topology.metric_space.cau_seq_filter | Mathlib porting status

Changes since the initial port

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

Changes in mathlib3

f2ce6086

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

10bf4f82

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -61,7 +61,7 @@ theorem CauchySeq.isCauSeq {f : ℕ → β} (hf : CauchySeq f) : IsCauSeq norm f
   cases' cauchy_iff.1 hf with hf1 hf2
   intro ε hε
   rcases hf2 {x | dist x.1 x.2 < ε} (dist_mem_uniformity hε) with ⟨t, ⟨ht, htsub⟩⟩
-  simp at ht ; cases' ht with N hN
+  simp at ht; cases' ht with N hN
   exists N
   intro j hj
   rw [← dist_eq_norm]
@@ -81,7 +81,7 @@ theorem CauSeq.cauchySeq (f : CauSeq β norm) : CauchySeq f :=
   constructor
   · exists N; intro b hb; exists b; simp [hb]
   · rintro ⟨a, b⟩ ⟨⟨a', ⟨ha'1, ha'2⟩⟩, ⟨b', ⟨hb'1, hb'2⟩⟩⟩
-    dsimp at ha'1 ha'2 hb'1 hb'2 
+    dsimp at ha'1 ha'2 hb'1 hb'2
     rw [← ha'2, ← hb'2]
     apply hεs
     rw [dist_eq_norm]

10bf4f82

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Robert Y. Lewis, Sébastien Gouëzel
 -/
-import Mathbin.Analysis.Normed.Field.Basic
+import Analysis.Normed.Field.Basic
 
 #align_import topology.metric_space.cau_seq_filter from "leanprover-community/mathlib"@"10bf4f825ad729c5653adc039dafa3622e7f93c9"

10bf4f82

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Robert Y. Lewis, Sébastien Gouëzel
-
-! This file was ported from Lean 3 source module topology.metric_space.cau_seq_filter
-! leanprover-community/mathlib commit 10bf4f825ad729c5653adc039dafa3622e7f93c9
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Normed.Field.Basic
 
+#align_import topology.metric_space.cau_seq_filter from "leanprover-community/mathlib"@"10bf4f825ad729c5653adc039dafa3622e7f93c9"
+
 /-!
 # Completeness in terms of `cauchy` filters vs `is_cau_seq` sequences

10bf4f82

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -30,6 +30,7 @@ open scoped Topology Classical
 
 variable {β : Type v}
 
+#print CauSeq.tendsto_limit /-
 theorem CauSeq.tendsto_limit [NormedRing β] [hn : IsAbsoluteValue (norm : β → ℝ)]
     (f : CauSeq β norm) [CauSeq.IsComplete β norm] : Tendsto f atTop (𝓝 f.lim) :=
   tendsto_nhds.mpr
@@ -44,6 +45,7 @@ theorem CauSeq.tendsto_limit [NormedRing β] [hn : IsAbsoluteValue (norm : β 
       dsimp [Metric.ball]; rw [dist_comm, dist_eq_norm]
       solve_by_elim)
 #align cau_seq.tendsto_limit CauSeq.tendsto_limit
+-/
 
 variable [NormedField β]
 
@@ -56,6 +58,7 @@ variable [NormedField β]
 -/
 open Metric
 
+#print CauchySeq.isCauSeq /-
 theorem CauchySeq.isCauSeq {f : ℕ → β} (hf : CauchySeq f) : IsCauSeq norm f :=
   by
   cases' cauchy_iff.1 hf with hf1 hf2
@@ -68,7 +71,9 @@ theorem CauchySeq.isCauSeq {f : ℕ → β} (hf : CauchySeq f) : IsCauSeq norm f
   apply @htsub (f j, f N)
   apply Set.mk_mem_prod <;> solve_by_elim [le_refl]
 #align cauchy_seq.is_cau_seq CauchySeq.isCauSeq
+-/
 
+#print CauSeq.cauchySeq /-
 theorem CauSeq.cauchySeq (f : CauSeq β norm) : CauchySeq f :=
   by
   refine' cauchy_iff.2 ⟨by infer_instance, fun s hs => _⟩
@@ -85,13 +90,17 @@ theorem CauSeq.cauchySeq (f : CauSeq β norm) : CauchySeq f :=
     rw [dist_eq_norm]
     apply hN <;> assumption
 #align cau_seq.cauchy_seq CauSeq.cauchySeq
+-/
 
+#print isCauSeq_iff_cauchySeq /-
 /-- In a normed field, `cau_seq` coincides with the usual notion of Cauchy sequences. -/
 theorem isCauSeq_iff_cauchySeq {α : Type u} [NormedField α] {u : ℕ → α} :
     IsCauSeq norm u ↔ CauchySeq u :=
   ⟨fun h => CauSeq.cauchySeq ⟨u, h⟩, fun h => h.IsCauSeq⟩
 #align cau_seq_iff_cauchy_seq isCauSeq_iff_cauchySeq
+-/
 
+#print completeSpace_of_cauSeq_isComplete /-
 -- see Note [lower instance priority]
 /-- A complete normed field is complete as a metric space, as Cauchy sequences converge by
 assumption and this suffices to characterize completeness. -/
@@ -107,4 +116,5 @@ instance (priority := 100) completeSpace_of_cauSeq_isComplete [CauSeq.IsComplete
   exists N
   simpa [dist_eq_norm] using hN
 #align complete_space_of_cau_seq_complete completeSpace_of_cauSeq_isComplete
+-/

10bf4f82

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -60,7 +60,7 @@ theorem CauchySeq.isCauSeq {f : ℕ → β} (hf : CauchySeq f) : IsCauSeq norm f
   by
   cases' cauchy_iff.1 hf with hf1 hf2
   intro ε hε
-  rcases hf2 { x | dist x.1 x.2 < ε } (dist_mem_uniformity hε) with ⟨t, ⟨ht, htsub⟩⟩
+  rcases hf2 {x | dist x.1 x.2 < ε} (dist_mem_uniformity hε) with ⟨t, ⟨ht, htsub⟩⟩
   simp at ht ; cases' ht with N hN
   exists N
   intro j hj
@@ -74,7 +74,7 @@ theorem CauSeq.cauchySeq (f : CauSeq β norm) : CauchySeq f :=
   refine' cauchy_iff.2 ⟨by infer_instance, fun s hs => _⟩
   rcases mem_uniformity_dist.1 hs with ⟨ε, ⟨hε, hεs⟩⟩
   cases' CauSeq.cauchy₂ f hε with N hN
-  exists { n | n ≥ N }.image f
+  exists {n | n ≥ N}.image f
   simp only [exists_prop, mem_at_top_sets, mem_map, mem_image, ge_iff_le, mem_set_of_eq]
   constructor
   · exists N; intro b hb; exists b; simp [hb]

10bf4f82

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -61,7 +61,7 @@ theorem CauchySeq.isCauSeq {f : ℕ → β} (hf : CauchySeq f) : IsCauSeq norm f
   cases' cauchy_iff.1 hf with hf1 hf2
   intro ε hε
   rcases hf2 { x | dist x.1 x.2 < ε } (dist_mem_uniformity hε) with ⟨t, ⟨ht, htsub⟩⟩
-  simp at ht; cases' ht with N hN
+  simp at ht ; cases' ht with N hN
   exists N
   intro j hj
   rw [← dist_eq_norm]
@@ -79,7 +79,7 @@ theorem CauSeq.cauchySeq (f : CauSeq β norm) : CauchySeq f :=
   constructor
   · exists N; intro b hb; exists b; simp [hb]
   · rintro ⟨a, b⟩ ⟨⟨a', ⟨ha'1, ha'2⟩⟩, ⟨b', ⟨hb'1, hb'2⟩⟩⟩
-    dsimp at ha'1 ha'2 hb'1 hb'2
+    dsimp at ha'1 ha'2 hb'1 hb'2 
     rw [← ha'2, ← hb'2]
     apply hεs
     rw [dist_eq_norm]

10bf4f82

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -26,7 +26,7 @@ universe u v
 
 open Set Filter
 
-open Topology Classical
+open scoped Topology Classical
 
 variable {β : Type v}

10bf4f82

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -30,12 +30,6 @@ open Topology Classical
 
 variable {β : Type v}
 
-/- warning: cau_seq.tendsto_limit -> CauSeq.tendsto_limit is a dubious translation:
-lean 3 declaration is
-  forall {β : Type.{u1}} [_inst_1 : NormedRing.{u1} β] [hn : IsAbsoluteValue.{0, u1} Real Real.orderedSemiring β (Ring.toSemiring.{u1} β (NormedRing.toRing.{u1} β _inst_1)) (Norm.norm.{u1} β (NormedRing.toHasNorm.{u1} β _inst_1))] (f : CauSeq.{0, u1} Real Real.linearOrderedField β (NormedRing.toRing.{u1} β _inst_1) (Norm.norm.{u1} β (NormedRing.toHasNorm.{u1} β _inst_1))) [_inst_2 : CauSeq.IsComplete.{0, u1} Real Real.linearOrderedField β (NormedRing.toRing.{u1} β _inst_1) (Norm.norm.{u1} β (NormedRing.toHasNorm.{u1} β _inst_1)) hn], Filter.Tendsto.{0, u1} Nat β (coeFn.{succ u1, succ u1} (CauSeq.{0, u1} Real Real.linearOrderedField β (NormedRing.toRing.{u1} β _inst_1) (Norm.norm.{u1} β (NormedRing.toHasNorm.{u1} β _inst_1))) (fun (_x : CauSeq.{0, u1} Real Real.linearOrderedField β (NormedRing.toRing.{u1} β _inst_1) (Norm.norm.{u1} β (NormedRing.toHasNorm.{u1} β _inst_1))) => Nat -> β) (CauSeq.hasCoeToFun.{0, u1} Real β Real.linearOrderedField (NormedRing.toRing.{u1} β _inst_1) (Norm.norm.{u1} β (NormedRing.toHasNorm.{u1} β _inst_1))) f) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} β (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (SeminormedRing.toPseudoMetricSpace.{u1} β (NormedRing.toSeminormedRing.{u1} β _inst_1)))) (CauSeq.lim.{0, u1} Real Real.linearOrderedField β (NormedRing.toRing.{u1} β _inst_1) (Norm.norm.{u1} β (NormedRing.toHasNorm.{u1} β _inst_1)) hn _inst_2 f))
-but is expected to have type
-  forall {β : Type.{u1}} [_inst_1 : NormedRing.{u1} β] [hn : IsAbsoluteValue.{0, u1} Real Real.orderedSemiring β (Ring.toSemiring.{u1} β (NormedRing.toRing.{u1} β _inst_1)) (Norm.norm.{u1} β (NormedRing.toNorm.{u1} β _inst_1))] (f : CauSeq.{0, u1} Real Real.instLinearOrderedFieldReal β (NormedRing.toRing.{u1} β _inst_1) (Norm.norm.{u1} β (NormedRing.toNorm.{u1} β _inst_1))) [_inst_2 : CauSeq.IsComplete.{0, u1} Real Real.instLinearOrderedFieldReal β (NormedRing.toRing.{u1} β _inst_1) (Norm.norm.{u1} β (NormedRing.toNorm.{u1} β _inst_1)) hn], Filter.Tendsto.{0, u1} Nat β (Subtype.val.{succ u1} (Nat -> β) (fun (f : Nat -> β) => IsCauSeq.{0, u1} Real Real.instLinearOrderedFieldReal β (NormedRing.toRing.{u1} β _inst_1) (Norm.norm.{u1} β (NormedRing.toNorm.{u1} β _inst_1)) f) f) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} β (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (SeminormedRing.toPseudoMetricSpace.{u1} β (NormedRing.toSeminormedRing.{u1} β _inst_1)))) (CauSeq.lim.{0, u1} Real Real.instLinearOrderedFieldReal β (NormedRing.toRing.{u1} β _inst_1) (Norm.norm.{u1} β (NormedRing.toNorm.{u1} β _inst_1)) hn _inst_2 f))
-Case conversion may be inaccurate. Consider using '#align cau_seq.tendsto_limit CauSeq.tendsto_limitₓ'. -/
 theorem CauSeq.tendsto_limit [NormedRing β] [hn : IsAbsoluteValue (norm : β → ℝ)]
     (f : CauSeq β norm) [CauSeq.IsComplete β norm] : Tendsto f atTop (𝓝 f.lim) :=
   tendsto_nhds.mpr
@@ -62,12 +56,6 @@ variable [NormedField β]
 -/
 open Metric
 
-/- warning: cauchy_seq.is_cau_seq -> CauchySeq.isCauSeq is a dubious translation:
-lean 3 declaration is
-  forall {β : Type.{u1}} [_inst_1 : NormedField.{u1} β] {f : Nat -> β}, (CauchySeq.{u1, 0} β Nat (PseudoMetricSpace.toUniformSpace.{u1} β (SeminormedRing.toPseudoMetricSpace.{u1} β (SeminormedCommRing.toSemiNormedRing.{u1} β (NormedCommRing.toSeminormedCommRing.{u1} β (NormedField.toNormedCommRing.{u1} β _inst_1))))) (CanonicallyLinearOrderedAddMonoid.semilatticeSup.{0} Nat Nat.canonicallyLinearOrderedAddMonoid) f) -> (IsCauSeq.{0, u1} Real Real.linearOrderedField β (NormedRing.toRing.{u1} β (NormedCommRing.toNormedRing.{u1} β (NormedField.toNormedCommRing.{u1} β _inst_1))) (Norm.norm.{u1} β (NormedField.toHasNorm.{u1} β _inst_1)) f)
-but is expected to have type
-  forall {β : Type.{u1}} [_inst_1 : NormedField.{u1} β] {f : Nat -> β}, (CauchySeq.{u1, 0} β Nat (PseudoMetricSpace.toUniformSpace.{u1} β (SeminormedRing.toPseudoMetricSpace.{u1} β (SeminormedCommRing.toSeminormedRing.{u1} β (NormedCommRing.toSeminormedCommRing.{u1} β (NormedField.toNormedCommRing.{u1} β _inst_1))))) (Lattice.toSemilatticeSup.{0} Nat Nat.instLatticeNat) f) -> (IsCauSeq.{0, u1} Real Real.instLinearOrderedFieldReal β (NormedRing.toRing.{u1} β (NormedCommRing.toNormedRing.{u1} β (NormedField.toNormedCommRing.{u1} β _inst_1))) (Norm.norm.{u1} β (NormedField.toNorm.{u1} β _inst_1)) f)
-Case conversion may be inaccurate. Consider using '#align cauchy_seq.is_cau_seq CauchySeq.isCauSeqₓ'. -/
 theorem CauchySeq.isCauSeq {f : ℕ → β} (hf : CauchySeq f) : IsCauSeq norm f :=
   by
   cases' cauchy_iff.1 hf with hf1 hf2
@@ -81,12 +69,6 @@ theorem CauchySeq.isCauSeq {f : ℕ → β} (hf : CauchySeq f) : IsCauSeq norm f
   apply Set.mk_mem_prod <;> solve_by_elim [le_refl]
 #align cauchy_seq.is_cau_seq CauchySeq.isCauSeq
 
-/- warning: cau_seq.cauchy_seq -> CauSeq.cauchySeq is a dubious translation:
-lean 3 declaration is
-  forall {β : Type.{u1}} [_inst_1 : NormedField.{u1} β] (f : CauSeq.{0, u1} Real Real.linearOrderedField β (NormedRing.toRing.{u1} β (NormedCommRing.toNormedRing.{u1} β (NormedField.toNormedCommRing.{u1} β _inst_1))) (Norm.norm.{u1} β (NormedField.toHasNorm.{u1} β _inst_1))), CauchySeq.{u1, 0} β Nat (PseudoMetricSpace.toUniformSpace.{u1} β (SeminormedRing.toPseudoMetricSpace.{u1} β (SeminormedCommRing.toSemiNormedRing.{u1} β (NormedCommRing.toSeminormedCommRing.{u1} β (NormedField.toNormedCommRing.{u1} β _inst_1))))) (CanonicallyLinearOrderedAddMonoid.semilatticeSup.{0} Nat Nat.canonicallyLinearOrderedAddMonoid) (coeFn.{succ u1, succ u1} (CauSeq.{0, u1} Real Real.linearOrderedField β (NormedRing.toRing.{u1} β (NormedCommRing.toNormedRing.{u1} β (NormedField.toNormedCommRing.{u1} β _inst_1))) (Norm.norm.{u1} β (NormedField.toHasNorm.{u1} β _inst_1))) (fun (_x : CauSeq.{0, u1} Real Real.linearOrderedField β (NormedRing.toRing.{u1} β (NormedCommRing.toNormedRing.{u1} β (NormedField.toNormedCommRing.{u1} β _inst_1))) (Norm.norm.{u1} β (NormedField.toHasNorm.{u1} β _inst_1))) => Nat -> β) (CauSeq.hasCoeToFun.{0, u1} Real β Real.linearOrderedField (NormedRing.toRing.{u1} β (NormedCommRing.toNormedRing.{u1} β (NormedField.toNormedCommRing.{u1} β _inst_1))) (Norm.norm.{u1} β (NormedField.toHasNorm.{u1} β _inst_1))) f)
-but is expected to have type
-  forall {β : Type.{u1}} [_inst_1 : NormedField.{u1} β] (f : CauSeq.{0, u1} Real Real.instLinearOrderedFieldReal β (NormedRing.toRing.{u1} β (NormedCommRing.toNormedRing.{u1} β (NormedField.toNormedCommRing.{u1} β _inst_1))) (Norm.norm.{u1} β (NormedField.toNorm.{u1} β _inst_1))), CauchySeq.{u1, 0} β Nat (PseudoMetricSpace.toUniformSpace.{u1} β (SeminormedRing.toPseudoMetricSpace.{u1} β (SeminormedCommRing.toSeminormedRing.{u1} β (NormedCommRing.toSeminormedCommRing.{u1} β (NormedField.toNormedCommRing.{u1} β _inst_1))))) (Lattice.toSemilatticeSup.{0} Nat Nat.instLatticeNat) (Subtype.val.{succ u1} (Nat -> β) (fun (f : Nat -> β) => IsCauSeq.{0, u1} Real Real.instLinearOrderedFieldReal β (NormedRing.toRing.{u1} β (NormedCommRing.toNormedRing.{u1} β (NormedField.toNormedCommRing.{u1} β _inst_1))) (Norm.norm.{u1} β (NormedField.toNorm.{u1} β _inst_1)) f) f)
-Case conversion may be inaccurate. Consider using '#align cau_seq.cauchy_seq CauSeq.cauchySeqₓ'. -/
 theorem CauSeq.cauchySeq (f : CauSeq β norm) : CauchySeq f :=
   by
   refine' cauchy_iff.2 ⟨by infer_instance, fun s hs => _⟩
@@ -104,24 +86,12 @@ theorem CauSeq.cauchySeq (f : CauSeq β norm) : CauchySeq f :=
     apply hN <;> assumption
 #align cau_seq.cauchy_seq CauSeq.cauchySeq
 
-/- warning: cau_seq_iff_cauchy_seq -> isCauSeq_iff_cauchySeq is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_2 : NormedField.{u1} α] {u : Nat -> α}, Iff (IsCauSeq.{0, u1} Real Real.linearOrderedField α (NormedRing.toRing.{u1} α (NormedCommRing.toNormedRing.{u1} α (NormedField.toNormedCommRing.{u1} α _inst_2))) (Norm.norm.{u1} α (NormedField.toHasNorm.{u1} α _inst_2)) u) (CauchySeq.{u1, 0} α Nat (PseudoMetricSpace.toUniformSpace.{u1} α (SeminormedRing.toPseudoMetricSpace.{u1} α (SeminormedCommRing.toSemiNormedRing.{u1} α (NormedCommRing.toSeminormedCommRing.{u1} α (NormedField.toNormedCommRing.{u1} α _inst_2))))) (CanonicallyLinearOrderedAddMonoid.semilatticeSup.{0} Nat Nat.canonicallyLinearOrderedAddMonoid) u)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_2 : NormedField.{u1} α] {u : Nat -> α}, Iff (IsCauSeq.{0, u1} Real Real.instLinearOrderedFieldReal α (NormedRing.toRing.{u1} α (NormedCommRing.toNormedRing.{u1} α (NormedField.toNormedCommRing.{u1} α _inst_2))) (Norm.norm.{u1} α (NormedField.toNorm.{u1} α _inst_2)) u) (CauchySeq.{u1, 0} α Nat (PseudoMetricSpace.toUniformSpace.{u1} α (SeminormedRing.toPseudoMetricSpace.{u1} α (SeminormedCommRing.toSeminormedRing.{u1} α (NormedCommRing.toSeminormedCommRing.{u1} α (NormedField.toNormedCommRing.{u1} α _inst_2))))) (Lattice.toSemilatticeSup.{0} Nat Nat.instLatticeNat) u)
-Case conversion may be inaccurate. Consider using '#align cau_seq_iff_cauchy_seq isCauSeq_iff_cauchySeqₓ'. -/
 /-- In a normed field, `cau_seq` coincides with the usual notion of Cauchy sequences. -/
 theorem isCauSeq_iff_cauchySeq {α : Type u} [NormedField α] {u : ℕ → α} :
     IsCauSeq norm u ↔ CauchySeq u :=
   ⟨fun h => CauSeq.cauchySeq ⟨u, h⟩, fun h => h.IsCauSeq⟩
 #align cau_seq_iff_cauchy_seq isCauSeq_iff_cauchySeq
 
-/- warning: complete_space_of_cau_seq_complete -> completeSpace_of_cauSeq_isComplete is a dubious translation:
-lean 3 declaration is
-  forall {β : Type.{u1}} [_inst_1 : NormedField.{u1} β] [_inst_2 : CauSeq.IsComplete.{0, u1} Real Real.linearOrderedField β (NormedRing.toRing.{u1} β (NormedCommRing.toNormedRing.{u1} β (NormedField.toNormedCommRing.{u1} β _inst_1))) (Norm.norm.{u1} β (NormedField.toHasNorm.{u1} β _inst_1)) (isAbsoluteValue_norm.{u1} β (NormedField.toNormedDivisionRing.{u1} β _inst_1))], CompleteSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (SeminormedRing.toPseudoMetricSpace.{u1} β (SeminormedCommRing.toSemiNormedRing.{u1} β (NormedCommRing.toSeminormedCommRing.{u1} β (NormedField.toNormedCommRing.{u1} β _inst_1)))))
-but is expected to have type
-  forall {β : Type.{u1}} [_inst_1 : NormedField.{u1} β] [_inst_2 : CauSeq.IsComplete.{0, u1} Real Real.instLinearOrderedFieldReal β (NormedRing.toRing.{u1} β (NormedCommRing.toNormedRing.{u1} β (NormedField.toNormedCommRing.{u1} β _inst_1))) (Norm.norm.{u1} β (NormedField.toNorm.{u1} β _inst_1)) (isAbsoluteValue_norm.{u1} β (NormedField.toNormedDivisionRing.{u1} β _inst_1))], CompleteSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (SeminormedRing.toPseudoMetricSpace.{u1} β (SeminormedCommRing.toSeminormedRing.{u1} β (NormedCommRing.toSeminormedCommRing.{u1} β (NormedField.toNormedCommRing.{u1} β _inst_1)))))
-Case conversion may be inaccurate. Consider using '#align complete_space_of_cau_seq_complete completeSpace_of_cauSeq_isCompleteₓ'. -/
 -- see Note [lower instance priority]
 /-- A complete normed field is complete as a metric space, as Cauchy sequences converge by
 assumption and this suffices to characterize completeness. -/

10bf4f82

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -47,8 +47,7 @@ theorem CauSeq.tendsto_limit [NormedRing β] [hn : IsAbsoluteValue (norm : β 
       exists N
       intro b hb
       apply hεs
-      dsimp [Metric.ball]
-      rw [dist_comm, dist_eq_norm]
+      dsimp [Metric.ball]; rw [dist_comm, dist_eq_norm]
       solve_by_elim)
 #align cau_seq.tendsto_limit CauSeq.tendsto_limit
 
@@ -96,10 +95,7 @@ theorem CauSeq.cauchySeq (f : CauSeq β norm) : CauchySeq f :=
   exists { n | n ≥ N }.image f
   simp only [exists_prop, mem_at_top_sets, mem_map, mem_image, ge_iff_le, mem_set_of_eq]
   constructor
-  · exists N
-    intro b hb
-    exists b
-    simp [hb]
+  · exists N; intro b hb; exists b; simp [hb]
   · rintro ⟨a, b⟩ ⟨⟨a', ⟨ha'1, ha'2⟩⟩, ⟨b', ⟨hb'1, hb'2⟩⟩⟩
     dsimp at ha'1 ha'2 hb'1 hb'2
     rw [← ha'2, ← hb'2]

10bf4f82

bump to nightly-2023-04-12-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/039ef89bef6e58b32b62898dd48e9d1a4312bb65

0809e5be

Diff

@@ -108,37 +108,37 @@ theorem CauSeq.cauchySeq (f : CauSeq β norm) : CauchySeq f :=
     apply hN <;> assumption
 #align cau_seq.cauchy_seq CauSeq.cauchySeq
 
-/- warning: cau_seq_iff_cauchy_seq -> cau_seq_iff_cauchySeq is a dubious translation:
+/- warning: cau_seq_iff_cauchy_seq -> isCauSeq_iff_cauchySeq is a dubious translation:
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_2 : NormedField.{u1} α] {u : Nat -> α}, Iff (IsCauSeq.{0, u1} Real Real.linearOrderedField α (NormedRing.toRing.{u1} α (NormedCommRing.toNormedRing.{u1} α (NormedField.toNormedCommRing.{u1} α _inst_2))) (Norm.norm.{u1} α (NormedField.toHasNorm.{u1} α _inst_2)) u) (CauchySeq.{u1, 0} α Nat (PseudoMetricSpace.toUniformSpace.{u1} α (SeminormedRing.toPseudoMetricSpace.{u1} α (SeminormedCommRing.toSemiNormedRing.{u1} α (NormedCommRing.toSeminormedCommRing.{u1} α (NormedField.toNormedCommRing.{u1} α _inst_2))))) (CanonicallyLinearOrderedAddMonoid.semilatticeSup.{0} Nat Nat.canonicallyLinearOrderedAddMonoid) u)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_2 : NormedField.{u1} α] {u : Nat -> α}, Iff (IsCauSeq.{0, u1} Real Real.instLinearOrderedFieldReal α (NormedRing.toRing.{u1} α (NormedCommRing.toNormedRing.{u1} α (NormedField.toNormedCommRing.{u1} α _inst_2))) (Norm.norm.{u1} α (NormedField.toNorm.{u1} α _inst_2)) u) (CauchySeq.{u1, 0} α Nat (PseudoMetricSpace.toUniformSpace.{u1} α (SeminormedRing.toPseudoMetricSpace.{u1} α (SeminormedCommRing.toSeminormedRing.{u1} α (NormedCommRing.toSeminormedCommRing.{u1} α (NormedField.toNormedCommRing.{u1} α _inst_2))))) (Lattice.toSemilatticeSup.{0} Nat Nat.instLatticeNat) u)
-Case conversion may be inaccurate. Consider using '#align cau_seq_iff_cauchy_seq cau_seq_iff_cauchySeqₓ'. -/
+Case conversion may be inaccurate. Consider using '#align cau_seq_iff_cauchy_seq isCauSeq_iff_cauchySeqₓ'. -/
 /-- In a normed field, `cau_seq` coincides with the usual notion of Cauchy sequences. -/
-theorem cau_seq_iff_cauchySeq {α : Type u} [NormedField α] {u : ℕ → α} :
+theorem isCauSeq_iff_cauchySeq {α : Type u} [NormedField α] {u : ℕ → α} :
     IsCauSeq norm u ↔ CauchySeq u :=
   ⟨fun h => CauSeq.cauchySeq ⟨u, h⟩, fun h => h.IsCauSeq⟩
-#align cau_seq_iff_cauchy_seq cau_seq_iff_cauchySeq
+#align cau_seq_iff_cauchy_seq isCauSeq_iff_cauchySeq
 
-/- warning: complete_space_of_cau_seq_complete -> completeSpace_of_cau_seq_complete is a dubious translation:
+/- warning: complete_space_of_cau_seq_complete -> completeSpace_of_cauSeq_isComplete is a dubious translation:
 lean 3 declaration is
   forall {β : Type.{u1}} [_inst_1 : NormedField.{u1} β] [_inst_2 : CauSeq.IsComplete.{0, u1} Real Real.linearOrderedField β (NormedRing.toRing.{u1} β (NormedCommRing.toNormedRing.{u1} β (NormedField.toNormedCommRing.{u1} β _inst_1))) (Norm.norm.{u1} β (NormedField.toHasNorm.{u1} β _inst_1)) (isAbsoluteValue_norm.{u1} β (NormedField.toNormedDivisionRing.{u1} β _inst_1))], CompleteSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (SeminormedRing.toPseudoMetricSpace.{u1} β (SeminormedCommRing.toSemiNormedRing.{u1} β (NormedCommRing.toSeminormedCommRing.{u1} β (NormedField.toNormedCommRing.{u1} β _inst_1)))))
 but is expected to have type
   forall {β : Type.{u1}} [_inst_1 : NormedField.{u1} β] [_inst_2 : CauSeq.IsComplete.{0, u1} Real Real.instLinearOrderedFieldReal β (NormedRing.toRing.{u1} β (NormedCommRing.toNormedRing.{u1} β (NormedField.toNormedCommRing.{u1} β _inst_1))) (Norm.norm.{u1} β (NormedField.toNorm.{u1} β _inst_1)) (isAbsoluteValue_norm.{u1} β (NormedField.toNormedDivisionRing.{u1} β _inst_1))], CompleteSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (SeminormedRing.toPseudoMetricSpace.{u1} β (SeminormedCommRing.toSeminormedRing.{u1} β (NormedCommRing.toSeminormedCommRing.{u1} β (NormedField.toNormedCommRing.{u1} β _inst_1)))))
-Case conversion may be inaccurate. Consider using '#align complete_space_of_cau_seq_complete completeSpace_of_cau_seq_completeₓ'. -/
+Case conversion may be inaccurate. Consider using '#align complete_space_of_cau_seq_complete completeSpace_of_cauSeq_isCompleteₓ'. -/
 -- see Note [lower instance priority]
 /-- A complete normed field is complete as a metric space, as Cauchy sequences converge by
 assumption and this suffices to characterize completeness. -/
-instance (priority := 100) completeSpace_of_cau_seq_complete [CauSeq.IsComplete β norm] :
+instance (priority := 100) completeSpace_of_cauSeq_isComplete [CauSeq.IsComplete β norm] :
     CompleteSpace β := by
   apply complete_of_cauchy_seq_tendsto
   intro u hu
-  have C : IsCauSeq norm u := cau_seq_iff_cauchySeq.2 hu
+  have C : IsCauSeq norm u := isCauSeq_iff_cauchySeq.2 hu
   exists CauSeq.lim ⟨u, C⟩
   rw [Metric.tendsto_atTop]
   intro ε εpos
   cases' (CauSeq.equiv_lim ⟨u, C⟩) _ εpos with N hN
   exists N
   simpa [dist_eq_norm] using hN
-#align complete_space_of_cau_seq_complete completeSpace_of_cau_seq_complete
+#align complete_space_of_cau_seq_complete completeSpace_of_cauSeq_isComplete

10bf4f82

bump to nightly-2023-03-16-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

8ae28b0b

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Robert Y. Lewis, Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module topology.metric_space.cau_seq_filter
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 10bf4f825ad729c5653adc039dafa3622e7f93c9
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.Analysis.Normed.Field.Basic
 /-!
 # Completeness in terms of `cauchy` filters vs `is_cau_seq` sequences
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we apply `metric.complete_of_cauchy_seq_tendsto` to prove that a `normed_ring`
 is complete in terms of `cauchy` filter if and only if it is complete in terms
 of `cau_seq` Cauchy sequences.

f2ce6086

bump to nightly-2023-03-14-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/2196ab363eb097c008d4497125e0dde23fb36db2

d4b38a42

Diff

@@ -27,6 +27,12 @@ open Topology Classical
 
 variable {β : Type v}
 
+/- warning: cau_seq.tendsto_limit -> CauSeq.tendsto_limit is a dubious translation:
+lean 3 declaration is
+  forall {β : Type.{u1}} [_inst_1 : NormedRing.{u1} β] [hn : IsAbsoluteValue.{0, u1} Real Real.orderedSemiring β (Ring.toSemiring.{u1} β (NormedRing.toRing.{u1} β _inst_1)) (Norm.norm.{u1} β (NormedRing.toHasNorm.{u1} β _inst_1))] (f : CauSeq.{0, u1} Real Real.linearOrderedField β (NormedRing.toRing.{u1} β _inst_1) (Norm.norm.{u1} β (NormedRing.toHasNorm.{u1} β _inst_1))) [_inst_2 : CauSeq.IsComplete.{0, u1} Real Real.linearOrderedField β (NormedRing.toRing.{u1} β _inst_1) (Norm.norm.{u1} β (NormedRing.toHasNorm.{u1} β _inst_1)) hn], Filter.Tendsto.{0, u1} Nat β (coeFn.{succ u1, succ u1} (CauSeq.{0, u1} Real Real.linearOrderedField β (NormedRing.toRing.{u1} β _inst_1) (Norm.norm.{u1} β (NormedRing.toHasNorm.{u1} β _inst_1))) (fun (_x : CauSeq.{0, u1} Real Real.linearOrderedField β (NormedRing.toRing.{u1} β _inst_1) (Norm.norm.{u1} β (NormedRing.toHasNorm.{u1} β _inst_1))) => Nat -> β) (CauSeq.hasCoeToFun.{0, u1} Real β Real.linearOrderedField (NormedRing.toRing.{u1} β _inst_1) (Norm.norm.{u1} β (NormedRing.toHasNorm.{u1} β _inst_1))) f) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} β (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (SeminormedRing.toPseudoMetricSpace.{u1} β (NormedRing.toSeminormedRing.{u1} β _inst_1)))) (CauSeq.lim.{0, u1} Real Real.linearOrderedField β (NormedRing.toRing.{u1} β _inst_1) (Norm.norm.{u1} β (NormedRing.toHasNorm.{u1} β _inst_1)) hn _inst_2 f))
+but is expected to have type
+  forall {β : Type.{u1}} [_inst_1 : NormedRing.{u1} β] [hn : IsAbsoluteValue.{0, u1} Real Real.orderedSemiring β (Ring.toSemiring.{u1} β (NormedRing.toRing.{u1} β _inst_1)) (Norm.norm.{u1} β (NormedRing.toNorm.{u1} β _inst_1))] (f : CauSeq.{0, u1} Real Real.instLinearOrderedFieldReal β (NormedRing.toRing.{u1} β _inst_1) (Norm.norm.{u1} β (NormedRing.toNorm.{u1} β _inst_1))) [_inst_2 : CauSeq.IsComplete.{0, u1} Real Real.instLinearOrderedFieldReal β (NormedRing.toRing.{u1} β _inst_1) (Norm.norm.{u1} β (NormedRing.toNorm.{u1} β _inst_1)) hn], Filter.Tendsto.{0, u1} Nat β (Subtype.val.{succ u1} (Nat -> β) (fun (f : Nat -> β) => IsCauSeq.{0, u1} Real Real.instLinearOrderedFieldReal β (NormedRing.toRing.{u1} β _inst_1) (Norm.norm.{u1} β (NormedRing.toNorm.{u1} β _inst_1)) f) f) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} β (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (SeminormedRing.toPseudoMetricSpace.{u1} β (NormedRing.toSeminormedRing.{u1} β _inst_1)))) (CauSeq.lim.{0, u1} Real Real.instLinearOrderedFieldReal β (NormedRing.toRing.{u1} β _inst_1) (Norm.norm.{u1} β (NormedRing.toNorm.{u1} β _inst_1)) hn _inst_2 f))
+Case conversion may be inaccurate. Consider using '#align cau_seq.tendsto_limit CauSeq.tendsto_limitₓ'. -/
 theorem CauSeq.tendsto_limit [NormedRing β] [hn : IsAbsoluteValue (norm : β → ℝ)]
     (f : CauSeq β norm) [CauSeq.IsComplete β norm] : Tendsto f atTop (𝓝 f.lim) :=
   tendsto_nhds.mpr
@@ -54,6 +60,12 @@ variable [NormedField β]
 -/
 open Metric
 
+/- warning: cauchy_seq.is_cau_seq -> CauchySeq.isCauSeq is a dubious translation:
+lean 3 declaration is
+  forall {β : Type.{u1}} [_inst_1 : NormedField.{u1} β] {f : Nat -> β}, (CauchySeq.{u1, 0} β Nat (PseudoMetricSpace.toUniformSpace.{u1} β (SeminormedRing.toPseudoMetricSpace.{u1} β (SeminormedCommRing.toSemiNormedRing.{u1} β (NormedCommRing.toSeminormedCommRing.{u1} β (NormedField.toNormedCommRing.{u1} β _inst_1))))) (CanonicallyLinearOrderedAddMonoid.semilatticeSup.{0} Nat Nat.canonicallyLinearOrderedAddMonoid) f) -> (IsCauSeq.{0, u1} Real Real.linearOrderedField β (NormedRing.toRing.{u1} β (NormedCommRing.toNormedRing.{u1} β (NormedField.toNormedCommRing.{u1} β _inst_1))) (Norm.norm.{u1} β (NormedField.toHasNorm.{u1} β _inst_1)) f)
+but is expected to have type
+  forall {β : Type.{u1}} [_inst_1 : NormedField.{u1} β] {f : Nat -> β}, (CauchySeq.{u1, 0} β Nat (PseudoMetricSpace.toUniformSpace.{u1} β (SeminormedRing.toPseudoMetricSpace.{u1} β (SeminormedCommRing.toSeminormedRing.{u1} β (NormedCommRing.toSeminormedCommRing.{u1} β (NormedField.toNormedCommRing.{u1} β _inst_1))))) (Lattice.toSemilatticeSup.{0} Nat Nat.instLatticeNat) f) -> (IsCauSeq.{0, u1} Real Real.instLinearOrderedFieldReal β (NormedRing.toRing.{u1} β (NormedCommRing.toNormedRing.{u1} β (NormedField.toNormedCommRing.{u1} β _inst_1))) (Norm.norm.{u1} β (NormedField.toNorm.{u1} β _inst_1)) f)
+Case conversion may be inaccurate. Consider using '#align cauchy_seq.is_cau_seq CauchySeq.isCauSeqₓ'. -/
 theorem CauchySeq.isCauSeq {f : ℕ → β} (hf : CauchySeq f) : IsCauSeq norm f :=
   by
   cases' cauchy_iff.1 hf with hf1 hf2
@@ -67,6 +79,12 @@ theorem CauchySeq.isCauSeq {f : ℕ → β} (hf : CauchySeq f) : IsCauSeq norm f
   apply Set.mk_mem_prod <;> solve_by_elim [le_refl]
 #align cauchy_seq.is_cau_seq CauchySeq.isCauSeq
 
+/- warning: cau_seq.cauchy_seq -> CauSeq.cauchySeq is a dubious translation:
+lean 3 declaration is
+  forall {β : Type.{u1}} [_inst_1 : NormedField.{u1} β] (f : CauSeq.{0, u1} Real Real.linearOrderedField β (NormedRing.toRing.{u1} β (NormedCommRing.toNormedRing.{u1} β (NormedField.toNormedCommRing.{u1} β _inst_1))) (Norm.norm.{u1} β (NormedField.toHasNorm.{u1} β _inst_1))), CauchySeq.{u1, 0} β Nat (PseudoMetricSpace.toUniformSpace.{u1} β (SeminormedRing.toPseudoMetricSpace.{u1} β (SeminormedCommRing.toSemiNormedRing.{u1} β (NormedCommRing.toSeminormedCommRing.{u1} β (NormedField.toNormedCommRing.{u1} β _inst_1))))) (CanonicallyLinearOrderedAddMonoid.semilatticeSup.{0} Nat Nat.canonicallyLinearOrderedAddMonoid) (coeFn.{succ u1, succ u1} (CauSeq.{0, u1} Real Real.linearOrderedField β (NormedRing.toRing.{u1} β (NormedCommRing.toNormedRing.{u1} β (NormedField.toNormedCommRing.{u1} β _inst_1))) (Norm.norm.{u1} β (NormedField.toHasNorm.{u1} β _inst_1))) (fun (_x : CauSeq.{0, u1} Real Real.linearOrderedField β (NormedRing.toRing.{u1} β (NormedCommRing.toNormedRing.{u1} β (NormedField.toNormedCommRing.{u1} β _inst_1))) (Norm.norm.{u1} β (NormedField.toHasNorm.{u1} β _inst_1))) => Nat -> β) (CauSeq.hasCoeToFun.{0, u1} Real β Real.linearOrderedField (NormedRing.toRing.{u1} β (NormedCommRing.toNormedRing.{u1} β (NormedField.toNormedCommRing.{u1} β _inst_1))) (Norm.norm.{u1} β (NormedField.toHasNorm.{u1} β _inst_1))) f)
+but is expected to have type
+  forall {β : Type.{u1}} [_inst_1 : NormedField.{u1} β] (f : CauSeq.{0, u1} Real Real.instLinearOrderedFieldReal β (NormedRing.toRing.{u1} β (NormedCommRing.toNormedRing.{u1} β (NormedField.toNormedCommRing.{u1} β _inst_1))) (Norm.norm.{u1} β (NormedField.toNorm.{u1} β _inst_1))), CauchySeq.{u1, 0} β Nat (PseudoMetricSpace.toUniformSpace.{u1} β (SeminormedRing.toPseudoMetricSpace.{u1} β (SeminormedCommRing.toSeminormedRing.{u1} β (NormedCommRing.toSeminormedCommRing.{u1} β (NormedField.toNormedCommRing.{u1} β _inst_1))))) (Lattice.toSemilatticeSup.{0} Nat Nat.instLatticeNat) (Subtype.val.{succ u1} (Nat -> β) (fun (f : Nat -> β) => IsCauSeq.{0, u1} Real Real.instLinearOrderedFieldReal β (NormedRing.toRing.{u1} β (NormedCommRing.toNormedRing.{u1} β (NormedField.toNormedCommRing.{u1} β _inst_1))) (Norm.norm.{u1} β (NormedField.toNorm.{u1} β _inst_1)) f) f)
+Case conversion may be inaccurate. Consider using '#align cau_seq.cauchy_seq CauSeq.cauchySeqₓ'. -/
 theorem CauSeq.cauchySeq (f : CauSeq β norm) : CauchySeq f :=
   by
   refine' cauchy_iff.2 ⟨by infer_instance, fun s hs => _⟩
@@ -87,12 +105,24 @@ theorem CauSeq.cauchySeq (f : CauSeq β norm) : CauchySeq f :=
     apply hN <;> assumption
 #align cau_seq.cauchy_seq CauSeq.cauchySeq
 
+/- warning: cau_seq_iff_cauchy_seq -> cau_seq_iff_cauchySeq is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_2 : NormedField.{u1} α] {u : Nat -> α}, Iff (IsCauSeq.{0, u1} Real Real.linearOrderedField α (NormedRing.toRing.{u1} α (NormedCommRing.toNormedRing.{u1} α (NormedField.toNormedCommRing.{u1} α _inst_2))) (Norm.norm.{u1} α (NormedField.toHasNorm.{u1} α _inst_2)) u) (CauchySeq.{u1, 0} α Nat (PseudoMetricSpace.toUniformSpace.{u1} α (SeminormedRing.toPseudoMetricSpace.{u1} α (SeminormedCommRing.toSemiNormedRing.{u1} α (NormedCommRing.toSeminormedCommRing.{u1} α (NormedField.toNormedCommRing.{u1} α _inst_2))))) (CanonicallyLinearOrderedAddMonoid.semilatticeSup.{0} Nat Nat.canonicallyLinearOrderedAddMonoid) u)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_2 : NormedField.{u1} α] {u : Nat -> α}, Iff (IsCauSeq.{0, u1} Real Real.instLinearOrderedFieldReal α (NormedRing.toRing.{u1} α (NormedCommRing.toNormedRing.{u1} α (NormedField.toNormedCommRing.{u1} α _inst_2))) (Norm.norm.{u1} α (NormedField.toNorm.{u1} α _inst_2)) u) (CauchySeq.{u1, 0} α Nat (PseudoMetricSpace.toUniformSpace.{u1} α (SeminormedRing.toPseudoMetricSpace.{u1} α (SeminormedCommRing.toSeminormedRing.{u1} α (NormedCommRing.toSeminormedCommRing.{u1} α (NormedField.toNormedCommRing.{u1} α _inst_2))))) (Lattice.toSemilatticeSup.{0} Nat Nat.instLatticeNat) u)
+Case conversion may be inaccurate. Consider using '#align cau_seq_iff_cauchy_seq cau_seq_iff_cauchySeqₓ'. -/
 /-- In a normed field, `cau_seq` coincides with the usual notion of Cauchy sequences. -/
 theorem cau_seq_iff_cauchySeq {α : Type u} [NormedField α] {u : ℕ → α} :
     IsCauSeq norm u ↔ CauchySeq u :=
   ⟨fun h => CauSeq.cauchySeq ⟨u, h⟩, fun h => h.IsCauSeq⟩
 #align cau_seq_iff_cauchy_seq cau_seq_iff_cauchySeq
 
+/- warning: complete_space_of_cau_seq_complete -> completeSpace_of_cau_seq_complete is a dubious translation:
+lean 3 declaration is
+  forall {β : Type.{u1}} [_inst_1 : NormedField.{u1} β] [_inst_2 : CauSeq.IsComplete.{0, u1} Real Real.linearOrderedField β (NormedRing.toRing.{u1} β (NormedCommRing.toNormedRing.{u1} β (NormedField.toNormedCommRing.{u1} β _inst_1))) (Norm.norm.{u1} β (NormedField.toHasNorm.{u1} β _inst_1)) (isAbsoluteValue_norm.{u1} β (NormedField.toNormedDivisionRing.{u1} β _inst_1))], CompleteSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (SeminormedRing.toPseudoMetricSpace.{u1} β (SeminormedCommRing.toSemiNormedRing.{u1} β (NormedCommRing.toSeminormedCommRing.{u1} β (NormedField.toNormedCommRing.{u1} β _inst_1)))))
+but is expected to have type
+  forall {β : Type.{u1}} [_inst_1 : NormedField.{u1} β] [_inst_2 : CauSeq.IsComplete.{0, u1} Real Real.instLinearOrderedFieldReal β (NormedRing.toRing.{u1} β (NormedCommRing.toNormedRing.{u1} β (NormedField.toNormedCommRing.{u1} β _inst_1))) (Norm.norm.{u1} β (NormedField.toNorm.{u1} β _inst_1)) (isAbsoluteValue_norm.{u1} β (NormedField.toNormedDivisionRing.{u1} β _inst_1))], CompleteSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (SeminormedRing.toPseudoMetricSpace.{u1} β (SeminormedCommRing.toSeminormedRing.{u1} β (NormedCommRing.toSeminormedCommRing.{u1} β (NormedField.toNormedCommRing.{u1} β _inst_1)))))
+Case conversion may be inaccurate. Consider using '#align complete_space_of_cau_seq_complete completeSpace_of_cau_seq_completeₓ'. -/
 -- see Note [lower instance priority]
 /-- A complete normed field is complete as a metric space, as Cauchy sequences converge by
 assumption and this suffices to characterize completeness. -/

f2ce6086

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

f2ce6086

chore: scope open Classical (#11199)

We remove all but one open Classicals, instead preferring to use open scoped Classical. The only real side-effect this led to is moving a couple declarations to use Exists.choose instead of Classical.choose.

The first few commits are explicitly labelled regex replaces for ease of review.

c747be0a

Diff

@@ -20,7 +20,8 @@ universe u v
 
 open Set Filter
 
-open Topology Classical
+open scoped Classical
+open Topology
 
 variable {β : Type v}

f2ce6086

chore: Remove nonterminal simp at (#7795)

Removes nonterminal uses of simp at. Replaces most of these with instances of simp? ... says.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com>

4160b2aa

Diff

@@ -55,7 +55,7 @@ theorem CauchySeq.isCauSeq {f : ℕ → β} (hf : CauchySeq f) : IsCauSeq norm f
   cases' cauchy_iff.1 hf with hf1 hf2
   intro ε hε
   rcases hf2 { x | dist x.1 x.2 < ε } (dist_mem_uniformity hε) with ⟨t, ⟨ht, htsub⟩⟩
-  simp at ht; cases' ht with N hN
+  simp only [mem_map, mem_atTop_sets, ge_iff_le, mem_preimage] at ht; cases' ht with N hN
   exists N
   intro j hj
   rw [← dist_eq_norm]

f2ce6086

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

depends on: #5966

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

89aa3a3b

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Robert Y. Lewis, Sébastien Gouëzel
-
-! This file was ported from Lean 3 source module topology.metric_space.cau_seq_filter
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.Normed.Field.Basic
 
+#align_import topology.metric_space.cau_seq_filter from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
+
 /-!
 # Completeness in terms of `Cauchy` filters vs `isCauSeq` sequences

f2ce6086

chore: tidy various files (#3408)

7e7ba10b

Diff

@@ -85,23 +85,23 @@ theorem CauSeq.cauchySeq (f : CauSeq β norm) : CauchySeq f := by
 #align cau_seq.cauchy_seq CauSeq.cauchySeq
 
 /-- In a normed field, `CauSeq` coincides with the usual notion of Cauchy sequences. -/
-theorem cau_seq_iff_cauchySeq {α : Type u} [NormedField α] {u : ℕ → α} :
+theorem isCauSeq_iff_cauchySeq {α : Type u} [NormedField α] {u : ℕ → α} :
     IsCauSeq norm u ↔ CauchySeq u :=
   ⟨fun h => CauSeq.cauchySeq ⟨u, h⟩, fun h => h.isCauSeq⟩
-#align cau_seq_iff_cauchy_seq cau_seq_iff_cauchySeq
+#align cau_seq_iff_cauchy_seq isCauSeq_iff_cauchySeq
 
 -- see Note [lower instance priority]
 /-- A complete normed field is complete as a metric space, as Cauchy sequences converge by
 assumption and this suffices to characterize completeness. -/
-instance (priority := 100) completeSpace_of_cau_seq_complete [CauSeq.IsComplete β norm] :
+instance (priority := 100) completeSpace_of_cauSeq_isComplete [CauSeq.IsComplete β norm] :
     CompleteSpace β := by
   apply complete_of_cauchySeq_tendsto
   intro u hu
-  have C : IsCauSeq norm u := cau_seq_iff_cauchySeq.2 hu
+  have C : IsCauSeq norm u := isCauSeq_iff_cauchySeq.2 hu
   exists CauSeq.lim ⟨u, C⟩
   rw [Metric.tendsto_atTop]
   intro ε εpos
   cases' (CauSeq.equiv_lim ⟨u, C⟩) _ εpos with N hN
   exists N
   simpa [dist_eq_norm] using hN
-#align complete_space_of_cau_seq_complete completeSpace_of_cau_seq_complete
+#align complete_space_of_cau_seq_complete completeSpace_of_cauSeq_isComplete

f2ce6086

feat: port Topology.MetricSpace.CauSeqFilter (#2852)

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

1c543ada

`topology.metric_space.cau_seq_filter` ⟷ `Mathlib.Topology.MetricSpace.CauSeqFilter`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 601

topology.metric_space.cau_seq_filter ⟷ Mathlib.Topology.MetricSpace.CauSeqFilter

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 601

`topology.metric_space.cau_seq_filter` ⟷ `Mathlib.Topology.MetricSpace.CauSeqFilter`