter_basis
-! leanprover-community/mathlib commit 531db2ef0fdddf8b3c8dcdcd87138fe969e1a81a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Topology.Algebra.FilterBasis
import Mathlib.Topology.Algebra.UniformGroup
+#align_import topology.algebra.uniform_filter_basis from "leanprover-community/mathlib"@"531db2ef0fdddf8b3c8dcdcd87138fe969e1a81a"
+
/-!
# Uniform properties of neighborhood bases in topological algebra
SProd
to implement overloaded notation · ×ˢ ·
(#4200)
Currently, the following notations are changed from · ×ˢ ·
because Lean 4 can't deal with ambiguous notations.
| Definition | Notation |
| :
Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: Chris Hughes <chrishughes24@gmail.com>
@@ -47,7 +47,7 @@ theorem cauchy_iff {F : Filter G} :
F.NeBot ∧ ∀ U ∈ B, ∃ M ∈ F, ∀ (x) (_ : x ∈ M) (y) (_ : y ∈ M), y - x ∈ U := by
letI := B.uniformSpace
haveI := B.uniformAddGroup
- suffices F ×ᶠ F ≤ uniformity G ↔ ∀ U ∈ B, ∃ M ∈ F, ∀ (x) (_ : x ∈ M) (y) (_ : y ∈ M), y - x ∈ U by
+ suffices F ×ˢ F ≤ uniformity G ↔ ∀ U ∈ B, ∃ M ∈ F, ∀ (x) (_ : x ∈ M) (y) (_ : y ∈ M), y - x ∈ U by
constructor <;> rintro ⟨h', h⟩ <;> refine' ⟨h', _⟩ <;> [rwa [← this]; rwa [this]]
rw [uniformity_eq_comap_nhds_zero G, ← map_le_iff_le_comap]
change Tendsto _ _ _ ↔ _
The main breaking change is that tac <;> [t1, t2]
is now written tac <;> [t1; t2]
, to avoid clashing with tactics like cases
and use
that take comma-separated lists.
@@ -48,7 +48,7 @@ theorem cauchy_iff {F : Filter G} :
letI := B.uniformSpace
haveI := B.uniformAddGroup
suffices F ×ᶠ F ≤ uniformity G ↔ ∀ U ∈ B, ∃ M ∈ F, ∀ (x) (_ : x ∈ M) (y) (_ : y ∈ M), y - x ∈ U by
- constructor <;> rintro ⟨h', h⟩ <;> refine' ⟨h', _⟩ <;> [rwa [← this], rwa [this]]
+ constructor <;> rintro ⟨h', h⟩ <;> refine' ⟨h', _⟩ <;> [rwa [← this]; rwa [this]]
rw [uniformity_eq_comap_nhds_zero G, ← map_le_iff_le_comap]
change Tendsto _ _ _ ↔ _
simp [(basis_sets F).prod_self.tendsto_iff B.nhds_zero_hasBasis, @forall_swap (_ ∈ _) G]
The unported dependencies are