topology.metric_space.equicontinuity ⟷ Mathlib.Topology.MetricSpace.Equicontinuity

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

@@ -62,7 +62,7 @@ theorem equicontinuousAt_iff {ι : Type _} [PseudoMetricSpace β] {F : ι → β
 #align metric.equicontinuous_at_iff Metric.equicontinuousAt_iff
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x x' «expr ∈ » U) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x x' «expr ∈ » U) -/
 #print Metric.equicontinuousAt_iff_pair /-
 /-- Reformulation of `equicontinuous_at_iff_pair` for families of functions taking values in a
 (pseudo) metric space. -/

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.MetricSpace.Basic
-import Mathbin.Topology.UniformSpace.Equicontinuity
+import Topology.MetricSpace.Basic
+import Topology.UniformSpace.Equicontinuity
 
 #align_import topology.metric_space.equicontinuity from "leanprover-community/mathlib"@"f47581155c818e6361af4e4fda60d27d020c226b"
 
@@ -62,7 +62,7 @@ theorem equicontinuousAt_iff {ι : Type _} [PseudoMetricSpace β] {F : ι → β
 #align metric.equicontinuous_at_iff Metric.equicontinuousAt_iff
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x x' «expr ∈ » U) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x x' «expr ∈ » U) -/
 #print Metric.equicontinuousAt_iff_pair /-
 /-- Reformulation of `equicontinuous_at_iff_pair` for families of functions taking values in a
 (pseudo) metric space. -/

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 topology.metric_space.equicontinuity
-! leanprover-community/mathlib commit f47581155c818e6361af4e4fda60d27d020c226b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Topology.MetricSpace.Basic
 import Mathbin.Topology.UniformSpace.Equicontinuity
 
+#align_import topology.metric_space.equicontinuity from "leanprover-community/mathlib"@"f47581155c818e6361af4e4fda60d27d020c226b"
+
 /-!
 # Equicontinuity in metric spaces
 
@@ -65,7 +62,7 @@ theorem equicontinuousAt_iff {ι : Type _} [PseudoMetricSpace β] {F : ι → β
 #align metric.equicontinuous_at_iff Metric.equicontinuousAt_iff
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x x' «expr ∈ » U) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x x' «expr ∈ » U) -/
 #print Metric.equicontinuousAt_iff_pair /-
 /-- Reformulation of `equicontinuous_at_iff_pair` for families of functions taking values in a
 (pseudo) metric space. -/

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

@@ -48,20 +48,25 @@ variable {α β ι : Type _} [PseudoMetricSpace α]
 
 namespace Metric
 
+#print Metric.equicontinuousAt_iff_right /-
 /-- Characterization of equicontinuity for families of functions taking values in a (pseudo) metric
 space. -/
 theorem equicontinuousAt_iff_right {ι : Type _} [TopologicalSpace β] {F : ι → β → α} {x₀ : β} :
     EquicontinuousAt F x₀ ↔ ∀ ε > 0, ∀ᶠ x in 𝓝 x₀, ∀ i, dist (F i x₀) (F i x) < ε :=
   uniformity_basis_dist.equicontinuousAt_iff_right
 #align metric.equicontinuous_at_iff_right Metric.equicontinuousAt_iff_right
+-/
 
+#print Metric.equicontinuousAt_iff /-
 /-- Characterization of equicontinuity for families of functions between (pseudo) metric spaces. -/
 theorem equicontinuousAt_iff {ι : Type _} [PseudoMetricSpace β] {F : ι → β → α} {x₀ : β} :
     EquicontinuousAt F x₀ ↔ ∀ ε > 0, ∃ δ > 0, ∀ x, dist x x₀ < δ → ∀ i, dist (F i x₀) (F i x) < ε :=
   nhds_basis_ball.equicontinuousAt_iff uniformity_basis_dist
 #align metric.equicontinuous_at_iff Metric.equicontinuousAt_iff
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x x' «expr ∈ » U) -/
+#print Metric.equicontinuousAt_iff_pair /-
 /-- Reformulation of `equicontinuous_at_iff_pair` for families of functions taking values in a
 (pseudo) metric space. -/
 protected theorem equicontinuousAt_iff_pair {ι : Type _} [TopologicalSpace β] {F : ι → β → α}
@@ -79,14 +84,18 @@ protected theorem equicontinuousAt_iff_pair {ι : Type _} [TopologicalSpace β]
     refine' Exists.imp (fun V => Exists.imp fun hV h => _) (H _ hε)
     exact fun x hx x' hx' i => hεU (h _ hx _ hx' i)
 #align metric.equicontinuous_at_iff_pair Metric.equicontinuousAt_iff_pair
+-/
 
+#print Metric.uniformEquicontinuous_iff_right /-
 /-- Characterization of uniform equicontinuity for families of functions taking values in a
 (pseudo) metric space. -/
 theorem uniformEquicontinuous_iff_right {ι : Type _} [UniformSpace β] {F : ι → β → α} :
     UniformEquicontinuous F ↔ ∀ ε > 0, ∀ᶠ xy : β × β in 𝓤 β, ∀ i, dist (F i xy.1) (F i xy.2) < ε :=
   uniformity_basis_dist.uniformEquicontinuous_iff_right
 #align metric.uniform_equicontinuous_iff_right Metric.uniformEquicontinuous_iff_right
+-/
 
+#print Metric.uniformEquicontinuous_iff /-
 /-- Characterization of uniform equicontinuity for families of functions between
 (pseudo) metric spaces. -/
 theorem uniformEquicontinuous_iff {ι : Type _} [PseudoMetricSpace β] {F : ι → β → α} :
@@ -94,7 +103,9 @@ theorem uniformEquicontinuous_iff {ι : Type _} [PseudoMetricSpace β] {F : ι 
       ∀ ε > 0, ∃ δ > 0, ∀ x y, dist x y < δ → ∀ i, dist (F i x) (F i y) < ε :=
   uniformity_basis_dist.uniformEquicontinuous_iff uniformity_basis_dist
 #align metric.uniform_equicontinuous_iff Metric.uniformEquicontinuous_iff
+-/
 
+#print Metric.equicontinuousAt_of_continuity_modulus /-
 /-- For a family of functions to a (pseudo) metric spaces, a convenient way to prove
 equicontinuity at a point is to show that all of the functions share a common *local* continuity
 modulus. -/
@@ -106,7 +117,9 @@ theorem equicontinuousAt_of_continuity_modulus {ι : Type _} [TopologicalSpace 
   intro ε ε0
   filter_upwards [b_lim (Iio_mem_nhds ε0), H] using fun x hx₁ hx₂ i => (hx₂ i).trans_lt hx₁
 #align metric.equicontinuous_at_of_continuity_modulus Metric.equicontinuousAt_of_continuity_modulus
+-/
 
+#print Metric.uniformEquicontinuous_of_continuity_modulus /-
 /-- For a family of functions between (pseudo) metric spaces, a convenient way to prove
 uniform equicontinuity is to show that all of the functions share a common *global* continuity
 modulus. -/
@@ -124,7 +137,9 @@ theorem uniformEquicontinuous_of_continuity_modulus {ι : Type _} [PseudoMetricS
     _ = dist (b (dist x y)) 0 := by simp [Real.dist_eq]
     _ < ε := hδ (by simpa only [Real.dist_eq, tsub_zero, abs_dist] using hxy)
 #align metric.uniform_equicontinuous_of_continuity_modulus Metric.uniformEquicontinuous_of_continuity_modulus
+-/
 
+#print Metric.equicontinuous_of_continuity_modulus /-
 /-- For a family of functions between (pseudo) metric spaces, a convenient way to prove
 equicontinuity is to show that all of the functions share a common *global* continuity modulus. -/
 theorem equicontinuous_of_continuity_modulus {ι : Type _} [PseudoMetricSpace β] (b : ℝ → ℝ)
@@ -132,6 +147,7 @@ theorem equicontinuous_of_continuity_modulus {ι : Type _} [PseudoMetricSpace β
     (H : ∀ (x y : β) (i), dist (F i x) (F i y) ≤ b (dist x y)) : Equicontinuous F :=
   (uniformEquicontinuous_of_continuity_modulus b b_lim F H).Equicontinuous
 #align metric.equicontinuous_of_continuity_modulus Metric.equicontinuous_of_continuity_modulus
+-/
 
 end Metric
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

@@ -123,7 +123,6 @@ theorem uniformEquicontinuous_of_continuity_modulus {ι : Type _} [PseudoMetricS
     _ ≤ |b (dist x y)| := (le_abs_self _)
     _ = dist (b (dist x y)) 0 := by simp [Real.dist_eq]
     _ < ε := hδ (by simpa only [Real.dist_eq, tsub_zero, abs_dist] using hxy)
-    
 #align metric.uniform_equicontinuous_of_continuity_modulus Metric.uniformEquicontinuous_of_continuity_modulus
 
 /-- For a family of functions between (pseudo) metric spaces, a convenient way to prove

mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004

@@ -61,7 +61,7 @@ theorem equicontinuousAt_iff {ι : Type _} [PseudoMetricSpace β] {F : ι → β
   nhds_basis_ball.equicontinuousAt_iff uniformity_basis_dist
 #align metric.equicontinuous_at_iff Metric.equicontinuousAt_iff
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x x' «expr ∈ » U) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x x' «expr ∈ » U) -/
 /-- Reformulation of `equicontinuous_at_iff_pair` for families of functions taking values in a
 (pseudo) metric space. -/
 protected theorem equicontinuousAt_iff_pair {ι : Type _} [TopologicalSpace β] {F : ι → β → α}

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

@@ -104,7 +104,7 @@ theorem equicontinuousAt_of_continuity_modulus {ι : Type _} [TopologicalSpace 
   by
   rw [Metric.equicontinuousAt_iff_right]
   intro ε ε0
-  filter_upwards [b_lim (Iio_mem_nhds ε0), H]using fun x hx₁ hx₂ i => (hx₂ i).trans_lt hx₁
+  filter_upwards [b_lim (Iio_mem_nhds ε0), H] using fun x hx₁ hx₂ i => (hx₂ i).trans_lt hx₁
 #align metric.equicontinuous_at_of_continuity_modulus Metric.equicontinuousAt_of_continuity_modulus
 
 /-- For a family of functions between (pseudo) metric spaces, a convenient way to prove

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

@@ -42,7 +42,7 @@ equicontinuity, continuity modulus
 
 open Filter
 
-open Topology uniformity
+open scoped Topology uniformity
 
 variable {α β ι : Type _} [PseudoMetricSpace α]
 

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

@@ -48,12 +48,6 @@ variable {α β ι : Type _} [PseudoMetricSpace α]
 
 namespace Metric
 
-/- warning: metric.equicontinuous_at_iff_right -> Metric.equicontinuousAt_iff_right is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoMetricSpace.{u1} α] {ι : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} β] {F : ι -> β -> α} {x₀ : β}, Iff (EquicontinuousAt.{u3, u2, u1} ι β α _inst_2 (PseudoMetricSpace.toUniformSpace.{u1} α _inst_1) F x₀) (forall (ε : Real), (GT.gt.{0} Real Real.hasLt ε (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (Filter.Eventually.{u2} β (fun (x : β) => forall (i : ι), LT.lt.{0} Real Real.hasLt (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1) (F i x₀) (F i x)) ε) (nhds.{u2} β _inst_2 x₀)))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoMetricSpace.{u1} α] {ι : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} β] {F : ι -> β -> α} {x₀ : β}, Iff (EquicontinuousAt.{u3, u2, u1} ι β α _inst_2 (PseudoMetricSpace.toUniformSpace.{u1} α _inst_1) F x₀) (forall (ε : Real), (GT.gt.{0} Real Real.instLTReal ε (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (Filter.Eventually.{u2} β (fun (x : β) => forall (i : ι), LT.lt.{0} Real Real.instLTReal (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1) (F i x₀) (F i x)) ε) (nhds.{u2} β _inst_2 x₀)))
-Case conversion may be inaccurate. Consider using '#align metric.equicontinuous_at_iff_right Metric.equicontinuousAt_iff_rightₓ'. -/
 /-- Characterization of equicontinuity for families of functions taking values in a (pseudo) metric
 space. -/
 theorem equicontinuousAt_iff_right {ι : Type _} [TopologicalSpace β] {F : ι → β → α} {x₀ : β} :
@@ -61,24 +55,12 @@ theorem equicontinuousAt_iff_right {ι : Type _} [TopologicalSpace β] {F : ι 
   uniformity_basis_dist.equicontinuousAt_iff_right
 #align metric.equicontinuous_at_iff_right Metric.equicontinuousAt_iff_right
 
-/- warning: metric.equicontinuous_at_iff -> Metric.equicontinuousAt_iff is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoMetricSpace.{u1} α] {ι : Type.{u3}} [_inst_2 : PseudoMetricSpace.{u2} β] {F : ι -> β -> α} {x₀ : β}, Iff (EquicontinuousAt.{u3, u2, u1} ι β α (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_2)) (PseudoMetricSpace.toUniformSpace.{u1} α _inst_1) F x₀) (forall (ε : Real), (GT.gt.{0} Real Real.hasLt ε (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (Exists.{1} Real (fun (δ : Real) => Exists.{0} (GT.gt.{0} Real Real.hasLt δ (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (fun (H : GT.gt.{0} Real Real.hasLt δ (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) => forall (x : β), (LT.lt.{0} Real Real.hasLt (Dist.dist.{u2} β (PseudoMetricSpace.toHasDist.{u2} β _inst_2) x x₀) δ) -> (forall (i : ι), LT.lt.{0} Real Real.hasLt (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1) (F i x₀) (F i x)) ε)))))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoMetricSpace.{u1} α] {ι : Type.{u3}} [_inst_2 : PseudoMetricSpace.{u2} β] {F : ι -> β -> α} {x₀ : β}, Iff (EquicontinuousAt.{u3, u2, u1} ι β α (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_2)) (PseudoMetricSpace.toUniformSpace.{u1} α _inst_1) F x₀) (forall (ε : Real), (GT.gt.{0} Real Real.instLTReal ε (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (Exists.{1} Real (fun (δ : Real) => And (GT.gt.{0} Real Real.instLTReal δ (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (forall (x : β), (LT.lt.{0} Real Real.instLTReal (Dist.dist.{u2} β (PseudoMetricSpace.toDist.{u2} β _inst_2) x x₀) δ) -> (forall (i : ι), LT.lt.{0} Real Real.instLTReal (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1) (F i x₀) (F i x)) ε)))))
-Case conversion may be inaccurate. Consider using '#align metric.equicontinuous_at_iff Metric.equicontinuousAt_iffₓ'. -/
 /-- Characterization of equicontinuity for families of functions between (pseudo) metric spaces. -/
 theorem equicontinuousAt_iff {ι : Type _} [PseudoMetricSpace β] {F : ι → β → α} {x₀ : β} :
     EquicontinuousAt F x₀ ↔ ∀ ε > 0, ∃ δ > 0, ∀ x, dist x x₀ < δ → ∀ i, dist (F i x₀) (F i x) < ε :=
   nhds_basis_ball.equicontinuousAt_iff uniformity_basis_dist
 #align metric.equicontinuous_at_iff Metric.equicontinuousAt_iff
 
-/- warning: metric.equicontinuous_at_iff_pair -> Metric.equicontinuousAt_iff_pair is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoMetricSpace.{u1} α] {ι : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} β] {F : ι -> β -> α} {x₀ : β}, Iff (EquicontinuousAt.{u3, u2, u1} ι β α _inst_2 (PseudoMetricSpace.toUniformSpace.{u1} α _inst_1) F x₀) (forall (ε : Real), (GT.gt.{0} Real Real.hasLt ε (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (Exists.{succ u2} (Set.{u2} β) (fun (U : Set.{u2} β) => Exists.{0} (Membership.Mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (Filter.hasMem.{u2} β) U (nhds.{u2} β _inst_2 x₀)) (fun (H : Membership.Mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (Filter.hasMem.{u2} β) U (nhds.{u2} β _inst_2 x₀)) => forall (x : β), (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x U) -> (forall (x' : β), (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x' U) -> (forall (i : ι), LT.lt.{0} Real Real.hasLt (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1) (F i x) (F i x')) ε))))))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoMetricSpace.{u1} α] {ι : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} β] {F : ι -> β -> α} {x₀ : β}, Iff (EquicontinuousAt.{u3, u2, u1} ι β α _inst_2 (PseudoMetricSpace.toUniformSpace.{u1} α _inst_1) F x₀) (forall (ε : Real), (GT.gt.{0} Real Real.instLTReal ε (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (Exists.{succ u2} (Set.{u2} β) (fun (U : Set.{u2} β) => And (Membership.mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (instMembershipSetFilter.{u2} β) U (nhds.{u2} β _inst_2 x₀)) (forall (x : β), (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x U) -> (forall (x' : β), (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x' U) -> (forall (i : ι), LT.lt.{0} Real Real.instLTReal (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1) (F i x) (F i x')) ε))))))
-Case conversion may be inaccurate. Consider using '#align metric.equicontinuous_at_iff_pair Metric.equicontinuousAt_iff_pairₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x x' «expr ∈ » U) -/
 /-- Reformulation of `equicontinuous_at_iff_pair` for families of functions taking values in a
 (pseudo) metric space. -/
@@ -98,12 +80,6 @@ protected theorem equicontinuousAt_iff_pair {ι : Type _} [TopologicalSpace β]
     exact fun x hx x' hx' i => hεU (h _ hx _ hx' i)
 #align metric.equicontinuous_at_iff_pair Metric.equicontinuousAt_iff_pair
 
-/- warning: metric.uniform_equicontinuous_iff_right -> Metric.uniformEquicontinuous_iff_right is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoMetricSpace.{u1} α] {ι : Type.{u3}} [_inst_2 : UniformSpace.{u2} β] {F : ι -> β -> α}, Iff (UniformEquicontinuous.{u3, u1, u2} ι α β (PseudoMetricSpace.toUniformSpace.{u1} α _inst_1) _inst_2 F) (forall (ε : Real), (GT.gt.{0} Real Real.hasLt ε (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (Filter.Eventually.{u2} (Prod.{u2, u2} β β) (fun (xy : Prod.{u2, u2} β β) => forall (i : ι), LT.lt.{0} Real Real.hasLt (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1) (F i (Prod.fst.{u2, u2} β β xy)) (F i (Prod.snd.{u2, u2} β β xy))) ε) (uniformity.{u2} β _inst_2)))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoMetricSpace.{u1} α] {ι : Type.{u3}} [_inst_2 : UniformSpace.{u2} β] {F : ι -> β -> α}, Iff (UniformEquicontinuous.{u3, u1, u2} ι α β (PseudoMetricSpace.toUniformSpace.{u1} α _inst_1) _inst_2 F) (forall (ε : Real), (GT.gt.{0} Real Real.instLTReal ε (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (Filter.Eventually.{u2} (Prod.{u2, u2} β β) (fun (xy : Prod.{u2, u2} β β) => forall (i : ι), LT.lt.{0} Real Real.instLTReal (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1) (F i (Prod.fst.{u2, u2} β β xy)) (F i (Prod.snd.{u2, u2} β β xy))) ε) (uniformity.{u2} β _inst_2)))
-Case conversion may be inaccurate. Consider using '#align metric.uniform_equicontinuous_iff_right Metric.uniformEquicontinuous_iff_rightₓ'. -/
 /-- Characterization of uniform equicontinuity for families of functions taking values in a
 (pseudo) metric space. -/
 theorem uniformEquicontinuous_iff_right {ι : Type _} [UniformSpace β] {F : ι → β → α} :
@@ -111,12 +87,6 @@ theorem uniformEquicontinuous_iff_right {ι : Type _} [UniformSpace β] {F : ι
   uniformity_basis_dist.uniformEquicontinuous_iff_right
 #align metric.uniform_equicontinuous_iff_right Metric.uniformEquicontinuous_iff_right
 
-/- warning: metric.uniform_equicontinuous_iff -> Metric.uniformEquicontinuous_iff is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoMetricSpace.{u1} α] {ι : Type.{u3}} [_inst_2 : PseudoMetricSpace.{u2} β] {F : ι -> β -> α}, Iff (UniformEquicontinuous.{u3, u1, u2} ι α β (PseudoMetricSpace.toUniformSpace.{u1} α _inst_1) (PseudoMetricSpace.toUniformSpace.{u2} β _inst_2) F) (forall (ε : Real), (GT.gt.{0} Real Real.hasLt ε (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (Exists.{1} Real (fun (δ : Real) => Exists.{0} (GT.gt.{0} Real Real.hasLt δ (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (fun (H : GT.gt.{0} Real Real.hasLt δ (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) => forall (x : β) (y : β), (LT.lt.{0} Real Real.hasLt (Dist.dist.{u2} β (PseudoMetricSpace.toHasDist.{u2} β _inst_2) x y) δ) -> (forall (i : ι), LT.lt.{0} Real Real.hasLt (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1) (F i x) (F i y)) ε)))))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoMetricSpace.{u1} α] {ι : Type.{u3}} [_inst_2 : PseudoMetricSpace.{u2} β] {F : ι -> β -> α}, Iff (UniformEquicontinuous.{u3, u1, u2} ι α β (PseudoMetricSpace.toUniformSpace.{u1} α _inst_1) (PseudoMetricSpace.toUniformSpace.{u2} β _inst_2) F) (forall (ε : Real), (GT.gt.{0} Real Real.instLTReal ε (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (Exists.{1} Real (fun (δ : Real) => And (GT.gt.{0} Real Real.instLTReal δ (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (forall (x : β) (y : β), (LT.lt.{0} Real Real.instLTReal (Dist.dist.{u2} β (PseudoMetricSpace.toDist.{u2} β _inst_2) x y) δ) -> (forall (i : ι), LT.lt.{0} Real Real.instLTReal (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1) (F i x) (F i y)) ε)))))
-Case conversion may be inaccurate. Consider using '#align metric.uniform_equicontinuous_iff Metric.uniformEquicontinuous_iffₓ'. -/
 /-- Characterization of uniform equicontinuity for families of functions between
 (pseudo) metric spaces. -/
 theorem uniformEquicontinuous_iff {ι : Type _} [PseudoMetricSpace β] {F : ι → β → α} :
@@ -125,12 +95,6 @@ theorem uniformEquicontinuous_iff {ι : Type _} [PseudoMetricSpace β] {F : ι 
   uniformity_basis_dist.uniformEquicontinuous_iff uniformity_basis_dist
 #align metric.uniform_equicontinuous_iff Metric.uniformEquicontinuous_iff
 
-/- warning: metric.equicontinuous_at_of_continuity_modulus -> Metric.equicontinuousAt_of_continuity_modulus is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoMetricSpace.{u1} α] {ι : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} β] {x₀ : β} (b : β -> Real), (Filter.Tendsto.{u2, 0} β Real b (nhds.{u2} β _inst_2 x₀) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (forall (F : ι -> β -> α), (Filter.Eventually.{u2} β (fun (x : β) => forall (i : ι), LE.le.{0} Real Real.hasLe (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1) (F i x₀) (F i x)) (b x)) (nhds.{u2} β _inst_2 x₀)) -> (EquicontinuousAt.{u3, u2, u1} ι β α _inst_2 (PseudoMetricSpace.toUniformSpace.{u1} α _inst_1) F x₀))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoMetricSpace.{u1} α] {ι : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} β] {x₀ : β} (b : β -> Real), (Filter.Tendsto.{u2, 0} β Real b (nhds.{u2} β _inst_2 x₀) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) -> (forall (F : ι -> β -> α), (Filter.Eventually.{u2} β (fun (x : β) => forall (i : ι), LE.le.{0} Real Real.instLEReal (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1) (F i x₀) (F i x)) (b x)) (nhds.{u2} β _inst_2 x₀)) -> (EquicontinuousAt.{u3, u2, u1} ι β α _inst_2 (PseudoMetricSpace.toUniformSpace.{u1} α _inst_1) F x₀))
-Case conversion may be inaccurate. Consider using '#align metric.equicontinuous_at_of_continuity_modulus Metric.equicontinuousAt_of_continuity_modulusₓ'. -/
 /-- For a family of functions to a (pseudo) metric spaces, a convenient way to prove
 equicontinuity at a point is to show that all of the functions share a common *local* continuity
 modulus. -/
@@ -143,12 +107,6 @@ theorem equicontinuousAt_of_continuity_modulus {ι : Type _} [TopologicalSpace 
   filter_upwards [b_lim (Iio_mem_nhds ε0), H]using fun x hx₁ hx₂ i => (hx₂ i).trans_lt hx₁
 #align metric.equicontinuous_at_of_continuity_modulus Metric.equicontinuousAt_of_continuity_modulus
 
-/- warning: metric.uniform_equicontinuous_of_continuity_modulus -> Metric.uniformEquicontinuous_of_continuity_modulus is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoMetricSpace.{u1} α] {ι : Type.{u3}} [_inst_2 : PseudoMetricSpace.{u2} β] (b : Real -> Real), (Filter.Tendsto.{0, 0} Real Real b (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (forall (F : ι -> β -> α), (forall (x : β) (y : β) (i : ι), LE.le.{0} Real Real.hasLe (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1) (F i x) (F i y)) (b (Dist.dist.{u2} β (PseudoMetricSpace.toHasDist.{u2} β _inst_2) x y))) -> (UniformEquicontinuous.{u3, u1, u2} ι α β (PseudoMetricSpace.toUniformSpace.{u1} α _inst_1) (PseudoMetricSpace.toUniformSpace.{u2} β _inst_2) F))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoMetricSpace.{u1} α] {ι : Type.{u3}} [_inst_2 : PseudoMetricSpace.{u2} β] (b : Real -> Real), (Filter.Tendsto.{0, 0} Real Real b (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) -> (forall (F : ι -> β -> α), (forall (x : β) (y : β) (i : ι), LE.le.{0} Real Real.instLEReal (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1) (F i x) (F i y)) (b (Dist.dist.{u2} β (PseudoMetricSpace.toDist.{u2} β _inst_2) x y))) -> (UniformEquicontinuous.{u3, u1, u2} ι α β (PseudoMetricSpace.toUniformSpace.{u1} α _inst_1) (PseudoMetricSpace.toUniformSpace.{u2} β _inst_2) F))
-Case conversion may be inaccurate. Consider using '#align metric.uniform_equicontinuous_of_continuity_modulus Metric.uniformEquicontinuous_of_continuity_modulusₓ'. -/
 /-- For a family of functions between (pseudo) metric spaces, a convenient way to prove
 uniform equicontinuity is to show that all of the functions share a common *global* continuity
 modulus. -/
@@ -168,12 +126,6 @@ theorem uniformEquicontinuous_of_continuity_modulus {ι : Type _} [PseudoMetricS
     
 #align metric.uniform_equicontinuous_of_continuity_modulus Metric.uniformEquicontinuous_of_continuity_modulus
 
-/- warning: metric.equicontinuous_of_continuity_modulus -> Metric.equicontinuous_of_continuity_modulus is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoMetricSpace.{u1} α] {ι : Type.{u3}} [_inst_2 : PseudoMetricSpace.{u2} β] (b : Real -> Real), (Filter.Tendsto.{0, 0} Real Real b (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (forall (F : ι -> β -> α), (forall (x : β) (y : β) (i : ι), LE.le.{0} Real Real.hasLe (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1) (F i x) (F i y)) (b (Dist.dist.{u2} β (PseudoMetricSpace.toHasDist.{u2} β _inst_2) x y))) -> (Equicontinuous.{u3, u2, u1} ι β α (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_2)) (PseudoMetricSpace.toUniformSpace.{u1} α _inst_1) F))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoMetricSpace.{u1} α] {ι : Type.{u3}} [_inst_2 : PseudoMetricSpace.{u2} β] (b : Real -> Real), (Filter.Tendsto.{0, 0} Real Real b (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) -> (forall (F : ι -> β -> α), (forall (x : β) (y : β) (i : ι), LE.le.{0} Real Real.instLEReal (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1) (F i x) (F i y)) (b (Dist.dist.{u2} β (PseudoMetricSpace.toDist.{u2} β _inst_2) x y))) -> (Equicontinuous.{u3, u2, u1} ι β α (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_2)) (PseudoMetricSpace.toUniformSpace.{u1} α _inst_1) F))
-Case conversion may be inaccurate. Consider using '#align metric.equicontinuous_of_continuity_modulus Metric.equicontinuous_of_continuity_modulusₓ'. -/
 /-- For a family of functions between (pseudo) metric spaces, a convenient way to prove
 equicontinuity is to show that all of the functions share a common *global* continuity modulus. -/
 theorem equicontinuous_of_continuity_modulus {ι : Type _} [PseudoMetricSpace β] (b : ℝ → ℝ)

mathlib commit https://github.com/leanprover-community/mathlib/commit/21e3562c5e12d846c7def5eff8cdbc520d7d4936

@@ -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 topology.metric_space.equicontinuity
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit f47581155c818e6361af4e4fda60d27d020c226b
 ! 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.UniformSpace.Equicontinuity
 /-!
 # Equicontinuity in metric spaces
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This files contains various facts about (uniform) equicontinuity in metric spaces. Most
 importantly, we prove the usual characterization of equicontinuity of `F` at `x₀` in the case of
 (pseudo) metric spaces: `∀ ε > 0, ∃ δ > 0, ∀ x, dist x x₀ < δ → ∀ i, dist (F i x₀) (F i x) < ε`,

mathlib commit https://github.com/leanprover-community/mathlib/commit/641b6a82006416ec431b2987b354af9311fed4f2

@@ -45,6 +45,12 @@ variable {α β ι : Type _} [PseudoMetricSpace α]
 
 namespace Metric
 
+/- warning: metric.equicontinuous_at_iff_right -> Metric.equicontinuousAt_iff_right is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoMetricSpace.{u1} α] {ι : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} β] {F : ι -> β -> α} {x₀ : β}, Iff (EquicontinuousAt.{u3, u2, u1} ι β α _inst_2 (PseudoMetricSpace.toUniformSpace.{u1} α _inst_1) F x₀) (forall (ε : Real), (GT.gt.{0} Real Real.hasLt ε (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (Filter.Eventually.{u2} β (fun (x : β) => forall (i : ι), LT.lt.{0} Real Real.hasLt (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1) (F i x₀) (F i x)) ε) (nhds.{u2} β _inst_2 x₀)))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoMetricSpace.{u1} α] {ι : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} β] {F : ι -> β -> α} {x₀ : β}, Iff (EquicontinuousAt.{u3, u2, u1} ι β α _inst_2 (PseudoMetricSpace.toUniformSpace.{u1} α _inst_1) F x₀) (forall (ε : Real), (GT.gt.{0} Real Real.instLTReal ε (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (Filter.Eventually.{u2} β (fun (x : β) => forall (i : ι), LT.lt.{0} Real Real.instLTReal (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1) (F i x₀) (F i x)) ε) (nhds.{u2} β _inst_2 x₀)))
+Case conversion may be inaccurate. Consider using '#align metric.equicontinuous_at_iff_right Metric.equicontinuousAt_iff_rightₓ'. -/
 /-- Characterization of equicontinuity for families of functions taking values in a (pseudo) metric
 space. -/
 theorem equicontinuousAt_iff_right {ι : Type _} [TopologicalSpace β] {F : ι → β → α} {x₀ : β} :
@@ -52,12 +58,24 @@ theorem equicontinuousAt_iff_right {ι : Type _} [TopologicalSpace β] {F : ι 
   uniformity_basis_dist.equicontinuousAt_iff_right
 #align metric.equicontinuous_at_iff_right Metric.equicontinuousAt_iff_right
 
+/- warning: metric.equicontinuous_at_iff -> Metric.equicontinuousAt_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoMetricSpace.{u1} α] {ι : Type.{u3}} [_inst_2 : PseudoMetricSpace.{u2} β] {F : ι -> β -> α} {x₀ : β}, Iff (EquicontinuousAt.{u3, u2, u1} ι β α (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_2)) (PseudoMetricSpace.toUniformSpace.{u1} α _inst_1) F x₀) (forall (ε : Real), (GT.gt.{0} Real Real.hasLt ε (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (Exists.{1} Real (fun (δ : Real) => Exists.{0} (GT.gt.{0} Real Real.hasLt δ (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (fun (H : GT.gt.{0} Real Real.hasLt δ (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) => forall (x : β), (LT.lt.{0} Real Real.hasLt (Dist.dist.{u2} β (PseudoMetricSpace.toHasDist.{u2} β _inst_2) x x₀) δ) -> (forall (i : ι), LT.lt.{0} Real Real.hasLt (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1) (F i x₀) (F i x)) ε)))))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoMetricSpace.{u1} α] {ι : Type.{u3}} [_inst_2 : PseudoMetricSpace.{u2} β] {F : ι -> β -> α} {x₀ : β}, Iff (EquicontinuousAt.{u3, u2, u1} ι β α (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_2)) (PseudoMetricSpace.toUniformSpace.{u1} α _inst_1) F x₀) (forall (ε : Real), (GT.gt.{0} Real Real.instLTReal ε (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (Exists.{1} Real (fun (δ : Real) => And (GT.gt.{0} Real Real.instLTReal δ (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (forall (x : β), (LT.lt.{0} Real Real.instLTReal (Dist.dist.{u2} β (PseudoMetricSpace.toDist.{u2} β _inst_2) x x₀) δ) -> (forall (i : ι), LT.lt.{0} Real Real.instLTReal (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1) (F i x₀) (F i x)) ε)))))
+Case conversion may be inaccurate. Consider using '#align metric.equicontinuous_at_iff Metric.equicontinuousAt_iffₓ'. -/
 /-- Characterization of equicontinuity for families of functions between (pseudo) metric spaces. -/
 theorem equicontinuousAt_iff {ι : Type _} [PseudoMetricSpace β] {F : ι → β → α} {x₀ : β} :
     EquicontinuousAt F x₀ ↔ ∀ ε > 0, ∃ δ > 0, ∀ x, dist x x₀ < δ → ∀ i, dist (F i x₀) (F i x) < ε :=
   nhds_basis_ball.equicontinuousAt_iff uniformity_basis_dist
 #align metric.equicontinuous_at_iff Metric.equicontinuousAt_iff
 
+/- warning: metric.equicontinuous_at_iff_pair -> Metric.equicontinuousAt_iff_pair is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoMetricSpace.{u1} α] {ι : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} β] {F : ι -> β -> α} {x₀ : β}, Iff (EquicontinuousAt.{u3, u2, u1} ι β α _inst_2 (PseudoMetricSpace.toUniformSpace.{u1} α _inst_1) F x₀) (forall (ε : Real), (GT.gt.{0} Real Real.hasLt ε (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (Exists.{succ u2} (Set.{u2} β) (fun (U : Set.{u2} β) => Exists.{0} (Membership.Mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (Filter.hasMem.{u2} β) U (nhds.{u2} β _inst_2 x₀)) (fun (H : Membership.Mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (Filter.hasMem.{u2} β) U (nhds.{u2} β _inst_2 x₀)) => forall (x : β), (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x U) -> (forall (x' : β), (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x' U) -> (forall (i : ι), LT.lt.{0} Real Real.hasLt (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1) (F i x) (F i x')) ε))))))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoMetricSpace.{u1} α] {ι : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} β] {F : ι -> β -> α} {x₀ : β}, Iff (EquicontinuousAt.{u3, u2, u1} ι β α _inst_2 (PseudoMetricSpace.toUniformSpace.{u1} α _inst_1) F x₀) (forall (ε : Real), (GT.gt.{0} Real Real.instLTReal ε (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (Exists.{succ u2} (Set.{u2} β) (fun (U : Set.{u2} β) => And (Membership.mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (instMembershipSetFilter.{u2} β) U (nhds.{u2} β _inst_2 x₀)) (forall (x : β), (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x U) -> (forall (x' : β), (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x' U) -> (forall (i : ι), LT.lt.{0} Real Real.instLTReal (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1) (F i x) (F i x')) ε))))))
+Case conversion may be inaccurate. Consider using '#align metric.equicontinuous_at_iff_pair Metric.equicontinuousAt_iff_pairₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x x' «expr ∈ » U) -/
 /-- Reformulation of `equicontinuous_at_iff_pair` for families of functions taking values in a
 (pseudo) metric space. -/
@@ -77,6 +95,12 @@ protected theorem equicontinuousAt_iff_pair {ι : Type _} [TopologicalSpace β]
     exact fun x hx x' hx' i => hεU (h _ hx _ hx' i)
 #align metric.equicontinuous_at_iff_pair Metric.equicontinuousAt_iff_pair
 
+/- warning: metric.uniform_equicontinuous_iff_right -> Metric.uniformEquicontinuous_iff_right is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoMetricSpace.{u1} α] {ι : Type.{u3}} [_inst_2 : UniformSpace.{u2} β] {F : ι -> β -> α}, Iff (UniformEquicontinuous.{u3, u1, u2} ι α β (PseudoMetricSpace.toUniformSpace.{u1} α _inst_1) _inst_2 F) (forall (ε : Real), (GT.gt.{0} Real Real.hasLt ε (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (Filter.Eventually.{u2} (Prod.{u2, u2} β β) (fun (xy : Prod.{u2, u2} β β) => forall (i : ι), LT.lt.{0} Real Real.hasLt (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1) (F i (Prod.fst.{u2, u2} β β xy)) (F i (Prod.snd.{u2, u2} β β xy))) ε) (uniformity.{u2} β _inst_2)))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoMetricSpace.{u1} α] {ι : Type.{u3}} [_inst_2 : UniformSpace.{u2} β] {F : ι -> β -> α}, Iff (UniformEquicontinuous.{u3, u1, u2} ι α β (PseudoMetricSpace.toUniformSpace.{u1} α _inst_1) _inst_2 F) (forall (ε : Real), (GT.gt.{0} Real Real.instLTReal ε (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (Filter.Eventually.{u2} (Prod.{u2, u2} β β) (fun (xy : Prod.{u2, u2} β β) => forall (i : ι), LT.lt.{0} Real Real.instLTReal (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1) (F i (Prod.fst.{u2, u2} β β xy)) (F i (Prod.snd.{u2, u2} β β xy))) ε) (uniformity.{u2} β _inst_2)))
+Case conversion may be inaccurate. Consider using '#align metric.uniform_equicontinuous_iff_right Metric.uniformEquicontinuous_iff_rightₓ'. -/
 /-- Characterization of uniform equicontinuity for families of functions taking values in a
 (pseudo) metric space. -/
 theorem uniformEquicontinuous_iff_right {ι : Type _} [UniformSpace β] {F : ι → β → α} :
@@ -84,6 +108,12 @@ theorem uniformEquicontinuous_iff_right {ι : Type _} [UniformSpace β] {F : ι
   uniformity_basis_dist.uniformEquicontinuous_iff_right
 #align metric.uniform_equicontinuous_iff_right Metric.uniformEquicontinuous_iff_right
 
+/- warning: metric.uniform_equicontinuous_iff -> Metric.uniformEquicontinuous_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoMetricSpace.{u1} α] {ι : Type.{u3}} [_inst_2 : PseudoMetricSpace.{u2} β] {F : ι -> β -> α}, Iff (UniformEquicontinuous.{u3, u1, u2} ι α β (PseudoMetricSpace.toUniformSpace.{u1} α _inst_1) (PseudoMetricSpace.toUniformSpace.{u2} β _inst_2) F) (forall (ε : Real), (GT.gt.{0} Real Real.hasLt ε (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (Exists.{1} Real (fun (δ : Real) => Exists.{0} (GT.gt.{0} Real Real.hasLt δ (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (fun (H : GT.gt.{0} Real Real.hasLt δ (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) => forall (x : β) (y : β), (LT.lt.{0} Real Real.hasLt (Dist.dist.{u2} β (PseudoMetricSpace.toHasDist.{u2} β _inst_2) x y) δ) -> (forall (i : ι), LT.lt.{0} Real Real.hasLt (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1) (F i x) (F i y)) ε)))))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoMetricSpace.{u1} α] {ι : Type.{u3}} [_inst_2 : PseudoMetricSpace.{u2} β] {F : ι -> β -> α}, Iff (UniformEquicontinuous.{u3, u1, u2} ι α β (PseudoMetricSpace.toUniformSpace.{u1} α _inst_1) (PseudoMetricSpace.toUniformSpace.{u2} β _inst_2) F) (forall (ε : Real), (GT.gt.{0} Real Real.instLTReal ε (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (Exists.{1} Real (fun (δ : Real) => And (GT.gt.{0} Real Real.instLTReal δ (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (forall (x : β) (y : β), (LT.lt.{0} Real Real.instLTReal (Dist.dist.{u2} β (PseudoMetricSpace.toDist.{u2} β _inst_2) x y) δ) -> (forall (i : ι), LT.lt.{0} Real Real.instLTReal (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1) (F i x) (F i y)) ε)))))
+Case conversion may be inaccurate. Consider using '#align metric.uniform_equicontinuous_iff Metric.uniformEquicontinuous_iffₓ'. -/
 /-- Characterization of uniform equicontinuity for families of functions between
 (pseudo) metric spaces. -/
 theorem uniformEquicontinuous_iff {ι : Type _} [PseudoMetricSpace β] {F : ι → β → α} :
@@ -92,6 +122,12 @@ theorem uniformEquicontinuous_iff {ι : Type _} [PseudoMetricSpace β] {F : ι 
   uniformity_basis_dist.uniformEquicontinuous_iff uniformity_basis_dist
 #align metric.uniform_equicontinuous_iff Metric.uniformEquicontinuous_iff
 
+/- warning: metric.equicontinuous_at_of_continuity_modulus -> Metric.equicontinuousAt_of_continuity_modulus is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoMetricSpace.{u1} α] {ι : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} β] {x₀ : β} (b : β -> Real), (Filter.Tendsto.{u2, 0} β Real b (nhds.{u2} β _inst_2 x₀) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (forall (F : ι -> β -> α), (Filter.Eventually.{u2} β (fun (x : β) => forall (i : ι), LE.le.{0} Real Real.hasLe (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1) (F i x₀) (F i x)) (b x)) (nhds.{u2} β _inst_2 x₀)) -> (EquicontinuousAt.{u3, u2, u1} ι β α _inst_2 (PseudoMetricSpace.toUniformSpace.{u1} α _inst_1) F x₀))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoMetricSpace.{u1} α] {ι : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} β] {x₀ : β} (b : β -> Real), (Filter.Tendsto.{u2, 0} β Real b (nhds.{u2} β _inst_2 x₀) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) -> (forall (F : ι -> β -> α), (Filter.Eventually.{u2} β (fun (x : β) => forall (i : ι), LE.le.{0} Real Real.instLEReal (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1) (F i x₀) (F i x)) (b x)) (nhds.{u2} β _inst_2 x₀)) -> (EquicontinuousAt.{u3, u2, u1} ι β α _inst_2 (PseudoMetricSpace.toUniformSpace.{u1} α _inst_1) F x₀))
+Case conversion may be inaccurate. Consider using '#align metric.equicontinuous_at_of_continuity_modulus Metric.equicontinuousAt_of_continuity_modulusₓ'. -/
 /-- For a family of functions to a (pseudo) metric spaces, a convenient way to prove
 equicontinuity at a point is to show that all of the functions share a common *local* continuity
 modulus. -/
@@ -104,6 +140,12 @@ theorem equicontinuousAt_of_continuity_modulus {ι : Type _} [TopologicalSpace 
   filter_upwards [b_lim (Iio_mem_nhds ε0), H]using fun x hx₁ hx₂ i => (hx₂ i).trans_lt hx₁
 #align metric.equicontinuous_at_of_continuity_modulus Metric.equicontinuousAt_of_continuity_modulus
 
+/- warning: metric.uniform_equicontinuous_of_continuity_modulus -> Metric.uniformEquicontinuous_of_continuity_modulus is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoMetricSpace.{u1} α] {ι : Type.{u3}} [_inst_2 : PseudoMetricSpace.{u2} β] (b : Real -> Real), (Filter.Tendsto.{0, 0} Real Real b (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (forall (F : ι -> β -> α), (forall (x : β) (y : β) (i : ι), LE.le.{0} Real Real.hasLe (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1) (F i x) (F i y)) (b (Dist.dist.{u2} β (PseudoMetricSpace.toHasDist.{u2} β _inst_2) x y))) -> (UniformEquicontinuous.{u3, u1, u2} ι α β (PseudoMetricSpace.toUniformSpace.{u1} α _inst_1) (PseudoMetricSpace.toUniformSpace.{u2} β _inst_2) F))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoMetricSpace.{u1} α] {ι : Type.{u3}} [_inst_2 : PseudoMetricSpace.{u2} β] (b : Real -> Real), (Filter.Tendsto.{0, 0} Real Real b (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) -> (forall (F : ι -> β -> α), (forall (x : β) (y : β) (i : ι), LE.le.{0} Real Real.instLEReal (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1) (F i x) (F i y)) (b (Dist.dist.{u2} β (PseudoMetricSpace.toDist.{u2} β _inst_2) x y))) -> (UniformEquicontinuous.{u3, u1, u2} ι α β (PseudoMetricSpace.toUniformSpace.{u1} α _inst_1) (PseudoMetricSpace.toUniformSpace.{u2} β _inst_2) F))
+Case conversion may be inaccurate. Consider using '#align metric.uniform_equicontinuous_of_continuity_modulus Metric.uniformEquicontinuous_of_continuity_modulusₓ'. -/
 /-- For a family of functions between (pseudo) metric spaces, a convenient way to prove
 uniform equicontinuity is to show that all of the functions share a common *global* continuity
 modulus. -/
@@ -123,6 +165,12 @@ theorem uniformEquicontinuous_of_continuity_modulus {ι : Type _} [PseudoMetricS
     
 #align metric.uniform_equicontinuous_of_continuity_modulus Metric.uniformEquicontinuous_of_continuity_modulus
 
+/- warning: metric.equicontinuous_of_continuity_modulus -> Metric.equicontinuous_of_continuity_modulus is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoMetricSpace.{u1} α] {ι : Type.{u3}} [_inst_2 : PseudoMetricSpace.{u2} β] (b : Real -> Real), (Filter.Tendsto.{0, 0} Real Real b (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (forall (F : ι -> β -> α), (forall (x : β) (y : β) (i : ι), LE.le.{0} Real Real.hasLe (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1) (F i x) (F i y)) (b (Dist.dist.{u2} β (PseudoMetricSpace.toHasDist.{u2} β _inst_2) x y))) -> (Equicontinuous.{u3, u2, u1} ι β α (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_2)) (PseudoMetricSpace.toUniformSpace.{u1} α _inst_1) F))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoMetricSpace.{u1} α] {ι : Type.{u3}} [_inst_2 : PseudoMetricSpace.{u2} β] (b : Real -> Real), (Filter.Tendsto.{0, 0} Real Real b (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) -> (forall (F : ι -> β -> α), (forall (x : β) (y : β) (i : ι), LE.le.{0} Real Real.instLEReal (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1) (F i x) (F i y)) (b (Dist.dist.{u2} β (PseudoMetricSpace.toDist.{u2} β _inst_2) x y))) -> (Equicontinuous.{u3, u2, u1} ι β α (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_2)) (PseudoMetricSpace.toUniformSpace.{u1} α _inst_1) F))
+Case conversion may be inaccurate. Consider using '#align metric.equicontinuous_of_continuity_modulus Metric.equicontinuous_of_continuity_modulusₓ'. -/
 /-- For a family of functions between (pseudo) metric spaces, a convenient way to prove
 equicontinuity is to show that all of the functions share a common *global* continuity modulus. -/
 theorem equicontinuous_of_continuity_modulus {ι : Type _} [PseudoMetricSpace β] (b : ℝ → ℝ)

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

@@ -58,7 +58,7 @@ theorem equicontinuousAt_iff {ι : Type _} [PseudoMetricSpace β] {F : ι → β
   nhds_basis_ball.equicontinuousAt_iff uniformity_basis_dist
 #align metric.equicontinuous_at_iff Metric.equicontinuousAt_iff
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x x' «expr ∈ » U) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x x' «expr ∈ » U) -/
 /-- Reformulation of `equicontinuous_at_iff_pair` for families of functions taking values in a
 (pseudo) metric space. -/
 protected theorem equicontinuousAt_iff_pair {ι : Type _} [TopologicalSpace β] {F : ι → β → α}
@@ -117,7 +117,7 @@ theorem uniformEquicontinuous_of_continuity_modulus {ι : Type _} [PseudoMetricS
   refine' ⟨δ, δ0, fun x y hxy i => _⟩
   calc
     dist (F i x) (F i y) ≤ b (dist x y) := H x y i
-    _ ≤ |b (dist x y)| := le_abs_self _
+    _ ≤ |b (dist x y)| := (le_abs_self _)
     _ = dist (b (dist x y)) 0 := by simp [Real.dist_eq]
     _ < ε := hδ (by simpa only [Real.dist_eq, tsub_zero, abs_dist] using hxy)
     

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

Co-authored-by: Moritz Firsching <firsching@google.com>

@@ -109,7 +109,7 @@ theorem uniformEquicontinuous_of_continuity_modulus {ι : Type*} [PseudoMetricSp
   refine' ⟨δ, δ0, fun x y hxy i => _⟩
   calc
     dist (F i x) (F i y) ≤ b (dist x y) := H x y i
-    _ ≤ |b (dist x y)| := (le_abs_self _)
+    _ ≤ |b (dist x y)| := le_abs_self _
     _ = dist (b (dist x y)) 0 := by simp [Real.dist_eq]
     _ < ε := hδ (by simpa only [Real.dist_eq, tsub_zero, abs_dist] using hxy)
 #align metric.uniform_equicontinuous_of_continuity_modulus Metric.uniformEquicontinuous_of_continuity_modulus

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

• converts "--porting note" into "-- Porting note";
• converts "porting note" into "Porting note".

@@ -92,7 +92,7 @@ theorem equicontinuousAt_of_continuity_modulus {ι : Type*} [TopologicalSpace β
     (H : ∀ᶠ x in 𝓝 x₀, ∀ i, dist (F i x₀) (F i x) ≤ b x) : EquicontinuousAt F x₀ := by
   rw [Metric.equicontinuousAt_iff_right]
   intro ε ε0
-  -- porting note: Lean 3 didn't need `Filter.mem_map.mp` here
+  -- Porting note: Lean 3 didn't need `Filter.mem_map.mp` here
   filter_upwards [Filter.mem_map.mp <| b_lim (Iio_mem_nhds ε0), H] using
     fun x hx₁ hx₂ i => (hx₂ i).trans_lt hx₁
 #align metric.equicontinuous_at_of_continuity_modulus Metric.equicontinuousAt_of_continuity_modulus

This reduces the main file from 3340 to 2220 lines. The remaining file is somewhat entangled, so splitting is less obvious. Help is welcome, though a follow-up PR is probably better :-)

I've kept copyright and authors as they were originally.

@@ -3,7 +3,7 @@ Copyright (c) 2022 Anatole Dedecker. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anatole Dedecker
 -/
-import Mathlib.Topology.MetricSpace.Basic
+import Mathlib.Topology.MetricSpace.PseudoMetric
 import Mathlib.Topology.UniformSpace.Equicontinuity
 
 #align_import topology.metric_space.equicontinuity from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

@@ -36,26 +36,26 @@ equicontinuity, continuity modulus
 
 open Filter Topology Uniformity
 
-variable {α β ι : Type _} [PseudoMetricSpace α]
+variable {α β ι : Type*} [PseudoMetricSpace α]
 
 namespace Metric
 
 /-- Characterization of equicontinuity for families of functions taking values in a (pseudo) metric
 space. -/
-theorem equicontinuousAt_iff_right {ι : Type _} [TopologicalSpace β] {F : ι → β → α} {x₀ : β} :
+theorem equicontinuousAt_iff_right {ι : Type*} [TopologicalSpace β] {F : ι → β → α} {x₀ : β} :
     EquicontinuousAt F x₀ ↔ ∀ ε > 0, ∀ᶠ x in 𝓝 x₀, ∀ i, dist (F i x₀) (F i x) < ε :=
   uniformity_basis_dist.equicontinuousAt_iff_right
 #align metric.equicontinuous_at_iff_right Metric.equicontinuousAt_iff_right
 
 /-- Characterization of equicontinuity for families of functions between (pseudo) metric spaces. -/
-theorem equicontinuousAt_iff {ι : Type _} [PseudoMetricSpace β] {F : ι → β → α} {x₀ : β} :
+theorem equicontinuousAt_iff {ι : Type*} [PseudoMetricSpace β] {F : ι → β → α} {x₀ : β} :
     EquicontinuousAt F x₀ ↔ ∀ ε > 0, ∃ δ > 0, ∀ x, dist x x₀ < δ → ∀ i, dist (F i x₀) (F i x) < ε :=
   nhds_basis_ball.equicontinuousAt_iff uniformity_basis_dist
 #align metric.equicontinuous_at_iff Metric.equicontinuousAt_iff
 
 /-- Reformulation of `equicontinuousAt_iff_pair` for families of functions taking values in a
 (pseudo) metric space. -/
-protected theorem equicontinuousAt_iff_pair {ι : Type _} [TopologicalSpace β] {F : ι → β → α}
+protected theorem equicontinuousAt_iff_pair {ι : Type*} [TopologicalSpace β] {F : ι → β → α}
     {x₀ : β} :
     EquicontinuousAt F x₀ ↔
       ∀ ε > 0, ∃ U ∈ 𝓝 x₀, ∀ x ∈ U, ∀ x' ∈ U, ∀ i, dist (F i x) (F i x') < ε := by
@@ -71,14 +71,14 @@ protected theorem equicontinuousAt_iff_pair {ι : Type _} [TopologicalSpace β]
 
 /-- Characterization of uniform equicontinuity for families of functions taking values in a
 (pseudo) metric space. -/
-theorem uniformEquicontinuous_iff_right {ι : Type _} [UniformSpace β] {F : ι → β → α} :
+theorem uniformEquicontinuous_iff_right {ι : Type*} [UniformSpace β] {F : ι → β → α} :
     UniformEquicontinuous F ↔ ∀ ε > 0, ∀ᶠ xy : β × β in 𝓤 β, ∀ i, dist (F i xy.1) (F i xy.2) < ε :=
   uniformity_basis_dist.uniformEquicontinuous_iff_right
 #align metric.uniform_equicontinuous_iff_right Metric.uniformEquicontinuous_iff_right
 
 /-- Characterization of uniform equicontinuity for families of functions between
 (pseudo) metric spaces. -/
-theorem uniformEquicontinuous_iff {ι : Type _} [PseudoMetricSpace β] {F : ι → β → α} :
+theorem uniformEquicontinuous_iff {ι : Type*} [PseudoMetricSpace β] {F : ι → β → α} :
     UniformEquicontinuous F ↔
       ∀ ε > 0, ∃ δ > 0, ∀ x y, dist x y < δ → ∀ i, dist (F i x) (F i y) < ε :=
   uniformity_basis_dist.uniformEquicontinuous_iff uniformity_basis_dist
@@ -87,7 +87,7 @@ theorem uniformEquicontinuous_iff {ι : Type _} [PseudoMetricSpace β] {F : ι 
 /-- For a family of functions to a (pseudo) metric spaces, a convenient way to prove
 equicontinuity at a point is to show that all of the functions share a common *local* continuity
 modulus. -/
-theorem equicontinuousAt_of_continuity_modulus {ι : Type _} [TopologicalSpace β] {x₀ : β}
+theorem equicontinuousAt_of_continuity_modulus {ι : Type*} [TopologicalSpace β] {x₀ : β}
     (b : β → ℝ) (b_lim : Tendsto b (𝓝 x₀) (𝓝 0)) (F : ι → β → α)
     (H : ∀ᶠ x in 𝓝 x₀, ∀ i, dist (F i x₀) (F i x) ≤ b x) : EquicontinuousAt F x₀ := by
   rw [Metric.equicontinuousAt_iff_right]
@@ -100,7 +100,7 @@ theorem equicontinuousAt_of_continuity_modulus {ι : Type _} [TopologicalSpace 
 /-- For a family of functions between (pseudo) metric spaces, a convenient way to prove
 uniform equicontinuity is to show that all of the functions share a common *global* continuity
 modulus. -/
-theorem uniformEquicontinuous_of_continuity_modulus {ι : Type _} [PseudoMetricSpace β] (b : ℝ → ℝ)
+theorem uniformEquicontinuous_of_continuity_modulus {ι : Type*} [PseudoMetricSpace β] (b : ℝ → ℝ)
     (b_lim : Tendsto b (𝓝 0) (𝓝 0)) (F : ι → β → α)
     (H : ∀ (x y : β) (i), dist (F i x) (F i y) ≤ b (dist x y)) : UniformEquicontinuous F := by
   rw [Metric.uniformEquicontinuous_iff]
@@ -116,7 +116,7 @@ theorem uniformEquicontinuous_of_continuity_modulus {ι : Type _} [PseudoMetricS
 
 /-- For a family of functions between (pseudo) metric spaces, a convenient way to prove
 equicontinuity is to show that all of the functions share a common *global* continuity modulus. -/
-theorem equicontinuous_of_continuity_modulus {ι : Type _} [PseudoMetricSpace β] (b : ℝ → ℝ)
+theorem equicontinuous_of_continuity_modulus {ι : Type*} [PseudoMetricSpace β] (b : ℝ → ℝ)
     (b_lim : Tendsto b (𝓝 0) (𝓝 0)) (F : ι → β → α)
     (H : ∀ (x y : β) (i), dist (F i x) (F i y) ≤ b (dist x y)) : Equicontinuous F :=
   (uniformEquicontinuous_of_continuity_modulus b b_lim F H).equicontinuous

• depends on: #5966

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

@@ -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 topology.metric_space.equicontinuity
-! 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.Topology.MetricSpace.Basic
 import Mathlib.Topology.UniformSpace.Equicontinuity
 
+#align_import topology.metric_space.equicontinuity from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
+
 /-!
 # Equicontinuity in metric spaces
 

This PR fixes two things:

• Most align statements for definitions and theorems and instances that are separated by two newlines from the relevant declaration (s/\n\n#align/\n#align). This is often seen in the mathport output after ending calc blocks.
• All remaining more-than-one-line #align statements. (This was needed for a script I wrote for #3630.)

@@ -115,8 +115,7 @@ theorem uniformEquicontinuous_of_continuity_modulus {ι : Type _} [PseudoMetricS
     _ ≤ |b (dist x y)| := (le_abs_self _)
     _ = dist (b (dist x y)) 0 := by simp [Real.dist_eq]
     _ < ε := hδ (by simpa only [Real.dist_eq, tsub_zero, abs_dist] using hxy)
-#align metric.uniform_equicontinuous_of_continuity_modulus
-  Metric.uniformEquicontinuous_of_continuity_modulus
+#align metric.uniform_equicontinuous_of_continuity_modulus Metric.uniformEquicontinuous_of_continuity_modulus
 
 /-- For a family of functions between (pseudo) metric spaces, a convenient way to prove
 equicontinuity is to show that all of the functions share a common *global* continuity modulus. -/

Also changed a few small things in Topology/UniformSpace/Equicontinuity