topology.uniform_space.uniform_convergence ⟷ Mathlib.Topology.UniformSpace.UniformConvergence

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

@@ -972,7 +972,7 @@ theorem TendstoLocallyUniformly.comp [TopologicalSpace γ] (h : TendstoLocallyUn
 #align tendsto_locally_uniformly.comp TendstoLocallyUniformly.comp
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (K «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (K «expr ⊆ » s) -/
 #print tendstoLocallyUniformlyOn_TFAE /-
 theorem tendstoLocallyUniformlyOn_TFAE [LocallyCompactSpace α] (G : ι → α → β) (g : α → β)
     (p : Filter ι) (hs : IsOpen s) :
@@ -996,7 +996,7 @@ theorem tendstoLocallyUniformlyOn_TFAE [LocallyCompactSpace α] (G : ι → α 
 #align tendsto_locally_uniformly_on_tfae tendstoLocallyUniformlyOn_TFAE
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (K «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (K «expr ⊆ » s) -/
 #print tendstoLocallyUniformlyOn_iff_forall_isCompact /-
 theorem tendstoLocallyUniformlyOn_iff_forall_isCompact [LocallyCompactSpace α] (hs : IsOpen s) :
     TendstoLocallyUniformlyOn F f p s ↔

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

@@ -265,7 +265,7 @@ theorem TendstoUniformlyOn.congr {F' : ι → α → β} (hf : TendstoUniformlyO
   rw [tendstoUniformlyOn_iff_tendstoUniformlyOnFilter] at hf ⊢
   refine' hf.congr _
   rw [eventually_iff] at hff' ⊢
-  simp only [Set.EqOn] at hff' 
+  simp only [Set.EqOn] at hff'
   simp only [mem_prod_principal, hff', mem_set_of_eq]
 #align tendsto_uniformly_on.congr TendstoUniformlyOn.congr
 -/
@@ -354,7 +354,7 @@ theorem TendstoUniformlyOnFilter.prod_map {ι' α' β' : Type _} [UniformSpace 
       (p.Prod q) (p'.Prod q') :=
   by
   intro u hu
-  rw [uniformity_prod_eq_prod, mem_map, mem_prod_iff] at hu 
+  rw [uniformity_prod_eq_prod, mem_map, mem_prod_iff] at hu
   obtain ⟨v, hv, w, hw, hvw⟩ := hu
   apply (tendsto_swap4_prod.eventually ((h v hv).prod_mk (h' w hw))).mono
   simp only [Prod_map, and_imp, Prod.forall]
@@ -474,7 +474,7 @@ theorem Filter.Tendsto.tendstoUniformlyOnFilter_const {g : ι → β} {b : β} (
     TendstoUniformlyOnFilter (fun n : ι => fun a : α => g n) (fun a : α => b) p p' :=
   by
   rw [tendstoUniformlyOnFilter_iff_tendsto]
-  rw [Uniform.tendsto_nhds_right] at hg 
+  rw [Uniform.tendsto_nhds_right] at hg
   exact
     (hg.comp (tendsto_fst.comp ((@tendsto_id ι p).Prod_map (@tendsto_id α p')))).congr fun x => by
       simp
@@ -604,7 +604,7 @@ theorem UniformCauchySeqOnFilter.tendstoUniformlyOnFilter_of_tendsto [NeBot p]
   -- Complete the proof
   intro x n hx hm'
   refine' Set.mem_of_mem_of_subset (mem_comp_rel.mpr _) htmem
-  rw [Uniform.tendsto_nhds_right] at hm' 
+  rw [Uniform.tendsto_nhds_right] at hm'
   have := hx.and (hm' ht)
   obtain ⟨m, hm⟩ := this.exists
   exact ⟨F m x, ⟨hm.2, htsymm hm.1⟩⟩
@@ -689,10 +689,10 @@ theorem UniformCauchySeqOn.prod_map {ι' α' β' : Type _} [UniformSpace β'] {F
     UniformCauchySeqOn (fun i : ι × ι' => Prod.map (F i.1) (F' i.2)) (p.Prod p') (s ×ˢ s') :=
   by
   intro u hu
-  rw [uniformity_prod_eq_prod, mem_map, mem_prod_iff] at hu 
+  rw [uniformity_prod_eq_prod, mem_map, mem_prod_iff] at hu
   obtain ⟨v, hv, w, hw, hvw⟩ := hu
   simp_rw [mem_prod, Prod_map, and_imp, Prod.forall]
-  rw [← Set.image_subset_iff] at hvw 
+  rw [← Set.image_subset_iff] at hvw
   apply (tendsto_swap4_prod.eventually ((h v hv).prod_mk (h' w hw))).mono
   intro x hx a b ha hb
   refine' hvw ⟨_, mk_mem_prod (hx.1 a ha) (hx.2 b hb), rfl⟩
@@ -740,9 +740,9 @@ theorem tendstoUniformlyOn_of_seq_tendstoUniformlyOn {l : Filter ι} [l.IsCounta
   by
   rw [tendstoUniformlyOn_iff_tendsto, tendsto_iff_seq_tendsto]
   intro u hu
-  rw [tendsto_prod_iff'] at hu 
+  rw [tendsto_prod_iff'] at hu
   specialize h (fun n => (u n).fst) hu.1
-  rw [tendstoUniformlyOn_iff_tendsto] at h 
+  rw [tendstoUniformlyOn_iff_tendsto] at h
   have :
     (fun q : ι × α => (f q.snd, F q.fst q.snd)) ∘ u =
       (fun q : ℕ × α => (f q.snd, F ((fun n : ℕ => (u n).fst) q.fst) q.snd)) ∘ fun n =>
@@ -876,7 +876,7 @@ theorem tendstoLocallyUniformlyOn_iUnion {S : γ → Set α} (hS : ∀ i, IsOpen
   rintro v hv x ⟨_, ⟨i, rfl⟩, hi : x ∈ S i⟩
   obtain ⟨t, ht, ht'⟩ := h i v hv x hi
   refine' ⟨t, _, ht'⟩
-  rw [(hS _).nhdsWithin_eq hi] at ht 
+  rw [(hS _).nhdsWithin_eq hi] at ht
   exact mem_nhdsWithin_of_mem_nhds ht
 #align tendsto_locally_uniformly_on_Union tendstoLocallyUniformlyOn_iUnion
 -/
@@ -927,10 +927,10 @@ theorem tendstoLocallyUniformly_iff_tendstoUniformly_of_compactSpace [CompactSpa
   choose U hU using h V hV
   obtain ⟨t, ht⟩ := is_compact_univ.elim_nhds_subcover' (fun k hk => U k) fun k hk => (hU k).1
   replace hU := fun x : t => (hU x).2
-  rw [← eventually_all] at hU 
+  rw [← eventually_all] at hU
   refine' hU.mono fun i hi x => _
   specialize ht (mem_univ x)
-  simp only [exists_prop, mem_Union, SetCoe.exists, exists_and_right, Subtype.coe_mk] at ht 
+  simp only [exists_prop, mem_Union, SetCoe.exists, exists_and_right, Subtype.coe_mk] at ht
   obtain ⟨y, ⟨hy₁, hy₂⟩, hy₃⟩ := ht
   exact hi ⟨⟨y, hy₁⟩, hy₂⟩ x hy₃
 #align tendsto_locally_uniformly_iff_tendsto_uniformly_of_compact_space tendstoLocallyUniformly_iff_tendstoUniformly_of_compactSpace
@@ -945,7 +945,7 @@ theorem tendstoLocallyUniformlyOn_iff_tendstoUniformlyOn_of_compact (hs : IsComp
   refine' ⟨fun h => _, TendstoUniformlyOn.tendstoLocallyUniformlyOn⟩
   rwa [tendstoLocallyUniformlyOn_iff_tendstoLocallyUniformly_comp_coe,
     tendstoLocallyUniformly_iff_tendstoUniformly_of_compactSpace, ←
-    tendstoUniformlyOn_iff_tendstoUniformly_comp_coe] at h 
+    tendstoUniformlyOn_iff_tendstoUniformly_comp_coe] at h
 #align tendsto_locally_uniformly_on_iff_tendsto_uniformly_on_of_compact tendstoLocallyUniformlyOn_iff_tendstoUniformlyOn_of_compact
 -/
 
@@ -967,7 +967,7 @@ theorem TendstoLocallyUniformly.comp [TopologicalSpace γ] (h : TendstoLocallyUn
     (g : γ → α) (cg : Continuous g) : TendstoLocallyUniformly (fun n => F n ∘ g) (f ∘ g) p :=
   by
   rw [← tendstoLocallyUniformlyOn_univ] at h ⊢
-  rw [continuous_iff_continuousOn_univ] at cg 
+  rw [continuous_iff_continuousOn_univ] at cg
   exact h.comp _ (maps_to_univ _ _) cg
 #align tendsto_locally_uniformly.comp TendstoLocallyUniformly.comp
 -/
@@ -1237,8 +1237,8 @@ theorem tendsto_comp_of_locally_uniform_limit (h : ContinuousAt f x) (hg : Tends
     (hunif : ∀ u ∈ 𝓤 β, ∃ t ∈ 𝓝 x, ∀ᶠ n in p, ∀ y ∈ t, (f y, F n y) ∈ u) :
     Tendsto (fun n => F n (g n)) p (𝓝 (f x)) :=
   by
-  rw [← continuousWithinAt_univ] at h 
-  rw [← nhdsWithin_univ] at hunif hg 
+  rw [← continuousWithinAt_univ] at h
+  rw [← nhdsWithin_univ] at hunif hg
   exact tendsto_comp_of_locally_uniform_limit_within h hg hunif
 #align tendsto_comp_of_locally_uniform_limit tendsto_comp_of_locally_uniform_limit
 -/

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

@@ -3,9 +3,9 @@ Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 -/
-import Mathbin.Topology.Separation
-import Mathbin.Topology.UniformSpace.Basic
-import Mathbin.Topology.UniformSpace.Cauchy
+import Topology.Separation
+import Topology.UniformSpace.Basic
+import Topology.UniformSpace.Cauchy
 
 #align_import topology.uniform_space.uniform_convergence from "leanprover-community/mathlib"@"0a0ec35061ed9960bf0e7ffb0335f44447b58977"
 
@@ -972,7 +972,7 @@ theorem TendstoLocallyUniformly.comp [TopologicalSpace γ] (h : TendstoLocallyUn
 #align tendsto_locally_uniformly.comp TendstoLocallyUniformly.comp
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (K «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (K «expr ⊆ » s) -/
 #print tendstoLocallyUniformlyOn_TFAE /-
 theorem tendstoLocallyUniformlyOn_TFAE [LocallyCompactSpace α] (G : ι → α → β) (g : α → β)
     (p : Filter ι) (hs : IsOpen s) :
@@ -996,7 +996,7 @@ theorem tendstoLocallyUniformlyOn_TFAE [LocallyCompactSpace α] (G : ι → α 
 #align tendsto_locally_uniformly_on_tfae tendstoLocallyUniformlyOn_TFAE
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (K «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (K «expr ⊆ » s) -/
 #print tendstoLocallyUniformlyOn_iff_forall_isCompact /-
 theorem tendstoLocallyUniformlyOn_iff_forall_isCompact [LocallyCompactSpace α] (hs : IsOpen s) :
     TendstoLocallyUniformlyOn F f p s ↔

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

@@ -127,8 +127,8 @@ theorem tendstoUniformlyOn_iff_tendstoUniformlyOnFilter :
 #align tendsto_uniformly_on_iff_tendsto_uniformly_on_filter tendstoUniformlyOn_iff_tendstoUniformlyOnFilter
 -/
 
-alias tendstoUniformlyOn_iff_tendstoUniformlyOnFilter ↔ TendstoUniformlyOn.tendstoUniformlyOnFilter
-  TendstoUniformlyOnFilter.tendstoUniformlyOn
+alias ⟨TendstoUniformlyOn.tendstoUniformlyOnFilter, TendstoUniformlyOnFilter.tendstoUniformlyOn⟩ :=
+  tendstoUniformlyOn_iff_tendstoUniformlyOnFilter
 #align tendsto_uniformly_on.tendsto_uniformly_on_filter TendstoUniformlyOn.tendstoUniformlyOnFilter
 #align tendsto_uniformly_on_filter.tendsto_uniformly_on TendstoUniformlyOnFilter.tendstoUniformlyOn
 

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

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
-
-! This file was ported from Lean 3 source module topology.uniform_space.uniform_convergence
-! leanprover-community/mathlib commit 0a0ec35061ed9960bf0e7ffb0335f44447b58977
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Topology.Separation
 import Mathbin.Topology.UniformSpace.Basic
 import Mathbin.Topology.UniformSpace.Cauchy
 
+#align_import topology.uniform_space.uniform_convergence from "leanprover-community/mathlib"@"0a0ec35061ed9960bf0e7ffb0335f44447b58977"
+
 /-!
 # Uniform convergence
 
@@ -975,7 +972,7 @@ theorem TendstoLocallyUniformly.comp [TopologicalSpace γ] (h : TendstoLocallyUn
 #align tendsto_locally_uniformly.comp TendstoLocallyUniformly.comp
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (K «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (K «expr ⊆ » s) -/
 #print tendstoLocallyUniformlyOn_TFAE /-
 theorem tendstoLocallyUniformlyOn_TFAE [LocallyCompactSpace α] (G : ι → α → β) (g : α → β)
     (p : Filter ι) (hs : IsOpen s) :
@@ -999,7 +996,7 @@ theorem tendstoLocallyUniformlyOn_TFAE [LocallyCompactSpace α] (G : ι → α 
 #align tendsto_locally_uniformly_on_tfae tendstoLocallyUniformlyOn_TFAE
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (K «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (K «expr ⊆ » s) -/
 #print tendstoLocallyUniformlyOn_iff_forall_isCompact /-
 theorem tendstoLocallyUniformlyOn_iff_forall_isCompact [LocallyCompactSpace α] (hs : IsOpen s) :
     TendstoLocallyUniformlyOn F f p s ↔

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

@@ -155,6 +155,7 @@ def TendstoUniformly (F : ι → α → β) (f : α → β) (p : Filter ι) :=
 #align tendsto_uniformly TendstoUniformly
 -/
 
+#print tendstoUniformly_iff_tendstoUniformlyOnFilter /-
 theorem tendstoUniformly_iff_tendstoUniformlyOnFilter :
     TendstoUniformly F f p ↔ TendstoUniformlyOnFilter F f p ⊤ :=
   by
@@ -163,10 +164,13 @@ theorem tendstoUniformly_iff_tendstoUniformlyOnFilter :
   simp_rw [← principal_univ, eventually_prod_principal_iff]
   simp
 #align tendsto_uniformly_iff_tendsto_uniformly_on_filter tendstoUniformly_iff_tendstoUniformlyOnFilter
+-/
 
+#print TendstoUniformly.tendstoUniformlyOnFilter /-
 theorem TendstoUniformly.tendstoUniformlyOnFilter (h : TendstoUniformly F f p) :
     TendstoUniformlyOnFilter F f p ⊤ := by rwa [← tendstoUniformly_iff_tendstoUniformlyOnFilter]
 #align tendsto_uniformly.tendsto_uniformly_on_filter TendstoUniformly.tendstoUniformlyOnFilter
+-/
 
 #print tendstoUniformlyOn_iff_tendstoUniformly_comp_coe /-
 theorem tendstoUniformlyOn_iff_tendstoUniformly_comp_coe :
@@ -178,6 +182,7 @@ theorem tendstoUniformlyOn_iff_tendstoUniformly_comp_coe :
 #align tendsto_uniformly_on_iff_tendsto_uniformly_comp_coe tendstoUniformlyOn_iff_tendstoUniformly_comp_coe
 -/
 
+#print tendstoUniformly_iff_tendsto /-
 /-- A sequence of functions `Fₙ` converges uniformly to a limiting function `f` w.r.t.
 filter `p` iff the function `(n, x) ↦ (f x, Fₙ x)` converges along `p ×ᶠ ⊤` to the uniformity.
 In other words: one knows nothing about the behavior of `x` in this limit.
@@ -186,7 +191,9 @@ theorem tendstoUniformly_iff_tendsto {F : ι → α → β} {f : α → β} {p :
     TendstoUniformly F f p ↔ Tendsto (fun q : ι × α => (f q.2, F q.1 q.2)) (p ×ᶠ ⊤) (𝓤 β) := by
   simp [tendstoUniformly_iff_tendstoUniformlyOnFilter, tendstoUniformlyOnFilter_iff_tendsto]
 #align tendsto_uniformly_iff_tendsto tendstoUniformly_iff_tendsto
+-/
 
+#print TendstoUniformlyOnFilter.tendsto_at /-
 /-- Uniform converence implies pointwise convergence. -/
 theorem TendstoUniformlyOnFilter.tendsto_at (h : TendstoUniformlyOnFilter F f p p')
     (hx : 𝓟 {x} ≤ p') : Tendsto (fun n => F n x) p <| 𝓝 (f x) :=
@@ -196,6 +203,7 @@ theorem TendstoUniformlyOnFilter.tendsto_at (h : TendstoUniformlyOnFilter F f p
   intro i h
   simpa using h.filter_mono hx
 #align tendsto_uniformly_on_filter.tendsto_at TendstoUniformlyOnFilter.tendsto_at
+-/
 
 #print TendstoUniformlyOn.tendsto_at /-
 /-- Uniform converence implies pointwise convergence. -/
@@ -220,15 +228,19 @@ theorem tendstoUniformlyOn_univ : TendstoUniformlyOn F f p univ ↔ TendstoUnifo
 #align tendsto_uniformly_on_univ tendstoUniformlyOn_univ
 -/
 
+#print TendstoUniformlyOnFilter.mono_left /-
 theorem TendstoUniformlyOnFilter.mono_left {p'' : Filter ι} (h : TendstoUniformlyOnFilter F f p p')
     (hp : p'' ≤ p) : TendstoUniformlyOnFilter F f p'' p' := fun u hu =>
   (h u hu).filter_mono (p'.prod_mono_left hp)
 #align tendsto_uniformly_on_filter.mono_left TendstoUniformlyOnFilter.mono_left
+-/
 
+#print TendstoUniformlyOnFilter.mono_right /-
 theorem TendstoUniformlyOnFilter.mono_right {p'' : Filter α} (h : TendstoUniformlyOnFilter F f p p')
     (hp : p'' ≤ p') : TendstoUniformlyOnFilter F f p p'' := fun u hu =>
   (h u hu).filter_mono (p.prod_mono_right hp)
 #align tendsto_uniformly_on_filter.mono_right TendstoUniformlyOnFilter.mono_right
+-/
 
 #print TendstoUniformlyOn.mono /-
 theorem TendstoUniformlyOn.mono {s' : Set α} (h : TendstoUniformlyOn F f p s) (h' : s' ⊆ s) :
@@ -337,6 +349,7 @@ theorem UniformContinuous.comp_tendstoUniformly [UniformSpace γ] {g : β → γ
 #align uniform_continuous.comp_tendsto_uniformly UniformContinuous.comp_tendstoUniformly
 -/
 
+#print TendstoUniformlyOnFilter.prod_map /-
 theorem TendstoUniformlyOnFilter.prod_map {ι' α' β' : Type _} [UniformSpace β'] {F' : ι' → α' → β'}
     {f' : α' → β'} {q : Filter ι'} {q' : Filter α'} (h : TendstoUniformlyOnFilter F f p p')
     (h' : TendstoUniformlyOnFilter F' f' q q') :
@@ -355,8 +368,10 @@ theorem TendstoUniformlyOnFilter.prod_map {ι' α' β' : Type _} [UniformSpace 
     mem_of_mem_of_subset (set.mem_prod.mpr ⟨hxv, hxw⟩) hvw
   exact hout
 #align tendsto_uniformly_on_filter.prod_map TendstoUniformlyOnFilter.prod_map
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print TendstoUniformlyOn.prod_map /-
 theorem TendstoUniformlyOn.prod_map {ι' α' β' : Type _} [UniformSpace β'] {F' : ι' → α' → β'}
     {f' : α' → β'} {p' : Filter ι'} {s' : Set α'} (h : TendstoUniformlyOn F f p s)
     (h' : TendstoUniformlyOn F' f' p' s') :
@@ -366,7 +381,9 @@ theorem TendstoUniformlyOn.prod_map {ι' α' β' : Type _} [UniformSpace β'] {F
   rw [tendstoUniformlyOn_iff_tendstoUniformlyOnFilter] at h h' ⊢
   simpa only [prod_principal_principal] using h.prod_map h'
 #align tendsto_uniformly_on.prod_map TendstoUniformlyOn.prod_map
+-/
 
+#print TendstoUniformly.prod_map /-
 theorem TendstoUniformly.prod_map {ι' α' β' : Type _} [UniformSpace β'] {F' : ι' → α' → β'}
     {f' : α' → β'} {p' : Filter ι'} (h : TendstoUniformly F f p) (h' : TendstoUniformly F' f' p') :
     TendstoUniformly (fun i : ι × ι' => Prod.map (F i.1) (F' i.2)) (Prod.map f f') (p.Prod p') :=
@@ -374,7 +391,9 @@ theorem TendstoUniformly.prod_map {ι' α' β' : Type _} [UniformSpace β'] {F'
   rw [← tendstoUniformlyOn_univ, ← univ_prod_univ] at *
   exact h.prod_map h'
 #align tendsto_uniformly.prod_map TendstoUniformly.prod_map
+-/
 
+#print TendstoUniformlyOnFilter.prod /-
 theorem TendstoUniformlyOnFilter.prod {ι' β' : Type _} [UniformSpace β'] {F' : ι' → α → β'}
     {f' : α → β'} {q : Filter ι'} (h : TendstoUniformlyOnFilter F f p p')
     (h' : TendstoUniformlyOnFilter F' f' q p') :
@@ -382,20 +401,25 @@ theorem TendstoUniformlyOnFilter.prod {ι' β' : Type _} [UniformSpace β'] {F'
       (p.Prod q) p' :=
   fun u hu => ((h.Prod_map h') u hu).diag_of_prod_right
 #align tendsto_uniformly_on_filter.prod TendstoUniformlyOnFilter.prod
+-/
 
+#print TendstoUniformlyOn.prod /-
 theorem TendstoUniformlyOn.prod {ι' β' : Type _} [UniformSpace β'] {F' : ι' → α → β'} {f' : α → β'}
     {p' : Filter ι'} (h : TendstoUniformlyOn F f p s) (h' : TendstoUniformlyOn F' f' p' s) :
     TendstoUniformlyOn (fun (i : ι × ι') a => (F i.1 a, F' i.2 a)) (fun a => (f a, f' a))
       (p.Prod p') s :=
   (congr_arg _ s.inter_self).mp ((h.Prod_map h').comp fun a => (a, a))
 #align tendsto_uniformly_on.prod TendstoUniformlyOn.prod
+-/
 
+#print TendstoUniformly.prod /-
 theorem TendstoUniformly.prod {ι' β' : Type _} [UniformSpace β'] {F' : ι' → α → β'} {f' : α → β'}
     {p' : Filter ι'} (h : TendstoUniformly F f p) (h' : TendstoUniformly F' f' p') :
     TendstoUniformly (fun (i : ι × ι') a => (F i.1 a, F' i.2 a)) (fun a => (f a, f' a))
       (p.Prod p') :=
   (h.Prod_map h').comp fun a => (a, a)
 #align tendsto_uniformly.prod TendstoUniformly.prod
+-/
 
 #print tendsto_prod_filter_iff /-
 /-- Uniform convergence on a filter `p'` to a constant function is equivalent to convergence in
@@ -419,6 +443,7 @@ theorem tendsto_prod_principal_iff {c : β} :
 #align tendsto_prod_principal_iff tendsto_prod_principal_iff
 -/
 
+#print tendsto_prod_top_iff /-
 /-- Uniform convergence to a constant function is equivalent to convergence in `p ×ᶠ ⊤`. -/
 theorem tendsto_prod_top_iff {c : β} :
     Tendsto (↿F) (p ×ᶠ ⊤) (𝓝 c) ↔ TendstoUniformly F (fun _ => c) p :=
@@ -426,6 +451,7 @@ theorem tendsto_prod_top_iff {c : β} :
   rw [tendstoUniformly_iff_tendstoUniformlyOnFilter]
   exact tendsto_prod_filter_iff
 #align tendsto_prod_top_iff tendsto_prod_top_iff
+-/
 
 #print tendstoUniformlyOn_empty /-
 /-- Uniform convergence on the empty set is vacuously true -/
@@ -468,6 +494,7 @@ theorem Filter.Tendsto.tendstoUniformlyOn_const {g : ι → β} {b : β} (hg : T
 -/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print UniformContinuousOn.tendstoUniformly /-
 theorem UniformContinuousOn.tendstoUniformly [UniformSpace α] [UniformSpace γ] {x : α} {U : Set α}
     (hU : U ∈ 𝓝 x) {F : α → β → γ} (hF : UniformContinuousOn (↿F) (U ×ˢ (univ : Set β))) :
     TendstoUniformly F (F x) (𝓝 x) :=
@@ -488,6 +515,7 @@ theorem UniformContinuousOn.tendstoUniformly [UniformSpace α] [UniformSpace γ]
     apply mem_of_superset (prod_mem_prod hU (mem_top.mpr rfl)) fun q h => _
     simp [h.1, mem_of_mem_nhds hU]
 #align uniform_continuous_on.tendsto_uniformly UniformContinuousOn.tendstoUniformly
+-/
 
 #print UniformContinuous₂.tendstoUniformly /-
 theorem UniformContinuous₂.tendstoUniformly [UniformSpace α] [UniformSpace γ] {f : α → β → γ}
@@ -595,6 +623,7 @@ theorem UniformCauchySeqOn.tendstoUniformlyOn_of_tendsto [NeBot p] (hF : Uniform
 #align uniform_cauchy_seq_on.tendsto_uniformly_on_of_tendsto UniformCauchySeqOn.tendstoUniformlyOn_of_tendsto
 -/
 
+#print UniformCauchySeqOnFilter.mono_left /-
 theorem UniformCauchySeqOnFilter.mono_left {p'' : Filter ι} (hf : UniformCauchySeqOnFilter F p p')
     (hp : p'' ≤ p) : UniformCauchySeqOnFilter F p'' p' :=
   by
@@ -602,7 +631,9 @@ theorem UniformCauchySeqOnFilter.mono_left {p'' : Filter ι} (hf : UniformCauchy
   have := (hf u hu).filter_mono (p'.prod_mono_left (Filter.prod_mono hp hp))
   exact this.mono (by simp)
 #align uniform_cauchy_seq_on_filter.mono_left UniformCauchySeqOnFilter.mono_left
+-/
 
+#print UniformCauchySeqOnFilter.mono_right /-
 theorem UniformCauchySeqOnFilter.mono_right {p'' : Filter α} (hf : UniformCauchySeqOnFilter F p p')
     (hp : p'' ≤ p') : UniformCauchySeqOnFilter F p p'' :=
   by
@@ -610,6 +641,7 @@ theorem UniformCauchySeqOnFilter.mono_right {p'' : Filter α} (hf : UniformCauch
   have := (hf u hu).filter_mono ((p ×ᶠ p).prod_mono_right hp)
   exact this.mono (by simp)
 #align uniform_cauchy_seq_on_filter.mono_right UniformCauchySeqOnFilter.mono_right
+-/
 
 #print UniformCauchySeqOn.mono /-
 theorem UniformCauchySeqOn.mono {s' : Set α} (hf : UniformCauchySeqOn F p s) (hss' : s' ⊆ s) :
@@ -620,6 +652,7 @@ theorem UniformCauchySeqOn.mono {s' : Set α} (hf : UniformCauchySeqOn F p s) (h
 #align uniform_cauchy_seq_on.mono UniformCauchySeqOn.mono
 -/
 
+#print UniformCauchySeqOnFilter.comp /-
 /-- Composing on the right by a function preserves uniform Cauchy sequences -/
 theorem UniformCauchySeqOnFilter.comp {γ : Type _} (hf : UniformCauchySeqOnFilter F p p')
     (g : γ → α) : UniformCauchySeqOnFilter (fun n => F n ∘ g) p (p'.comap g) :=
@@ -630,7 +663,9 @@ theorem UniformCauchySeqOnFilter.comp {γ : Type _} (hf : UniformCauchySeqOnFilt
   refine' ⟨pa, hpa, pb ∘ g, _, fun x hx y hy => hpapb hx hy⟩
   exact eventually_comap.mpr (hpb.mono fun x hx y hy => by simp only [hx, hy, Function.comp_apply])
 #align uniform_cauchy_seq_on_filter.comp UniformCauchySeqOnFilter.comp
+-/
 
+#print UniformCauchySeqOn.comp /-
 /-- Composing on the right by a function preserves uniform Cauchy sequences -/
 theorem UniformCauchySeqOn.comp {γ : Type _} (hf : UniformCauchySeqOn F p s) (g : γ → α) :
     UniformCauchySeqOn (fun n => F n ∘ g) p (g ⁻¹' s) :=
@@ -638,6 +673,7 @@ theorem UniformCauchySeqOn.comp {γ : Type _} (hf : UniformCauchySeqOn F p s) (g
   rw [uniformCauchySeqOn_iff_uniformCauchySeqOnFilter] at hf ⊢
   simpa only [UniformCauchySeqOn, comap_principal] using hf.comp g
 #align uniform_cauchy_seq_on.comp UniformCauchySeqOn.comp
+-/
 
 #print UniformContinuous.comp_uniformCauchySeqOn /-
 /-- Composing on the left by a uniformly continuous function preserves
@@ -649,6 +685,7 @@ theorem UniformContinuous.comp_uniformCauchySeqOn [UniformSpace γ] {g : β →
 -/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print UniformCauchySeqOn.prod_map /-
 theorem UniformCauchySeqOn.prod_map {ι' α' β' : Type _} [UniformSpace β'] {F' : ι' → α' → β'}
     {p' : Filter ι'} {s' : Set α'} (h : UniformCauchySeqOn F p s)
     (h' : UniformCauchySeqOn F' p' s') :
@@ -663,13 +700,17 @@ theorem UniformCauchySeqOn.prod_map {ι' α' β' : Type _} [UniformSpace β'] {F
   intro x hx a b ha hb
   refine' hvw ⟨_, mk_mem_prod (hx.1 a ha) (hx.2 b hb), rfl⟩
 #align uniform_cauchy_seq_on.prod_map UniformCauchySeqOn.prod_map
+-/
 
+#print UniformCauchySeqOn.prod /-
 theorem UniformCauchySeqOn.prod {ι' β' : Type _} [UniformSpace β'] {F' : ι' → α → β'}
     {p' : Filter ι'} (h : UniformCauchySeqOn F p s) (h' : UniformCauchySeqOn F' p' s) :
     UniformCauchySeqOn (fun (i : ι × ι') a => (F i.fst a, F' i.snd a)) (p ×ᶠ p') s :=
   (congr_arg _ s.inter_self).mp ((h.Prod_map h').comp fun a => (a, a))
 #align uniform_cauchy_seq_on.prod UniformCauchySeqOn.prod
+-/
 
+#print UniformCauchySeqOn.prod' /-
 theorem UniformCauchySeqOn.prod' {β' : Type _} [UniformSpace β'] {F' : ι → α → β'}
     (h : UniformCauchySeqOn F p s) (h' : UniformCauchySeqOn F' p s) :
     UniformCauchySeqOn (fun (i : ι) a => (F i a, F' i a)) p s :=
@@ -678,6 +719,7 @@ theorem UniformCauchySeqOn.prod' {β' : Type _} [UniformSpace β'] {F' : ι →
   have hh : tendsto (fun x : ι => (x, x)) p (p ×ᶠ p) := tendsto_diag
   exact (hh.prod_map hh).Eventually ((h.prod h') u hu)
 #align uniform_cauchy_seq_on.prod' UniformCauchySeqOn.prod'
+-/
 
 #print UniformCauchySeqOn.cauchy_map /-
 /-- If a sequence of functions is uniformly Cauchy on a set, then the values at each point form
@@ -830,6 +872,7 @@ theorem TendstoLocallyUniformlyOn.mono (h : TendstoLocallyUniformlyOn F f p s) (
 #align tendsto_locally_uniformly_on.mono TendstoLocallyUniformlyOn.mono
 -/
 
+#print tendstoLocallyUniformlyOn_iUnion /-
 theorem tendstoLocallyUniformlyOn_iUnion {S : γ → Set α} (hS : ∀ i, IsOpen (S i))
     (h : ∀ i, TendstoLocallyUniformlyOn F f p (S i)) : TendstoLocallyUniformlyOn F f p (⋃ i, S i) :=
   by
@@ -839,6 +882,7 @@ theorem tendstoLocallyUniformlyOn_iUnion {S : γ → Set α} (hS : ∀ i, IsOpen
   rw [(hS _).nhdsWithin_eq hi] at ht 
   exact mem_nhdsWithin_of_mem_nhds ht
 #align tendsto_locally_uniformly_on_Union tendstoLocallyUniformlyOn_iUnion
+-/
 
 #print tendstoLocallyUniformlyOn_biUnion /-
 theorem tendstoLocallyUniformlyOn_biUnion {s : Set γ} {S : γ → Set α} (hS : ∀ i ∈ s, IsOpen (S i))
@@ -855,11 +899,13 @@ theorem tendstoLocallyUniformlyOn_sUnion (S : Set (Set α)) (hS : ∀ s ∈ S, I
 #align tendsto_locally_uniformly_on_sUnion tendstoLocallyUniformlyOn_sUnion
 -/
 
+#print TendstoLocallyUniformlyOn.union /-
 theorem TendstoLocallyUniformlyOn.union {s₁ s₂ : Set α} (hs₁ : IsOpen s₁) (hs₂ : IsOpen s₂)
     (h₁ : TendstoLocallyUniformlyOn F f p s₁) (h₂ : TendstoLocallyUniformlyOn F f p s₂) :
     TendstoLocallyUniformlyOn F f p (s₁ ∪ s₂) := by rw [← sUnion_pair];
   refine' tendstoLocallyUniformlyOn_sUnion _ _ _ <;> simp [*]
 #align tendsto_locally_uniformly_on.union TendstoLocallyUniformlyOn.union
+-/
 
 #print tendstoLocallyUniformlyOn_univ /-
 theorem tendstoLocallyUniformlyOn_univ :
@@ -930,6 +976,7 @@ theorem TendstoLocallyUniformly.comp [TopologicalSpace γ] (h : TendstoLocallyUn
 -/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (K «expr ⊆ » s) -/
+#print tendstoLocallyUniformlyOn_TFAE /-
 theorem tendstoLocallyUniformlyOn_TFAE [LocallyCompactSpace α] (G : ι → α → β) (g : α → β)
     (p : Filter ι) (hs : IsOpen s) :
     TFAE
@@ -950,6 +997,7 @@ theorem tendstoLocallyUniformlyOn_TFAE [LocallyCompactSpace α] (G : ι → α 
     exact ⟨v, hv1, hv2 u hu⟩
   tfae_finish
 #align tendsto_locally_uniformly_on_tfae tendstoLocallyUniformlyOn_TFAE
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (K «expr ⊆ » s) -/
 #print tendstoLocallyUniformlyOn_iff_forall_isCompact /-
@@ -1031,6 +1079,7 @@ the statements are derived from a statement about locally uniform approximation
 a point, called `continuous_within_at_of_locally_uniform_approx_of_continuous_within_at`. -/
 
 
+#print continuousWithinAt_of_locally_uniform_approx_of_continuousWithinAt /-
 /-- A function which can be locally uniformly approximated by functions which are continuous
 within a set at a point is continuous within this set at this point. -/
 theorem continuousWithinAt_of_locally_uniform_approx_of_continuousWithinAt (hx : x ∈ s)
@@ -1052,7 +1101,9 @@ theorem continuousWithinAt_of_locally_uniform_approx_of_continuousWithinAt (hx :
     u₂₁ (prod_mk_mem_compRel (refl_mem_uniformity h₂) (hsymm (A.self_of_nhds_within hx)))
   exact C.mono fun y hy => u₁₀ (prod_mk_mem_compRel hy this)
 #align continuous_within_at_of_locally_uniform_approx_of_continuous_within_at continuousWithinAt_of_locally_uniform_approx_of_continuousWithinAt
+-/
 
+#print continuousAt_of_locally_uniform_approx_of_continuousAt /-
 /-- A function which can be locally uniformly approximated by functions which are continuous at
 a point is continuous at this point. -/
 theorem continuousAt_of_locally_uniform_approx_of_continuousAt
@@ -1062,7 +1113,9 @@ theorem continuousAt_of_locally_uniform_approx_of_continuousAt
   apply continuousWithinAt_of_locally_uniform_approx_of_continuousWithinAt (mem_univ _) _
   simpa only [exists_prop, nhdsWithin_univ, continuousWithinAt_univ] using L
 #align continuous_at_of_locally_uniform_approx_of_continuous_at continuousAt_of_locally_uniform_approx_of_continuousAt
+-/
 
+#print continuousOn_of_locally_uniform_approx_of_continuousWithinAt /-
 /-- A function which can be locally uniformly approximated by functions which are continuous
 on a set is continuous on this set. -/
 theorem continuousOn_of_locally_uniform_approx_of_continuousWithinAt
@@ -1071,6 +1124,7 @@ theorem continuousOn_of_locally_uniform_approx_of_continuousWithinAt
     ContinuousOn f s := fun x hx =>
   continuousWithinAt_of_locally_uniform_approx_of_continuousWithinAt hx (L x hx)
 #align continuous_on_of_locally_uniform_approx_of_continuous_within_at continuousOn_of_locally_uniform_approx_of_continuousWithinAt
+-/
 
 #print continuousOn_of_uniform_approx_of_continuousOn /-
 /-- A function which can be uniformly approximated by functions which are continuous on a set
@@ -1082,6 +1136,7 @@ theorem continuousOn_of_uniform_approx_of_continuousOn
 #align continuous_on_of_uniform_approx_of_continuous_on continuousOn_of_uniform_approx_of_continuousOn
 -/
 
+#print continuous_of_locally_uniform_approx_of_continuousAt /-
 /-- A function which can be locally uniformly approximated by continuous functions is continuous. -/
 theorem continuous_of_locally_uniform_approx_of_continuousAt
     (L : ∀ x : α, ∀ u ∈ 𝓤 β, ∃ t ∈ 𝓝 x, ∃ F, ContinuousAt F x ∧ ∀ y ∈ t, (f y, F y) ∈ u) :
@@ -1089,6 +1144,7 @@ theorem continuous_of_locally_uniform_approx_of_continuousAt
   continuous_iff_continuousAt.2 fun x =>
     continuousAt_of_locally_uniform_approx_of_continuousAt (L x)
 #align continuous_of_locally_uniform_approx_of_continuous_at continuous_of_locally_uniform_approx_of_continuousAt
+-/
 
 #print continuous_of_uniform_approx_of_continuous /-
 /-- A function which can be uniformly approximated by continuous functions is continuous. -/
@@ -1156,6 +1212,7 @@ this paragraph, we prove variations around this statement.
 -/
 
 
+#print tendsto_comp_of_locally_uniform_limit_within /-
 /-- If `Fₙ` converges locally uniformly on a neighborhood of `x` within a set `s` to a function `f`
 which is continuous at `x` within `s `, and `gₙ` tends to `x` within `s`, then `Fₙ (gₙ)` tends
 to `f x`. -/
@@ -1174,7 +1231,9 @@ theorem tendsto_comp_of_locally_uniform_limit_within (h : ContinuousWithinAt f s
   rcases hy with ⟨⟨H1, H2⟩, H3⟩
   exact u₁₀ (prod_mk_mem_compRel H3 (H1 _ H2))
 #align tendsto_comp_of_locally_uniform_limit_within tendsto_comp_of_locally_uniform_limit_within
+-/
 
+#print tendsto_comp_of_locally_uniform_limit /-
 /-- If `Fₙ` converges locally uniformly on a neighborhood of `x` to a function `f` which is
 continuous at `x`, and `gₙ` tends to `x`, then `Fₙ (gₙ)` tends to `f x`. -/
 theorem tendsto_comp_of_locally_uniform_limit (h : ContinuousAt f x) (hg : Tendsto g p (𝓝 x))
@@ -1185,6 +1244,7 @@ theorem tendsto_comp_of_locally_uniform_limit (h : ContinuousAt f x) (hg : Tends
   rw [← nhdsWithin_univ] at hunif hg 
   exact tendsto_comp_of_locally_uniform_limit_within h hg hunif
 #align tendsto_comp_of_locally_uniform_limit tendsto_comp_of_locally_uniform_limit
+-/
 
 #print TendstoLocallyUniformlyOn.tendsto_comp /-
 /-- If `Fₙ` tends locally uniformly to `f` on a set `s`, and `gₙ` tends to `x` within `s`, then

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

@@ -929,7 +929,7 @@ theorem TendstoLocallyUniformly.comp [TopologicalSpace γ] (h : TendstoLocallyUn
 #align tendsto_locally_uniformly.comp TendstoLocallyUniformly.comp
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (K «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (K «expr ⊆ » s) -/
 theorem tendstoLocallyUniformlyOn_TFAE [LocallyCompactSpace α] (G : ι → α → β) (g : α → β)
     (p : Filter ι) (hs : IsOpen s) :
     TFAE
@@ -951,7 +951,7 @@ theorem tendstoLocallyUniformlyOn_TFAE [LocallyCompactSpace α] (G : ι → α 
   tfae_finish
 #align tendsto_locally_uniformly_on_tfae tendstoLocallyUniformlyOn_TFAE
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (K «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (K «expr ⊆ » s) -/
 #print tendstoLocallyUniformlyOn_iff_forall_isCompact /-
 theorem tendstoLocallyUniformlyOn_iff_forall_isCompact [LocallyCompactSpace α] (hs : IsOpen s) :
     TendstoLocallyUniformlyOn F f p s ↔

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

@@ -130,8 +130,8 @@ theorem tendstoUniformlyOn_iff_tendstoUniformlyOnFilter :
 #align tendsto_uniformly_on_iff_tendsto_uniformly_on_filter tendstoUniformlyOn_iff_tendstoUniformlyOnFilter
 -/
 
-alias tendstoUniformlyOn_iff_tendstoUniformlyOnFilter ↔
-  TendstoUniformlyOn.tendstoUniformlyOnFilter TendstoUniformlyOnFilter.tendstoUniformlyOn
+alias tendstoUniformlyOn_iff_tendstoUniformlyOnFilter ↔ TendstoUniformlyOn.tendstoUniformlyOnFilter
+  TendstoUniformlyOnFilter.tendstoUniformlyOn
 #align tendsto_uniformly_on.tendsto_uniformly_on_filter TendstoUniformlyOn.tendstoUniformlyOnFilter
 #align tendsto_uniformly_on_filter.tendsto_uniformly_on TendstoUniformlyOnFilter.tendstoUniformlyOn
 
@@ -264,7 +264,7 @@ theorem TendstoUniformlyOn.congr {F' : ι → α → β} (hf : TendstoUniformlyO
 #print TendstoUniformlyOn.congr_right /-
 theorem TendstoUniformlyOn.congr_right {g : α → β} (hf : TendstoUniformlyOn F f p s)
     (hfg : EqOn f g s) : TendstoUniformlyOn F g p s := fun u hu => by
-  filter_upwards [hf u hu]with i hi a ha using hfg ha ▸ hi a ha
+  filter_upwards [hf u hu] with i hi a ha using hfg ha ▸ hi a ha
 #align tendsto_uniformly_on.congr_right TendstoUniformlyOn.congr_right
 -/
 
@@ -351,7 +351,7 @@ theorem TendstoUniformlyOnFilter.prod_map {ι' α' β' : Type _} [UniformSpace 
   intro n n' x hxv hxw
   have hout :
     ((f x.fst, F n x.fst), (f' x.snd, F' n' x.snd)) ∈
-      { x : (β × β) × β' × β' | ((x.fst.fst, x.snd.fst), x.fst.snd, x.snd.snd) ∈ u } :=
+      {x : (β × β) × β' × β' | ((x.fst.fst, x.snd.fst), x.fst.snd, x.snd.snd) ∈ u} :=
     mem_of_mem_of_subset (set.mem_prod.mpr ⟨hxv, hxw⟩) hvw
   exact hout
 #align tendsto_uniformly_on_filter.prod_map TendstoUniformlyOnFilter.prod_map
@@ -688,7 +688,7 @@ theorem UniformCauchySeqOn.cauchy_map [hp : NeBot p] (hf : UniformCauchySeqOn F
   simp only [cauchy_map_iff, hp, true_and_iff]
   intro u hu
   rw [mem_map]
-  filter_upwards [hf u hu]with p hp using hp x hx
+  filter_upwards [hf u hu] with p hp using hp x hx
 #align uniform_cauchy_seq_on.cauchy_map UniformCauchySeqOn.cauchy_map
 -/
 
@@ -804,7 +804,7 @@ theorem tendstoLocallyUniformly_iff_forall_tendsto :
   · rintro ⟨n, hn, hp⟩
     exact ⟨_, hp, n, hn, fun i hi a ha => hi a ha⟩
   · rintro ⟨I, hI, n, hn, hu⟩
-    exact ⟨n, hn, by filter_upwards [hI]using hu⟩
+    exact ⟨n, hn, by filter_upwards [hI] using hu⟩
 #align tendsto_locally_uniformly_iff_forall_tendsto tendstoLocallyUniformly_iff_forall_tendsto
 -/
 
@@ -914,7 +914,7 @@ theorem TendstoLocallyUniformlyOn.comp [TopologicalSpace γ] {t : Set γ}
   intro u hu x hx
   rcases h u hu (g x) (hg hx) with ⟨a, ha, H⟩
   have : g ⁻¹' a ∈ 𝓝[t] x :=
-    (cg x hx).preimage_mem_nhds_within' (nhdsWithin_mono (g x) hg.image_subset ha)
+    (cg x hx).preimage_mem_nhdsWithin' (nhdsWithin_mono (g x) hg.image_subset ha)
   exact ⟨g ⁻¹' a, this, H.mono fun n hn y hy => hn _ hy⟩
 #align tendsto_locally_uniformly_on.comp TendstoLocallyUniformlyOn.comp
 -/
@@ -1006,7 +1006,7 @@ theorem TendstoLocallyUniformlyOn.congr {G : ι → α → β} (hf : TendstoLoca
   rintro u hu x hx
   obtain ⟨t, ht, h⟩ := hf u hu x hx
   refine' ⟨s ∩ t, inter_mem self_mem_nhdsWithin ht, _⟩
-  filter_upwards [h]with i hi y hy using hg i hy.1 ▸ hi y hy.2
+  filter_upwards [h] with i hi y hy using hg i hy.1 ▸ hi y hy.2
 #align tendsto_locally_uniformly_on.congr TendstoLocallyUniformlyOn.congr
 -/
 
@@ -1017,7 +1017,7 @@ theorem TendstoLocallyUniformlyOn.congr_right {g : α → β} (hf : TendstoLocal
   rintro u hu x hx
   obtain ⟨t, ht, h⟩ := hf u hu x hx
   refine' ⟨s ∩ t, inter_mem self_mem_nhdsWithin ht, _⟩
-  filter_upwards [h]with i hi y hy using hg hy.1 ▸ hi y hy.2
+  filter_upwards [h] with i hi y hy using hg hy.1 ▸ hi y hy.2
 #align tendsto_locally_uniformly_on.congr_right TendstoLocallyUniformlyOn.congr_right
 -/
 

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

@@ -253,10 +253,10 @@ theorem TendstoUniformlyOnFilter.congr {F' : ι → α → β} (hf : TendstoUnif
 theorem TendstoUniformlyOn.congr {F' : ι → α → β} (hf : TendstoUniformlyOn F f p s)
     (hff' : ∀ᶠ n in p, Set.EqOn (F n) (F' n) s) : TendstoUniformlyOn F' f p s :=
   by
-  rw [tendstoUniformlyOn_iff_tendstoUniformlyOnFilter] at hf⊢
+  rw [tendstoUniformlyOn_iff_tendstoUniformlyOnFilter] at hf ⊢
   refine' hf.congr _
-  rw [eventually_iff] at hff'⊢
-  simp only [Set.EqOn] at hff'
+  rw [eventually_iff] at hff' ⊢
+  simp only [Set.EqOn] at hff' 
   simp only [mem_prod_principal, hff', mem_set_of_eq]
 #align tendsto_uniformly_on.congr TendstoUniformlyOn.congr
 -/
@@ -296,7 +296,7 @@ theorem TendstoUniformlyOnFilter.comp (h : TendstoUniformlyOnFilter F f p p') (g
 theorem TendstoUniformlyOn.comp (h : TendstoUniformlyOn F f p s) (g : γ → α) :
     TendstoUniformlyOn (fun n => F n ∘ g) (f ∘ g) p (g ⁻¹' s) :=
   by
-  rw [tendstoUniformlyOn_iff_tendstoUniformlyOnFilter] at h⊢
+  rw [tendstoUniformlyOn_iff_tendstoUniformlyOnFilter] at h ⊢
   simpa [TendstoUniformlyOn, comap_principal] using TendstoUniformlyOnFilter.comp h g
 #align tendsto_uniformly_on.comp TendstoUniformlyOn.comp
 -/
@@ -306,7 +306,7 @@ theorem TendstoUniformlyOn.comp (h : TendstoUniformlyOn F f p s) (g : γ → α)
 theorem TendstoUniformly.comp (h : TendstoUniformly F f p) (g : γ → α) :
     TendstoUniformly (fun n => F n ∘ g) (f ∘ g) p :=
   by
-  rw [tendstoUniformly_iff_tendstoUniformlyOnFilter] at h⊢
+  rw [tendstoUniformly_iff_tendstoUniformlyOnFilter] at h ⊢
   simpa [principal_univ, comap_principal] using h.comp g
 #align tendsto_uniformly.comp TendstoUniformly.comp
 -/
@@ -344,7 +344,7 @@ theorem TendstoUniformlyOnFilter.prod_map {ι' α' β' : Type _} [UniformSpace 
       (p.Prod q) (p'.Prod q') :=
   by
   intro u hu
-  rw [uniformity_prod_eq_prod, mem_map, mem_prod_iff] at hu
+  rw [uniformity_prod_eq_prod, mem_map, mem_prod_iff] at hu 
   obtain ⟨v, hv, w, hw, hvw⟩ := hu
   apply (tendsto_swap4_prod.eventually ((h v hv).prod_mk (h' w hw))).mono
   simp only [Prod_map, and_imp, Prod.forall]
@@ -363,7 +363,7 @@ theorem TendstoUniformlyOn.prod_map {ι' α' β' : Type _} [UniformSpace β'] {F
     TendstoUniformlyOn (fun i : ι × ι' => Prod.map (F i.1) (F' i.2)) (Prod.map f f') (p.Prod p')
       (s ×ˢ s') :=
   by
-  rw [tendstoUniformlyOn_iff_tendstoUniformlyOnFilter] at h h'⊢
+  rw [tendstoUniformlyOn_iff_tendstoUniformlyOnFilter] at h h' ⊢
   simpa only [prod_principal_principal] using h.prod_map h'
 #align tendsto_uniformly_on.prod_map TendstoUniformlyOn.prod_map
 
@@ -451,7 +451,7 @@ theorem Filter.Tendsto.tendstoUniformlyOnFilter_const {g : ι → β} {b : β} (
     TendstoUniformlyOnFilter (fun n : ι => fun a : α => g n) (fun a : α => b) p p' :=
   by
   rw [tendstoUniformlyOnFilter_iff_tendsto]
-  rw [Uniform.tendsto_nhds_right] at hg
+  rw [Uniform.tendsto_nhds_right] at hg 
   exact
     (hg.comp (tendsto_fst.comp ((@tendsto_id ι p).Prod_map (@tendsto_id α p')))).congr fun x => by
       simp
@@ -579,7 +579,7 @@ theorem UniformCauchySeqOnFilter.tendstoUniformlyOnFilter_of_tendsto [NeBot p]
   -- Complete the proof
   intro x n hx hm'
   refine' Set.mem_of_mem_of_subset (mem_comp_rel.mpr _) htmem
-  rw [Uniform.tendsto_nhds_right] at hm'
+  rw [Uniform.tendsto_nhds_right] at hm' 
   have := hx.and (hm' ht)
   obtain ⟨m, hm⟩ := this.exists
   exact ⟨F m x, ⟨hm.2, htsymm hm.1⟩⟩
@@ -615,7 +615,7 @@ theorem UniformCauchySeqOnFilter.mono_right {p'' : Filter α} (hf : UniformCauch
 theorem UniformCauchySeqOn.mono {s' : Set α} (hf : UniformCauchySeqOn F p s) (hss' : s' ⊆ s) :
     UniformCauchySeqOn F p s' :=
   by
-  rw [uniformCauchySeqOn_iff_uniformCauchySeqOnFilter] at hf⊢
+  rw [uniformCauchySeqOn_iff_uniformCauchySeqOnFilter] at hf ⊢
   exact hf.mono_right (le_principal_iff.mpr <| mem_principal.mpr hss')
 #align uniform_cauchy_seq_on.mono UniformCauchySeqOn.mono
 -/
@@ -635,7 +635,7 @@ theorem UniformCauchySeqOnFilter.comp {γ : Type _} (hf : UniformCauchySeqOnFilt
 theorem UniformCauchySeqOn.comp {γ : Type _} (hf : UniformCauchySeqOn F p s) (g : γ → α) :
     UniformCauchySeqOn (fun n => F n ∘ g) p (g ⁻¹' s) :=
   by
-  rw [uniformCauchySeqOn_iff_uniformCauchySeqOnFilter] at hf⊢
+  rw [uniformCauchySeqOn_iff_uniformCauchySeqOnFilter] at hf ⊢
   simpa only [UniformCauchySeqOn, comap_principal] using hf.comp g
 #align uniform_cauchy_seq_on.comp UniformCauchySeqOn.comp
 
@@ -655,10 +655,10 @@ theorem UniformCauchySeqOn.prod_map {ι' α' β' : Type _} [UniformSpace β'] {F
     UniformCauchySeqOn (fun i : ι × ι' => Prod.map (F i.1) (F' i.2)) (p.Prod p') (s ×ˢ s') :=
   by
   intro u hu
-  rw [uniformity_prod_eq_prod, mem_map, mem_prod_iff] at hu
+  rw [uniformity_prod_eq_prod, mem_map, mem_prod_iff] at hu 
   obtain ⟨v, hv, w, hw, hvw⟩ := hu
   simp_rw [mem_prod, Prod_map, and_imp, Prod.forall]
-  rw [← Set.image_subset_iff] at hvw
+  rw [← Set.image_subset_iff] at hvw 
   apply (tendsto_swap4_prod.eventually ((h v hv).prod_mk (h' w hw))).mono
   intro x hx a b ha hb
   refine' hvw ⟨_, mk_mem_prod (hx.1 a ha) (hx.2 b hb), rfl⟩
@@ -701,9 +701,9 @@ theorem tendstoUniformlyOn_of_seq_tendstoUniformlyOn {l : Filter ι} [l.IsCounta
   by
   rw [tendstoUniformlyOn_iff_tendsto, tendsto_iff_seq_tendsto]
   intro u hu
-  rw [tendsto_prod_iff'] at hu
+  rw [tendsto_prod_iff'] at hu 
   specialize h (fun n => (u n).fst) hu.1
-  rw [tendstoUniformlyOn_iff_tendsto] at h
+  rw [tendstoUniformlyOn_iff_tendsto] at h 
   have :
     (fun q : ι × α => (f q.snd, F q.fst q.snd)) ∘ u =
       (fun q : ℕ × α => (f q.snd, F ((fun n : ℕ => (u n).fst) q.fst) q.snd)) ∘ fun n =>
@@ -720,7 +720,7 @@ theorem tendstoUniformlyOn_of_seq_tendstoUniformlyOn {l : Filter ι} [l.IsCounta
 theorem TendstoUniformlyOn.seq_tendstoUniformlyOn {l : Filter ι} (h : TendstoUniformlyOn F f l s)
     (u : ℕ → ι) (hu : Tendsto u atTop l) : TendstoUniformlyOn (fun n => F (u n)) f atTop s :=
   by
-  rw [tendstoUniformlyOn_iff_tendsto] at h⊢
+  rw [tendstoUniformlyOn_iff_tendsto] at h ⊢
   have :
     (fun q : ℕ × α => (f q.snd, F (u q.fst) q.snd)) =
       (fun q : ι × α => (f q.snd, F q.fst q.snd)) ∘ fun p : ℕ × α => (u p.fst, p.snd) :=
@@ -836,7 +836,7 @@ theorem tendstoLocallyUniformlyOn_iUnion {S : γ → Set α} (hS : ∀ i, IsOpen
   rintro v hv x ⟨_, ⟨i, rfl⟩, hi : x ∈ S i⟩
   obtain ⟨t, ht, ht'⟩ := h i v hv x hi
   refine' ⟨t, _, ht'⟩
-  rw [(hS _).nhdsWithin_eq hi] at ht
+  rw [(hS _).nhdsWithin_eq hi] at ht 
   exact mem_nhdsWithin_of_mem_nhds ht
 #align tendsto_locally_uniformly_on_Union tendstoLocallyUniformlyOn_iUnion
 
@@ -884,10 +884,10 @@ theorem tendstoLocallyUniformly_iff_tendstoUniformly_of_compactSpace [CompactSpa
   choose U hU using h V hV
   obtain ⟨t, ht⟩ := is_compact_univ.elim_nhds_subcover' (fun k hk => U k) fun k hk => (hU k).1
   replace hU := fun x : t => (hU x).2
-  rw [← eventually_all] at hU
+  rw [← eventually_all] at hU 
   refine' hU.mono fun i hi x => _
   specialize ht (mem_univ x)
-  simp only [exists_prop, mem_Union, SetCoe.exists, exists_and_right, Subtype.coe_mk] at ht
+  simp only [exists_prop, mem_Union, SetCoe.exists, exists_and_right, Subtype.coe_mk] at ht 
   obtain ⟨y, ⟨hy₁, hy₂⟩, hy₃⟩ := ht
   exact hi ⟨⟨y, hy₁⟩, hy₂⟩ x hy₃
 #align tendsto_locally_uniformly_iff_tendsto_uniformly_of_compact_space tendstoLocallyUniformly_iff_tendstoUniformly_of_compactSpace
@@ -902,7 +902,7 @@ theorem tendstoLocallyUniformlyOn_iff_tendstoUniformlyOn_of_compact (hs : IsComp
   refine' ⟨fun h => _, TendstoUniformlyOn.tendstoLocallyUniformlyOn⟩
   rwa [tendstoLocallyUniformlyOn_iff_tendstoLocallyUniformly_comp_coe,
     tendstoLocallyUniformly_iff_tendstoUniformly_of_compactSpace, ←
-    tendstoUniformlyOn_iff_tendstoUniformly_comp_coe] at h
+    tendstoUniformlyOn_iff_tendstoUniformly_comp_coe] at h 
 #align tendsto_locally_uniformly_on_iff_tendsto_uniformly_on_of_compact tendstoLocallyUniformlyOn_iff_tendstoUniformlyOn_of_compact
 -/
 
@@ -923,8 +923,8 @@ theorem TendstoLocallyUniformlyOn.comp [TopologicalSpace γ] {t : Set γ}
 theorem TendstoLocallyUniformly.comp [TopologicalSpace γ] (h : TendstoLocallyUniformly F f p)
     (g : γ → α) (cg : Continuous g) : TendstoLocallyUniformly (fun n => F n ∘ g) (f ∘ g) p :=
   by
-  rw [← tendstoLocallyUniformlyOn_univ] at h⊢
-  rw [continuous_iff_continuousOn_univ] at cg
+  rw [← tendstoLocallyUniformlyOn_univ] at h ⊢
+  rw [continuous_iff_continuousOn_univ] at cg 
   exact h.comp _ (maps_to_univ _ _) cg
 #align tendsto_locally_uniformly.comp TendstoLocallyUniformly.comp
 -/
@@ -1038,10 +1038,10 @@ theorem continuousWithinAt_of_locally_uniform_approx_of_continuousWithinAt (hx :
     ContinuousWithinAt f s x :=
   by
   apply Uniform.continuousWithinAt_iff'_left.2 fun u₀ hu₀ => _
-  obtain ⟨u₁, h₁, u₁₀⟩ : ∃ (u : Set (β × β))(H : u ∈ 𝓤 β), compRel u u ⊆ u₀ :=
+  obtain ⟨u₁, h₁, u₁₀⟩ : ∃ (u : Set (β × β)) (H : u ∈ 𝓤 β), compRel u u ⊆ u₀ :=
     comp_mem_uniformity_sets hu₀
   obtain ⟨u₂, h₂, hsymm, u₂₁⟩ :
-    ∃ (u : Set (β × β))(H : u ∈ 𝓤 β), (∀ {a b}, (a, b) ∈ u → (b, a) ∈ u) ∧ compRel u u ⊆ u₁ :=
+    ∃ (u : Set (β × β)) (H : u ∈ 𝓤 β), (∀ {a b}, (a, b) ∈ u → (b, a) ∈ u) ∧ compRel u u ⊆ u₁ :=
     comp_symm_of_uniformity h₁
   rcases L u₂ h₂ with ⟨t, tx, F, hFc, hF⟩
   have A : ∀ᶠ y in 𝓝[s] x, (f y, F y) ∈ u₂ := eventually.mono tx hF
@@ -1165,7 +1165,7 @@ theorem tendsto_comp_of_locally_uniform_limit_within (h : ContinuousWithinAt f s
     Tendsto (fun n => F n (g n)) p (𝓝 (f x)) :=
   by
   apply Uniform.tendsto_nhds_right.2 fun u₀ hu₀ => _
-  obtain ⟨u₁, h₁, u₁₀⟩ : ∃ (u : Set (β × β))(H : u ∈ 𝓤 β), compRel u u ⊆ u₀ :=
+  obtain ⟨u₁, h₁, u₁₀⟩ : ∃ (u : Set (β × β)) (H : u ∈ 𝓤 β), compRel u u ⊆ u₀ :=
     comp_mem_uniformity_sets hu₀
   rcases hunif u₁ h₁ with ⟨s, sx, hs⟩
   have A : ∀ᶠ n in p, g n ∈ s := hg sx
@@ -1181,8 +1181,8 @@ theorem tendsto_comp_of_locally_uniform_limit (h : ContinuousAt f x) (hg : Tends
     (hunif : ∀ u ∈ 𝓤 β, ∃ t ∈ 𝓝 x, ∀ᶠ n in p, ∀ y ∈ t, (f y, F n y) ∈ u) :
     Tendsto (fun n => F n (g n)) p (𝓝 (f x)) :=
   by
-  rw [← continuousWithinAt_univ] at h
-  rw [← nhdsWithin_univ] at hunif hg
+  rw [← continuousWithinAt_univ] at h 
+  rw [← nhdsWithin_univ] at hunif hg 
   exact tendsto_comp_of_locally_uniform_limit_within h hg hunif
 #align tendsto_comp_of_locally_uniform_limit tendsto_comp_of_locally_uniform_limit
 

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

@@ -70,7 +70,7 @@ Uniform limit, uniform convergence, tends uniformly to
 
 noncomputable section
 
-open Topology Classical uniformity Filter
+open scoped Topology Classical uniformity Filter
 
 open Set Filter
 

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

@@ -155,12 +155,6 @@ def TendstoUniformly (F : ι → α → β) (f : α → β) (p : Filter ι) :=
 #align tendsto_uniformly TendstoUniformly
 -/
 
-/- warning: tendsto_uniformly_iff_tendsto_uniformly_on_filter -> tendstoUniformly_iff_tendstoUniformlyOnFilter is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {f : α -> β} {p : Filter.{u3} ι}, Iff (TendstoUniformly.{u1, u2, u3} α β ι _inst_1 F f p) (TendstoUniformlyOnFilter.{u1, u2, u3} α β ι _inst_1 F f p (Top.top.{u1} (Filter.{u1} α) (Filter.hasTop.{u1} α)))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {f : α -> β} {p : Filter.{u3} ι}, Iff (TendstoUniformly.{u1, u2, u3} α β ι _inst_1 F f p) (TendstoUniformlyOnFilter.{u1, u2, u3} α β ι _inst_1 F f p (Top.top.{u1} (Filter.{u1} α) (Filter.instTopFilter.{u1} α)))
-Case conversion may be inaccurate. Consider using '#align tendsto_uniformly_iff_tendsto_uniformly_on_filter tendstoUniformly_iff_tendstoUniformlyOnFilterₓ'. -/
 theorem tendstoUniformly_iff_tendstoUniformlyOnFilter :
     TendstoUniformly F f p ↔ TendstoUniformlyOnFilter F f p ⊤ :=
   by
@@ -170,12 +164,6 @@ theorem tendstoUniformly_iff_tendstoUniformlyOnFilter :
   simp
 #align tendsto_uniformly_iff_tendsto_uniformly_on_filter tendstoUniformly_iff_tendstoUniformlyOnFilter
 
-/- warning: tendsto_uniformly.tendsto_uniformly_on_filter -> TendstoUniformly.tendstoUniformlyOnFilter is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {f : α -> β} {p : Filter.{u3} ι}, (TendstoUniformly.{u1, u2, u3} α β ι _inst_1 F f p) -> (TendstoUniformlyOnFilter.{u1, u2, u3} α β ι _inst_1 F f p (Top.top.{u1} (Filter.{u1} α) (Filter.hasTop.{u1} α)))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {f : α -> β} {p : Filter.{u3} ι}, (TendstoUniformly.{u1, u2, u3} α β ι _inst_1 F f p) -> (TendstoUniformlyOnFilter.{u1, u2, u3} α β ι _inst_1 F f p (Top.top.{u1} (Filter.{u1} α) (Filter.instTopFilter.{u1} α)))
-Case conversion may be inaccurate. Consider using '#align tendsto_uniformly.tendsto_uniformly_on_filter TendstoUniformly.tendstoUniformlyOnFilterₓ'. -/
 theorem TendstoUniformly.tendstoUniformlyOnFilter (h : TendstoUniformly F f p) :
     TendstoUniformlyOnFilter F f p ⊤ := by rwa [← tendstoUniformly_iff_tendstoUniformlyOnFilter]
 #align tendsto_uniformly.tendsto_uniformly_on_filter TendstoUniformly.tendstoUniformlyOnFilter
@@ -190,12 +178,6 @@ theorem tendstoUniformlyOn_iff_tendstoUniformly_comp_coe :
 #align tendsto_uniformly_on_iff_tendsto_uniformly_comp_coe tendstoUniformlyOn_iff_tendstoUniformly_comp_coe
 -/
 
-/- warning: tendsto_uniformly_iff_tendsto -> tendstoUniformly_iff_tendsto is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {f : α -> β} {p : Filter.{u3} ι}, Iff (TendstoUniformly.{u1, u2, u3} α β ι _inst_1 F f p) (Filter.Tendsto.{max u3 u1, u2} (Prod.{u3, u1} ι α) (Prod.{u2, u2} β β) (fun (q : Prod.{u3, u1} ι α) => Prod.mk.{u2, u2} β β (f (Prod.snd.{u3, u1} ι α q)) (F (Prod.fst.{u3, u1} ι α q) (Prod.snd.{u3, u1} ι α q))) (Filter.prod.{u3, u1} ι α p (Top.top.{u1} (Filter.{u1} α) (Filter.hasTop.{u1} α))) (uniformity.{u2} β _inst_1))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {f : α -> β} {p : Filter.{u3} ι}, Iff (TendstoUniformly.{u1, u2, u3} α β ι _inst_1 F f p) (Filter.Tendsto.{max u1 u3, u2} (Prod.{u3, u1} ι α) (Prod.{u2, u2} β β) (fun (q : Prod.{u3, u1} ι α) => Prod.mk.{u2, u2} β β (f (Prod.snd.{u3, u1} ι α q)) (F (Prod.fst.{u3, u1} ι α q) (Prod.snd.{u3, u1} ι α q))) (Filter.prod.{u3, u1} ι α p (Top.top.{u1} (Filter.{u1} α) (Filter.instTopFilter.{u1} α))) (uniformity.{u2} β _inst_1))
-Case conversion may be inaccurate. Consider using '#align tendsto_uniformly_iff_tendsto tendstoUniformly_iff_tendstoₓ'. -/
 /-- A sequence of functions `Fₙ` converges uniformly to a limiting function `f` w.r.t.
 filter `p` iff the function `(n, x) ↦ (f x, Fₙ x)` converges along `p ×ᶠ ⊤` to the uniformity.
 In other words: one knows nothing about the behavior of `x` in this limit.
@@ -205,12 +187,6 @@ theorem tendstoUniformly_iff_tendsto {F : ι → α → β} {f : α → β} {p :
   simp [tendstoUniformly_iff_tendstoUniformlyOnFilter, tendstoUniformlyOnFilter_iff_tendsto]
 #align tendsto_uniformly_iff_tendsto tendstoUniformly_iff_tendsto
 
-/- warning: tendsto_uniformly_on_filter.tendsto_at -> TendstoUniformlyOnFilter.tendsto_at is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {f : α -> β} {x : α} {p : Filter.{u3} ι} {p' : Filter.{u1} α}, (TendstoUniformlyOnFilter.{u1, u2, u3} α β ι _inst_1 F f p p') -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) (Filter.principal.{u1} α (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) x)) p') -> (Filter.Tendsto.{u3, u2} ι β (fun (n : ι) => F n x) p (nhds.{u2} β (UniformSpace.toTopologicalSpace.{u2} β _inst_1) (f x)))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {f : α -> β} {x : α} {p : Filter.{u3} ι} {p' : Filter.{u1} α}, (TendstoUniformlyOnFilter.{u1, u2, u3} α β ι _inst_1 F f p p') -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) (Filter.principal.{u1} α (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) x)) p') -> (Filter.Tendsto.{u3, u2} ι β (fun (n : ι) => F n x) p (nhds.{u2} β (UniformSpace.toTopologicalSpace.{u2} β _inst_1) (f x)))
-Case conversion may be inaccurate. Consider using '#align tendsto_uniformly_on_filter.tendsto_at TendstoUniformlyOnFilter.tendsto_atₓ'. -/
 /-- Uniform converence implies pointwise convergence. -/
 theorem TendstoUniformlyOnFilter.tendsto_at (h : TendstoUniformlyOnFilter F f p p')
     (hx : 𝓟 {x} ≤ p') : Tendsto (fun n => F n x) p <| 𝓝 (f x) :=
@@ -244,23 +220,11 @@ theorem tendstoUniformlyOn_univ : TendstoUniformlyOn F f p univ ↔ TendstoUnifo
 #align tendsto_uniformly_on_univ tendstoUniformlyOn_univ
 -/
 
-/- warning: tendsto_uniformly_on_filter.mono_left -> TendstoUniformlyOnFilter.mono_left is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {f : α -> β} {p : Filter.{u3} ι} {p' : Filter.{u1} α} {p'' : Filter.{u3} ι}, (TendstoUniformlyOnFilter.{u1, u2, u3} α β ι _inst_1 F f p p') -> (LE.le.{u3} (Filter.{u3} ι) (Preorder.toHasLe.{u3} (Filter.{u3} ι) (PartialOrder.toPreorder.{u3} (Filter.{u3} ι) (Filter.partialOrder.{u3} ι))) p'' p) -> (TendstoUniformlyOnFilter.{u1, u2, u3} α β ι _inst_1 F f p'' p')
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {f : α -> β} {p : Filter.{u3} ι} {p' : Filter.{u1} α} {p'' : Filter.{u3} ι}, (TendstoUniformlyOnFilter.{u1, u2, u3} α β ι _inst_1 F f p p') -> (LE.le.{u3} (Filter.{u3} ι) (Preorder.toLE.{u3} (Filter.{u3} ι) (PartialOrder.toPreorder.{u3} (Filter.{u3} ι) (Filter.instPartialOrderFilter.{u3} ι))) p'' p) -> (TendstoUniformlyOnFilter.{u1, u2, u3} α β ι _inst_1 F f p'' p')
-Case conversion may be inaccurate. Consider using '#align tendsto_uniformly_on_filter.mono_left TendstoUniformlyOnFilter.mono_leftₓ'. -/
 theorem TendstoUniformlyOnFilter.mono_left {p'' : Filter ι} (h : TendstoUniformlyOnFilter F f p p')
     (hp : p'' ≤ p) : TendstoUniformlyOnFilter F f p'' p' := fun u hu =>
   (h u hu).filter_mono (p'.prod_mono_left hp)
 #align tendsto_uniformly_on_filter.mono_left TendstoUniformlyOnFilter.mono_left
 
-/- warning: tendsto_uniformly_on_filter.mono_right -> TendstoUniformlyOnFilter.mono_right is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {f : α -> β} {p : Filter.{u3} ι} {p' : Filter.{u1} α} {p'' : Filter.{u1} α}, (TendstoUniformlyOnFilter.{u1, u2, u3} α β ι _inst_1 F f p p') -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) p'' p') -> (TendstoUniformlyOnFilter.{u1, u2, u3} α β ι _inst_1 F f p p'')
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {f : α -> β} {p : Filter.{u3} ι} {p' : Filter.{u1} α} {p'' : Filter.{u1} α}, (TendstoUniformlyOnFilter.{u1, u2, u3} α β ι _inst_1 F f p p') -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) p'' p') -> (TendstoUniformlyOnFilter.{u1, u2, u3} α β ι _inst_1 F f p p'')
-Case conversion may be inaccurate. Consider using '#align tendsto_uniformly_on_filter.mono_right TendstoUniformlyOnFilter.mono_rightₓ'. -/
 theorem TendstoUniformlyOnFilter.mono_right {p'' : Filter α} (h : TendstoUniformlyOnFilter F f p p')
     (hp : p'' ≤ p') : TendstoUniformlyOnFilter F f p p'' := fun u hu =>
   (h u hu).filter_mono (p.prod_mono_right hp)
@@ -373,12 +337,6 @@ theorem UniformContinuous.comp_tendstoUniformly [UniformSpace γ] {g : β → γ
 #align uniform_continuous.comp_tendsto_uniformly UniformContinuous.comp_tendstoUniformly
 -/
 
-/- warning: tendsto_uniformly_on_filter.prod_map -> TendstoUniformlyOnFilter.prod_map is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {f : α -> β} {p : Filter.{u3} ι} {p' : Filter.{u1} α} {ι' : Type.{u4}} {α' : Type.{u5}} {β' : Type.{u6}} [_inst_2 : UniformSpace.{u6} β'] {F' : ι' -> α' -> β'} {f' : α' -> β'} {q : Filter.{u4} ι'} {q' : Filter.{u5} α'}, (TendstoUniformlyOnFilter.{u1, u2, u3} α β ι _inst_1 F f p p') -> (TendstoUniformlyOnFilter.{u5, u6, u4} α' β' ι' _inst_2 F' f' q q') -> (TendstoUniformlyOnFilter.{max u1 u5, max u2 u6, max u3 u4} (Prod.{u1, u5} α α') (Prod.{u2, u6} β β') (Prod.{u3, u4} ι ι') (Prod.uniformSpace.{u2, u6} β β' _inst_1 _inst_2) (fun (i : Prod.{u3, u4} ι ι') => Prod.map.{u1, u2, u5, u6} α β α' β' (F (Prod.fst.{u3, u4} ι ι' i)) (F' (Prod.snd.{u3, u4} ι ι' i))) (Prod.map.{u1, u2, u5, u6} α β α' β' f f') (Filter.prod.{u3, u4} ι ι' p q) (Filter.prod.{u1, u5} α α' p' q'))
-but is expected to have type
-  forall {α : Type.{u4}} {β : Type.{u5}} {ι : Type.{u6}} [_inst_1 : UniformSpace.{u5} β] {F : ι -> α -> β} {f : α -> β} {p : Filter.{u6} ι} {p' : Filter.{u4} α} {ι' : Type.{u3}} {α' : Type.{u2}} {β' : Type.{u1}} [_inst_2 : UniformSpace.{u1} β'] {F' : ι' -> α' -> β'} {f' : α' -> β'} {q : Filter.{u3} ι'} {q' : Filter.{u2} α'}, (TendstoUniformlyOnFilter.{u4, u5, u6} α β ι _inst_1 F f p p') -> (TendstoUniformlyOnFilter.{u2, u1, u3} α' β' ι' _inst_2 F' f' q q') -> (TendstoUniformlyOnFilter.{max u2 u4, max u1 u5, max u6 u3} (Prod.{u4, u2} α α') (Prod.{u5, u1} β β') (Prod.{u6, u3} ι ι') (instUniformSpaceProd.{u5, u1} β β' _inst_1 _inst_2) (fun (i : Prod.{u6, u3} ι ι') => Prod.map.{u4, u5, u2, u1} α β α' β' (F (Prod.fst.{u6, u3} ι ι' i)) (F' (Prod.snd.{u6, u3} ι ι' i))) (Prod.map.{u4, u5, u2, u1} α β α' β' f f') (Filter.prod.{u6, u3} ι ι' p q) (Filter.prod.{u4, u2} α α' p' q'))
-Case conversion may be inaccurate. Consider using '#align tendsto_uniformly_on_filter.prod_map TendstoUniformlyOnFilter.prod_mapₓ'. -/
 theorem TendstoUniformlyOnFilter.prod_map {ι' α' β' : Type _} [UniformSpace β'] {F' : ι' → α' → β'}
     {f' : α' → β'} {q : Filter ι'} {q' : Filter α'} (h : TendstoUniformlyOnFilter F f p p')
     (h' : TendstoUniformlyOnFilter F' f' q q') :
@@ -398,12 +356,6 @@ theorem TendstoUniformlyOnFilter.prod_map {ι' α' β' : Type _} [UniformSpace 
   exact hout
 #align tendsto_uniformly_on_filter.prod_map TendstoUniformlyOnFilter.prod_map
 
-/- warning: tendsto_uniformly_on.prod_map -> TendstoUniformlyOn.prod_map is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {f : α -> β} {s : Set.{u1} α} {p : Filter.{u3} ι} {ι' : Type.{u4}} {α' : Type.{u5}} {β' : Type.{u6}} [_inst_2 : UniformSpace.{u6} β'] {F' : ι' -> α' -> β'} {f' : α' -> β'} {p' : Filter.{u4} ι'} {s' : Set.{u5} α'}, (TendstoUniformlyOn.{u1, u2, u3} α β ι _inst_1 F f p s) -> (TendstoUniformlyOn.{u5, u6, u4} α' β' ι' _inst_2 F' f' p' s') -> (TendstoUniformlyOn.{max u1 u5, max u2 u6, max u3 u4} (Prod.{u1, u5} α α') (Prod.{u2, u6} β β') (Prod.{u3, u4} ι ι') (Prod.uniformSpace.{u2, u6} β β' _inst_1 _inst_2) (fun (i : Prod.{u3, u4} ι ι') => Prod.map.{u1, u2, u5, u6} α β α' β' (F (Prod.fst.{u3, u4} ι ι' i)) (F' (Prod.snd.{u3, u4} ι ι' i))) (Prod.map.{u1, u2, u5, u6} α β α' β' f f') (Filter.prod.{u3, u4} ι ι' p p') (Set.prod.{u1, u5} α α' s s'))
-but is expected to have type
-  forall {α : Type.{u4}} {β : Type.{u5}} {ι : Type.{u6}} [_inst_1 : UniformSpace.{u5} β] {F : ι -> α -> β} {f : α -> β} {s : Set.{u4} α} {p : Filter.{u6} ι} {ι' : Type.{u3}} {α' : Type.{u2}} {β' : Type.{u1}} [_inst_2 : UniformSpace.{u1} β'] {F' : ι' -> α' -> β'} {f' : α' -> β'} {p' : Filter.{u3} ι'} {s' : Set.{u2} α'}, (TendstoUniformlyOn.{u4, u5, u6} α β ι _inst_1 F f p s) -> (TendstoUniformlyOn.{u2, u1, u3} α' β' ι' _inst_2 F' f' p' s') -> (TendstoUniformlyOn.{max u2 u4, max u1 u5, max u6 u3} (Prod.{u4, u2} α α') (Prod.{u5, u1} β β') (Prod.{u6, u3} ι ι') (instUniformSpaceProd.{u5, u1} β β' _inst_1 _inst_2) (fun (i : Prod.{u6, u3} ι ι') => Prod.map.{u4, u5, u2, u1} α β α' β' (F (Prod.fst.{u6, u3} ι ι' i)) (F' (Prod.snd.{u6, u3} ι ι' i))) (Prod.map.{u4, u5, u2, u1} α β α' β' f f') (Filter.prod.{u6, u3} ι ι' p p') (Set.prod.{u4, u2} α α' s s'))
-Case conversion may be inaccurate. Consider using '#align tendsto_uniformly_on.prod_map TendstoUniformlyOn.prod_mapₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem TendstoUniformlyOn.prod_map {ι' α' β' : Type _} [UniformSpace β'] {F' : ι' → α' → β'}
     {f' : α' → β'} {p' : Filter ι'} {s' : Set α'} (h : TendstoUniformlyOn F f p s)
@@ -415,12 +367,6 @@ theorem TendstoUniformlyOn.prod_map {ι' α' β' : Type _} [UniformSpace β'] {F
   simpa only [prod_principal_principal] using h.prod_map h'
 #align tendsto_uniformly_on.prod_map TendstoUniformlyOn.prod_map
 
-/- warning: tendsto_uniformly.prod_map -> TendstoUniformly.prod_map is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {f : α -> β} {p : Filter.{u3} ι} {ι' : Type.{u4}} {α' : Type.{u5}} {β' : Type.{u6}} [_inst_2 : UniformSpace.{u6} β'] {F' : ι' -> α' -> β'} {f' : α' -> β'} {p' : Filter.{u4} ι'}, (TendstoUniformly.{u1, u2, u3} α β ι _inst_1 F f p) -> (TendstoUniformly.{u5, u6, u4} α' β' ι' _inst_2 F' f' p') -> (TendstoUniformly.{max u1 u5, max u2 u6, max u3 u4} (Prod.{u1, u5} α α') (Prod.{u2, u6} β β') (Prod.{u3, u4} ι ι') (Prod.uniformSpace.{u2, u6} β β' _inst_1 _inst_2) (fun (i : Prod.{u3, u4} ι ι') => Prod.map.{u1, u2, u5, u6} α β α' β' (F (Prod.fst.{u3, u4} ι ι' i)) (F' (Prod.snd.{u3, u4} ι ι' i))) (Prod.map.{u1, u2, u5, u6} α β α' β' f f') (Filter.prod.{u3, u4} ι ι' p p'))
-but is expected to have type
-  forall {α : Type.{u4}} {β : Type.{u5}} {ι : Type.{u6}} [_inst_1 : UniformSpace.{u5} β] {F : ι -> α -> β} {f : α -> β} {p : Filter.{u6} ι} {ι' : Type.{u3}} {α' : Type.{u2}} {β' : Type.{u1}} [_inst_2 : UniformSpace.{u1} β'] {F' : ι' -> α' -> β'} {f' : α' -> β'} {p' : Filter.{u3} ι'}, (TendstoUniformly.{u4, u5, u6} α β ι _inst_1 F f p) -> (TendstoUniformly.{u2, u1, u3} α' β' ι' _inst_2 F' f' p') -> (TendstoUniformly.{max u2 u4, max u1 u5, max u6 u3} (Prod.{u4, u2} α α') (Prod.{u5, u1} β β') (Prod.{u6, u3} ι ι') (instUniformSpaceProd.{u5, u1} β β' _inst_1 _inst_2) (fun (i : Prod.{u6, u3} ι ι') => Prod.map.{u4, u5, u2, u1} α β α' β' (F (Prod.fst.{u6, u3} ι ι' i)) (F' (Prod.snd.{u6, u3} ι ι' i))) (Prod.map.{u4, u5, u2, u1} α β α' β' f f') (Filter.prod.{u6, u3} ι ι' p p'))
-Case conversion may be inaccurate. Consider using '#align tendsto_uniformly.prod_map TendstoUniformly.prod_mapₓ'. -/
 theorem TendstoUniformly.prod_map {ι' α' β' : Type _} [UniformSpace β'] {F' : ι' → α' → β'}
     {f' : α' → β'} {p' : Filter ι'} (h : TendstoUniformly F f p) (h' : TendstoUniformly F' f' p') :
     TendstoUniformly (fun i : ι × ι' => Prod.map (F i.1) (F' i.2)) (Prod.map f f') (p.Prod p') :=
@@ -429,12 +375,6 @@ theorem TendstoUniformly.prod_map {ι' α' β' : Type _} [UniformSpace β'] {F'
   exact h.prod_map h'
 #align tendsto_uniformly.prod_map TendstoUniformly.prod_map
 
-/- warning: tendsto_uniformly_on_filter.prod -> TendstoUniformlyOnFilter.prod is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {f : α -> β} {p : Filter.{u3} ι} {p' : Filter.{u1} α} {ι' : Type.{u4}} {β' : Type.{u5}} [_inst_2 : UniformSpace.{u5} β'] {F' : ι' -> α -> β'} {f' : α -> β'} {q : Filter.{u4} ι'}, (TendstoUniformlyOnFilter.{u1, u2, u3} α β ι _inst_1 F f p p') -> (TendstoUniformlyOnFilter.{u1, u5, u4} α β' ι' _inst_2 F' f' q p') -> (TendstoUniformlyOnFilter.{u1, max u2 u5, max u3 u4} α (Prod.{u2, u5} β β') (Prod.{u3, u4} ι ι') (Prod.uniformSpace.{u2, u5} β β' _inst_1 _inst_2) (fun (i : Prod.{u3, u4} ι ι') (a : α) => Prod.mk.{u2, u5} β β' (F (Prod.fst.{u3, u4} ι ι' i) a) (F' (Prod.snd.{u3, u4} ι ι' i) a)) (fun (a : α) => Prod.mk.{u2, u5} β β' (f a) (f' a)) (Filter.prod.{u3, u4} ι ι' p q) p')
-but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u4}} {ι : Type.{u5}} [_inst_1 : UniformSpace.{u4} β] {F : ι -> α -> β} {f : α -> β} {p : Filter.{u5} ι} {p' : Filter.{u3} α} {ι' : Type.{u2}} {β' : Type.{u1}} [_inst_2 : UniformSpace.{u1} β'] {F' : ι' -> α -> β'} {f' : α -> β'} {q : Filter.{u2} ι'}, (TendstoUniformlyOnFilter.{u3, u4, u5} α β ι _inst_1 F f p p') -> (TendstoUniformlyOnFilter.{u3, u1, u2} α β' ι' _inst_2 F' f' q p') -> (TendstoUniformlyOnFilter.{u3, max u1 u4, max u5 u2} α (Prod.{u4, u1} β β') (Prod.{u5, u2} ι ι') (instUniformSpaceProd.{u4, u1} β β' _inst_1 _inst_2) (fun (i : Prod.{u5, u2} ι ι') (a : α) => Prod.mk.{u4, u1} β β' (F (Prod.fst.{u5, u2} ι ι' i) a) (F' (Prod.snd.{u5, u2} ι ι' i) a)) (fun (a : α) => Prod.mk.{u4, u1} β β' (f a) (f' a)) (Filter.prod.{u5, u2} ι ι' p q) p')
-Case conversion may be inaccurate. Consider using '#align tendsto_uniformly_on_filter.prod TendstoUniformlyOnFilter.prodₓ'. -/
 theorem TendstoUniformlyOnFilter.prod {ι' β' : Type _} [UniformSpace β'] {F' : ι' → α → β'}
     {f' : α → β'} {q : Filter ι'} (h : TendstoUniformlyOnFilter F f p p')
     (h' : TendstoUniformlyOnFilter F' f' q p') :
@@ -443,12 +383,6 @@ theorem TendstoUniformlyOnFilter.prod {ι' β' : Type _} [UniformSpace β'] {F'
   fun u hu => ((h.Prod_map h') u hu).diag_of_prod_right
 #align tendsto_uniformly_on_filter.prod TendstoUniformlyOnFilter.prod
 
-/- warning: tendsto_uniformly_on.prod -> TendstoUniformlyOn.prod is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {f : α -> β} {s : Set.{u1} α} {p : Filter.{u3} ι} {ι' : Type.{u4}} {β' : Type.{u5}} [_inst_2 : UniformSpace.{u5} β'] {F' : ι' -> α -> β'} {f' : α -> β'} {p' : Filter.{u4} ι'}, (TendstoUniformlyOn.{u1, u2, u3} α β ι _inst_1 F f p s) -> (TendstoUniformlyOn.{u1, u5, u4} α β' ι' _inst_2 F' f' p' s) -> (TendstoUniformlyOn.{u1, max u2 u5, max u3 u4} α (Prod.{u2, u5} β β') (Prod.{u3, u4} ι ι') (Prod.uniformSpace.{u2, u5} β β' _inst_1 _inst_2) (fun (i : Prod.{u3, u4} ι ι') (a : α) => Prod.mk.{u2, u5} β β' (F (Prod.fst.{u3, u4} ι ι' i) a) (F' (Prod.snd.{u3, u4} ι ι' i) a)) (fun (a : α) => Prod.mk.{u2, u5} β β' (f a) (f' a)) (Filter.prod.{u3, u4} ι ι' p p') s)
-but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u4}} {ι : Type.{u5}} [_inst_1 : UniformSpace.{u4} β] {F : ι -> α -> β} {f : α -> β} {s : Set.{u3} α} {p : Filter.{u5} ι} {ι' : Type.{u2}} {β' : Type.{u1}} [_inst_2 : UniformSpace.{u1} β'] {F' : ι' -> α -> β'} {f' : α -> β'} {p' : Filter.{u2} ι'}, (TendstoUniformlyOn.{u3, u4, u5} α β ι _inst_1 F f p s) -> (TendstoUniformlyOn.{u3, u1, u2} α β' ι' _inst_2 F' f' p' s) -> (TendstoUniformlyOn.{u3, max u1 u4, max u5 u2} α (Prod.{u4, u1} β β') (Prod.{u5, u2} ι ι') (instUniformSpaceProd.{u4, u1} β β' _inst_1 _inst_2) (fun (i : Prod.{u5, u2} ι ι') (a : α) => Prod.mk.{u4, u1} β β' (F (Prod.fst.{u5, u2} ι ι' i) a) (F' (Prod.snd.{u5, u2} ι ι' i) a)) (fun (a : α) => Prod.mk.{u4, u1} β β' (f a) (f' a)) (Filter.prod.{u5, u2} ι ι' p p') s)
-Case conversion may be inaccurate. Consider using '#align tendsto_uniformly_on.prod TendstoUniformlyOn.prodₓ'. -/
 theorem TendstoUniformlyOn.prod {ι' β' : Type _} [UniformSpace β'] {F' : ι' → α → β'} {f' : α → β'}
     {p' : Filter ι'} (h : TendstoUniformlyOn F f p s) (h' : TendstoUniformlyOn F' f' p' s) :
     TendstoUniformlyOn (fun (i : ι × ι') a => (F i.1 a, F' i.2 a)) (fun a => (f a, f' a))
@@ -456,12 +390,6 @@ theorem TendstoUniformlyOn.prod {ι' β' : Type _} [UniformSpace β'] {F' : ι'
   (congr_arg _ s.inter_self).mp ((h.Prod_map h').comp fun a => (a, a))
 #align tendsto_uniformly_on.prod TendstoUniformlyOn.prod
 
-/- warning: tendsto_uniformly.prod -> TendstoUniformly.prod is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {f : α -> β} {p : Filter.{u3} ι} {ι' : Type.{u4}} {β' : Type.{u5}} [_inst_2 : UniformSpace.{u5} β'] {F' : ι' -> α -> β'} {f' : α -> β'} {p' : Filter.{u4} ι'}, (TendstoUniformly.{u1, u2, u3} α β ι _inst_1 F f p) -> (TendstoUniformly.{u1, u5, u4} α β' ι' _inst_2 F' f' p') -> (TendstoUniformly.{u1, max u2 u5, max u3 u4} α (Prod.{u2, u5} β β') (Prod.{u3, u4} ι ι') (Prod.uniformSpace.{u2, u5} β β' _inst_1 _inst_2) (fun (i : Prod.{u3, u4} ι ι') (a : α) => Prod.mk.{u2, u5} β β' (F (Prod.fst.{u3, u4} ι ι' i) a) (F' (Prod.snd.{u3, u4} ι ι' i) a)) (fun (a : α) => Prod.mk.{u2, u5} β β' (f a) (f' a)) (Filter.prod.{u3, u4} ι ι' p p'))
-but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u4}} {ι : Type.{u5}} [_inst_1 : UniformSpace.{u4} β] {F : ι -> α -> β} {f : α -> β} {p : Filter.{u5} ι} {ι' : Type.{u2}} {β' : Type.{u1}} [_inst_2 : UniformSpace.{u1} β'] {F' : ι' -> α -> β'} {f' : α -> β'} {p' : Filter.{u2} ι'}, (TendstoUniformly.{u3, u4, u5} α β ι _inst_1 F f p) -> (TendstoUniformly.{u3, u1, u2} α β' ι' _inst_2 F' f' p') -> (TendstoUniformly.{u3, max u1 u4, max u5 u2} α (Prod.{u4, u1} β β') (Prod.{u5, u2} ι ι') (instUniformSpaceProd.{u4, u1} β β' _inst_1 _inst_2) (fun (i : Prod.{u5, u2} ι ι') (a : α) => Prod.mk.{u4, u1} β β' (F (Prod.fst.{u5, u2} ι ι' i) a) (F' (Prod.snd.{u5, u2} ι ι' i) a)) (fun (a : α) => Prod.mk.{u4, u1} β β' (f a) (f' a)) (Filter.prod.{u5, u2} ι ι' p p'))
-Case conversion may be inaccurate. Consider using '#align tendsto_uniformly.prod TendstoUniformly.prodₓ'. -/
 theorem TendstoUniformly.prod {ι' β' : Type _} [UniformSpace β'] {F' : ι' → α → β'} {f' : α → β'}
     {p' : Filter ι'} (h : TendstoUniformly F f p) (h' : TendstoUniformly F' f' p') :
     TendstoUniformly (fun (i : ι × ι') a => (F i.1 a, F' i.2 a)) (fun a => (f a, f' a))
@@ -491,12 +419,6 @@ theorem tendsto_prod_principal_iff {c : β} :
 #align tendsto_prod_principal_iff tendsto_prod_principal_iff
 -/
 
-/- warning: tendsto_prod_top_iff -> tendsto_prod_top_iff is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {p : Filter.{u3} ι} {c : β}, Iff (Filter.Tendsto.{max u3 u1, u2} (Prod.{u3, u1} ι α) β (Function.HasUncurry.uncurry.{max u3 u1 u2, max u3 u1, u2} (ι -> α -> β) (Prod.{u3, u1} ι α) β (Function.hasUncurryInduction.{u3, max u1 u2, u1, u2} ι (α -> β) α β (Function.hasUncurryBase.{u1, u2} α β)) F) (Filter.prod.{u3, u1} ι α p (Top.top.{u1} (Filter.{u1} α) (Filter.hasTop.{u1} α))) (nhds.{u2} β (UniformSpace.toTopologicalSpace.{u2} β _inst_1) c)) (TendstoUniformly.{u1, u2, u3} α β ι _inst_1 F (fun (_x : α) => c) p)
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {p : Filter.{u3} ι} {c : β}, Iff (Filter.Tendsto.{max u1 u3, u2} (Prod.{u3, u1} ι α) β (Function.HasUncurry.uncurry.{max (max u1 u2) u3, max u1 u3, u2} (ι -> α -> β) (Prod.{u3, u1} ι α) β (Function.hasUncurryInduction.{u3, max u1 u2, u1, u2} ι (α -> β) α β (Function.hasUncurryBase.{u1, u2} α β)) F) (Filter.prod.{u3, u1} ι α p (Top.top.{u1} (Filter.{u1} α) (Filter.instTopFilter.{u1} α))) (nhds.{u2} β (UniformSpace.toTopologicalSpace.{u2} β _inst_1) c)) (TendstoUniformly.{u1, u2, u3} α β ι _inst_1 F (fun (_x : α) => c) p)
-Case conversion may be inaccurate. Consider using '#align tendsto_prod_top_iff tendsto_prod_top_iffₓ'. -/
 /-- Uniform convergence to a constant function is equivalent to convergence in `p ×ᶠ ⊤`. -/
 theorem tendsto_prod_top_iff {c : β} :
     Tendsto (↿F) (p ×ᶠ ⊤) (𝓝 c) ↔ TendstoUniformly F (fun _ => c) p :=
@@ -545,12 +467,6 @@ theorem Filter.Tendsto.tendstoUniformlyOn_const {g : ι → β} {b : β} (hg : T
 #align filter.tendsto.tendsto_uniformly_on_const Filter.Tendsto.tendstoUniformlyOn_const
 -/
 
-/- warning: uniform_continuous_on.tendsto_uniformly -> UniformContinuousOn.tendstoUniformly is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] [_inst_2 : UniformSpace.{u1} α] [_inst_3 : UniformSpace.{u3} γ] {x : α} {U : Set.{u1} α}, (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) U (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_2) x)) -> (forall {F : α -> β -> γ}, (UniformContinuousOn.{max u1 u2, u3} (Prod.{u1, u2} α β) γ (Prod.uniformSpace.{u1, u2} α β _inst_2 _inst_1) _inst_3 (Function.HasUncurry.uncurry.{max u1 u2 u3, max u1 u2, u3} (α -> β -> γ) (Prod.{u1, u2} α β) γ (Function.hasUncurryInduction.{u1, max u2 u3, u2, u3} α (β -> γ) β γ (Function.hasUncurryBase.{u2, u3} β γ)) F) (Set.prod.{u1, u2} α β U (Set.univ.{u2} β))) -> (TendstoUniformly.{u2, u3, u1} β γ α _inst_3 F (F x) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_2) x)))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] [_inst_2 : UniformSpace.{u1} α] [_inst_3 : UniformSpace.{u3} γ] {x : α} {U : Set.{u1} α}, (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) U (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_2) x)) -> (forall {F : α -> β -> γ}, (UniformContinuousOn.{max u1 u2, u3} (Prod.{u1, u2} α β) γ (instUniformSpaceProd.{u1, u2} α β _inst_2 _inst_1) _inst_3 (Function.HasUncurry.uncurry.{max (max u1 u2) u3, max u1 u2, u3} (α -> β -> γ) (Prod.{u1, u2} α β) γ (Function.hasUncurryInduction.{u1, max u2 u3, u2, u3} α (β -> γ) β γ (Function.hasUncurryBase.{u2, u3} β γ)) F) (Set.prod.{u1, u2} α β U (Set.univ.{u2} β))) -> (TendstoUniformly.{u2, u3, u1} β γ α _inst_3 F (F x) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_2) x)))
-Case conversion may be inaccurate. Consider using '#align uniform_continuous_on.tendsto_uniformly UniformContinuousOn.tendstoUniformlyₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem UniformContinuousOn.tendstoUniformly [UniformSpace α] [UniformSpace γ] {x : α} {U : Set α}
     (hU : U ∈ 𝓝 x) {F : α → β → γ} (hF : UniformContinuousOn (↿F) (U ×ˢ (univ : Set β))) :
@@ -679,12 +595,6 @@ theorem UniformCauchySeqOn.tendstoUniformlyOn_of_tendsto [NeBot p] (hF : Uniform
 #align uniform_cauchy_seq_on.tendsto_uniformly_on_of_tendsto UniformCauchySeqOn.tendstoUniformlyOn_of_tendsto
 -/
 
-/- warning: uniform_cauchy_seq_on_filter.mono_left -> UniformCauchySeqOnFilter.mono_left is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {p : Filter.{u3} ι} {p' : Filter.{u1} α} {p'' : Filter.{u3} ι}, (UniformCauchySeqOnFilter.{u1, u2, u3} α β ι _inst_1 F p p') -> (LE.le.{u3} (Filter.{u3} ι) (Preorder.toHasLe.{u3} (Filter.{u3} ι) (PartialOrder.toPreorder.{u3} (Filter.{u3} ι) (Filter.partialOrder.{u3} ι))) p'' p) -> (UniformCauchySeqOnFilter.{u1, u2, u3} α β ι _inst_1 F p'' p')
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {p : Filter.{u3} ι} {p' : Filter.{u1} α} {p'' : Filter.{u3} ι}, (UniformCauchySeqOnFilter.{u1, u2, u3} α β ι _inst_1 F p p') -> (LE.le.{u3} (Filter.{u3} ι) (Preorder.toLE.{u3} (Filter.{u3} ι) (PartialOrder.toPreorder.{u3} (Filter.{u3} ι) (Filter.instPartialOrderFilter.{u3} ι))) p'' p) -> (UniformCauchySeqOnFilter.{u1, u2, u3} α β ι _inst_1 F p'' p')
-Case conversion may be inaccurate. Consider using '#align uniform_cauchy_seq_on_filter.mono_left UniformCauchySeqOnFilter.mono_leftₓ'. -/
 theorem UniformCauchySeqOnFilter.mono_left {p'' : Filter ι} (hf : UniformCauchySeqOnFilter F p p')
     (hp : p'' ≤ p) : UniformCauchySeqOnFilter F p'' p' :=
   by
@@ -693,12 +603,6 @@ theorem UniformCauchySeqOnFilter.mono_left {p'' : Filter ι} (hf : UniformCauchy
   exact this.mono (by simp)
 #align uniform_cauchy_seq_on_filter.mono_left UniformCauchySeqOnFilter.mono_left
 
-/- warning: uniform_cauchy_seq_on_filter.mono_right -> UniformCauchySeqOnFilter.mono_right is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {p : Filter.{u3} ι} {p' : Filter.{u1} α} {p'' : Filter.{u1} α}, (UniformCauchySeqOnFilter.{u1, u2, u3} α β ι _inst_1 F p p') -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) p'' p') -> (UniformCauchySeqOnFilter.{u1, u2, u3} α β ι _inst_1 F p p'')
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {p : Filter.{u3} ι} {p' : Filter.{u1} α} {p'' : Filter.{u1} α}, (UniformCauchySeqOnFilter.{u1, u2, u3} α β ι _inst_1 F p p') -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) p'' p') -> (UniformCauchySeqOnFilter.{u1, u2, u3} α β ι _inst_1 F p p'')
-Case conversion may be inaccurate. Consider using '#align uniform_cauchy_seq_on_filter.mono_right UniformCauchySeqOnFilter.mono_rightₓ'. -/
 theorem UniformCauchySeqOnFilter.mono_right {p'' : Filter α} (hf : UniformCauchySeqOnFilter F p p')
     (hp : p'' ≤ p') : UniformCauchySeqOnFilter F p p'' :=
   by
@@ -716,12 +620,6 @@ theorem UniformCauchySeqOn.mono {s' : Set α} (hf : UniformCauchySeqOn F p s) (h
 #align uniform_cauchy_seq_on.mono UniformCauchySeqOn.mono
 -/
 
-/- warning: uniform_cauchy_seq_on_filter.comp -> UniformCauchySeqOnFilter.comp is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {p : Filter.{u3} ι} {p' : Filter.{u1} α} {γ : Type.{u4}}, (UniformCauchySeqOnFilter.{u1, u2, u3} α β ι _inst_1 F p p') -> (forall (g : γ -> α), UniformCauchySeqOnFilter.{u4, u2, u3} γ β ι _inst_1 (fun (n : ι) => Function.comp.{succ u4, succ u1, succ u2} γ α β (F n) g) p (Filter.comap.{u4, u1} γ α g p'))
-but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u3}} {ι : Type.{u4}} [_inst_1 : UniformSpace.{u3} β] {F : ι -> α -> β} {p : Filter.{u4} ι} {p' : Filter.{u2} α} {γ : Type.{u1}}, (UniformCauchySeqOnFilter.{u2, u3, u4} α β ι _inst_1 F p p') -> (forall (g : γ -> α), UniformCauchySeqOnFilter.{u1, u3, u4} γ β ι _inst_1 (fun (n : ι) => Function.comp.{succ u1, succ u2, succ u3} γ α β (F n) g) p (Filter.comap.{u1, u2} γ α g p'))
-Case conversion may be inaccurate. Consider using '#align uniform_cauchy_seq_on_filter.comp UniformCauchySeqOnFilter.compₓ'. -/
 /-- Composing on the right by a function preserves uniform Cauchy sequences -/
 theorem UniformCauchySeqOnFilter.comp {γ : Type _} (hf : UniformCauchySeqOnFilter F p p')
     (g : γ → α) : UniformCauchySeqOnFilter (fun n => F n ∘ g) p (p'.comap g) :=
@@ -733,12 +631,6 @@ theorem UniformCauchySeqOnFilter.comp {γ : Type _} (hf : UniformCauchySeqOnFilt
   exact eventually_comap.mpr (hpb.mono fun x hx y hy => by simp only [hx, hy, Function.comp_apply])
 #align uniform_cauchy_seq_on_filter.comp UniformCauchySeqOnFilter.comp
 
-/- warning: uniform_cauchy_seq_on.comp -> UniformCauchySeqOn.comp is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {s : Set.{u1} α} {p : Filter.{u3} ι} {γ : Type.{u4}}, (UniformCauchySeqOn.{u1, u2, u3} α β ι _inst_1 F p s) -> (forall (g : γ -> α), UniformCauchySeqOn.{u4, u2, u3} γ β ι _inst_1 (fun (n : ι) => Function.comp.{succ u4, succ u1, succ u2} γ α β (F n) g) p (Set.preimage.{u4, u1} γ α g s))
-but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u3}} {ι : Type.{u4}} [_inst_1 : UniformSpace.{u3} β] {F : ι -> α -> β} {s : Set.{u2} α} {p : Filter.{u4} ι} {γ : Type.{u1}}, (UniformCauchySeqOn.{u2, u3, u4} α β ι _inst_1 F p s) -> (forall (g : γ -> α), UniformCauchySeqOn.{u1, u3, u4} γ β ι _inst_1 (fun (n : ι) => Function.comp.{succ u1, succ u2, succ u3} γ α β (F n) g) p (Set.preimage.{u1, u2} γ α g s))
-Case conversion may be inaccurate. Consider using '#align uniform_cauchy_seq_on.comp UniformCauchySeqOn.compₓ'. -/
 /-- Composing on the right by a function preserves uniform Cauchy sequences -/
 theorem UniformCauchySeqOn.comp {γ : Type _} (hf : UniformCauchySeqOn F p s) (g : γ → α) :
     UniformCauchySeqOn (fun n => F n ∘ g) p (g ⁻¹' s) :=
@@ -756,12 +648,6 @@ theorem UniformContinuous.comp_uniformCauchySeqOn [UniformSpace γ] {g : β →
 #align uniform_continuous.comp_uniform_cauchy_seq_on UniformContinuous.comp_uniformCauchySeqOn
 -/
 
-/- warning: uniform_cauchy_seq_on.prod_map -> UniformCauchySeqOn.prod_map is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {s : Set.{u1} α} {p : Filter.{u3} ι} {ι' : Type.{u4}} {α' : Type.{u5}} {β' : Type.{u6}} [_inst_2 : UniformSpace.{u6} β'] {F' : ι' -> α' -> β'} {p' : Filter.{u4} ι'} {s' : Set.{u5} α'}, (UniformCauchySeqOn.{u1, u2, u3} α β ι _inst_1 F p s) -> (UniformCauchySeqOn.{u5, u6, u4} α' β' ι' _inst_2 F' p' s') -> (UniformCauchySeqOn.{max u1 u5, max u2 u6, max u3 u4} (Prod.{u1, u5} α α') (Prod.{u2, u6} β β') (Prod.{u3, u4} ι ι') (Prod.uniformSpace.{u2, u6} β β' _inst_1 _inst_2) (fun (i : Prod.{u3, u4} ι ι') => Prod.map.{u1, u2, u5, u6} α β α' β' (F (Prod.fst.{u3, u4} ι ι' i)) (F' (Prod.snd.{u3, u4} ι ι' i))) (Filter.prod.{u3, u4} ι ι' p p') (Set.prod.{u1, u5} α α' s s'))
-but is expected to have type
-  forall {α : Type.{u4}} {β : Type.{u5}} {ι : Type.{u6}} [_inst_1 : UniformSpace.{u5} β] {F : ι -> α -> β} {s : Set.{u4} α} {p : Filter.{u6} ι} {ι' : Type.{u3}} {α' : Type.{u2}} {β' : Type.{u1}} [_inst_2 : UniformSpace.{u1} β'] {F' : ι' -> α' -> β'} {p' : Filter.{u3} ι'} {s' : Set.{u2} α'}, (UniformCauchySeqOn.{u4, u5, u6} α β ι _inst_1 F p s) -> (UniformCauchySeqOn.{u2, u1, u3} α' β' ι' _inst_2 F' p' s') -> (UniformCauchySeqOn.{max u2 u4, max u1 u5, max u6 u3} (Prod.{u4, u2} α α') (Prod.{u5, u1} β β') (Prod.{u6, u3} ι ι') (instUniformSpaceProd.{u5, u1} β β' _inst_1 _inst_2) (fun (i : Prod.{u6, u3} ι ι') => Prod.map.{u4, u5, u2, u1} α β α' β' (F (Prod.fst.{u6, u3} ι ι' i)) (F' (Prod.snd.{u6, u3} ι ι' i))) (Filter.prod.{u6, u3} ι ι' p p') (Set.prod.{u4, u2} α α' s s'))
-Case conversion may be inaccurate. Consider using '#align uniform_cauchy_seq_on.prod_map UniformCauchySeqOn.prod_mapₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem UniformCauchySeqOn.prod_map {ι' α' β' : Type _} [UniformSpace β'] {F' : ι' → α' → β'}
     {p' : Filter ι'} {s' : Set α'} (h : UniformCauchySeqOn F p s)
@@ -778,24 +664,12 @@ theorem UniformCauchySeqOn.prod_map {ι' α' β' : Type _} [UniformSpace β'] {F
   refine' hvw ⟨_, mk_mem_prod (hx.1 a ha) (hx.2 b hb), rfl⟩
 #align uniform_cauchy_seq_on.prod_map UniformCauchySeqOn.prod_map
 
-/- warning: uniform_cauchy_seq_on.prod -> UniformCauchySeqOn.prod is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {s : Set.{u1} α} {p : Filter.{u3} ι} {ι' : Type.{u4}} {β' : Type.{u5}} [_inst_2 : UniformSpace.{u5} β'] {F' : ι' -> α -> β'} {p' : Filter.{u4} ι'}, (UniformCauchySeqOn.{u1, u2, u3} α β ι _inst_1 F p s) -> (UniformCauchySeqOn.{u1, u5, u4} α β' ι' _inst_2 F' p' s) -> (UniformCauchySeqOn.{u1, max u2 u5, max u3 u4} α (Prod.{u2, u5} β β') (Prod.{u3, u4} ι ι') (Prod.uniformSpace.{u2, u5} β β' _inst_1 _inst_2) (fun (i : Prod.{u3, u4} ι ι') (a : α) => Prod.mk.{u2, u5} β β' (F (Prod.fst.{u3, u4} ι ι' i) a) (F' (Prod.snd.{u3, u4} ι ι' i) a)) (Filter.prod.{u3, u4} ι ι' p p') s)
-but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u4}} {ι : Type.{u5}} [_inst_1 : UniformSpace.{u4} β] {F : ι -> α -> β} {s : Set.{u3} α} {p : Filter.{u5} ι} {ι' : Type.{u2}} {β' : Type.{u1}} [_inst_2 : UniformSpace.{u1} β'] {F' : ι' -> α -> β'} {p' : Filter.{u2} ι'}, (UniformCauchySeqOn.{u3, u4, u5} α β ι _inst_1 F p s) -> (UniformCauchySeqOn.{u3, u1, u2} α β' ι' _inst_2 F' p' s) -> (UniformCauchySeqOn.{u3, max u1 u4, max u5 u2} α (Prod.{u4, u1} β β') (Prod.{u5, u2} ι ι') (instUniformSpaceProd.{u4, u1} β β' _inst_1 _inst_2) (fun (i : Prod.{u5, u2} ι ι') (a : α) => Prod.mk.{u4, u1} β β' (F (Prod.fst.{u5, u2} ι ι' i) a) (F' (Prod.snd.{u5, u2} ι ι' i) a)) (Filter.prod.{u5, u2} ι ι' p p') s)
-Case conversion may be inaccurate. Consider using '#align uniform_cauchy_seq_on.prod UniformCauchySeqOn.prodₓ'. -/
 theorem UniformCauchySeqOn.prod {ι' β' : Type _} [UniformSpace β'] {F' : ι' → α → β'}
     {p' : Filter ι'} (h : UniformCauchySeqOn F p s) (h' : UniformCauchySeqOn F' p' s) :
     UniformCauchySeqOn (fun (i : ι × ι') a => (F i.fst a, F' i.snd a)) (p ×ᶠ p') s :=
   (congr_arg _ s.inter_self).mp ((h.Prod_map h').comp fun a => (a, a))
 #align uniform_cauchy_seq_on.prod UniformCauchySeqOn.prod
 
-/- warning: uniform_cauchy_seq_on.prod' -> UniformCauchySeqOn.prod' is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {s : Set.{u1} α} {p : Filter.{u3} ι} {β' : Type.{u4}} [_inst_2 : UniformSpace.{u4} β'] {F' : ι -> α -> β'}, (UniformCauchySeqOn.{u1, u2, u3} α β ι _inst_1 F p s) -> (UniformCauchySeqOn.{u1, u4, u3} α β' ι _inst_2 F' p s) -> (UniformCauchySeqOn.{u1, max u2 u4, u3} α (Prod.{u2, u4} β β') ι (Prod.uniformSpace.{u2, u4} β β' _inst_1 _inst_2) (fun (i : ι) (a : α) => Prod.mk.{u2, u4} β β' (F i a) (F' i a)) p s)
-but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u3}} {ι : Type.{u4}} [_inst_1 : UniformSpace.{u3} β] {F : ι -> α -> β} {s : Set.{u2} α} {p : Filter.{u4} ι} {β' : Type.{u1}} [_inst_2 : UniformSpace.{u1} β'] {F' : ι -> α -> β'}, (UniformCauchySeqOn.{u2, u3, u4} α β ι _inst_1 F p s) -> (UniformCauchySeqOn.{u2, u1, u4} α β' ι _inst_2 F' p s) -> (UniformCauchySeqOn.{u2, max u1 u3, u4} α (Prod.{u3, u1} β β') ι (instUniformSpaceProd.{u3, u1} β β' _inst_1 _inst_2) (fun (i : ι) (a : α) => Prod.mk.{u3, u1} β β' (F i a) (F' i a)) p s)
-Case conversion may be inaccurate. Consider using '#align uniform_cauchy_seq_on.prod' UniformCauchySeqOn.prod'ₓ'. -/
 theorem UniformCauchySeqOn.prod' {β' : Type _} [UniformSpace β'] {F' : ι → α → β'}
     (h : UniformCauchySeqOn F p s) (h' : UniformCauchySeqOn F' p s) :
     UniformCauchySeqOn (fun (i : ι) a => (F i a, F' i a)) p s :=
@@ -956,12 +830,6 @@ theorem TendstoLocallyUniformlyOn.mono (h : TendstoLocallyUniformlyOn F f p s) (
 #align tendsto_locally_uniformly_on.mono TendstoLocallyUniformlyOn.mono
 -/
 
-/- warning: tendsto_locally_uniformly_on_Union -> tendstoLocallyUniformlyOn_iUnion is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} {ι : Type.{u4}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {f : α -> β} {p : Filter.{u4} ι} [_inst_2 : TopologicalSpace.{u1} α] {S : γ -> (Set.{u1} α)}, (forall (i : γ), IsOpen.{u1} α _inst_2 (S i)) -> (forall (i : γ), TendstoLocallyUniformlyOn.{u1, u2, u4} α β ι _inst_1 _inst_2 F f p (S i)) -> (TendstoLocallyUniformlyOn.{u1, u2, u4} α β ι _inst_1 _inst_2 F f p (Set.iUnion.{u1, succ u3} α γ (fun (i : γ) => S i)))
-but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u3}} {γ : Type.{u4}} [ι : UniformSpace.{u3} β] {_inst_1 : γ -> α -> β} {F : α -> β} {f : Filter.{u4} γ} [p : TopologicalSpace.{u2} α] {_inst_2 : Sort.{u1}} {S : _inst_2 -> (Set.{u2} α)}, (forall (i : _inst_2), IsOpen.{u2} α p (S i)) -> (forall (i : _inst_2), TendstoLocallyUniformlyOn.{u2, u3, u4} α β γ ι p _inst_1 F f (S i)) -> (TendstoLocallyUniformlyOn.{u2, u3, u4} α β γ ι p _inst_1 F f (Set.iUnion.{u2, u1} α _inst_2 (fun (i : _inst_2) => S i)))
-Case conversion may be inaccurate. Consider using '#align tendsto_locally_uniformly_on_Union tendstoLocallyUniformlyOn_iUnionₓ'. -/
 theorem tendstoLocallyUniformlyOn_iUnion {S : γ → Set α} (hS : ∀ i, IsOpen (S i))
     (h : ∀ i, TendstoLocallyUniformlyOn F f p (S i)) : TendstoLocallyUniformlyOn F f p (⋃ i, S i) :=
   by
@@ -987,12 +855,6 @@ theorem tendstoLocallyUniformlyOn_sUnion (S : Set (Set α)) (hS : ∀ s ∈ S, I
 #align tendsto_locally_uniformly_on_sUnion tendstoLocallyUniformlyOn_sUnion
 -/
 
-/- warning: tendsto_locally_uniformly_on.union -> TendstoLocallyUniformlyOn.union is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {f : α -> β} {p : Filter.{u3} ι} [_inst_2 : TopologicalSpace.{u1} α] {s₁ : Set.{u1} α} {s₂ : Set.{u1} α}, (IsOpen.{u1} α _inst_2 s₁) -> (IsOpen.{u1} α _inst_2 s₂) -> (TendstoLocallyUniformlyOn.{u1, u2, u3} α β ι _inst_1 _inst_2 F f p s₁) -> (TendstoLocallyUniformlyOn.{u1, u2, u3} α β ι _inst_1 _inst_2 F f p s₂) -> (TendstoLocallyUniformlyOn.{u1, u2, u3} α β ι _inst_1 _inst_2 F f p (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s₁ s₂))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {f : α -> β} {p : Filter.{u3} ι} [_inst_2 : TopologicalSpace.{u1} α] {s₁ : Set.{u1} α} {s₂ : Set.{u1} α}, (IsOpen.{u1} α _inst_2 s₁) -> (IsOpen.{u1} α _inst_2 s₂) -> (TendstoLocallyUniformlyOn.{u1, u2, u3} α β ι _inst_1 _inst_2 F f p s₁) -> (TendstoLocallyUniformlyOn.{u1, u2, u3} α β ι _inst_1 _inst_2 F f p s₂) -> (TendstoLocallyUniformlyOn.{u1, u2, u3} α β ι _inst_1 _inst_2 F f p (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s₁ s₂))
-Case conversion may be inaccurate. Consider using '#align tendsto_locally_uniformly_on.union TendstoLocallyUniformlyOn.unionₓ'. -/
 theorem TendstoLocallyUniformlyOn.union {s₁ s₂ : Set α} (hs₁ : IsOpen s₁) (hs₂ : IsOpen s₂)
     (h₁ : TendstoLocallyUniformlyOn F f p s₁) (h₂ : TendstoLocallyUniformlyOn F f p s₂) :
     TendstoLocallyUniformlyOn F f p (s₁ ∪ s₂) := by rw [← sUnion_pair];
@@ -1067,12 +929,6 @@ theorem TendstoLocallyUniformly.comp [TopologicalSpace γ] (h : TendstoLocallyUn
 #align tendsto_locally_uniformly.comp TendstoLocallyUniformly.comp
 -/
 
-/- warning: tendsto_locally_uniformly_on_tfae -> tendstoLocallyUniformlyOn_TFAE is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {s : Set.{u1} α} [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : LocallyCompactSpace.{u1} α _inst_2] (G : ι -> α -> β) (g : α -> β) (p : Filter.{u3} ι), (IsOpen.{u1} α _inst_2 s) -> (List.TFAE (List.cons.{0} Prop (TendstoLocallyUniformlyOn.{u1, u2, u3} α β ι _inst_1 _inst_2 G g p s) (List.cons.{0} Prop (forall (K : Set.{u1} α), (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) K s) -> (IsCompact.{u1} α _inst_2 K) -> (TendstoUniformlyOn.{u1, u2, u3} α β ι _inst_1 G g p K)) (List.cons.{0} Prop (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (Exists.{succ u1} (Set.{u1} α) (fun (v : Set.{u1} α) => Exists.{0} (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) v (nhdsWithin.{u1} α _inst_2 x s)) (fun (H : Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) v (nhdsWithin.{u1} α _inst_2 x s)) => TendstoUniformlyOn.{u1, u2, u3} α β ι _inst_1 G g p v)))) (List.nil.{0} Prop)))))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {s : Set.{u1} α} [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : LocallyCompactSpace.{u1} α _inst_2] (G : ι -> α -> β) (g : α -> β) (p : Filter.{u3} ι), (IsOpen.{u1} α _inst_2 s) -> (List.TFAE (List.cons.{0} Prop (TendstoLocallyUniformlyOn.{u1, u2, u3} α β ι _inst_1 _inst_2 G g p s) (List.cons.{0} Prop (forall (K : Set.{u1} α), (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) K s) -> (IsCompact.{u1} α _inst_2 K) -> (TendstoUniformlyOn.{u1, u2, u3} α β ι _inst_1 G g p K)) (List.cons.{0} Prop (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (Exists.{succ u1} (Set.{u1} α) (fun (v : Set.{u1} α) => And (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) v (nhdsWithin.{u1} α _inst_2 x s)) (TendstoUniformlyOn.{u1, u2, u3} α β ι _inst_1 G g p v)))) (List.nil.{0} Prop)))))
-Case conversion may be inaccurate. Consider using '#align tendsto_locally_uniformly_on_tfae tendstoLocallyUniformlyOn_TFAEₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (K «expr ⊆ » s) -/
 theorem tendstoLocallyUniformlyOn_TFAE [LocallyCompactSpace α] (G : ι → α → β) (g : α → β)
     (p : Filter ι) (hs : IsOpen s) :
@@ -1175,12 +1031,6 @@ the statements are derived from a statement about locally uniform approximation
 a point, called `continuous_within_at_of_locally_uniform_approx_of_continuous_within_at`. -/
 
 
-/- warning: continuous_within_at_of_locally_uniform_approx_of_continuous_within_at -> continuousWithinAt_of_locally_uniform_approx_of_continuousWithinAt is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u2} β] {f : α -> β} {s : Set.{u1} α} {x : α} [_inst_2 : TopologicalSpace.{u1} α], (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall (u : Set.{u2} (Prod.{u2, u2} β β)), (Membership.Mem.{u2, u2} (Set.{u2} (Prod.{u2, u2} β β)) (Filter.{u2} (Prod.{u2, u2} β β)) (Filter.hasMem.{u2} (Prod.{u2, u2} β β)) u (uniformity.{u2} β _inst_1)) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => Exists.{0} (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) t (nhdsWithin.{u1} α _inst_2 x s)) (fun (H : Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) t (nhdsWithin.{u1} α _inst_2 x s)) => Exists.{max (succ u1) (succ u2)} (α -> β) (fun (F : α -> β) => And (ContinuousWithinAt.{u1, u2} α β _inst_2 (UniformSpace.toTopologicalSpace.{u2} β _inst_1) F s x) (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) -> (Membership.Mem.{u2, u2} (Prod.{u2, u2} β β) (Set.{u2} (Prod.{u2, u2} β β)) (Set.hasMem.{u2} (Prod.{u2, u2} β β)) (Prod.mk.{u2, u2} β β (f y) (F y)) u))))))) -> (ContinuousWithinAt.{u1, u2} α β _inst_2 (UniformSpace.toTopologicalSpace.{u2} β _inst_1) f s x)
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u2} β] {f : α -> β} {s : Set.{u1} α} {x : α} [_inst_2 : TopologicalSpace.{u1} α], (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (forall (u : Set.{u2} (Prod.{u2, u2} β β)), (Membership.mem.{u2, u2} (Set.{u2} (Prod.{u2, u2} β β)) (Filter.{u2} (Prod.{u2, u2} β β)) (instMembershipSetFilter.{u2} (Prod.{u2, u2} β β)) u (uniformity.{u2} β _inst_1)) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) t (nhdsWithin.{u1} α _inst_2 x s)) (Exists.{max (succ u1) (succ u2)} (α -> β) (fun (F : α -> β) => And (ContinuousWithinAt.{u1, u2} α β _inst_2 (UniformSpace.toTopologicalSpace.{u2} β _inst_1) F s x) (forall (y : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) -> (Membership.mem.{u2, u2} (Prod.{u2, u2} β β) (Set.{u2} (Prod.{u2, u2} β β)) (Set.instMembershipSet.{u2} (Prod.{u2, u2} β β)) (Prod.mk.{u2, u2} β β (f y) (F y)) u))))))) -> (ContinuousWithinAt.{u1, u2} α β _inst_2 (UniformSpace.toTopologicalSpace.{u2} β _inst_1) f s x)
-Case conversion may be inaccurate. Consider using '#align continuous_within_at_of_locally_uniform_approx_of_continuous_within_at continuousWithinAt_of_locally_uniform_approx_of_continuousWithinAtₓ'. -/
 /-- A function which can be locally uniformly approximated by functions which are continuous
 within a set at a point is continuous within this set at this point. -/
 theorem continuousWithinAt_of_locally_uniform_approx_of_continuousWithinAt (hx : x ∈ s)
@@ -1203,12 +1053,6 @@ theorem continuousWithinAt_of_locally_uniform_approx_of_continuousWithinAt (hx :
   exact C.mono fun y hy => u₁₀ (prod_mk_mem_compRel hy this)
 #align continuous_within_at_of_locally_uniform_approx_of_continuous_within_at continuousWithinAt_of_locally_uniform_approx_of_continuousWithinAt
 
-/- warning: continuous_at_of_locally_uniform_approx_of_continuous_at -> continuousAt_of_locally_uniform_approx_of_continuousAt is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u2} β] {f : α -> β} {x : α} [_inst_2 : TopologicalSpace.{u1} α], (forall (u : Set.{u2} (Prod.{u2, u2} β β)), (Membership.Mem.{u2, u2} (Set.{u2} (Prod.{u2, u2} β β)) (Filter.{u2} (Prod.{u2, u2} β β)) (Filter.hasMem.{u2} (Prod.{u2, u2} β β)) u (uniformity.{u2} β _inst_1)) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => Exists.{0} (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) t (nhds.{u1} α _inst_2 x)) (fun (H : Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) t (nhds.{u1} α _inst_2 x)) => Exists.{max (succ u1) (succ u2)} (α -> β) (fun (F : α -> β) => And (ContinuousAt.{u1, u2} α β _inst_2 (UniformSpace.toTopologicalSpace.{u2} β _inst_1) F x) (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) -> (Membership.Mem.{u2, u2} (Prod.{u2, u2} β β) (Set.{u2} (Prod.{u2, u2} β β)) (Set.hasMem.{u2} (Prod.{u2, u2} β β)) (Prod.mk.{u2, u2} β β (f y) (F y)) u))))))) -> (ContinuousAt.{u1, u2} α β _inst_2 (UniformSpace.toTopologicalSpace.{u2} β _inst_1) f x)
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u2} β] {f : α -> β} {x : α} [_inst_2 : TopologicalSpace.{u1} α], (forall (u : Set.{u2} (Prod.{u2, u2} β β)), (Membership.mem.{u2, u2} (Set.{u2} (Prod.{u2, u2} β β)) (Filter.{u2} (Prod.{u2, u2} β β)) (instMembershipSetFilter.{u2} (Prod.{u2, u2} β β)) u (uniformity.{u2} β _inst_1)) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) t (nhds.{u1} α _inst_2 x)) (Exists.{max (succ u2) (succ u1)} (α -> β) (fun (F : α -> β) => And (ContinuousAt.{u1, u2} α β _inst_2 (UniformSpace.toTopologicalSpace.{u2} β _inst_1) F x) (forall (y : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) -> (Membership.mem.{u2, u2} (Prod.{u2, u2} β β) (Set.{u2} (Prod.{u2, u2} β β)) (Set.instMembershipSet.{u2} (Prod.{u2, u2} β β)) (Prod.mk.{u2, u2} β β (f y) (F y)) u))))))) -> (ContinuousAt.{u1, u2} α β _inst_2 (UniformSpace.toTopologicalSpace.{u2} β _inst_1) f x)
-Case conversion may be inaccurate. Consider using '#align continuous_at_of_locally_uniform_approx_of_continuous_at continuousAt_of_locally_uniform_approx_of_continuousAtₓ'. -/
 /-- A function which can be locally uniformly approximated by functions which are continuous at
 a point is continuous at this point. -/
 theorem continuousAt_of_locally_uniform_approx_of_continuousAt
@@ -1219,12 +1063,6 @@ theorem continuousAt_of_locally_uniform_approx_of_continuousAt
   simpa only [exists_prop, nhdsWithin_univ, continuousWithinAt_univ] using L
 #align continuous_at_of_locally_uniform_approx_of_continuous_at continuousAt_of_locally_uniform_approx_of_continuousAt
 
-/- warning: continuous_on_of_locally_uniform_approx_of_continuous_within_at -> continuousOn_of_locally_uniform_approx_of_continuousWithinAt is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u2} β] {f : α -> β} {s : Set.{u1} α} [_inst_2 : TopologicalSpace.{u1} α], (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall (u : Set.{u2} (Prod.{u2, u2} β β)), (Membership.Mem.{u2, u2} (Set.{u2} (Prod.{u2, u2} β β)) (Filter.{u2} (Prod.{u2, u2} β β)) (Filter.hasMem.{u2} (Prod.{u2, u2} β β)) u (uniformity.{u2} β _inst_1)) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => Exists.{0} (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) t (nhdsWithin.{u1} α _inst_2 x s)) (fun (H : Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) t (nhdsWithin.{u1} α _inst_2 x s)) => Exists.{max (succ u1) (succ u2)} (α -> β) (fun (F : α -> β) => And (ContinuousWithinAt.{u1, u2} α β _inst_2 (UniformSpace.toTopologicalSpace.{u2} β _inst_1) F s x) (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) -> (Membership.Mem.{u2, u2} (Prod.{u2, u2} β β) (Set.{u2} (Prod.{u2, u2} β β)) (Set.hasMem.{u2} (Prod.{u2, u2} β β)) (Prod.mk.{u2, u2} β β (f y) (F y)) u)))))))) -> (ContinuousOn.{u1, u2} α β _inst_2 (UniformSpace.toTopologicalSpace.{u2} β _inst_1) f s)
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u2} β] {f : α -> β} {s : Set.{u1} α} [_inst_2 : TopologicalSpace.{u1} α], (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (forall (u : Set.{u2} (Prod.{u2, u2} β β)), (Membership.mem.{u2, u2} (Set.{u2} (Prod.{u2, u2} β β)) (Filter.{u2} (Prod.{u2, u2} β β)) (instMembershipSetFilter.{u2} (Prod.{u2, u2} β β)) u (uniformity.{u2} β _inst_1)) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) t (nhdsWithin.{u1} α _inst_2 x s)) (Exists.{max (succ u2) (succ u1)} (α -> β) (fun (F : α -> β) => And (ContinuousWithinAt.{u1, u2} α β _inst_2 (UniformSpace.toTopologicalSpace.{u2} β _inst_1) F s x) (forall (y : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) -> (Membership.mem.{u2, u2} (Prod.{u2, u2} β β) (Set.{u2} (Prod.{u2, u2} β β)) (Set.instMembershipSet.{u2} (Prod.{u2, u2} β β)) (Prod.mk.{u2, u2} β β (f y) (F y)) u)))))))) -> (ContinuousOn.{u1, u2} α β _inst_2 (UniformSpace.toTopologicalSpace.{u2} β _inst_1) f s)
-Case conversion may be inaccurate. Consider using '#align continuous_on_of_locally_uniform_approx_of_continuous_within_at continuousOn_of_locally_uniform_approx_of_continuousWithinAtₓ'. -/
 /-- A function which can be locally uniformly approximated by functions which are continuous
 on a set is continuous on this set. -/
 theorem continuousOn_of_locally_uniform_approx_of_continuousWithinAt
@@ -1244,12 +1082,6 @@ theorem continuousOn_of_uniform_approx_of_continuousOn
 #align continuous_on_of_uniform_approx_of_continuous_on continuousOn_of_uniform_approx_of_continuousOn
 -/
 
-/- warning: continuous_of_locally_uniform_approx_of_continuous_at -> continuous_of_locally_uniform_approx_of_continuousAt is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u2} β] {f : α -> β} [_inst_2 : TopologicalSpace.{u1} α], (forall (x : α) (u : Set.{u2} (Prod.{u2, u2} β β)), (Membership.Mem.{u2, u2} (Set.{u2} (Prod.{u2, u2} β β)) (Filter.{u2} (Prod.{u2, u2} β β)) (Filter.hasMem.{u2} (Prod.{u2, u2} β β)) u (uniformity.{u2} β _inst_1)) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => Exists.{0} (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) t (nhds.{u1} α _inst_2 x)) (fun (H : Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) t (nhds.{u1} α _inst_2 x)) => Exists.{max (succ u1) (succ u2)} (α -> β) (fun (F : α -> β) => And (ContinuousAt.{u1, u2} α β _inst_2 (UniformSpace.toTopologicalSpace.{u2} β _inst_1) F x) (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) -> (Membership.Mem.{u2, u2} (Prod.{u2, u2} β β) (Set.{u2} (Prod.{u2, u2} β β)) (Set.hasMem.{u2} (Prod.{u2, u2} β β)) (Prod.mk.{u2, u2} β β (f y) (F y)) u))))))) -> (Continuous.{u1, u2} α β _inst_2 (UniformSpace.toTopologicalSpace.{u2} β _inst_1) f)
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u2} β] {f : α -> β} [_inst_2 : TopologicalSpace.{u1} α], (forall (x : α) (u : Set.{u2} (Prod.{u2, u2} β β)), (Membership.mem.{u2, u2} (Set.{u2} (Prod.{u2, u2} β β)) (Filter.{u2} (Prod.{u2, u2} β β)) (instMembershipSetFilter.{u2} (Prod.{u2, u2} β β)) u (uniformity.{u2} β _inst_1)) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) t (nhds.{u1} α _inst_2 x)) (Exists.{max (succ u2) (succ u1)} (α -> β) (fun (F : α -> β) => And (ContinuousAt.{u1, u2} α β _inst_2 (UniformSpace.toTopologicalSpace.{u2} β _inst_1) F x) (forall (y : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) -> (Membership.mem.{u2, u2} (Prod.{u2, u2} β β) (Set.{u2} (Prod.{u2, u2} β β)) (Set.instMembershipSet.{u2} (Prod.{u2, u2} β β)) (Prod.mk.{u2, u2} β β (f y) (F y)) u))))))) -> (Continuous.{u1, u2} α β _inst_2 (UniformSpace.toTopologicalSpace.{u2} β _inst_1) f)
-Case conversion may be inaccurate. Consider using '#align continuous_of_locally_uniform_approx_of_continuous_at continuous_of_locally_uniform_approx_of_continuousAtₓ'. -/
 /-- A function which can be locally uniformly approximated by continuous functions is continuous. -/
 theorem continuous_of_locally_uniform_approx_of_continuousAt
     (L : ∀ x : α, ∀ u ∈ 𝓤 β, ∃ t ∈ 𝓝 x, ∃ F, ContinuousAt F x ∧ ∀ y ∈ t, (f y, F y) ∈ u) :
@@ -1324,9 +1156,6 @@ this paragraph, we prove variations around this statement.
 -/
 
 
-/- warning: tendsto_comp_of_locally_uniform_limit_within -> tendsto_comp_of_locally_uniform_limit_within is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tendsto_comp_of_locally_uniform_limit_within tendsto_comp_of_locally_uniform_limit_withinₓ'. -/
 /-- If `Fₙ` converges locally uniformly on a neighborhood of `x` within a set `s` to a function `f`
 which is continuous at `x` within `s `, and `gₙ` tends to `x` within `s`, then `Fₙ (gₙ)` tends
 to `f x`. -/
@@ -1346,9 +1175,6 @@ theorem tendsto_comp_of_locally_uniform_limit_within (h : ContinuousWithinAt f s
   exact u₁₀ (prod_mk_mem_compRel H3 (H1 _ H2))
 #align tendsto_comp_of_locally_uniform_limit_within tendsto_comp_of_locally_uniform_limit_within
 
-/- warning: tendsto_comp_of_locally_uniform_limit -> tendsto_comp_of_locally_uniform_limit is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tendsto_comp_of_locally_uniform_limit tendsto_comp_of_locally_uniform_limitₓ'. -/
 /-- If `Fₙ` converges locally uniformly on a neighborhood of `x` to a function `f` which is
 continuous at `x`, and `gₙ` tends to `x`, then `Fₙ (gₙ)` tends to `f x`. -/
 theorem tendsto_comp_of_locally_uniform_limit (h : ContinuousAt f x) (hg : Tendsto g p (𝓝 x))

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

@@ -561,13 +561,9 @@ theorem UniformContinuousOn.tendstoUniformly [UniformSpace α] [UniformSpace γ]
     show (fun q : α × β => (F x q.2, F q.1 q.2)) = Prod.map (↿F) ↿F ∘ φ by ext <;> simpa]
   apply hF.comp (tendsto_inf.mpr ⟨_, _⟩)
   · rw [uniformity_prod, tendsto_inf, tendsto_comap_iff, tendsto_comap_iff,
-      show (fun p : (α × β) × α × β => (p.1.1, p.2.1)) ∘ φ = (fun a => (x, a)) ∘ Prod.fst
-        by
-        ext
+      show (fun p : (α × β) × α × β => (p.1.1, p.2.1)) ∘ φ = (fun a => (x, a)) ∘ Prod.fst by ext;
         simp,
-      show (fun p : (α × β) × α × β => (p.1.2, p.2.2)) ∘ φ = (fun b => (b, b)) ∘ Prod.snd
-        by
-        ext
+      show (fun p : (α × β) × α × β => (p.1.2, p.2.2)) ∘ φ = (fun b => (b, b)) ∘ Prod.snd by ext;
         simp]
     exact
       ⟨tendsto_left_nhds_uniformity.comp tendsto_fst,
@@ -838,9 +834,7 @@ theorem tendstoUniformlyOn_of_seq_tendstoUniformlyOn {l : Filter ι} [l.IsCounta
     (fun q : ι × α => (f q.snd, F q.fst q.snd)) ∘ u =
       (fun q : ℕ × α => (f q.snd, F ((fun n : ℕ => (u n).fst) q.fst) q.snd)) ∘ fun n =>
         (n, (u n).snd) :=
-    by
-    ext1 n
-    simp
+    by ext1 n; simp
   rw [this]
   refine' tendsto.comp h _
   rw [tendsto_prod_iff']
@@ -856,9 +850,7 @@ theorem TendstoUniformlyOn.seq_tendstoUniformlyOn {l : Filter ι} (h : TendstoUn
   have :
     (fun q : ℕ × α => (f q.snd, F (u q.fst) q.snd)) =
       (fun q : ι × α => (f q.snd, F q.fst q.snd)) ∘ fun p : ℕ × α => (u p.fst, p.snd) :=
-    by
-    ext1 x
-    simp
+    by ext1 x; simp
   rw [this]
   refine' h.comp _
   rw [tendsto_prod_iff']
@@ -983,19 +975,15 @@ theorem tendstoLocallyUniformlyOn_iUnion {S : γ → Set α} (hS : ∀ i, IsOpen
 #print tendstoLocallyUniformlyOn_biUnion /-
 theorem tendstoLocallyUniformlyOn_biUnion {s : Set γ} {S : γ → Set α} (hS : ∀ i ∈ s, IsOpen (S i))
     (h : ∀ i ∈ s, TendstoLocallyUniformlyOn F f p (S i)) :
-    TendstoLocallyUniformlyOn F f p (⋃ i ∈ s, S i) :=
-  by
-  rw [bUnion_eq_Union]
+    TendstoLocallyUniformlyOn F f p (⋃ i ∈ s, S i) := by rw [bUnion_eq_Union];
   exact tendstoLocallyUniformlyOn_iUnion (fun i => hS _ i.2) fun i => h _ i.2
 #align tendsto_locally_uniformly_on_bUnion tendstoLocallyUniformlyOn_biUnion
 -/
 
 #print tendstoLocallyUniformlyOn_sUnion /-
 theorem tendstoLocallyUniformlyOn_sUnion (S : Set (Set α)) (hS : ∀ s ∈ S, IsOpen s)
-    (h : ∀ s ∈ S, TendstoLocallyUniformlyOn F f p s) : TendstoLocallyUniformlyOn F f p (⋃₀ S) :=
-  by
-  rw [sUnion_eq_bUnion]
-  exact tendstoLocallyUniformlyOn_biUnion hS h
+    (h : ∀ s ∈ S, TendstoLocallyUniformlyOn F f p s) : TendstoLocallyUniformlyOn F f p (⋃₀ S) := by
+  rw [sUnion_eq_bUnion]; exact tendstoLocallyUniformlyOn_biUnion hS h
 #align tendsto_locally_uniformly_on_sUnion tendstoLocallyUniformlyOn_sUnion
 -/
 
@@ -1007,9 +995,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align tendsto_locally_uniformly_on.union TendstoLocallyUniformlyOn.unionₓ'. -/
 theorem TendstoLocallyUniformlyOn.union {s₁ s₂ : Set α} (hs₁ : IsOpen s₁) (hs₂ : IsOpen s₂)
     (h₁ : TendstoLocallyUniformlyOn F f p s₁) (h₂ : TendstoLocallyUniformlyOn F f p s₂) :
-    TendstoLocallyUniformlyOn F f p (s₁ ∪ s₂) :=
-  by
-  rw [← sUnion_pair]
+    TendstoLocallyUniformlyOn F f p (s₁ ∪ s₂) := by rw [← sUnion_pair];
   refine' tendstoLocallyUniformlyOn_sUnion _ _ _ <;> simp [*]
 #align tendsto_locally_uniformly_on.union TendstoLocallyUniformlyOn.union
 

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

@@ -1339,10 +1339,7 @@ this paragraph, we prove variations around this statement.
 
 
 /- warning: tendsto_comp_of_locally_uniform_limit_within -> tendsto_comp_of_locally_uniform_limit_within is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {f : α -> β} {s : Set.{u1} α} {x : α} {p : Filter.{u3} ι} {g : ι -> α} [_inst_2 : TopologicalSpace.{u1} α], (ContinuousWithinAt.{u1, u2} α β _inst_2 (UniformSpace.toTopologicalSpace.{u2} β _inst_1) f s x) -> (Filter.Tendsto.{u3, u1} ι α g p (nhdsWithin.{u1} α _inst_2 x s)) -> (forall (u : Set.{u2} (Prod.{u2, u2} β β)), (Membership.Mem.{u2, u2} (Set.{u2} (Prod.{u2, u2} β β)) (Filter.{u2} (Prod.{u2, u2} β β)) (Filter.hasMem.{u2} (Prod.{u2, u2} β β)) u (uniformity.{u2} β _inst_1)) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => Exists.{0} (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) t (nhdsWithin.{u1} α _inst_2 x s)) (fun (H : Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) t (nhdsWithin.{u1} α _inst_2 x s)) => Filter.Eventually.{u3} ι (fun (n : ι) => forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) -> (Membership.Mem.{u2, u2} (Prod.{u2, u2} β β) (Set.{u2} (Prod.{u2, u2} β β)) (Set.hasMem.{u2} (Prod.{u2, u2} β β)) (Prod.mk.{u2, u2} β β (f y) (F n y)) u)) p)))) -> (Filter.Tendsto.{u3, u2} ι β (fun (n : ι) => F n (g n)) p (nhds.{u2} β (UniformSpace.toTopologicalSpace.{u2} β _inst_1) (f x)))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {f : α -> β} {s : Set.{u1} α} {x : α} {p : Filter.{u3} ι} {g : ι -> α} [_inst_2 : TopologicalSpace.{u1} α], (ContinuousWithinAt.{u1, u2} α β _inst_2 (UniformSpace.toTopologicalSpace.{u2} β _inst_1) f s x) -> (Filter.Tendsto.{u3, u1} ι α g p (nhdsWithin.{u1} α _inst_2 x s)) -> (forall (u : Set.{u2} (Prod.{u2, u2} β β)), (Membership.mem.{u2, u2} (Set.{u2} (Prod.{u2, u2} β β)) (Filter.{u2} (Prod.{u2, u2} β β)) (instMembershipSetFilter.{u2} (Prod.{u2, u2} β β)) u (uniformity.{u2} β _inst_1)) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) t (nhdsWithin.{u1} α _inst_2 x s)) (Filter.Eventually.{u3} ι (fun (n : ι) => forall (y : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) -> (Membership.mem.{u2, u2} (Prod.{u2, u2} β β) (Set.{u2} (Prod.{u2, u2} β β)) (Set.instMembershipSet.{u2} (Prod.{u2, u2} β β)) (Prod.mk.{u2, u2} β β (f y) (F n y)) u)) p)))) -> (Filter.Tendsto.{u3, u2} ι β (fun (n : ι) => F n (g n)) p (nhds.{u2} β (UniformSpace.toTopologicalSpace.{u2} β _inst_1) (f x)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align tendsto_comp_of_locally_uniform_limit_within tendsto_comp_of_locally_uniform_limit_withinₓ'. -/
 /-- If `Fₙ` converges locally uniformly on a neighborhood of `x` within a set `s` to a function `f`
 which is continuous at `x` within `s `, and `gₙ` tends to `x` within `s`, then `Fₙ (gₙ)` tends
@@ -1364,10 +1361,7 @@ theorem tendsto_comp_of_locally_uniform_limit_within (h : ContinuousWithinAt f s
 #align tendsto_comp_of_locally_uniform_limit_within tendsto_comp_of_locally_uniform_limit_within
 
 /- warning: tendsto_comp_of_locally_uniform_limit -> tendsto_comp_of_locally_uniform_limit is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {f : α -> β} {x : α} {p : Filter.{u3} ι} {g : ι -> α} [_inst_2 : TopologicalSpace.{u1} α], (ContinuousAt.{u1, u2} α β _inst_2 (UniformSpace.toTopologicalSpace.{u2} β _inst_1) f x) -> (Filter.Tendsto.{u3, u1} ι α g p (nhds.{u1} α _inst_2 x)) -> (forall (u : Set.{u2} (Prod.{u2, u2} β β)), (Membership.Mem.{u2, u2} (Set.{u2} (Prod.{u2, u2} β β)) (Filter.{u2} (Prod.{u2, u2} β β)) (Filter.hasMem.{u2} (Prod.{u2, u2} β β)) u (uniformity.{u2} β _inst_1)) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => Exists.{0} (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) t (nhds.{u1} α _inst_2 x)) (fun (H : Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) t (nhds.{u1} α _inst_2 x)) => Filter.Eventually.{u3} ι (fun (n : ι) => forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) -> (Membership.Mem.{u2, u2} (Prod.{u2, u2} β β) (Set.{u2} (Prod.{u2, u2} β β)) (Set.hasMem.{u2} (Prod.{u2, u2} β β)) (Prod.mk.{u2, u2} β β (f y) (F n y)) u)) p)))) -> (Filter.Tendsto.{u3, u2} ι β (fun (n : ι) => F n (g n)) p (nhds.{u2} β (UniformSpace.toTopologicalSpace.{u2} β _inst_1) (f x)))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {f : α -> β} {x : α} {p : Filter.{u3} ι} {g : ι -> α} [_inst_2 : TopologicalSpace.{u1} α], (ContinuousAt.{u1, u2} α β _inst_2 (UniformSpace.toTopologicalSpace.{u2} β _inst_1) f x) -> (Filter.Tendsto.{u3, u1} ι α g p (nhds.{u1} α _inst_2 x)) -> (forall (u : Set.{u2} (Prod.{u2, u2} β β)), (Membership.mem.{u2, u2} (Set.{u2} (Prod.{u2, u2} β β)) (Filter.{u2} (Prod.{u2, u2} β β)) (instMembershipSetFilter.{u2} (Prod.{u2, u2} β β)) u (uniformity.{u2} β _inst_1)) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) t (nhds.{u1} α _inst_2 x)) (Filter.Eventually.{u3} ι (fun (n : ι) => forall (y : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) -> (Membership.mem.{u2, u2} (Prod.{u2, u2} β β) (Set.{u2} (Prod.{u2, u2} β β)) (Set.instMembershipSet.{u2} (Prod.{u2, u2} β β)) (Prod.mk.{u2, u2} β β (f y) (F n y)) u)) p)))) -> (Filter.Tendsto.{u3, u2} ι β (fun (n : ι) => F n (g n)) p (nhds.{u2} β (UniformSpace.toTopologicalSpace.{u2} β _inst_1) (f x)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align tendsto_comp_of_locally_uniform_limit tendsto_comp_of_locally_uniform_limitₓ'. -/
 /-- If `Fₙ` converges locally uniformly on a neighborhood of `x` to a function `f` which is
 continuous at `x`, and `gₙ` tends to `x`, then `Fₙ (gₙ)` tends to `f x`. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

@@ -207,7 +207,7 @@ theorem tendstoUniformly_iff_tendsto {F : ι → α → β} {f : α → β} {p :
 
 /- warning: tendsto_uniformly_on_filter.tendsto_at -> TendstoUniformlyOnFilter.tendsto_at is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {f : α -> β} {x : α} {p : Filter.{u3} ι} {p' : Filter.{u1} α}, (TendstoUniformlyOnFilter.{u1, u2, u3} α β ι _inst_1 F f p p') -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) (Filter.principal.{u1} α (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) x)) p') -> (Filter.Tendsto.{u3, u2} ι β (fun (n : ι) => F n x) p (nhds.{u2} β (UniformSpace.toTopologicalSpace.{u2} β _inst_1) (f x)))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {f : α -> β} {x : α} {p : Filter.{u3} ι} {p' : Filter.{u1} α}, (TendstoUniformlyOnFilter.{u1, u2, u3} α β ι _inst_1 F f p p') -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) (Filter.principal.{u1} α (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) x)) p') -> (Filter.Tendsto.{u3, u2} ι β (fun (n : ι) => F n x) p (nhds.{u2} β (UniformSpace.toTopologicalSpace.{u2} β _inst_1) (f x)))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {f : α -> β} {x : α} {p : Filter.{u3} ι} {p' : Filter.{u1} α}, (TendstoUniformlyOnFilter.{u1, u2, u3} α β ι _inst_1 F f p p') -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) (Filter.principal.{u1} α (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) x)) p') -> (Filter.Tendsto.{u3, u2} ι β (fun (n : ι) => F n x) p (nhds.{u2} β (UniformSpace.toTopologicalSpace.{u2} β _inst_1) (f x)))
 Case conversion may be inaccurate. Consider using '#align tendsto_uniformly_on_filter.tendsto_at TendstoUniformlyOnFilter.tendsto_atₓ'. -/
@@ -246,7 +246,7 @@ theorem tendstoUniformlyOn_univ : TendstoUniformlyOn F f p univ ↔ TendstoUnifo
 
 /- warning: tendsto_uniformly_on_filter.mono_left -> TendstoUniformlyOnFilter.mono_left is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {f : α -> β} {p : Filter.{u3} ι} {p' : Filter.{u1} α} {p'' : Filter.{u3} ι}, (TendstoUniformlyOnFilter.{u1, u2, u3} α β ι _inst_1 F f p p') -> (LE.le.{u3} (Filter.{u3} ι) (Preorder.toLE.{u3} (Filter.{u3} ι) (PartialOrder.toPreorder.{u3} (Filter.{u3} ι) (Filter.partialOrder.{u3} ι))) p'' p) -> (TendstoUniformlyOnFilter.{u1, u2, u3} α β ι _inst_1 F f p'' p')
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {f : α -> β} {p : Filter.{u3} ι} {p' : Filter.{u1} α} {p'' : Filter.{u3} ι}, (TendstoUniformlyOnFilter.{u1, u2, u3} α β ι _inst_1 F f p p') -> (LE.le.{u3} (Filter.{u3} ι) (Preorder.toHasLe.{u3} (Filter.{u3} ι) (PartialOrder.toPreorder.{u3} (Filter.{u3} ι) (Filter.partialOrder.{u3} ι))) p'' p) -> (TendstoUniformlyOnFilter.{u1, u2, u3} α β ι _inst_1 F f p'' p')
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {f : α -> β} {p : Filter.{u3} ι} {p' : Filter.{u1} α} {p'' : Filter.{u3} ι}, (TendstoUniformlyOnFilter.{u1, u2, u3} α β ι _inst_1 F f p p') -> (LE.le.{u3} (Filter.{u3} ι) (Preorder.toLE.{u3} (Filter.{u3} ι) (PartialOrder.toPreorder.{u3} (Filter.{u3} ι) (Filter.instPartialOrderFilter.{u3} ι))) p'' p) -> (TendstoUniformlyOnFilter.{u1, u2, u3} α β ι _inst_1 F f p'' p')
 Case conversion may be inaccurate. Consider using '#align tendsto_uniformly_on_filter.mono_left TendstoUniformlyOnFilter.mono_leftₓ'. -/
@@ -257,7 +257,7 @@ theorem TendstoUniformlyOnFilter.mono_left {p'' : Filter ι} (h : TendstoUniform
 
 /- warning: tendsto_uniformly_on_filter.mono_right -> TendstoUniformlyOnFilter.mono_right is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {f : α -> β} {p : Filter.{u3} ι} {p' : Filter.{u1} α} {p'' : Filter.{u1} α}, (TendstoUniformlyOnFilter.{u1, u2, u3} α β ι _inst_1 F f p p') -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) p'' p') -> (TendstoUniformlyOnFilter.{u1, u2, u3} α β ι _inst_1 F f p p'')
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {f : α -> β} {p : Filter.{u3} ι} {p' : Filter.{u1} α} {p'' : Filter.{u1} α}, (TendstoUniformlyOnFilter.{u1, u2, u3} α β ι _inst_1 F f p p') -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) p'' p') -> (TendstoUniformlyOnFilter.{u1, u2, u3} α β ι _inst_1 F f p p'')
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {f : α -> β} {p : Filter.{u3} ι} {p' : Filter.{u1} α} {p'' : Filter.{u1} α}, (TendstoUniformlyOnFilter.{u1, u2, u3} α β ι _inst_1 F f p p') -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) p'' p') -> (TendstoUniformlyOnFilter.{u1, u2, u3} α β ι _inst_1 F f p p'')
 Case conversion may be inaccurate. Consider using '#align tendsto_uniformly_on_filter.mono_right TendstoUniformlyOnFilter.mono_rightₓ'. -/
@@ -685,7 +685,7 @@ theorem UniformCauchySeqOn.tendstoUniformlyOn_of_tendsto [NeBot p] (hF : Uniform
 
 /- warning: uniform_cauchy_seq_on_filter.mono_left -> UniformCauchySeqOnFilter.mono_left is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {p : Filter.{u3} ι} {p' : Filter.{u1} α} {p'' : Filter.{u3} ι}, (UniformCauchySeqOnFilter.{u1, u2, u3} α β ι _inst_1 F p p') -> (LE.le.{u3} (Filter.{u3} ι) (Preorder.toLE.{u3} (Filter.{u3} ι) (PartialOrder.toPreorder.{u3} (Filter.{u3} ι) (Filter.partialOrder.{u3} ι))) p'' p) -> (UniformCauchySeqOnFilter.{u1, u2, u3} α β ι _inst_1 F p'' p')
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {p : Filter.{u3} ι} {p' : Filter.{u1} α} {p'' : Filter.{u3} ι}, (UniformCauchySeqOnFilter.{u1, u2, u3} α β ι _inst_1 F p p') -> (LE.le.{u3} (Filter.{u3} ι) (Preorder.toHasLe.{u3} (Filter.{u3} ι) (PartialOrder.toPreorder.{u3} (Filter.{u3} ι) (Filter.partialOrder.{u3} ι))) p'' p) -> (UniformCauchySeqOnFilter.{u1, u2, u3} α β ι _inst_1 F p'' p')
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {p : Filter.{u3} ι} {p' : Filter.{u1} α} {p'' : Filter.{u3} ι}, (UniformCauchySeqOnFilter.{u1, u2, u3} α β ι _inst_1 F p p') -> (LE.le.{u3} (Filter.{u3} ι) (Preorder.toLE.{u3} (Filter.{u3} ι) (PartialOrder.toPreorder.{u3} (Filter.{u3} ι) (Filter.instPartialOrderFilter.{u3} ι))) p'' p) -> (UniformCauchySeqOnFilter.{u1, u2, u3} α β ι _inst_1 F p'' p')
 Case conversion may be inaccurate. Consider using '#align uniform_cauchy_seq_on_filter.mono_left UniformCauchySeqOnFilter.mono_leftₓ'. -/
@@ -699,7 +699,7 @@ theorem UniformCauchySeqOnFilter.mono_left {p'' : Filter ι} (hf : UniformCauchy
 
 /- warning: uniform_cauchy_seq_on_filter.mono_right -> UniformCauchySeqOnFilter.mono_right is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {p : Filter.{u3} ι} {p' : Filter.{u1} α} {p'' : Filter.{u1} α}, (UniformCauchySeqOnFilter.{u1, u2, u3} α β ι _inst_1 F p p') -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) p'' p') -> (UniformCauchySeqOnFilter.{u1, u2, u3} α β ι _inst_1 F p p'')
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {p : Filter.{u3} ι} {p' : Filter.{u1} α} {p'' : Filter.{u1} α}, (UniformCauchySeqOnFilter.{u1, u2, u3} α β ι _inst_1 F p p') -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) p'' p') -> (UniformCauchySeqOnFilter.{u1, u2, u3} α β ι _inst_1 F p p'')
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {p : Filter.{u3} ι} {p' : Filter.{u1} α} {p'' : Filter.{u1} α}, (UniformCauchySeqOnFilter.{u1, u2, u3} α β ι _inst_1 F p p') -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) p'' p') -> (UniformCauchySeqOnFilter.{u1, u2, u3} α β ι _inst_1 F p p'')
 Case conversion may be inaccurate. Consider using '#align uniform_cauchy_seq_on_filter.mono_right UniformCauchySeqOnFilter.mono_rightₓ'. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee

@@ -964,13 +964,13 @@ theorem TendstoLocallyUniformlyOn.mono (h : TendstoLocallyUniformlyOn F f p s) (
 #align tendsto_locally_uniformly_on.mono TendstoLocallyUniformlyOn.mono
 -/
 
-/- warning: tendsto_locally_uniformly_on_Union -> tendstoLocallyUniformlyOn_unionᵢ is a dubious translation:
+/- warning: tendsto_locally_uniformly_on_Union -> tendstoLocallyUniformlyOn_iUnion is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} {ι : Type.{u4}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {f : α -> β} {p : Filter.{u4} ι} [_inst_2 : TopologicalSpace.{u1} α] {S : γ -> (Set.{u1} α)}, (forall (i : γ), IsOpen.{u1} α _inst_2 (S i)) -> (forall (i : γ), TendstoLocallyUniformlyOn.{u1, u2, u4} α β ι _inst_1 _inst_2 F f p (S i)) -> (TendstoLocallyUniformlyOn.{u1, u2, u4} α β ι _inst_1 _inst_2 F f p (Set.unionᵢ.{u1, succ u3} α γ (fun (i : γ) => S i)))
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} {ι : Type.{u4}} [_inst_1 : UniformSpace.{u2} β] {F : ι -> α -> β} {f : α -> β} {p : Filter.{u4} ι} [_inst_2 : TopologicalSpace.{u1} α] {S : γ -> (Set.{u1} α)}, (forall (i : γ), IsOpen.{u1} α _inst_2 (S i)) -> (forall (i : γ), TendstoLocallyUniformlyOn.{u1, u2, u4} α β ι _inst_1 _inst_2 F f p (S i)) -> (TendstoLocallyUniformlyOn.{u1, u2, u4} α β ι _inst_1 _inst_2 F f p (Set.iUnion.{u1, succ u3} α γ (fun (i : γ) => S i)))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u3}} {γ : Type.{u4}} [ι : UniformSpace.{u3} β] {_inst_1 : γ -> α -> β} {F : α -> β} {f : Filter.{u4} γ} [p : TopologicalSpace.{u2} α] {_inst_2 : Sort.{u1}} {S : _inst_2 -> (Set.{u2} α)}, (forall (i : _inst_2), IsOpen.{u2} α p (S i)) -> (forall (i : _inst_2), TendstoLocallyUniformlyOn.{u2, u3, u4} α β γ ι p _inst_1 F f (S i)) -> (TendstoLocallyUniformlyOn.{u2, u3, u4} α β γ ι p _inst_1 F f (Set.unionᵢ.{u2, u1} α _inst_2 (fun (i : _inst_2) => S i)))
-Case conversion may be inaccurate. Consider using '#align tendsto_locally_uniformly_on_Union tendstoLocallyUniformlyOn_unionᵢₓ'. -/
-theorem tendstoLocallyUniformlyOn_unionᵢ {S : γ → Set α} (hS : ∀ i, IsOpen (S i))
+  forall {α : Type.{u2}} {β : Type.{u3}} {γ : Type.{u4}} [ι : UniformSpace.{u3} β] {_inst_1 : γ -> α -> β} {F : α -> β} {f : Filter.{u4} γ} [p : TopologicalSpace.{u2} α] {_inst_2 : Sort.{u1}} {S : _inst_2 -> (Set.{u2} α)}, (forall (i : _inst_2), IsOpen.{u2} α p (S i)) -> (forall (i : _inst_2), TendstoLocallyUniformlyOn.{u2, u3, u4} α β γ ι p _inst_1 F f (S i)) -> (TendstoLocallyUniformlyOn.{u2, u3, u4} α β γ ι p _inst_1 F f (Set.iUnion.{u2, u1} α _inst_2 (fun (i : _inst_2) => S i)))
+Case conversion may be inaccurate. Consider using '#align tendsto_locally_uniformly_on_Union tendstoLocallyUniformlyOn_iUnionₓ'. -/
+theorem tendstoLocallyUniformlyOn_iUnion {S : γ → Set α} (hS : ∀ i, IsOpen (S i))
     (h : ∀ i, TendstoLocallyUniformlyOn F f p (S i)) : TendstoLocallyUniformlyOn F f p (⋃ i, S i) :=
   by
   rintro v hv x ⟨_, ⟨i, rfl⟩, hi : x ∈ S i⟩
@@ -978,25 +978,25 @@ theorem tendstoLocallyUniformlyOn_unionᵢ {S : γ → Set α} (hS : ∀ i, IsOp
   refine' ⟨t, _, ht'⟩
   rw [(hS _).nhdsWithin_eq hi] at ht
   exact mem_nhdsWithin_of_mem_nhds ht
-#align tendsto_locally_uniformly_on_Union tendstoLocallyUniformlyOn_unionᵢ
+#align tendsto_locally_uniformly_on_Union tendstoLocallyUniformlyOn_iUnion
 
-#print tendstoLocallyUniformlyOn_bunionᵢ /-
-theorem tendstoLocallyUniformlyOn_bunionᵢ {s : Set γ} {S : γ → Set α} (hS : ∀ i ∈ s, IsOpen (S i))
+#print tendstoLocallyUniformlyOn_biUnion /-
+theorem tendstoLocallyUniformlyOn_biUnion {s : Set γ} {S : γ → Set α} (hS : ∀ i ∈ s, IsOpen (S i))
     (h : ∀ i ∈ s, TendstoLocallyUniformlyOn F f p (S i)) :
     TendstoLocallyUniformlyOn F f p (⋃ i ∈ s, S i) :=
   by
   rw [bUnion_eq_Union]
-  exact tendstoLocallyUniformlyOn_unionᵢ (fun i => hS _ i.2) fun i => h _ i.2
-#align tendsto_locally_uniformly_on_bUnion tendstoLocallyUniformlyOn_bunionᵢ
+  exact tendstoLocallyUniformlyOn_iUnion (fun i => hS _ i.2) fun i => h _ i.2
+#align tendsto_locally_uniformly_on_bUnion tendstoLocallyUniformlyOn_biUnion
 -/
 
-#print tendstoLocallyUniformlyOn_unionₛ /-
-theorem tendstoLocallyUniformlyOn_unionₛ (S : Set (Set α)) (hS : ∀ s ∈ S, IsOpen s)
+#print tendstoLocallyUniformlyOn_sUnion /-
+theorem tendstoLocallyUniformlyOn_sUnion (S : Set (Set α)) (hS : ∀ s ∈ S, IsOpen s)
     (h : ∀ s ∈ S, TendstoLocallyUniformlyOn F f p s) : TendstoLocallyUniformlyOn F f p (⋃₀ S) :=
   by
   rw [sUnion_eq_bUnion]
-  exact tendstoLocallyUniformlyOn_bunionᵢ hS h
-#align tendsto_locally_uniformly_on_sUnion tendstoLocallyUniformlyOn_unionₛ
+  exact tendstoLocallyUniformlyOn_biUnion hS h
+#align tendsto_locally_uniformly_on_sUnion tendstoLocallyUniformlyOn_sUnion
 -/
 
 /- warning: tendsto_locally_uniformly_on.union -> TendstoLocallyUniformlyOn.union is a dubious translation:
@@ -1010,7 +1010,7 @@ theorem TendstoLocallyUniformlyOn.union {s₁ s₂ : Set α} (hs₁ : IsOpen s
     TendstoLocallyUniformlyOn F f p (s₁ ∪ s₂) :=
   by
   rw [← sUnion_pair]
-  refine' tendstoLocallyUniformlyOn_unionₛ _ _ _ <;> simp [*]
+  refine' tendstoLocallyUniformlyOn_sUnion _ _ _ <;> simp [*]
 #align tendsto_locally_uniformly_on.union TendstoLocallyUniformlyOn.union
 
 #print tendstoLocallyUniformlyOn_univ /-

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

@@ -1087,7 +1087,7 @@ lean 3 declaration is
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : UniformSpace.{u2} β] {s : Set.{u1} α} [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : LocallyCompactSpace.{u1} α _inst_2] (G : ι -> α -> β) (g : α -> β) (p : Filter.{u3} ι), (IsOpen.{u1} α _inst_2 s) -> (List.TFAE (List.cons.{0} Prop (TendstoLocallyUniformlyOn.{u1, u2, u3} α β ι _inst_1 _inst_2 G g p s) (List.cons.{0} Prop (forall (K : Set.{u1} α), (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) K s) -> (IsCompact.{u1} α _inst_2 K) -> (TendstoUniformlyOn.{u1, u2, u3} α β ι _inst_1 G g p K)) (List.cons.{0} Prop (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (Exists.{succ u1} (Set.{u1} α) (fun (v : Set.{u1} α) => And (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) v (nhdsWithin.{u1} α _inst_2 x s)) (TendstoUniformlyOn.{u1, u2, u3} α β ι _inst_1 G g p v)))) (List.nil.{0} Prop)))))
 Case conversion may be inaccurate. Consider using '#align tendsto_locally_uniformly_on_tfae tendstoLocallyUniformlyOn_TFAEₓ'. -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (K «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (K «expr ⊆ » s) -/
 theorem tendstoLocallyUniformlyOn_TFAE [LocallyCompactSpace α] (G : ι → α → β) (g : α → β)
     (p : Filter ι) (hs : IsOpen s) :
     TFAE
@@ -1109,7 +1109,7 @@ theorem tendstoLocallyUniformlyOn_TFAE [LocallyCompactSpace α] (G : ι → α 
   tfae_finish
 #align tendsto_locally_uniformly_on_tfae tendstoLocallyUniformlyOn_TFAE
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (K «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (K «expr ⊆ » s) -/
 #print tendstoLocallyUniformlyOn_iff_forall_isCompact /-
 theorem tendstoLocallyUniformlyOn_iff_forall_isCompact [LocallyCompactSpace α] (hs : IsOpen s) :
     TendstoLocallyUniformlyOn F f p s ↔

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

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

@@ -68,7 +68,6 @@ open Topology Uniformity Filter Set
 
 universe u v w x
 variable {α : Type u} {β : Type v} {γ : Type w} {ι : Type x} [UniformSpace β]
-
 variable {F : ι → α → β} {f : α → β} {s s' : Set α} {x : α} {p : Filter ι} {p' : Filter α}
   {g : ι → α}
 

Classifies by adding issue number #10756 to porting notes claiming anything semantically equivalent to:

• "new lemma"
• "added lemma"

@@ -367,7 +367,7 @@ theorem Filter.Tendsto.tendstoUniformlyOn_const {g : ι → β} {b : β} (hg : T
   tendstoUniformlyOn_iff_tendstoUniformlyOnFilter.mpr (hg.tendstoUniformlyOnFilter_const (𝓟 s))
 #align filter.tendsto.tendsto_uniformly_on_const Filter.Tendsto.tendstoUniformlyOn_const
 
--- Porting note: new lemma
+-- Porting note (#10756): new lemma
 theorem UniformContinuousOn.tendstoUniformlyOn [UniformSpace α] [UniformSpace γ] {x : α} {U : Set α}
     {V : Set β} {F : α → β → γ} (hF : UniformContinuousOn (↿F) (U ×ˢ V)) (hU : x ∈ U) :
     TendstoUniformlyOn F (F x) (𝓝[U] x) V := by
@@ -613,7 +613,7 @@ theorem tendstoLocallyUniformlyOn_univ :
   simp [TendstoLocallyUniformlyOn, TendstoLocallyUniformly, nhdsWithin_univ]
 #align tendsto_locally_uniformly_on_univ tendstoLocallyUniformlyOn_univ
 
--- Porting note: new lemma
+-- Porting note (#10756): new lemma
 theorem tendstoLocallyUniformlyOn_iff_forall_tendsto :
     TendstoLocallyUniformlyOn F f p s ↔
       ∀ x ∈ s, Tendsto (fun y : ι × α => (f y.2, F y.1 y.2)) (p ×ˢ 𝓝[s] x) (𝓤 β) :=

We have UniformCauchySeqOn.cauchy_map. This is the special case of that if one wants exactly CauchySeq, which is a Cauchy map specialized to atTop.

@@ -551,6 +551,13 @@ theorem UniformCauchySeqOn.cauchy_map [hp : NeBot p] (hf : UniformCauchySeqOn F
   filter_upwards [hf u hu] with p hp using hp x hx
 #align uniform_cauchy_seq_on.cauchy_map UniformCauchySeqOn.cauchy_map
 
+/-- If a sequence of functions is uniformly Cauchy on a set, then the values at each point form
+a Cauchy sequence.  See `UniformCauchSeqOn.cauchy_map` for the non-`atTop` case. -/
+theorem UniformCauchySeqOn.cauchySeq [Nonempty ι] [SemilatticeSup ι]
+    (hf : UniformCauchySeqOn F atTop s) (hx : x ∈ s) :
+    CauchySeq fun i ↦ F i x :=
+  hf.cauchy_map (hp := atTop_neBot) hx
+
 section SeqTendsto
 
 theorem tendstoUniformlyOn_of_seq_tendstoUniformlyOn {l : Filter ι} [l.IsCountablyGenerated]

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".

@@ -134,7 +134,7 @@ def TendstoUniformly (F : ι → α → β) (f : α → β) (p : Filter ι) :=
   ∀ u ∈ 𝓤 β, ∀ᶠ n in p, ∀ x : α, (f x, F n x) ∈ u
 #align tendsto_uniformly TendstoUniformly
 
--- porting note: moved from below
+-- Porting note: moved from below
 theorem tendstoUniformlyOn_univ : TendstoUniformlyOn F f p univ ↔ TendstoUniformly F f p := by
   simp [TendstoUniformlyOn, TendstoUniformly]
 #align tendsto_uniformly_on_univ tendstoUniformlyOn_univ
@@ -184,7 +184,7 @@ theorem TendstoUniformly.tendsto_at (h : TendstoUniformly F f p) (x : α) :
   h.tendstoUniformlyOnFilter.tendsto_at le_top
 #align tendsto_uniformly.tendsto_at TendstoUniformly.tendsto_at
 
--- porting note: tendstoUniformlyOn_univ moved up
+-- Porting note: tendstoUniformlyOn_univ moved up
 
 theorem TendstoUniformlyOnFilter.mono_left {p'' : Filter ι} (h : TendstoUniformlyOnFilter F f p p')
     (hp : p'' ≤ p) : TendstoUniformlyOnFilter F f p'' p' := fun u hu =>
@@ -367,7 +367,7 @@ theorem Filter.Tendsto.tendstoUniformlyOn_const {g : ι → β} {b : β} (hg : T
   tendstoUniformlyOn_iff_tendstoUniformlyOnFilter.mpr (hg.tendstoUniformlyOnFilter_const (𝓟 s))
 #align filter.tendsto.tendsto_uniformly_on_const Filter.Tendsto.tendstoUniformlyOn_const
 
--- porting note: new lemma
+-- Porting note: new lemma
 theorem UniformContinuousOn.tendstoUniformlyOn [UniformSpace α] [UniformSpace γ] {x : α} {U : Set α}
     {V : Set β} {F : α → β → γ} (hF : UniformContinuousOn (↿F) (U ×ˢ V)) (hU : x ∈ U) :
     TendstoUniformlyOn F (F x) (𝓝[U] x) V := by
@@ -606,7 +606,7 @@ theorem tendstoLocallyUniformlyOn_univ :
   simp [TendstoLocallyUniformlyOn, TendstoLocallyUniformly, nhdsWithin_univ]
 #align tendsto_locally_uniformly_on_univ tendstoLocallyUniformlyOn_univ
 
--- porting note: new lemma
+-- Porting note: new lemma
 theorem tendstoLocallyUniformlyOn_iff_forall_tendsto :
     TendstoLocallyUniformlyOn F f p s ↔
       ∀ x ∈ s, Tendsto (fun y : ι × α => (f y.2, F y.1 y.2)) (p ×ˢ 𝓝[s] x) (𝓤 β) :=
@@ -648,7 +648,7 @@ theorem TendstoLocallyUniformlyOn.mono (h : TendstoLocallyUniformlyOn F f p s) (
   exact ⟨t, nhdsWithin_mono x h' ht, H.mono fun n => id⟩
 #align tendsto_locally_uniformly_on.mono TendstoLocallyUniformlyOn.mono
 
--- porting note: generalized from `Type` to `Sort`
+-- Porting note: generalized from `Type` to `Sort`
 theorem tendstoLocallyUniformlyOn_iUnion {ι' : Sort*} {S : ι' → Set α} (hS : ∀ i, IsOpen (S i))
     (h : ∀ i, TendstoLocallyUniformlyOn F f p (S i)) :
     TendstoLocallyUniformlyOn F f p (⋃ i, S i) :=
@@ -677,7 +677,7 @@ theorem TendstoLocallyUniformlyOn.union {s₁ s₂ : Set α} (hs₁ : IsOpen s
   refine' tendstoLocallyUniformlyOn_sUnion _ _ _ <;> simp [*]
 #align tendsto_locally_uniformly_on.union TendstoLocallyUniformlyOn.union
 
--- porting note: tendstoLocallyUniformlyOn_univ moved up
+-- Porting note: tendstoLocallyUniformlyOn_univ moved up
 
 protected theorem TendstoLocallyUniformly.tendstoLocallyUniformlyOn
     (h : TendstoLocallyUniformly F f p) : TendstoLocallyUniformlyOn F f p s :=

I replaced a few "terminal" refine/refine's with exact.

The strategy was very simple-minded: essentially any refine whose following line had smaller indentation got replaced by exact and then I cleaned up the mess.

This PR certainly leaves some further terminal refines, but maybe the current change is beneficial.

@@ -449,7 +449,7 @@ theorem UniformCauchySeqOnFilter.tendstoUniformlyOnFilter_of_tendsto [NeBot p]
   -- But we need to promote hF' to the full product filter to use it
   have hmc : ∀ᶠ x in (p ×ˢ p) ×ˢ p', Tendsto (fun n : ι => F n x.snd) p (𝓝 (f x.snd)) := by
     rw [eventually_prod_iff]
-    refine' ⟨fun _ => True, by simp, _, hF', by simp⟩
+    exact ⟨fun _ => True, by simp, _, hF', by simp⟩
   -- To apply filter operations we'll need to do some order manipulation
   rw [Filter.eventually_swap_iff]
   have := tendsto_prodAssoc.eventually (tendsto_prod_swap.eventually ((hF t ht).and hmc))
@@ -525,7 +525,7 @@ theorem UniformCauchySeqOn.prod_map {ι' α' β' : Type*} [UniformSpace β'] {F'
   rw [← Set.image_subset_iff] at hvw
   apply (tendsto_swap4_prod.eventually ((h v hv).prod_mk (h' w hw))).mono
   intro x hx a b ha hb
-  refine' hvw ⟨_, mk_mem_prod (hx.1 a ha) (hx.2 b hb), rfl⟩
+  exact hvw ⟨_, mk_mem_prod (hx.1 a ha) (hx.2 b hb), rfl⟩
 #align uniform_cauchy_seq_on.prod_map UniformCauchySeqOn.prod_map
 
 theorem UniformCauchySeqOn.prod {ι' β' : Type*} [UniformSpace β'] {F' : ι' → α → β'}
@@ -738,7 +738,7 @@ theorem tendstoLocallyUniformlyOn_TFAE [LocallyCompactSpace α] (G : ι → α 
   tfae_have 2 → 3
   · rintro h x hx
     obtain ⟨K, ⟨hK1, hK2⟩, hK3⟩ := (compact_basis_nhds x).mem_iff.mp (hs.mem_nhds hx)
-    refine' ⟨K, nhdsWithin_le_nhds hK1, h K hK3 hK2⟩
+    exact ⟨K, nhdsWithin_le_nhds hK1, h K hK3 hK2⟩
   tfae_have 3 → 1
   · rintro h u hu x hx
     obtain ⟨v, hv1, hv2⟩ := h x hx
@@ -760,7 +760,7 @@ theorem tendstoLocallyUniformlyOn_iff_filter :
     exact ⟨_, hs2, _, eventually_of_mem hs1 fun x => id, fun hi y hy => hi y hy⟩
   · rintro h u hu x hx
     obtain ⟨pa, hpa, pb, hpb, h⟩ := h x hx u hu
-    refine' ⟨pb, hpb, eventually_of_mem hpa fun i hi y hy => h hi hy⟩
+    exact ⟨pb, hpb, eventually_of_mem hpa fun i hi y hy => h hi hy⟩
 #align tendsto_locally_uniformly_on_iff_filter tendstoLocallyUniformlyOn_iff_filter
 
 theorem tendstoLocallyUniformly_iff_filter :

Subset of #9319

@@ -150,7 +150,7 @@ theorem TendstoUniformly.tendstoUniformlyOnFilter (h : TendstoUniformly F f p) :
 
 theorem tendstoUniformlyOn_iff_tendstoUniformly_comp_coe :
     TendstoUniformlyOn F f p s ↔ TendstoUniformly (fun i (x : s) => F i x) (f ∘ (↑)) p :=
-  forall₂_congr <| fun u _ => by simp
+  forall₂_congr fun u _ => by simp
 #align tendsto_uniformly_on_iff_tendsto_uniformly_comp_coe tendstoUniformlyOn_iff_tendstoUniformly_comp_coe
 
 /-- A sequence of functions `Fₙ` converges uniformly to a limiting function `f` w.r.t.
@@ -376,7 +376,7 @@ theorem UniformContinuousOn.tendstoUniformlyOn [UniformSpace α] [UniformSpace 
   change Tendsto (Prod.map (↿F) ↿F ∘ φ) (𝓝[U] x ×ˢ 𝓟 V) (𝓤 γ)
   simp only [nhdsWithin, SProd.sprod, Filter.prod, comap_inf, inf_assoc, comap_principal,
     inf_principal]
-  refine hF.comp (Tendsto.inf ?_ <| tendsto_principal_principal.2 <| fun x hx => ⟨⟨hU, hx.2⟩, hx⟩)
+  refine hF.comp (Tendsto.inf ?_ <| tendsto_principal_principal.2 fun x hx => ⟨⟨hU, hx.2⟩, hx⟩)
   simp only [uniformity_prod_eq_comap_prod, tendsto_comap_iff, (· ∘ ·),
     nhds_eq_comap_uniformity, comap_comap]
   exact tendsto_comap.prod_mk (tendsto_diag_uniformity _ _)
@@ -652,7 +652,7 @@ theorem TendstoLocallyUniformlyOn.mono (h : TendstoLocallyUniformlyOn F f p s) (
 theorem tendstoLocallyUniformlyOn_iUnion {ι' : Sort*} {S : ι' → Set α} (hS : ∀ i, IsOpen (S i))
     (h : ∀ i, TendstoLocallyUniformlyOn F f p (S i)) :
     TendstoLocallyUniformlyOn F f p (⋃ i, S i) :=
-  (isOpen_iUnion hS).tendstoLocallyUniformlyOn_iff_forall_tendsto.2 $ fun _x hx =>
+  (isOpen_iUnion hS).tendstoLocallyUniformlyOn_iff_forall_tendsto.2 fun _x hx =>
     let ⟨i, hi⟩ := mem_iUnion.1 hx
     (hS i).tendstoLocallyUniformlyOn_iff_forall_tendsto.1 (h i) _ hi
 #align tendsto_locally_uniformly_on_Union tendstoLocallyUniformlyOn_iUnion

mathport was forgetting a space in filter_upwards [...]with instead of filter_upwards [...] with.

@@ -221,7 +221,7 @@ theorem TendstoUniformlyOn.congr {F' : ι → α → β} (hf : TendstoUniformlyO
 
 theorem TendstoUniformlyOn.congr_right {g : α → β} (hf : TendstoUniformlyOn F f p s)
     (hfg : EqOn f g s) : TendstoUniformlyOn F g p s := fun u hu => by
-  filter_upwards [hf u hu]with i hi a ha using hfg ha ▸ hi a ha
+  filter_upwards [hf u hu] with i hi a ha using hfg ha ▸ hi a ha
 #align tendsto_uniformly_on.congr_right TendstoUniformlyOn.congr_right
 
 protected theorem TendstoUniformly.tendstoUniformlyOn (h : TendstoUniformly F f p) :
@@ -548,7 +548,7 @@ theorem UniformCauchySeqOn.cauchy_map [hp : NeBot p] (hf : UniformCauchySeqOn F
   simp only [cauchy_map_iff, hp, true_and_iff]
   intro u hu
   rw [mem_map]
-  filter_upwards [hf u hu]with p hp using hp x hx
+  filter_upwards [hf u hu] with p hp using hp x hx
 #align uniform_cauchy_seq_on.cauchy_map UniformCauchySeqOn.cauchy_map
 
 section SeqTendsto
@@ -785,7 +785,7 @@ theorem TendstoLocallyUniformlyOn.congr {G : ι → α → β} (hf : TendstoLoca
   rintro u hu x hx
   obtain ⟨t, ht, h⟩ := hf u hu x hx
   refine' ⟨s ∩ t, inter_mem self_mem_nhdsWithin ht, _⟩
-  filter_upwards [h]with i hi y hy using hg i hy.1 ▸ hi y hy.2
+  filter_upwards [h] with i hi y hy using hg i hy.1 ▸ hi y hy.2
 #align tendsto_locally_uniformly_on.congr TendstoLocallyUniformlyOn.congr
 
 theorem TendstoLocallyUniformlyOn.congr_right {g : α → β} (hf : TendstoLocallyUniformlyOn F f p s)
@@ -793,7 +793,7 @@ theorem TendstoLocallyUniformlyOn.congr_right {g : α → β} (hf : TendstoLocal
   rintro u hu x hx
   obtain ⟨t, ht, h⟩ := hf u hu x hx
   refine' ⟨s ∩ t, inter_mem self_mem_nhdsWithin ht, _⟩
-  filter_upwards [h]with i hi y hy using hg hy.1 ▸ hi y hy.2
+  filter_upwards [h] with i hi y hy using hg hy.1 ▸ hi y hy.2
 #align tendsto_locally_uniformly_on.congr_right TendstoLocallyUniformlyOn.congr_right
 
 /-!

This will improve spaces in the mathlib4 docs.

@@ -916,7 +916,7 @@ this paragraph, we prove variations around this statement.
 
 
 /-- If `Fₙ` converges locally uniformly on a neighborhood of `x` within a set `s` to a function `f`
-which is continuous at `x` within `s `, and `gₙ` tends to `x` within `s`, then `Fₙ (gₙ)` tends
+which is continuous at `x` within `s`, and `gₙ` tends to `x` within `s`, then `Fₙ (gₙ)` tends
 to `f x`. -/
 theorem tendsto_comp_of_locally_uniform_limit_within (h : ContinuousWithinAt f s x)
     (hg : Tendsto g p (𝓝[s] x))

@@ -112,8 +112,9 @@ theorem tendstoUniformlyOn_iff_tendstoUniformlyOnFilter :
   simp
 #align tendsto_uniformly_on_iff_tendsto_uniformly_on_filter tendstoUniformlyOn_iff_tendstoUniformlyOnFilter
 
-alias tendstoUniformlyOn_iff_tendstoUniformlyOnFilter ↔
-  TendstoUniformlyOn.tendstoUniformlyOnFilter TendstoUniformlyOnFilter.tendstoUniformlyOn
+
+alias ⟨TendstoUniformlyOn.tendstoUniformlyOnFilter, TendstoUniformlyOnFilter.tendstoUniformlyOn⟩ :=
+  tendstoUniformlyOn_iff_tendstoUniformlyOnFilter
 #align tendsto_uniformly_on.tendsto_uniformly_on_filter TendstoUniformlyOn.tendstoUniformlyOnFilter
 #align tendsto_uniformly_on_filter.tendsto_uniformly_on TendstoUniformlyOnFilter.tendstoUniformlyOn
 

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

This has nice performance benefits.

@@ -269,7 +269,7 @@ theorem UniformContinuous.comp_tendstoUniformly [UniformSpace γ] {g : β → γ
     TendstoUniformly (fun i => g ∘ F i) (g ∘ f) p := fun _u hu => h _ (hg hu)
 #align uniform_continuous.comp_tendsto_uniformly UniformContinuous.comp_tendstoUniformly
 
-theorem TendstoUniformlyOnFilter.prod_map {ι' α' β' : Type _} [UniformSpace β'] {F' : ι' → α' → β'}
+theorem TendstoUniformlyOnFilter.prod_map {ι' α' β' : Type*} [UniformSpace β'] {F' : ι' → α' → β'}
     {f' : α' → β'} {q : Filter ι'} {q' : Filter α'} (h : TendstoUniformlyOnFilter F f p p')
     (h' : TendstoUniformlyOnFilter F' f' q q') :
     TendstoUniformlyOnFilter (fun i : ι × ι' => Prod.map (F i.1) (F' i.2)) (Prod.map f f')
@@ -279,7 +279,7 @@ theorem TendstoUniformlyOnFilter.prod_map {ι' α' β' : Type _} [UniformSpace 
   convert h.prod_map h' -- seems to be faster than `exact` here
 #align tendsto_uniformly_on_filter.prod_map TendstoUniformlyOnFilter.prod_map
 
-theorem TendstoUniformlyOn.prod_map {ι' α' β' : Type _} [UniformSpace β'] {F' : ι' → α' → β'}
+theorem TendstoUniformlyOn.prod_map {ι' α' β' : Type*} [UniformSpace β'] {F' : ι' → α' → β'}
     {f' : α' → β'} {p' : Filter ι'} {s' : Set α'} (h : TendstoUniformlyOn F f p s)
     (h' : TendstoUniformlyOn F' f' p' s') :
     TendstoUniformlyOn (fun i : ι × ι' => Prod.map (F i.1) (F' i.2)) (Prod.map f f') (p ×ˢ p')
@@ -288,14 +288,14 @@ theorem TendstoUniformlyOn.prod_map {ι' α' β' : Type _} [UniformSpace β'] {F
   simpa only [prod_principal_principal] using h.prod_map h'
 #align tendsto_uniformly_on.prod_map TendstoUniformlyOn.prod_map
 
-theorem TendstoUniformly.prod_map {ι' α' β' : Type _} [UniformSpace β'] {F' : ι' → α' → β'}
+theorem TendstoUniformly.prod_map {ι' α' β' : Type*} [UniformSpace β'] {F' : ι' → α' → β'}
     {f' : α' → β'} {p' : Filter ι'} (h : TendstoUniformly F f p) (h' : TendstoUniformly F' f' p') :
     TendstoUniformly (fun i : ι × ι' => Prod.map (F i.1) (F' i.2)) (Prod.map f f') (p ×ˢ p') := by
   rw [← tendstoUniformlyOn_univ, ← univ_prod_univ] at *
   exact h.prod_map h'
 #align tendsto_uniformly.prod_map TendstoUniformly.prod_map
 
-theorem TendstoUniformlyOnFilter.prod {ι' β' : Type _} [UniformSpace β'] {F' : ι' → α → β'}
+theorem TendstoUniformlyOnFilter.prod {ι' β' : Type*} [UniformSpace β'] {F' : ι' → α → β'}
     {f' : α → β'} {q : Filter ι'} (h : TendstoUniformlyOnFilter F f p p')
     (h' : TendstoUniformlyOnFilter F' f' q p') :
     TendstoUniformlyOnFilter (fun (i : ι × ι') a => (F i.1 a, F' i.2 a)) (fun a => (f a, f' a))
@@ -303,14 +303,14 @@ theorem TendstoUniformlyOnFilter.prod {ι' β' : Type _} [UniformSpace β'] {F'
   fun u hu => ((h.prod_map h') u hu).diag_of_prod_right
 #align tendsto_uniformly_on_filter.prod TendstoUniformlyOnFilter.prod
 
-theorem TendstoUniformlyOn.prod {ι' β' : Type _} [UniformSpace β'] {F' : ι' → α → β'} {f' : α → β'}
+theorem TendstoUniformlyOn.prod {ι' β' : Type*} [UniformSpace β'] {F' : ι' → α → β'} {f' : α → β'}
     {p' : Filter ι'} (h : TendstoUniformlyOn F f p s) (h' : TendstoUniformlyOn F' f' p' s) :
     TendstoUniformlyOn (fun (i : ι × ι') a => (F i.1 a, F' i.2 a)) (fun a => (f a, f' a))
       (p.prod p') s :=
   (congr_arg _ s.inter_self).mp ((h.prod_map h').comp fun a => (a, a))
 #align tendsto_uniformly_on.prod TendstoUniformlyOn.prod
 
-theorem TendstoUniformly.prod {ι' β' : Type _} [UniformSpace β'] {F' : ι' → α → β'} {f' : α → β'}
+theorem TendstoUniformly.prod {ι' β' : Type*} [UniformSpace β'] {F' : ι' → α → β'} {f' : α → β'}
     {p' : Filter ι'} (h : TendstoUniformly F f p) (h' : TendstoUniformly F' f' p') :
     TendstoUniformly (fun (i : ι × ι') a => (F i.1 a, F' i.2 a)) (fun a => (f a, f' a))
       (p ×ˢ p') :=
@@ -491,7 +491,7 @@ theorem UniformCauchySeqOn.mono {s' : Set α} (hf : UniformCauchySeqOn F p s) (h
 #align uniform_cauchy_seq_on.mono UniformCauchySeqOn.mono
 
 /-- Composing on the right by a function preserves uniform Cauchy sequences -/
-theorem UniformCauchySeqOnFilter.comp {γ : Type _} (hf : UniformCauchySeqOnFilter F p p')
+theorem UniformCauchySeqOnFilter.comp {γ : Type*} (hf : UniformCauchySeqOnFilter F p p')
     (g : γ → α) : UniformCauchySeqOnFilter (fun n => F n ∘ g) p (p'.comap g) := fun u hu => by
   obtain ⟨pa, hpa, pb, hpb, hpapb⟩ := eventually_prod_iff.mp (hf u hu)
   rw [eventually_prod_iff]
@@ -500,7 +500,7 @@ theorem UniformCauchySeqOnFilter.comp {γ : Type _} (hf : UniformCauchySeqOnFilt
 #align uniform_cauchy_seq_on_filter.comp UniformCauchySeqOnFilter.comp
 
 /-- Composing on the right by a function preserves uniform Cauchy sequences -/
-theorem UniformCauchySeqOn.comp {γ : Type _} (hf : UniformCauchySeqOn F p s) (g : γ → α) :
+theorem UniformCauchySeqOn.comp {γ : Type*} (hf : UniformCauchySeqOn F p s) (g : γ → α) :
     UniformCauchySeqOn (fun n => F n ∘ g) p (g ⁻¹' s) := by
   rw [uniformCauchySeqOn_iff_uniformCauchySeqOnFilter] at hf ⊢
   simpa only [UniformCauchySeqOn, comap_principal] using hf.comp g
@@ -513,7 +513,7 @@ theorem UniformContinuous.comp_uniformCauchySeqOn [UniformSpace γ] {g : β →
     UniformCauchySeqOn (fun n => g ∘ F n) p s := fun _u hu => hf _ (hg hu)
 #align uniform_continuous.comp_uniform_cauchy_seq_on UniformContinuous.comp_uniformCauchySeqOn
 
-theorem UniformCauchySeqOn.prod_map {ι' α' β' : Type _} [UniformSpace β'] {F' : ι' → α' → β'}
+theorem UniformCauchySeqOn.prod_map {ι' α' β' : Type*} [UniformSpace β'] {F' : ι' → α' → β'}
     {p' : Filter ι'} {s' : Set α'} (h : UniformCauchySeqOn F p s)
     (h' : UniformCauchySeqOn F' p' s') :
     UniformCauchySeqOn (fun i : ι × ι' => Prod.map (F i.1) (F' i.2)) (p ×ˢ p') (s ×ˢ s') := by
@@ -527,13 +527,13 @@ theorem UniformCauchySeqOn.prod_map {ι' α' β' : Type _} [UniformSpace β'] {F
   refine' hvw ⟨_, mk_mem_prod (hx.1 a ha) (hx.2 b hb), rfl⟩
 #align uniform_cauchy_seq_on.prod_map UniformCauchySeqOn.prod_map
 
-theorem UniformCauchySeqOn.prod {ι' β' : Type _} [UniformSpace β'] {F' : ι' → α → β'}
+theorem UniformCauchySeqOn.prod {ι' β' : Type*} [UniformSpace β'] {F' : ι' → α → β'}
     {p' : Filter ι'} (h : UniformCauchySeqOn F p s) (h' : UniformCauchySeqOn F' p' s) :
     UniformCauchySeqOn (fun (i : ι × ι') a => (F i.fst a, F' i.snd a)) (p ×ˢ p') s :=
   (congr_arg _ s.inter_self).mp ((h.prod_map h').comp fun a => (a, a))
 #align uniform_cauchy_seq_on.prod UniformCauchySeqOn.prod
 
-theorem UniformCauchySeqOn.prod' {β' : Type _} [UniformSpace β'] {F' : ι → α → β'}
+theorem UniformCauchySeqOn.prod' {β' : Type*} [UniformSpace β'] {F' : ι → α → β'}
     (h : UniformCauchySeqOn F p s) (h' : UniformCauchySeqOn F' p s) :
     UniformCauchySeqOn (fun (i : ι) a => (F i a, F' i a)) p s := fun u hu =>
   have hh : Tendsto (fun x : ι => (x, x)) p (p ×ˢ p) := tendsto_diag
@@ -648,7 +648,7 @@ theorem TendstoLocallyUniformlyOn.mono (h : TendstoLocallyUniformlyOn F f p s) (
 #align tendsto_locally_uniformly_on.mono TendstoLocallyUniformlyOn.mono
 
 -- porting note: generalized from `Type` to `Sort`
-theorem tendstoLocallyUniformlyOn_iUnion {ι' : Sort _} {S : ι' → Set α} (hS : ∀ i, IsOpen (S i))
+theorem tendstoLocallyUniformlyOn_iUnion {ι' : Sort*} {S : ι' → Set α} (hS : ∀ i, IsOpen (S i))
     (h : ∀ i, TendstoLocallyUniformlyOn F f p (S i)) :
     TendstoLocallyUniformlyOn F f p (⋃ i, S i) :=
   (isOpen_iUnion hS).tendstoLocallyUniformlyOn_iff_forall_tendsto.2 $ fun _x hx =>

• depends on: #5966

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

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
-
-! This file was ported from Lean 3 source module topology.uniform_space.uniform_convergence
-! leanprover-community/mathlib commit 2705404e701abc6b3127da906f40bae062a169c9
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Topology.Separation
 import Mathlib.Topology.UniformSpace.Basic
 import Mathlib.Topology.UniformSpace.Cauchy
 
+#align_import topology.uniform_space.uniform_convergence from "leanprover-community/mathlib"@"2705404e701abc6b3127da906f40bae062a169c9"
+
 /-!
 # Uniform convergence
 

Changes are of the form

• some_tactic at h⊢ -> some_tactic at h ⊢
• some_tactic at h -> some_tactic at h

@@ -214,9 +214,9 @@ theorem TendstoUniformlyOnFilter.congr {F' : ι → α → β} (hf : TendstoUnif
 
 theorem TendstoUniformlyOn.congr {F' : ι → α → β} (hf : TendstoUniformlyOn F f p s)
     (hff' : ∀ᶠ n in p, Set.EqOn (F n) (F' n) s) : TendstoUniformlyOn F' f p s := by
-  rw [tendstoUniformlyOn_iff_tendstoUniformlyOnFilter] at hf⊢
+  rw [tendstoUniformlyOn_iff_tendstoUniformlyOnFilter] at hf ⊢
   refine' hf.congr _
-  rw [eventually_iff] at hff'⊢
+  rw [eventually_iff] at hff' ⊢
   simp only [Set.EqOn] at hff'
   simp only [mem_prod_principal, hff', mem_setOf_eq]
 #align tendsto_uniformly_on.congr TendstoUniformlyOn.congr
@@ -241,14 +241,14 @@ theorem TendstoUniformlyOnFilter.comp (h : TendstoUniformlyOnFilter F f p p') (g
 /-- Composing on the right by a function preserves uniform convergence on a set -/
 theorem TendstoUniformlyOn.comp (h : TendstoUniformlyOn F f p s) (g : γ → α) :
     TendstoUniformlyOn (fun n => F n ∘ g) (f ∘ g) p (g ⁻¹' s) := by
-  rw [tendstoUniformlyOn_iff_tendstoUniformlyOnFilter] at h⊢
+  rw [tendstoUniformlyOn_iff_tendstoUniformlyOnFilter] at h ⊢
   simpa [TendstoUniformlyOn, comap_principal] using TendstoUniformlyOnFilter.comp h g
 #align tendsto_uniformly_on.comp TendstoUniformlyOn.comp
 
 /-- Composing on the right by a function preserves uniform convergence -/
 theorem TendstoUniformly.comp (h : TendstoUniformly F f p) (g : γ → α) :
     TendstoUniformly (fun n => F n ∘ g) (f ∘ g) p := by
-  rw [tendstoUniformly_iff_tendstoUniformlyOnFilter] at h⊢
+  rw [tendstoUniformly_iff_tendstoUniformlyOnFilter] at h ⊢
   simpa [principal_univ, comap_principal] using h.comp g
 #align tendsto_uniformly.comp TendstoUniformly.comp
 
@@ -287,7 +287,7 @@ theorem TendstoUniformlyOn.prod_map {ι' α' β' : Type _} [UniformSpace β'] {F
     (h' : TendstoUniformlyOn F' f' p' s') :
     TendstoUniformlyOn (fun i : ι × ι' => Prod.map (F i.1) (F' i.2)) (Prod.map f f') (p ×ˢ p')
       (s ×ˢ s') := by
-  rw [tendstoUniformlyOn_iff_tendstoUniformlyOnFilter] at h h'⊢
+  rw [tendstoUniformlyOn_iff_tendstoUniformlyOnFilter] at h h' ⊢
   simpa only [prod_principal_principal] using h.prod_map h'
 #align tendsto_uniformly_on.prod_map TendstoUniformlyOn.prod_map
 
@@ -489,7 +489,7 @@ theorem UniformCauchySeqOnFilter.mono_right {p'' : Filter α} (hf : UniformCauch
 
 theorem UniformCauchySeqOn.mono {s' : Set α} (hf : UniformCauchySeqOn F p s) (hss' : s' ⊆ s) :
     UniformCauchySeqOn F p s' := by
-  rw [uniformCauchySeqOn_iff_uniformCauchySeqOnFilter] at hf⊢
+  rw [uniformCauchySeqOn_iff_uniformCauchySeqOnFilter] at hf ⊢
   exact hf.mono_right (le_principal_iff.mpr <| mem_principal.mpr hss')
 #align uniform_cauchy_seq_on.mono UniformCauchySeqOn.mono
 
@@ -505,7 +505,7 @@ theorem UniformCauchySeqOnFilter.comp {γ : Type _} (hf : UniformCauchySeqOnFilt
 /-- Composing on the right by a function preserves uniform Cauchy sequences -/
 theorem UniformCauchySeqOn.comp {γ : Type _} (hf : UniformCauchySeqOn F p s) (g : γ → α) :
     UniformCauchySeqOn (fun n => F n ∘ g) p (g ⁻¹' s) := by
-  rw [uniformCauchySeqOn_iff_uniformCauchySeqOnFilter] at hf⊢
+  rw [uniformCauchySeqOn_iff_uniformCauchySeqOnFilter] at hf ⊢
   simpa only [UniformCauchySeqOn, comap_principal] using hf.comp g
 #align uniform_cauchy_seq_on.comp UniformCauchySeqOn.comp
 
@@ -568,7 +568,7 @@ theorem tendstoUniformlyOn_of_seq_tendstoUniformlyOn {l : Filter ι} [l.IsCounta
 
 theorem TendstoUniformlyOn.seq_tendstoUniformlyOn {l : Filter ι} (h : TendstoUniformlyOn F f l s)
     (u : ℕ → ι) (hu : Tendsto u atTop l) : TendstoUniformlyOn (fun n => F (u n)) f atTop s := by
-  rw [tendstoUniformlyOn_iff_tendsto] at h⊢
+  rw [tendstoUniformlyOn_iff_tendsto] at h ⊢
   exact h.comp ((hu.comp tendsto_fst).prod_mk tendsto_snd)
 #align tendsto_uniformly_on.seq_tendsto_uniformly_on TendstoUniformlyOn.seq_tendstoUniformlyOn
 
@@ -723,7 +723,7 @@ theorem TendstoLocallyUniformlyOn.comp [TopologicalSpace γ] {t : Set γ}
 
 theorem TendstoLocallyUniformly.comp [TopologicalSpace γ] (h : TendstoLocallyUniformly F f p)
     (g : γ → α) (cg : Continuous g) : TendstoLocallyUniformly (fun n => F n ∘ g) (f ∘ g) p := by
-  rw [← tendstoLocallyUniformlyOn_univ] at h⊢
+  rw [← tendstoLocallyUniformlyOn_univ] at h ⊢
   rw [continuous_iff_continuousOn_univ] at cg
   exact h.comp _ (mapsTo_univ _ _) cg
 #align tendsto_locally_uniformly.comp TendstoLocallyUniformly.comp

Found with git grep -n "λ [a-zA-Z_ ]*,"

@@ -355,7 +355,7 @@ theorem tendstoUniformlyOn_singleton_iff_tendsto :
 #align tendsto_uniformly_on_singleton_iff_tendsto tendstoUniformlyOn_singleton_iff_tendsto
 
 /-- If a sequence `g` converges to some `b`, then the sequence of constant functions
-`λ n, λ a, g n` converges to the constant function `λ a, b` on any set `s` -/
+`fun n ↦ fun a ↦ g n` converges to the constant function `fun a ↦ b` on any set `s` -/
 theorem Filter.Tendsto.tendstoUniformlyOnFilter_const {g : ι → β} {b : β} (hg : Tendsto g p (𝓝 b))
     (p' : Filter α) :
     TendstoUniformlyOnFilter (fun n : ι => fun _ : α => g n) (fun _ : α => b) p p' := by
@@ -363,7 +363,7 @@ theorem Filter.Tendsto.tendstoUniformlyOnFilter_const {g : ι → β} {b : β} (
 #align filter.tendsto.tendsto_uniformly_on_filter_const Filter.Tendsto.tendstoUniformlyOnFilter_const
 
 /-- If a sequence `g` converges to some `b`, then the sequence of constant functions
-`λ n, λ a, g n` converges to the constant function `λ a, b` on any set `s` -/
+`fun n ↦ fun a ↦ g n` converges to the constant function `fun a ↦ b` on any set `s` -/
 theorem Filter.Tendsto.tendstoUniformlyOn_const {g : ι → β} {b : β} (hg : Tendsto g p (𝓝 b))
     (s : Set α) : TendstoUniformlyOn (fun n : ι => fun _ : α => g n) (fun _ : α => b) p s :=
   tendstoUniformlyOn_iff_tendstoUniformlyOnFilter.mpr (hg.tendstoUniformlyOnFilter_const (𝓟 s))

• Protect HasFTaylorSeriesUpToOn.fderivWithin, IsBoundedBilinearMap.fderiv, and IsBoundedBilinearMap.fderivWithin.

• Rename

  • isBoundedBilinearMapSmul -> isBoundedBilinearMap_smul;
  • isBoundedBilinearMapMul -> isBoundedBilinearMap_mul;
  • isBoundedBilinearMapComp -> isBoundedBilinearMap_comp;
  • isBoundedBilinearMapSmulRight -> isBoundedBilinearMap_smulRight;
  • isBoundedBilinearMapCompMultilinear -> isBoundedBilinearMap_compMultilinear;
  • ContinuousLinearMap.mulLeftRightIsBoundedBilinear -> ContinuousLinearMap.mulLeftRight_isBoundedBilinear;
  • nhdsWithin_eq_nhds_within' -> nhdsWithin_eq_nhdsWithin';
  • ContinuousWithinAt.preimage_mem_nhds_within' -> ContinuousWithinAt.preimage_mem_nhdsWithin'.

Co-authored-by: Floris van Doorn <fpvdoorn@gmail.com> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

@@ -717,7 +717,7 @@ theorem TendstoLocallyUniformlyOn.comp [TopologicalSpace γ] {t : Set γ}
   intro u hu x hx
   rcases h u hu (g x) (hg hx) with ⟨a, ha, H⟩
   have : g ⁻¹' a ∈ 𝓝[t] x :=
-    (cg x hx).preimage_mem_nhds_within' (nhdsWithin_mono (g x) hg.image_subset ha)
+    (cg x hx).preimage_mem_nhdsWithin' (nhdsWithin_mono (g x) hg.image_subset ha)
   exact ⟨g ⁻¹' a, this, H.mono fun n hn y hy => hn _ hy⟩
 #align tendsto_locally_uniformly_on.comp TendstoLocallyUniformlyOn.comp
 

@@ -728,21 +728,24 @@ theorem TendstoLocallyUniformly.comp [TopologicalSpace γ] (h : TendstoLocallyUn
   exact h.comp _ (mapsTo_univ _ _) cg
 #align tendsto_locally_uniformly.comp TendstoLocallyUniformly.comp
 
-open List in
 theorem tendstoLocallyUniformlyOn_TFAE [LocallyCompactSpace α] (G : ι → α → β) (g : α → β)
     (p : Filter ι) (hs : IsOpen s) :
-    TFAE [TendstoLocallyUniformlyOn G g p s,
-          ∀ K, K ⊆ s → IsCompact K → TendstoUniformlyOn G g p K,
-          ∀ x ∈ s, ∃ v ∈ 𝓝[s] x, TendstoUniformlyOn G g p v] := by
-  apply_rules [tfae_of_cycle, Chain.cons, Chain.nil] -- porting note: todo: use `tfae_have` or not?
-  · exact fun h K hKs hKc =>
-      (tendstoLocallyUniformlyOn_iff_tendstoUniformlyOn_of_compact hKc).mp (h.mono hKs)
+    List.TFAE [
+      TendstoLocallyUniformlyOn G g p s,
+      ∀ K, K ⊆ s → IsCompact K → TendstoUniformlyOn G g p K,
+      ∀ x ∈ s, ∃ v ∈ 𝓝[s] x, TendstoUniformlyOn G g p v] := by
+  tfae_have 1 → 2
+  · rintro h K hK1 hK2
+    exact (tendstoLocallyUniformlyOn_iff_tendstoUniformlyOn_of_compact hK2).mp (h.mono hK1)
+  tfae_have 2 → 3
   · rintro h x hx
-    obtain ⟨K, ⟨hK1, hK2⟩ ,hK3⟩ := (compact_basis_nhds x).mem_iff.mp (hs.mem_nhds hx)
-    refine' ⟨K, nhdsWithin_le_nhds hK1 , h K hK3 hK2 ⟩
+    obtain ⟨K, ⟨hK1, hK2⟩, hK3⟩ := (compact_basis_nhds x).mem_iff.mp (hs.mem_nhds hx)
+    refine' ⟨K, nhdsWithin_le_nhds hK1, h K hK3 hK2⟩
+  tfae_have 3 → 1
   · rintro h u hu x hx
     obtain ⟨v, hv1, hv2⟩ := h x hx
     exact ⟨v, hv1, hv2 u hu⟩
+  tfae_finish
 #align tendsto_locally_uniformly_on_tfae tendstoLocallyUniformlyOn_TFAE
 
 theorem tendstoLocallyUniformlyOn_iff_forall_isCompact [LocallyCompactSpace α] (hs : IsOpen s) :

Currently, the following notations are changed from · ×ˢ · because Lean 4 can't deal with ambiguous notations. | Definition | Notation | | :

Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: Chris Hughes <chrishughes24@gmail.com>

@@ -84,19 +84,19 @@ We define uniform convergence and locally uniform convergence, on a set or in th
 
 /-- A sequence of functions `Fₙ` converges uniformly on a filter `p'` to a limiting function `f`
 with respect to the filter `p` if, for any entourage of the diagonal `u`, one has
-`p ×ᶠ p'`-eventually `(f x, Fₙ x) ∈ u`. -/
+`p ×ˢ p'`-eventually `(f x, Fₙ x) ∈ u`. -/
 def TendstoUniformlyOnFilter (F : ι → α → β) (f : α → β) (p : Filter ι) (p' : Filter α) :=
-  ∀ u ∈ 𝓤 β, ∀ᶠ n : ι × α in p ×ᶠ p', (f n.snd, F n.fst n.snd) ∈ u
+  ∀ u ∈ 𝓤 β, ∀ᶠ n : ι × α in p ×ˢ p', (f n.snd, F n.fst n.snd) ∈ u
 #align tendsto_uniformly_on_filter TendstoUniformlyOnFilter
 
 /--
 A sequence of functions `Fₙ` converges uniformly on a filter `p'` to a limiting function `f` w.r.t.
-filter `p` iff the function `(n, x) ↦ (f x, Fₙ x)` converges along `p ×ᶠ p'` to the uniformity.
+filter `p` iff the function `(n, x) ↦ (f x, Fₙ x)` converges along `p ×ˢ p'` to the uniformity.
 In other words: one knows nothing about the behavior of `x` in this limit besides it being in `p'`.
 -/
 theorem tendstoUniformlyOnFilter_iff_tendsto :
     TendstoUniformlyOnFilter F f p p' ↔
-      Tendsto (fun q : ι × α => (f q.2, F q.1 q.2)) (p ×ᶠ p') (𝓤 β) :=
+      Tendsto (fun q : ι × α => (f q.2, F q.1 q.2)) (p ×ˢ p') (𝓤 β) :=
   Iff.rfl
 #align tendsto_uniformly_on_filter_iff_tendsto tendstoUniformlyOnFilter_iff_tendsto
 
@@ -121,11 +121,11 @@ alias tendstoUniformlyOn_iff_tendstoUniformlyOnFilter ↔
 #align tendsto_uniformly_on_filter.tendsto_uniformly_on TendstoUniformlyOnFilter.tendstoUniformlyOn
 
 /-- A sequence of functions `Fₙ` converges uniformly on a set `s` to a limiting function `f` w.r.t.
-filter `p` iff the function `(n, x) ↦ (f x, Fₙ x)` converges along `p ×ᶠ 𝓟 s` to the uniformity.
+filter `p` iff the function `(n, x) ↦ (f x, Fₙ x)` converges along `p ×ˢ 𝓟 s` to the uniformity.
 In other words: one knows nothing about the behavior of `x` in this limit besides it being in `s`.
 -/
 theorem tendstoUniformlyOn_iff_tendsto {F : ι → α → β} {f : α → β} {p : Filter ι} {s : Set α} :
-    TendstoUniformlyOn F f p s ↔ Tendsto (fun q : ι × α => (f q.2, F q.1 q.2)) (p ×ᶠ 𝓟 s) (𝓤 β) :=
+    TendstoUniformlyOn F f p s ↔ Tendsto (fun q : ι × α => (f q.2, F q.1 q.2)) (p ×ˢ 𝓟 s) (𝓤 β) :=
   by simp [tendstoUniformlyOn_iff_tendstoUniformlyOnFilter, tendstoUniformlyOnFilter_iff_tendsto]
 #align tendsto_uniformly_on_iff_tendsto tendstoUniformlyOn_iff_tendsto
 
@@ -156,11 +156,11 @@ theorem tendstoUniformlyOn_iff_tendstoUniformly_comp_coe :
 #align tendsto_uniformly_on_iff_tendsto_uniformly_comp_coe tendstoUniformlyOn_iff_tendstoUniformly_comp_coe
 
 /-- A sequence of functions `Fₙ` converges uniformly to a limiting function `f` w.r.t.
-filter `p` iff the function `(n, x) ↦ (f x, Fₙ x)` converges along `p ×ᶠ ⊤` to the uniformity.
+filter `p` iff the function `(n, x) ↦ (f x, Fₙ x)` converges along `p ×ˢ ⊤` to the uniformity.
 In other words: one knows nothing about the behavior of `x` in this limit.
 -/
 theorem tendstoUniformly_iff_tendsto {F : ι → α → β} {f : α → β} {p : Filter ι} :
-    TendstoUniformly F f p ↔ Tendsto (fun q : ι × α => (f q.2, F q.1 q.2)) (p ×ᶠ ⊤) (𝓤 β) := by
+    TendstoUniformly F f p ↔ Tendsto (fun q : ι × α => (f q.2, F q.1 q.2)) (p ×ˢ ⊤) (𝓤 β) := by
   simp [tendstoUniformly_iff_tendstoUniformlyOnFilter, tendstoUniformlyOnFilter_iff_tendsto]
 #align tendsto_uniformly_iff_tendsto tendstoUniformly_iff_tendsto
 
@@ -205,7 +205,7 @@ theorem TendstoUniformlyOn.mono {s' : Set α} (h : TendstoUniformlyOn F f p s) (
 #align tendsto_uniformly_on.mono TendstoUniformlyOn.mono
 
 theorem TendstoUniformlyOnFilter.congr {F' : ι → α → β} (hf : TendstoUniformlyOnFilter F f p p')
-    (hff' : ∀ᶠ n : ι × α in p ×ᶠ p', F n.fst n.snd = F' n.fst n.snd) :
+    (hff' : ∀ᶠ n : ι × α in p ×ˢ p', F n.fst n.snd = F' n.fst n.snd) :
     TendstoUniformlyOnFilter F' f p p' := by
   refine' fun u hu => ((hf u hu).and hff').mono fun n h => _
   rw [← h.right]
@@ -276,7 +276,7 @@ theorem TendstoUniformlyOnFilter.prod_map {ι' α' β' : Type _} [UniformSpace 
     {f' : α' → β'} {q : Filter ι'} {q' : Filter α'} (h : TendstoUniformlyOnFilter F f p p')
     (h' : TendstoUniformlyOnFilter F' f' q q') :
     TendstoUniformlyOnFilter (fun i : ι × ι' => Prod.map (F i.1) (F' i.2)) (Prod.map f f')
-      (p ×ᶠ q) (p' ×ᶠ q') := by
+      (p ×ˢ q) (p' ×ˢ q') := by
   rw [tendstoUniformlyOnFilter_iff_tendsto] at h h' ⊢
   rw [uniformity_prod_eq_comap_prod, tendsto_comap_iff, ← map_swap4_prod, tendsto_map'_iff]
   convert h.prod_map h' -- seems to be faster than `exact` here
@@ -285,7 +285,7 @@ theorem TendstoUniformlyOnFilter.prod_map {ι' α' β' : Type _} [UniformSpace 
 theorem TendstoUniformlyOn.prod_map {ι' α' β' : Type _} [UniformSpace β'] {F' : ι' → α' → β'}
     {f' : α' → β'} {p' : Filter ι'} {s' : Set α'} (h : TendstoUniformlyOn F f p s)
     (h' : TendstoUniformlyOn F' f' p' s') :
-    TendstoUniformlyOn (fun i : ι × ι' => Prod.map (F i.1) (F' i.2)) (Prod.map f f') (p ×ᶠ p')
+    TendstoUniformlyOn (fun i : ι × ι' => Prod.map (F i.1) (F' i.2)) (Prod.map f f') (p ×ˢ p')
       (s ×ˢ s') := by
   rw [tendstoUniformlyOn_iff_tendstoUniformlyOnFilter] at h h'⊢
   simpa only [prod_principal_principal] using h.prod_map h'
@@ -293,7 +293,7 @@ theorem TendstoUniformlyOn.prod_map {ι' α' β' : Type _} [UniformSpace β'] {F
 
 theorem TendstoUniformly.prod_map {ι' α' β' : Type _} [UniformSpace β'] {F' : ι' → α' → β'}
     {f' : α' → β'} {p' : Filter ι'} (h : TendstoUniformly F f p) (h' : TendstoUniformly F' f' p') :
-    TendstoUniformly (fun i : ι × ι' => Prod.map (F i.1) (F' i.2)) (Prod.map f f') (p ×ᶠ p') := by
+    TendstoUniformly (fun i : ι × ι' => Prod.map (F i.1) (F' i.2)) (Prod.map f f') (p ×ˢ p') := by
   rw [← tendstoUniformlyOn_univ, ← univ_prod_univ] at *
   exact h.prod_map h'
 #align tendsto_uniformly.prod_map TendstoUniformly.prod_map
@@ -302,7 +302,7 @@ theorem TendstoUniformlyOnFilter.prod {ι' β' : Type _} [UniformSpace β'] {F'
     {f' : α → β'} {q : Filter ι'} (h : TendstoUniformlyOnFilter F f p p')
     (h' : TendstoUniformlyOnFilter F' f' q p') :
     TendstoUniformlyOnFilter (fun (i : ι × ι') a => (F i.1 a, F' i.2 a)) (fun a => (f a, f' a))
-      (p ×ᶠ q) p' :=
+      (p ×ˢ q) p' :=
   fun u hu => ((h.prod_map h') u hu).diag_of_prod_right
 #align tendsto_uniformly_on_filter.prod TendstoUniformlyOnFilter.prod
 
@@ -316,29 +316,29 @@ theorem TendstoUniformlyOn.prod {ι' β' : Type _} [UniformSpace β'] {F' : ι'
 theorem TendstoUniformly.prod {ι' β' : Type _} [UniformSpace β'] {F' : ι' → α → β'} {f' : α → β'}
     {p' : Filter ι'} (h : TendstoUniformly F f p) (h' : TendstoUniformly F' f' p') :
     TendstoUniformly (fun (i : ι × ι') a => (F i.1 a, F' i.2 a)) (fun a => (f a, f' a))
-      (p ×ᶠ p') :=
+      (p ×ˢ p') :=
   (h.prod_map h').comp fun a => (a, a)
 #align tendsto_uniformly.prod TendstoUniformly.prod
 
 /-- Uniform convergence on a filter `p'` to a constant function is equivalent to convergence in
-`p ×ᶠ p'`. -/
+`p ×ˢ p'`. -/
 theorem tendsto_prod_filter_iff {c : β} :
-    Tendsto (↿F) (p ×ᶠ p') (𝓝 c) ↔ TendstoUniformlyOnFilter F (fun _ => c) p p' := by
+    Tendsto (↿F) (p ×ˢ p') (𝓝 c) ↔ TendstoUniformlyOnFilter F (fun _ => c) p p' := by
   simp_rw [nhds_eq_comap_uniformity, tendsto_comap_iff]
   rfl
 #align tendsto_prod_filter_iff tendsto_prod_filter_iff
 
 /-- Uniform convergence on a set `s` to a constant function is equivalent to convergence in
-`p ×ᶠ 𝓟 s`. -/
+`p ×ˢ 𝓟 s`. -/
 theorem tendsto_prod_principal_iff {c : β} :
-    Tendsto (↿F) (p ×ᶠ 𝓟 s) (𝓝 c) ↔ TendstoUniformlyOn F (fun _ => c) p s := by
+    Tendsto (↿F) (p ×ˢ 𝓟 s) (𝓝 c) ↔ TendstoUniformlyOn F (fun _ => c) p s := by
   rw [tendstoUniformlyOn_iff_tendstoUniformlyOnFilter]
   exact tendsto_prod_filter_iff
 #align tendsto_prod_principal_iff tendsto_prod_principal_iff
 
-/-- Uniform convergence to a constant function is equivalent to convergence in `p ×ᶠ ⊤`. -/
+/-- Uniform convergence to a constant function is equivalent to convergence in `p ×ˢ ⊤`. -/
 theorem tendsto_prod_top_iff {c : β} :
-    Tendsto (↿F) (p ×ᶠ ⊤) (𝓝 c) ↔ TendstoUniformly F (fun _ => c) p := by
+    Tendsto (↿F) (p ×ˢ ⊤) (𝓝 c) ↔ TendstoUniformly F (fun _ => c) p := by
   rw [tendstoUniformly_iff_tendstoUniformlyOnFilter]
   exact tendsto_prod_filter_iff
 #align tendsto_prod_top_iff tendsto_prod_top_iff
@@ -375,8 +375,9 @@ theorem UniformContinuousOn.tendstoUniformlyOn [UniformSpace α] [UniformSpace 
     TendstoUniformlyOn F (F x) (𝓝[U] x) V := by
   set φ := fun q : α × β => ((x, q.2), q)
   rw [tendstoUniformlyOn_iff_tendsto]
-  change Tendsto (Prod.map (↿F) ↿F ∘ φ) (𝓝[U] x ×ᶠ 𝓟 V) (𝓤 γ)
-  simp only [nhdsWithin, Filter.prod, comap_inf, inf_assoc, comap_principal, inf_principal]
+  change Tendsto (Prod.map (↿F) ↿F ∘ φ) (𝓝[U] x ×ˢ 𝓟 V) (𝓤 γ)
+  simp only [nhdsWithin, SProd.sprod, Filter.prod, comap_inf, inf_assoc, comap_principal,
+    inf_principal]
   refine hF.comp (Tendsto.inf ?_ <| tendsto_principal_principal.2 <| fun x hx => ⟨⟨hU, hx.2⟩, hx⟩)
   simp only [uniformity_prod_eq_comap_prod, tendsto_comap_iff, (· ∘ ·),
     nhds_eq_comap_uniformity, comap_comap]
@@ -397,13 +398,13 @@ theorem UniformContinuous₂.tendstoUniformly [UniformSpace α] [UniformSpace γ
 /-- A sequence is uniformly Cauchy if eventually all of its pairwise differences are
 uniformly bounded -/
 def UniformCauchySeqOnFilter (F : ι → α → β) (p : Filter ι) (p' : Filter α) : Prop :=
-  ∀ u ∈ 𝓤 β, ∀ᶠ m : (ι × ι) × α in (p ×ᶠ p) ×ᶠ p', (F m.fst.fst m.snd, F m.fst.snd m.snd) ∈ u
+  ∀ u ∈ 𝓤 β, ∀ᶠ m : (ι × ι) × α in (p ×ˢ p) ×ˢ p', (F m.fst.fst m.snd, F m.fst.snd m.snd) ∈ u
 #align uniform_cauchy_seq_on_filter UniformCauchySeqOnFilter
 
 /-- A sequence is uniformly Cauchy if eventually all of its pairwise differences are
 uniformly bounded -/
 def UniformCauchySeqOn (F : ι → α → β) (p : Filter ι) (s : Set α) : Prop :=
-  ∀ u ∈ 𝓤 β, ∀ᶠ m : ι × ι in p ×ᶠ p, ∀ x : α, x ∈ s → (F m.fst x, F m.snd x) ∈ u
+  ∀ u ∈ 𝓤 β, ∀ᶠ m : ι × ι in p ×ˢ p, ∀ x : α, x ∈ s → (F m.fst x, F m.snd x) ∈ u
 #align uniform_cauchy_seq_on UniformCauchySeqOn
 
 theorem uniformCauchySeqOn_iff_uniformCauchySeqOnFilter :
@@ -448,7 +449,7 @@ theorem UniformCauchySeqOnFilter.tendstoUniformlyOnFilter_of_tendsto [NeBot p]
   rcases comp_symm_of_uniformity hu with ⟨t, ht, htsymm, htmem⟩
   -- We will choose n, x, and m simultaneously. n and x come from hF. m comes from hF'
   -- But we need to promote hF' to the full product filter to use it
-  have hmc : ∀ᶠ x in (p ×ᶠ p) ×ᶠ p', Tendsto (fun n : ι => F n x.snd) p (𝓝 (f x.snd)) := by
+  have hmc : ∀ᶠ x in (p ×ˢ p) ×ˢ p', Tendsto (fun n : ι => F n x.snd) p (𝓝 (f x.snd)) := by
     rw [eventually_prod_iff]
     refine' ⟨fun _ => True, by simp, _, hF', by simp⟩
   -- To apply filter operations we'll need to do some order manipulation
@@ -482,7 +483,7 @@ theorem UniformCauchySeqOnFilter.mono_left {p'' : Filter ι} (hf : UniformCauchy
 
 theorem UniformCauchySeqOnFilter.mono_right {p'' : Filter α} (hf : UniformCauchySeqOnFilter F p p')
     (hp : p'' ≤ p') : UniformCauchySeqOnFilter F p p'' := fun u hu =>
-  have := (hf u hu).filter_mono ((p ×ᶠ p).prod_mono_right hp)
+  have := (hf u hu).filter_mono ((p ×ˢ p).prod_mono_right hp)
   this.mono (by simp)
 #align uniform_cauchy_seq_on_filter.mono_right UniformCauchySeqOnFilter.mono_right
 
@@ -518,7 +519,7 @@ theorem UniformContinuous.comp_uniformCauchySeqOn [UniformSpace γ] {g : β →
 theorem UniformCauchySeqOn.prod_map {ι' α' β' : Type _} [UniformSpace β'] {F' : ι' → α' → β'}
     {p' : Filter ι'} {s' : Set α'} (h : UniformCauchySeqOn F p s)
     (h' : UniformCauchySeqOn F' p' s') :
-    UniformCauchySeqOn (fun i : ι × ι' => Prod.map (F i.1) (F' i.2)) (p ×ᶠ p') (s ×ˢ s') := by
+    UniformCauchySeqOn (fun i : ι × ι' => Prod.map (F i.1) (F' i.2)) (p ×ˢ p') (s ×ˢ s') := by
   intro u hu
   rw [uniformity_prod_eq_prod, mem_map, mem_prod_iff] at hu
   obtain ⟨v, hv, w, hw, hvw⟩ := hu
@@ -531,14 +532,14 @@ theorem UniformCauchySeqOn.prod_map {ι' α' β' : Type _} [UniformSpace β'] {F
 
 theorem UniformCauchySeqOn.prod {ι' β' : Type _} [UniformSpace β'] {F' : ι' → α → β'}
     {p' : Filter ι'} (h : UniformCauchySeqOn F p s) (h' : UniformCauchySeqOn F' p' s) :
-    UniformCauchySeqOn (fun (i : ι × ι') a => (F i.fst a, F' i.snd a)) (p ×ᶠ p') s :=
+    UniformCauchySeqOn (fun (i : ι × ι') a => (F i.fst a, F' i.snd a)) (p ×ˢ p') s :=
   (congr_arg _ s.inter_self).mp ((h.prod_map h').comp fun a => (a, a))
 #align uniform_cauchy_seq_on.prod UniformCauchySeqOn.prod
 
 theorem UniformCauchySeqOn.prod' {β' : Type _} [UniformSpace β'] {F' : ι → α → β'}
     (h : UniformCauchySeqOn F p s) (h' : UniformCauchySeqOn F' p s) :
     UniformCauchySeqOn (fun (i : ι) a => (F i a, F' i a)) p s := fun u hu =>
-  have hh : Tendsto (fun x : ι => (x, x)) p (p ×ᶠ p) := tendsto_diag
+  have hh : Tendsto (fun x : ι => (x, x)) p (p ×ˢ p) := tendsto_diag
   (hh.prod_map hh).eventually ((h.prod h') u hu)
 #align uniform_cauchy_seq_on.prod' UniformCauchySeqOn.prod'
 
@@ -610,19 +611,19 @@ theorem tendstoLocallyUniformlyOn_univ :
 -- porting note: new lemma
 theorem tendstoLocallyUniformlyOn_iff_forall_tendsto :
     TendstoLocallyUniformlyOn F f p s ↔
-      ∀ x ∈ s, Tendsto (fun y : ι × α => (f y.2, F y.1 y.2)) (p ×ᶠ 𝓝[s] x) (𝓤 β) :=
+      ∀ x ∈ s, Tendsto (fun y : ι × α => (f y.2, F y.1 y.2)) (p ×ˢ 𝓝[s] x) (𝓤 β) :=
   forall₂_swap.trans <| forall₄_congr fun _ _ _ _ => by
     rw [mem_map, mem_prod_iff_right]; rfl
 
 nonrec theorem IsOpen.tendstoLocallyUniformlyOn_iff_forall_tendsto (hs : IsOpen s) :
     TendstoLocallyUniformlyOn F f p s ↔
-      ∀ x ∈ s, Tendsto (fun y : ι × α => (f y.2, F y.1 y.2)) (p ×ᶠ 𝓝 x) (𝓤 β) :=
+      ∀ x ∈ s, Tendsto (fun y : ι × α => (f y.2, F y.1 y.2)) (p ×ˢ 𝓝 x) (𝓤 β) :=
   tendstoLocallyUniformlyOn_iff_forall_tendsto.trans <| forall₂_congr fun x hx => by
     rw [hs.nhdsWithin_eq hx]
 
 theorem tendstoLocallyUniformly_iff_forall_tendsto :
     TendstoLocallyUniformly F f p ↔
-      ∀ x, Tendsto (fun y : ι × α => (f y.2, F y.1 y.2)) (p ×ᶠ 𝓝 x) (𝓤 β) := by
+      ∀ x, Tendsto (fun y : ι × α => (f y.2, F y.1 y.2)) (p ×ˢ 𝓝 x) (𝓤 β) := by
   simp [← tendstoLocallyUniformlyOn_univ, isOpen_univ.tendstoLocallyUniformlyOn_iff_forall_tendsto]
 #align tendsto_locally_uniformly_iff_forall_tendsto tendstoLocallyUniformly_iff_forall_tendsto
 

As discussed on Zulip

Renames

• supₛ → sSup
• infₛ → sInf
• supᵢ → iSup
• infᵢ → iInf
• bsupₛ → bsSup
• binfₛ → bsInf
• bsupᵢ → biSup
• binfᵢ → biInf
• csupₛ → csSup
• cinfₛ → csInf
• csupᵢ → ciSup
• cinfᵢ → ciInf
• unionₛ → sUnion
• interₛ → sInter
• unionᵢ → iUnion
• interᵢ → iInter
• bunionₛ → bsUnion
• binterₛ → bsInter
• bunionᵢ → biUnion
• binterᵢ → biInter

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

@@ -650,32 +650,32 @@ theorem TendstoLocallyUniformlyOn.mono (h : TendstoLocallyUniformlyOn F f p s) (
 #align tendsto_locally_uniformly_on.mono TendstoLocallyUniformlyOn.mono
 
 -- porting note: generalized from `Type` to `Sort`
-theorem tendstoLocallyUniformlyOn_unionᵢ {ι' : Sort _} {S : ι' → Set α} (hS : ∀ i, IsOpen (S i))
+theorem tendstoLocallyUniformlyOn_iUnion {ι' : Sort _} {S : ι' → Set α} (hS : ∀ i, IsOpen (S i))
     (h : ∀ i, TendstoLocallyUniformlyOn F f p (S i)) :
     TendstoLocallyUniformlyOn F f p (⋃ i, S i) :=
-  (isOpen_unionᵢ hS).tendstoLocallyUniformlyOn_iff_forall_tendsto.2 $ fun _x hx =>
-    let ⟨i, hi⟩ := mem_unionᵢ.1 hx
+  (isOpen_iUnion hS).tendstoLocallyUniformlyOn_iff_forall_tendsto.2 $ fun _x hx =>
+    let ⟨i, hi⟩ := mem_iUnion.1 hx
     (hS i).tendstoLocallyUniformlyOn_iff_forall_tendsto.1 (h i) _ hi
-#align tendsto_locally_uniformly_on_Union tendstoLocallyUniformlyOn_unionᵢ
+#align tendsto_locally_uniformly_on_Union tendstoLocallyUniformlyOn_iUnion
 
-theorem tendstoLocallyUniformlyOn_bunionᵢ {s : Set γ} {S : γ → Set α} (hS : ∀ i ∈ s, IsOpen (S i))
+theorem tendstoLocallyUniformlyOn_biUnion {s : Set γ} {S : γ → Set α} (hS : ∀ i ∈ s, IsOpen (S i))
     (h : ∀ i ∈ s, TendstoLocallyUniformlyOn F f p (S i)) :
     TendstoLocallyUniformlyOn F f p (⋃ i ∈ s, S i) :=
-  tendstoLocallyUniformlyOn_unionᵢ (fun i => isOpen_unionᵢ (hS i)) fun i =>
-   tendstoLocallyUniformlyOn_unionᵢ (hS i) (h i)
-#align tendsto_locally_uniformly_on_bUnion tendstoLocallyUniformlyOn_bunionᵢ
+  tendstoLocallyUniformlyOn_iUnion (fun i => isOpen_iUnion (hS i)) fun i =>
+   tendstoLocallyUniformlyOn_iUnion (hS i) (h i)
+#align tendsto_locally_uniformly_on_bUnion tendstoLocallyUniformlyOn_biUnion
 
-theorem tendstoLocallyUniformlyOn_unionₛ (S : Set (Set α)) (hS : ∀ s ∈ S, IsOpen s)
+theorem tendstoLocallyUniformlyOn_sUnion (S : Set (Set α)) (hS : ∀ s ∈ S, IsOpen s)
     (h : ∀ s ∈ S, TendstoLocallyUniformlyOn F f p s) : TendstoLocallyUniformlyOn F f p (⋃₀ S) := by
-  rw [unionₛ_eq_bunionᵢ]
-  exact tendstoLocallyUniformlyOn_bunionᵢ hS h
-#align tendsto_locally_uniformly_on_sUnion tendstoLocallyUniformlyOn_unionₛ
+  rw [sUnion_eq_biUnion]
+  exact tendstoLocallyUniformlyOn_biUnion hS h
+#align tendsto_locally_uniformly_on_sUnion tendstoLocallyUniformlyOn_sUnion
 
 theorem TendstoLocallyUniformlyOn.union {s₁ s₂ : Set α} (hs₁ : IsOpen s₁) (hs₂ : IsOpen s₂)
     (h₁ : TendstoLocallyUniformlyOn F f p s₁) (h₂ : TendstoLocallyUniformlyOn F f p s₂) :
     TendstoLocallyUniformlyOn F f p (s₁ ∪ s₂) := by
-  rw [← unionₛ_pair]
-  refine' tendstoLocallyUniformlyOn_unionₛ _ _ _ <;> simp [*]
+  rw [← sUnion_pair]
+  refine' tendstoLocallyUniformlyOn_sUnion _ _ _ <;> simp [*]
 #align tendsto_locally_uniformly_on.union TendstoLocallyUniformlyOn.union
 
 -- porting note: tendstoLocallyUniformlyOn_univ moved up
@@ -695,7 +695,7 @@ theorem tendstoLocallyUniformly_iff_tendstoUniformly_of_compactSpace [CompactSpa
   rw [← eventually_all] at hU
   refine' hU.mono fun i hi x => _
   specialize ht (mem_univ x)
-  simp only [exists_prop, mem_unionᵢ, SetCoe.exists, exists_and_right, Subtype.coe_mk] at ht
+  simp only [exists_prop, mem_iUnion, SetCoe.exists, exists_and_right, Subtype.coe_mk] at ht
   obtain ⟨y, ⟨hy₁, hy₂⟩, hy₃⟩ := ht
   exact hi ⟨⟨y, hy₁⟩, hy₂⟩ x hy₃
 #align tendsto_locally_uniformly_iff_tendsto_uniformly_of_compact_space tendstoLocallyUniformly_iff_tendstoUniformly_of_compactSpace

closes #3680, see https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Stepping.20through.20simp_rw/near/326712986

@@ -324,7 +324,7 @@ theorem TendstoUniformly.prod {ι' β' : Type _} [UniformSpace β'] {F' : ι' 
 `p ×ᶠ p'`. -/
 theorem tendsto_prod_filter_iff {c : β} :
     Tendsto (↿F) (p ×ᶠ p') (𝓝 c) ↔ TendstoUniformlyOnFilter F (fun _ => c) p p' := by
-  simp_rw [nhds_eq_comap_uniformity, tendsto_comap_iff, map_map, le_def, mem_map]
+  simp_rw [nhds_eq_comap_uniformity, tendsto_comap_iff]
   rfl
 #align tendsto_prod_filter_iff tendsto_prod_filter_iff
 

Co-authored-by: Anatole Dedecker <anatolededecker@gmail.com> Co-authored-by: Johan Commelin <johan@commelin.net>