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

@@ -46,7 +46,7 @@ section
 
 You should extend this class when you extend `continuous_map`. -/
 class ContinuousMapClass (F : Type _) (α β : outParam <| Type _) [TopologicalSpace α]
-    [TopologicalSpace β] extends FunLike F α fun _ => β where
+    [TopologicalSpace β] extends DFunLike F α fun _ => β where
   map_continuous (f : F) : Continuous f
 #align continuous_map_class ContinuousMapClass
 -/
@@ -97,7 +97,7 @@ instance : ContinuousMapClass C(α, β) α β
 /-- Helper instance for when there's too many metavariables to apply `fun_like.has_coe_to_fun`
 directly. -/
 instance : CoeFun C(α, β) fun _ => α → β :=
-  FunLike.hasCoeToFun
+  DFunLike.hasCoeToFun
 
 #print ContinuousMap.toFun_eq_coe /-
 @[simp]
@@ -119,7 +119,7 @@ theorem coe_coe {F : Type _} [ContinuousMapClass F α β] (f : F) : ⇑(f : C(α
 #print ContinuousMap.ext /-
 @[ext]
 theorem ext {f g : C(α, β)} (h : ∀ a, f a = g a) : f = g :=
-  FunLike.ext _ _ h
+  DFunLike.ext _ _ h
 #align continuous_map.ext ContinuousMap.ext
 -/
 
@@ -142,7 +142,7 @@ theorem coe_copy (f : C(α, β)) (f' : α → β) (h : f' = f) : ⇑(f.copy f' h
 
 #print ContinuousMap.copy_eq /-
 theorem copy_eq (f : C(α, β)) (f' : α → β) (h : f' = f) : f.copy f' h = f :=
-  FunLike.ext' h
+  DFunLike.ext' h
 #align continuous_map.copy_eq ContinuousMap.copy_eq
 -/
 
@@ -328,7 +328,7 @@ theorem comp_const (f : C(β, γ)) (b : β) : f.comp (const α b) = const α (f
 #print ContinuousMap.cancel_right /-
 theorem cancel_right {f₁ f₂ : C(β, γ)} {g : C(α, β)} (hg : Surjective g) :
     f₁.comp g = f₂.comp g ↔ f₁ = f₂ :=
-  ⟨fun h => ext <| hg.forall.2 <| FunLike.ext_iff.1 h, congr_arg _⟩
+  ⟨fun h => ext <| hg.forall.2 <| DFunLike.ext_iff.1 h, congr_arg _⟩
 #align continuous_map.cancel_right ContinuousMap.cancel_right
 -/
 
@@ -341,7 +341,7 @@ theorem cancel_left {f : C(β, γ)} {g₁ g₂ : C(α, β)} (hf : Injective f) :
 
 instance [Nonempty α] [Nontrivial β] : Nontrivial C(α, β) :=
   ⟨let ⟨b₁, b₂, hb⟩ := exists_pair_ne β
-    ⟨const _ b₁, const _ b₂, fun h => hb <| FunLike.congr_fun h <| Classical.arbitrary α⟩⟩
+    ⟨const _ b₁, const _ b₂, fun h => hb <| DFunLike.congr_fun h <| Classical.arbitrary α⟩⟩
 
 section Prod
 

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

@@ -3,8 +3,8 @@ Copyright © 2020 Nicolò Cavalleri. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Nicolò Cavalleri
 -/
-import Mathbin.Data.Set.UnionLift
-import Mathbin.Topology.Homeomorph
+import Data.Set.UnionLift
+import Topology.Homeomorph
 
 #align_import topology.continuous_function.basic from "leanprover-community/mathlib"@"55d771df074d0dd020139ee1cd4b95521422df9f"
 

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

@@ -2,15 +2,12 @@
 Copyright © 2020 Nicolò Cavalleri. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Nicolò Cavalleri
-
-! This file was ported from Lean 3 source module topology.continuous_function.basic
-! leanprover-community/mathlib commit 55d771df074d0dd020139ee1cd4b95521422df9f
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Set.UnionLift
 import Mathbin.Topology.Homeomorph
 
+#align_import topology.continuous_function.basic from "leanprover-community/mathlib"@"55d771df074d0dd020139ee1cd4b95521422df9f"
+
 /-!
 # Continuous bundled maps
 

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

@@ -40,7 +40,6 @@ structure ContinuousMap (α β : Type _) [TopologicalSpace α] [TopologicalSpace
 #align continuous_map ContinuousMap
 -/
 
--- mathport name: «exprC( , )»
 notation "C(" α ", " β ")" => ContinuousMap α β
 
 section
@@ -65,15 +64,17 @@ section ContinuousMapClass
 
 variable {F α β : Type _} [TopologicalSpace α] [TopologicalSpace β] [ContinuousMapClass F α β]
 
-include β
-
+#print map_continuousAt /-
 theorem map_continuousAt (f : F) (a : α) : ContinuousAt f a :=
   (map_continuous f).ContinuousAt
 #align map_continuous_at map_continuousAt
+-/
 
+#print map_continuousWithinAt /-
 theorem map_continuousWithinAt (f : F) (s : Set α) (a : α) : ContinuousWithinAt f s a :=
   (map_continuous f).ContinuousWithinAt
 #align map_continuous_within_at map_continuousWithinAt
+-/
 
 instance : CoeTC F C(α, β) :=
   ⟨fun f =>
@@ -101,24 +102,31 @@ directly. -/
 instance : CoeFun C(α, β) fun _ => α → β :=
   FunLike.hasCoeToFun
 
+#print ContinuousMap.toFun_eq_coe /-
 @[simp]
 theorem toFun_eq_coe {f : C(α, β)} : f.toFun = (f : α → β) :=
   rfl
 #align continuous_map.to_fun_eq_coe ContinuousMap.toFun_eq_coe
+-/
 
 -- this must come after the coe_to_fun definition
 initialize_simps_projections ContinuousMap (toFun → apply)
 
+#print ContinuousMap.coe_coe /-
 @[protected, simp, norm_cast]
 theorem coe_coe {F : Type _} [ContinuousMapClass F α β] (f : F) : ⇑(f : C(α, β)) = f :=
   rfl
 #align continuous_map.coe_coe ContinuousMap.coe_coe
+-/
 
+#print ContinuousMap.ext /-
 @[ext]
 theorem ext {f g : C(α, β)} (h : ∀ a, f a = g a) : f = g :=
   FunLike.ext _ _ h
 #align continuous_map.ext ContinuousMap.ext
+-/
 
+#print ContinuousMap.copy /-
 /-- Copy of a `continuous_map` with a new `to_fun` equal to the old one. Useful to fix definitional
 equalities. -/
 protected def copy (f : C(α, β)) (f' : α → β) (h : f' = f) : C(α, β)
@@ -126,55 +134,76 @@ protected def copy (f : C(α, β)) (f' : α → β) (h : f' = f) : C(α, β)
   toFun := f'
   continuous_toFun := h.symm ▸ f.continuous_toFun
 #align continuous_map.copy ContinuousMap.copy
+-/
 
+#print ContinuousMap.coe_copy /-
 @[simp]
 theorem coe_copy (f : C(α, β)) (f' : α → β) (h : f' = f) : ⇑(f.copy f' h) = f' :=
   rfl
 #align continuous_map.coe_copy ContinuousMap.coe_copy
+-/
 
+#print ContinuousMap.copy_eq /-
 theorem copy_eq (f : C(α, β)) (f' : α → β) (h : f' = f) : f.copy f' h = f :=
   FunLike.ext' h
 #align continuous_map.copy_eq ContinuousMap.copy_eq
+-/
 
 variable {α β} {f g : C(α, β)}
 
+#print ContinuousMap.continuous /-
 /-- Deprecated. Use `map_continuous` instead. -/
 protected theorem continuous (f : C(α, β)) : Continuous f :=
   f.continuous_toFun
 #align continuous_map.continuous ContinuousMap.continuous
+-/
 
+#print ContinuousMap.continuous_set_coe /-
 @[continuity]
 theorem continuous_set_coe (s : Set C(α, β)) (f : s) : Continuous f :=
   f.1.Continuous
 #align continuous_map.continuous_set_coe ContinuousMap.continuous_set_coe
+-/
 
+#print ContinuousMap.continuousAt /-
 /-- Deprecated. Use `map_continuous_at` instead. -/
 protected theorem continuousAt (f : C(α, β)) (x : α) : ContinuousAt f x :=
   f.Continuous.ContinuousAt
 #align continuous_map.continuous_at ContinuousMap.continuousAt
+-/
 
+#print ContinuousMap.congr_fun /-
 /-- Deprecated. Use `fun_like.congr_fun` instead. -/
 protected theorem congr_fun {f g : C(α, β)} (H : f = g) (x : α) : f x = g x :=
   H ▸ rfl
 #align continuous_map.congr_fun ContinuousMap.congr_fun
+-/
 
+#print ContinuousMap.congr_arg /-
 /-- Deprecated. Use `fun_like.congr_arg` instead. -/
 protected theorem congr_arg (f : C(α, β)) {x y : α} (h : x = y) : f x = f y :=
   h ▸ rfl
 #align continuous_map.congr_arg ContinuousMap.congr_arg
+-/
 
+#print ContinuousMap.coe_injective /-
 theorem coe_injective : @Function.Injective C(α, β) (α → β) coeFn := fun f g h => by
   cases f <;> cases g <;> congr
 #align continuous_map.coe_injective ContinuousMap.coe_injective
+-/
 
+#print ContinuousMap.coe_mk /-
 @[simp]
 theorem coe_mk (f : α → β) (h : Continuous f) : ⇑(⟨f, h⟩ : C(α, β)) = f :=
   rfl
 #align continuous_map.coe_mk ContinuousMap.coe_mk
+-/
 
+#print ContinuousMap.map_specializes /-
 theorem map_specializes (f : C(α, β)) {x y : α} (h : x ⤳ y) : f x ⤳ f y :=
   h.map f.2
 #align continuous_map.map_specializes ContinuousMap.map_specializes
+-/
 
 section
 
@@ -202,10 +231,12 @@ protected def id : C(α, α) :=
 #align continuous_map.id ContinuousMap.id
 -/
 
+#print ContinuousMap.coe_id /-
 @[simp]
 theorem coe_id : ⇑(ContinuousMap.id α) = id :=
   rfl
 #align continuous_map.coe_id ContinuousMap.coe_id
+-/
 
 #print ContinuousMap.const /-
 /-- The constant map as a continuous map. -/
@@ -214,25 +245,31 @@ def const (b : β) : C(α, β) :=
 #align continuous_map.const ContinuousMap.const
 -/
 
+#print ContinuousMap.coe_const /-
 @[simp]
 theorem coe_const (b : β) : ⇑(const α b) = Function.const α b :=
   rfl
 #align continuous_map.coe_const ContinuousMap.coe_const
+-/
 
 instance [Inhabited β] : Inhabited C(α, β) :=
   ⟨const α default⟩
 
 variable {α}
 
+#print ContinuousMap.id_apply /-
 @[simp]
 theorem id_apply (a : α) : ContinuousMap.id α a = a :=
   rfl
 #align continuous_map.id_apply ContinuousMap.id_apply
+-/
 
+#print ContinuousMap.const_apply /-
 @[simp]
 theorem const_apply (b : β) (a : α) : const α b a = b :=
   rfl
 #align continuous_map.const_apply ContinuousMap.const_apply
+-/
 
 #print ContinuousMap.comp /-
 /-- The composition of continuous maps, as a continuous map. -/
@@ -241,51 +278,69 @@ def comp (f : C(β, γ)) (g : C(α, β)) : C(α, γ) :=
 #align continuous_map.comp ContinuousMap.comp
 -/
 
+#print ContinuousMap.coe_comp /-
 @[simp]
 theorem coe_comp (f : C(β, γ)) (g : C(α, β)) : ⇑(comp f g) = f ∘ g :=
   rfl
 #align continuous_map.coe_comp ContinuousMap.coe_comp
+-/
 
+#print ContinuousMap.comp_apply /-
 @[simp]
 theorem comp_apply (f : C(β, γ)) (g : C(α, β)) (a : α) : comp f g a = f (g a) :=
   rfl
 #align continuous_map.comp_apply ContinuousMap.comp_apply
+-/
 
+#print ContinuousMap.comp_assoc /-
 @[simp]
 theorem comp_assoc (f : C(γ, δ)) (g : C(β, γ)) (h : C(α, β)) :
     (f.comp g).comp h = f.comp (g.comp h) :=
   rfl
 #align continuous_map.comp_assoc ContinuousMap.comp_assoc
+-/
 
+#print ContinuousMap.id_comp /-
 @[simp]
 theorem id_comp (f : C(α, β)) : (ContinuousMap.id _).comp f = f :=
   ext fun _ => rfl
 #align continuous_map.id_comp ContinuousMap.id_comp
+-/
 
+#print ContinuousMap.comp_id /-
 @[simp]
 theorem comp_id (f : C(α, β)) : f.comp (ContinuousMap.id _) = f :=
   ext fun _ => rfl
 #align continuous_map.comp_id ContinuousMap.comp_id
+-/
 
+#print ContinuousMap.const_comp /-
 @[simp]
 theorem const_comp (c : γ) (f : C(α, β)) : (const β c).comp f = const α c :=
   ext fun _ => rfl
 #align continuous_map.const_comp ContinuousMap.const_comp
+-/
 
+#print ContinuousMap.comp_const /-
 @[simp]
 theorem comp_const (f : C(β, γ)) (b : β) : f.comp (const α b) = const α (f b) :=
   ext fun _ => rfl
 #align continuous_map.comp_const ContinuousMap.comp_const
+-/
 
+#print ContinuousMap.cancel_right /-
 theorem cancel_right {f₁ f₂ : C(β, γ)} {g : C(α, β)} (hg : Surjective g) :
     f₁.comp g = f₂.comp g ↔ f₁ = f₂ :=
   ⟨fun h => ext <| hg.forall.2 <| FunLike.ext_iff.1 h, congr_arg _⟩
 #align continuous_map.cancel_right ContinuousMap.cancel_right
+-/
 
+#print ContinuousMap.cancel_left /-
 theorem cancel_left {f : C(β, γ)} {g₁ g₂ : C(α, β)} (hf : Injective f) :
     f.comp g₁ = f.comp g₂ ↔ g₁ = g₂ :=
   ⟨fun h => ext fun a => hf <| by rw [← comp_apply, h, comp_apply], congr_arg _⟩
 #align continuous_map.cancel_left ContinuousMap.cancel_left
+-/
 
 instance [Nonempty α] [Nontrivial β] : Nontrivial C(α, β) :=
   ⟨let ⟨b₁, b₂, hb⟩ := exists_pair_ne β
@@ -296,13 +351,16 @@ section Prod
 variable {α₁ α₂ β₁ β₂ : Type _} [TopologicalSpace α₁] [TopologicalSpace α₂] [TopologicalSpace β₁]
   [TopologicalSpace β₂]
 
+#print ContinuousMap.prodMk /-
 /-- Given two continuous maps `f` and `g`, this is the continuous map `x ↦ (f x, g x)`. -/
 def prodMk (f : C(α, β₁)) (g : C(α, β₂)) : C(α, β₁ × β₂)
     where
   toFun x := (f x, g x)
   continuous_toFun := Continuous.prod_mk f.Continuous g.Continuous
 #align continuous_map.prod_mk ContinuousMap.prodMk
+-/
 
+#print ContinuousMap.prodMap /-
 /-- Given two continuous maps `f` and `g`, this is the continuous map `(x, y) ↦ (f x, g y)`. -/
 @[simps]
 def prodMap (f : C(α₁, α₂)) (g : C(β₁, β₂)) : C(α₁ × β₁, α₂ × β₂)
@@ -310,11 +368,14 @@ def prodMap (f : C(α₁, α₂)) (g : C(β₁, β₂)) : C(α₁ × β₁, α
   toFun := Prod.map f g
   continuous_toFun := Continuous.prod_map f.Continuous g.Continuous
 #align continuous_map.prod_map ContinuousMap.prodMap
+-/
 
+#print ContinuousMap.prod_eval /-
 @[simp]
 theorem prod_eval (f : C(α, β₁)) (g : C(α, β₂)) (a : α) : (prodMk f g) a = (f a, g a) :=
   rfl
 #align continuous_map.prod_eval ContinuousMap.prod_eval
+-/
 
 end Prod
 
@@ -328,10 +389,12 @@ def pi (f : ∀ i, C(A, X i)) : C(A, ∀ i, X i) where toFun (a : A) (i : I) :=
 #align continuous_map.pi ContinuousMap.pi
 -/
 
+#print ContinuousMap.pi_eval /-
 @[simp]
 theorem pi_eval (f : ∀ i, C(A, X i)) (a : A) : (pi f) a = fun i : I => (f i) a :=
   rfl
 #align continuous_map.pi_eval ContinuousMap.pi_eval
+-/
 
 end Pi
 
@@ -346,27 +409,35 @@ def restrict (f : C(α, β)) : C(s, β) :=
 #align continuous_map.restrict ContinuousMap.restrict
 -/
 
+#print ContinuousMap.coe_restrict /-
 @[simp]
 theorem coe_restrict (f : C(α, β)) : ⇑(f.restrict s) = f ∘ coe :=
   rfl
 #align continuous_map.coe_restrict ContinuousMap.coe_restrict
+-/
 
+#print ContinuousMap.restrict_apply /-
 @[simp]
 theorem restrict_apply (f : C(α, β)) (s : Set α) (x : s) : f.restrict s x = f x :=
   rfl
 #align continuous_map.restrict_apply ContinuousMap.restrict_apply
+-/
 
+#print ContinuousMap.restrict_apply_mk /-
 @[simp]
 theorem restrict_apply_mk (f : C(α, β)) (s : Set α) (x : α) (hx : x ∈ s) :
     f.restrict s ⟨x, hx⟩ = f x :=
   rfl
 #align continuous_map.restrict_apply_mk ContinuousMap.restrict_apply_mk
+-/
 
+#print ContinuousMap.restrictPreimage /-
 /-- The restriction of a continuous map to the preimage of a set. -/
 @[simps]
 def restrictPreimage (f : C(α, β)) (s : Set β) : C(f ⁻¹' s, s) :=
   ⟨s.restrictPreimage f, continuous_iff_continuousAt.mpr fun x => f.2.ContinuousAt.restrictPreimage⟩
 #align continuous_map.restrict_preimage ContinuousMap.restrictPreimage
+-/
 
 end Restrict
 
@@ -376,8 +447,7 @@ variable {ι : Type _} (S : ι → Set α) (φ : ∀ i : ι, C(S i, β))
   (hφ : ∀ (i j) (x : α) (hxi : x ∈ S i) (hxj : x ∈ S j), φ i ⟨x, hxi⟩ = φ j ⟨x, hxj⟩)
   (hS : ∀ x : α, ∃ i, S i ∈ nhds x)
 
-include hφ hS
-
+#print ContinuousMap.liftCover /-
 /-- A family `φ i` of continuous maps `C(S i, β)`, where the domains `S i` contain a neighbourhood
 of each point in `α` and the functions `φ i` agree pairwise on intersections, can be glued to
 construct a continuous map in `C(α, β)`. -/
@@ -393,20 +463,23 @@ noncomputable def liftCover : C(α, β) :=
   rw [continuousOn_iff_continuous_restrict]
   simpa only [Set.restrict, Set.liftCover_coe] using (φ i).Continuous
 #align continuous_map.lift_cover ContinuousMap.liftCover
+-/
 
 variable {S φ hφ hS}
 
+#print ContinuousMap.liftCover_coe /-
 @[simp]
 theorem liftCover_coe {i : ι} (x : S i) : liftCover S φ hφ hS x = φ i x :=
   Set.liftCover_coe _
 #align continuous_map.lift_cover_coe ContinuousMap.liftCover_coe
+-/
 
+#print ContinuousMap.liftCover_restrict /-
 @[simp]
 theorem liftCover_restrict {i : ι} : (liftCover S φ hφ hS).restrict (S i) = φ i :=
   ext <| liftCover_coe
 #align continuous_map.lift_cover_restrict ContinuousMap.liftCover_restrict
-
-omit hφ hS
+-/
 
 variable (A : Set (Set α)) (F : ∀ (s : Set α) (hi : s ∈ A), C(s, β))
   (hF :
@@ -414,8 +487,7 @@ variable (A : Set (Set α)) (F : ∀ (s : Set α) (hi : s ∈ A), C(s, β))
       F s hs ⟨x, hxi⟩ = F t ht ⟨x, hxj⟩)
   (hA : ∀ x : α, ∃ i ∈ A, i ∈ nhds x)
 
-include hF hA
-
+#print ContinuousMap.liftCover' /-
 /-- A family `F s` of continuous maps `C(s, β)`, where (1) the domains `s` are taken from a set `A`
 of sets in `α` which contain a neighbourhood of each point in `α` and (2) the functions `F s` agree
 pairwise on intersections, can be glued to construct a continuous map in `C(α, β)`. -/
@@ -428,19 +500,24 @@ noncomputable def liftCover' : C(α, β) :=
   obtain ⟨s, hs, hsx⟩ := hA x
   exact ⟨⟨s, hs⟩, hsx⟩
 #align continuous_map.lift_cover' ContinuousMap.liftCover'
+-/
 
 variable {A F hF hA}
 
+#print ContinuousMap.liftCover_coe' /-
 @[simp]
 theorem liftCover_coe' {s : Set α} {hs : s ∈ A} (x : s) : liftCover' A F hF hA x = F s hs x :=
   let x' : (coe : A → Set α) ⟨s, hs⟩ := x
   liftCover_coe x'
 #align continuous_map.lift_cover_coe' ContinuousMap.liftCover_coe'
+-/
 
+#print ContinuousMap.liftCover_restrict' /-
 @[simp]
 theorem liftCover_restrict' {s : Set α} {hs : s ∈ A} : (liftCover' A F hF hA).restrict s = F s hs :=
   ext <| liftCover_coe'
 #align continuous_map.lift_cover_restrict' ContinuousMap.liftCover_restrict'
+-/
 
 end Gluing
 
@@ -475,16 +552,20 @@ theorem coe_refl : (Homeomorph.refl α : C(α, α)) = ContinuousMap.id α :=
 #align homeomorph.coe_refl Homeomorph.coe_refl
 -/
 
+#print Homeomorph.coe_trans /-
 @[simp]
 theorem coe_trans : (f.trans g : C(α, γ)) = (g : C(β, γ)).comp f :=
   rfl
 #align homeomorph.coe_trans Homeomorph.coe_trans
+-/
 
+#print Homeomorph.symm_comp_toContinuousMap /-
 /-- Left inverse to a continuous map from a homeomorphism, mirroring `equiv.symm_comp_self`. -/
 @[simp]
 theorem symm_comp_toContinuousMap : (f.symm : C(β, α)).comp (f : C(α, β)) = ContinuousMap.id α := by
   rw [← coeTrans, self_trans_symm, coe_refl]
 #align homeomorph.symm_comp_to_continuous_map Homeomorph.symm_comp_toContinuousMap
+-/
 
 #print Homeomorph.toContinuousMap_comp_symm /-
 /-- Right inverse to a continuous map from a homeomorphism, mirroring `equiv.self_comp_symm`. -/

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

@@ -50,7 +50,7 @@ section
 
 You should extend this class when you extend `continuous_map`. -/
 class ContinuousMapClass (F : Type _) (α β : outParam <| Type _) [TopologicalSpace α]
-  [TopologicalSpace β] extends FunLike F α fun _ => β where
+    [TopologicalSpace β] extends FunLike F α fun _ => β where
   map_continuous (f : F) : Continuous f
 #align continuous_map_class ContinuousMapClass
 -/

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

@@ -464,11 +464,9 @@ def toContinuousMap (e : α ≃ₜ β) : C(α, β) :=
 instance : Coe (α ≃ₜ β) C(α, β) :=
   ⟨Homeomorph.toContinuousMap⟩
 
-/- warning: homeomorph.to_continuous_map_as_coe clashes with [anonymous] -> [anonymous]
-Case conversion may be inaccurate. Consider using '#align homeomorph.to_continuous_map_as_coe [anonymous]ₓ'. -/
-theorem [anonymous] : f.toContinuousMap = f :=
+theorem toContinuousMap_as_coe : f.toContinuousMap = f :=
   rfl
-#align homeomorph.to_continuous_map_as_coe [anonymous]
+#align homeomorph.to_continuous_map_as_coe Homeomorph.toContinuousMap_as_coe
 
 #print Homeomorph.coe_refl /-
 @[simp]

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

@@ -67,22 +67,10 @@ variable {F α β : Type _} [TopologicalSpace α] [TopologicalSpace β] [Continu
 
 include β
 
-/- warning: map_continuous_at -> map_continuousAt is a dubious translation:
-lean 3 declaration is
-  forall {F : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : TopologicalSpace.{u3} β] [_inst_3 : ContinuousMapClass.{u1, u2, u3} F α β _inst_1 _inst_2] (f : F) (a : α), ContinuousAt.{u2, u3} α β _inst_1 _inst_2 (coeFn.{succ u1, max (succ u2) (succ u3)} F (fun (_x : F) => α -> β) (FunLike.hasCoeToFun.{succ u1, succ u2, succ u3} F α (fun (_x : α) => β) (ContinuousMapClass.toFunLike.{u1, u2, u3} F α β _inst_1 _inst_2 _inst_3)) f) a
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 theorem map_continuousAt (f : F) (a : α) : ContinuousAt f a :=
   (map_continuous f).ContinuousAt
 #align map_continuous_at map_continuousAt
 
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 theorem map_continuousWithinAt (f : F) (s : Set α) (a : α) : ContinuousWithinAt f s a :=
   (map_continuous f).ContinuousWithinAt
 #align map_continuous_within_at map_continuousWithinAt
@@ -113,12 +101,6 @@ directly. -/
 instance : CoeFun C(α, β) fun _ => α → β :=
   FunLike.hasCoeToFun
 
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 @[simp]
 theorem toFun_eq_coe {f : C(α, β)} : f.toFun = (f : α → β) :=
   rfl
@@ -127,34 +109,16 @@ theorem toFun_eq_coe {f : C(α, β)} : f.toFun = (f : α → β) :=
 -- this must come after the coe_to_fun definition
 initialize_simps_projections ContinuousMap (toFun → apply)
 
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 @[protected, simp, norm_cast]
 theorem coe_coe {F : Type _} [ContinuousMapClass F α β] (f : F) : ⇑(f : C(α, β)) = f :=
   rfl
 #align continuous_map.coe_coe ContinuousMap.coe_coe
 
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 @[ext]
 theorem ext {f g : C(α, β)} (h : ∀ a, f a = g a) : f = g :=
   FunLike.ext _ _ h
 #align continuous_map.ext ContinuousMap.ext
 
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 /-- Copy of a `continuous_map` with a new `to_fun` equal to the old one. Useful to fix definitional
 equalities. -/
 protected def copy (f : C(α, β)) (f' : α → β) (h : f' = f) : C(α, β)
@@ -163,111 +127,51 @@ protected def copy (f : C(α, β)) (f' : α → β) (h : f' = f) : C(α, β)
   continuous_toFun := h.symm ▸ f.continuous_toFun
 #align continuous_map.copy ContinuousMap.copy
 
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 @[simp]
 theorem coe_copy (f : C(α, β)) (f' : α → β) (h : f' = f) : ⇑(f.copy f' h) = f' :=
   rfl
 #align continuous_map.coe_copy ContinuousMap.coe_copy
 
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 theorem copy_eq (f : C(α, β)) (f' : α → β) (h : f' = f) : f.copy f' h = f :=
   FunLike.ext' h
 #align continuous_map.copy_eq ContinuousMap.copy_eq
 
 variable {α β} {f g : C(α, β)}
 
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 /-- Deprecated. Use `map_continuous` instead. -/
 protected theorem continuous (f : C(α, β)) : Continuous f :=
   f.continuous_toFun
 #align continuous_map.continuous ContinuousMap.continuous
 
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 @[continuity]
 theorem continuous_set_coe (s : Set C(α, β)) (f : s) : Continuous f :=
   f.1.Continuous
 #align continuous_map.continuous_set_coe ContinuousMap.continuous_set_coe
 
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 /-- Deprecated. Use `map_continuous_at` instead. -/
 protected theorem continuousAt (f : C(α, β)) (x : α) : ContinuousAt f x :=
   f.Continuous.ContinuousAt
 #align continuous_map.continuous_at ContinuousMap.continuousAt
 
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 /-- Deprecated. Use `fun_like.congr_fun` instead. -/
 protected theorem congr_fun {f g : C(α, β)} (H : f = g) (x : α) : f x = g x :=
   H ▸ rfl
 #align continuous_map.congr_fun ContinuousMap.congr_fun
 
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 /-- Deprecated. Use `fun_like.congr_arg` instead. -/
 protected theorem congr_arg (f : C(α, β)) {x y : α} (h : x = y) : f x = f y :=
   h ▸ rfl
 #align continuous_map.congr_arg ContinuousMap.congr_arg
 
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 theorem coe_injective : @Function.Injective C(α, β) (α → β) coeFn := fun f g h => by
   cases f <;> cases g <;> congr
 #align continuous_map.coe_injective ContinuousMap.coe_injective
 
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 @[simp]
 theorem coe_mk (f : α → β) (h : Continuous f) : ⇑(⟨f, h⟩ : C(α, β)) = f :=
   rfl
 #align continuous_map.coe_mk ContinuousMap.coe_mk
 
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 theorem map_specializes (f : C(α, β)) {x y : α} (h : x ⤳ y) : f x ⤳ f y :=
   h.map f.2
 #align continuous_map.map_specializes ContinuousMap.map_specializes
@@ -298,12 +202,6 @@ protected def id : C(α, α) :=
 #align continuous_map.id ContinuousMap.id
 -/
 
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 @[simp]
 theorem coe_id : ⇑(ContinuousMap.id α) = id :=
   rfl
@@ -316,12 +214,6 @@ def const (b : β) : C(α, β) :=
 #align continuous_map.const ContinuousMap.const
 -/
 
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 @[simp]
 theorem coe_const (b : β) : ⇑(const α b) = Function.const α b :=
   rfl
@@ -332,23 +224,11 @@ instance [Inhabited β] : Inhabited C(α, β) :=
 
 variable {α}
 
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 @[simp]
 theorem id_apply (a : α) : ContinuousMap.id α a = a :=
   rfl
 #align continuous_map.id_apply ContinuousMap.id_apply
 
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 @[simp]
 theorem const_apply (b : β) (a : α) : const α b a = b :=
   rfl
@@ -361,101 +241,47 @@ def comp (f : C(β, γ)) (g : C(α, β)) : C(α, γ) :=
 #align continuous_map.comp ContinuousMap.comp
 -/
 
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 @[simp]
 theorem coe_comp (f : C(β, γ)) (g : C(α, β)) : ⇑(comp f g) = f ∘ g :=
   rfl
 #align continuous_map.coe_comp ContinuousMap.coe_comp
 
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 @[simp]
 theorem comp_apply (f : C(β, γ)) (g : C(α, β)) (a : α) : comp f g a = f (g a) :=
   rfl
 #align continuous_map.comp_apply ContinuousMap.comp_apply
 
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 @[simp]
 theorem comp_assoc (f : C(γ, δ)) (g : C(β, γ)) (h : C(α, β)) :
     (f.comp g).comp h = f.comp (g.comp h) :=
   rfl
 #align continuous_map.comp_assoc ContinuousMap.comp_assoc
 
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 @[simp]
 theorem id_comp (f : C(α, β)) : (ContinuousMap.id _).comp f = f :=
   ext fun _ => rfl
 #align continuous_map.id_comp ContinuousMap.id_comp
 
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 @[simp]
 theorem comp_id (f : C(α, β)) : f.comp (ContinuousMap.id _) = f :=
   ext fun _ => rfl
 #align continuous_map.comp_id ContinuousMap.comp_id
 
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 @[simp]
 theorem const_comp (c : γ) (f : C(α, β)) : (const β c).comp f = const α c :=
   ext fun _ => rfl
 #align continuous_map.const_comp ContinuousMap.const_comp
 
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 @[simp]
 theorem comp_const (f : C(β, γ)) (b : β) : f.comp (const α b) = const α (f b) :=
   ext fun _ => rfl
 #align continuous_map.comp_const ContinuousMap.comp_const
 
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 theorem cancel_right {f₁ f₂ : C(β, γ)} {g : C(α, β)} (hg : Surjective g) :
     f₁.comp g = f₂.comp g ↔ f₁ = f₂ :=
   ⟨fun h => ext <| hg.forall.2 <| FunLike.ext_iff.1 h, congr_arg _⟩
 #align continuous_map.cancel_right ContinuousMap.cancel_right
 
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 theorem cancel_left {f : C(β, γ)} {g₁ g₂ : C(α, β)} (hf : Injective f) :
     f.comp g₁ = f.comp g₂ ↔ g₁ = g₂ :=
   ⟨fun h => ext fun a => hf <| by rw [← comp_apply, h, comp_apply], congr_arg _⟩
@@ -470,12 +296,6 @@ section Prod
 variable {α₁ α₂ β₁ β₂ : Type _} [TopologicalSpace α₁] [TopologicalSpace α₂] [TopologicalSpace β₁]
   [TopologicalSpace β₂]
 
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 /-- Given two continuous maps `f` and `g`, this is the continuous map `x ↦ (f x, g x)`. -/
 def prodMk (f : C(α, β₁)) (g : C(α, β₂)) : C(α, β₁ × β₂)
     where
@@ -483,12 +303,6 @@ def prodMk (f : C(α, β₁)) (g : C(α, β₂)) : C(α, β₁ × β₂)
   continuous_toFun := Continuous.prod_mk f.Continuous g.Continuous
 #align continuous_map.prod_mk ContinuousMap.prodMk
 
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 /-- Given two continuous maps `f` and `g`, this is the continuous map `(x, y) ↦ (f x, g y)`. -/
 @[simps]
 def prodMap (f : C(α₁, α₂)) (g : C(β₁, β₂)) : C(α₁ × β₁, α₂ × β₂)
@@ -497,12 +311,6 @@ def prodMap (f : C(α₁, α₂)) (g : C(β₁, β₂)) : C(α₁ × β₁, α
   continuous_toFun := Continuous.prod_map f.Continuous g.Continuous
 #align continuous_map.prod_map ContinuousMap.prodMap
 
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 @[simp]
 theorem prod_eval (f : C(α, β₁)) (g : C(α, β₂)) (a : α) : (prodMk f g) a = (f a, g a) :=
   rfl
@@ -520,12 +328,6 @@ def pi (f : ∀ i, C(A, X i)) : C(A, ∀ i, X i) where toFun (a : A) (i : I) :=
 #align continuous_map.pi ContinuousMap.pi
 -/
 
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 @[simp]
 theorem pi_eval (f : ∀ i, C(A, X i)) (a : A) : (pi f) a = fun i : I => (f i) a :=
   rfl
@@ -544,46 +346,22 @@ def restrict (f : C(α, β)) : C(s, β) :=
 #align continuous_map.restrict ContinuousMap.restrict
 -/
 
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 @[simp]
 theorem coe_restrict (f : C(α, β)) : ⇑(f.restrict s) = f ∘ coe :=
   rfl
 #align continuous_map.coe_restrict ContinuousMap.coe_restrict
 
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 @[simp]
 theorem restrict_apply (f : C(α, β)) (s : Set α) (x : s) : f.restrict s x = f x :=
   rfl
 #align continuous_map.restrict_apply ContinuousMap.restrict_apply
 
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 @[simp]
 theorem restrict_apply_mk (f : C(α, β)) (s : Set α) (x : α) (hx : x ∈ s) :
     f.restrict s ⟨x, hx⟩ = f x :=
   rfl
 #align continuous_map.restrict_apply_mk ContinuousMap.restrict_apply_mk
 
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 /-- The restriction of a continuous map to the preimage of a set. -/
 @[simps]
 def restrictPreimage (f : C(α, β)) (s : Set β) : C(f ⁻¹' s, s) :=
@@ -600,9 +378,6 @@ variable {ι : Type _} (S : ι → Set α) (φ : ∀ i : ι, C(S i, β))
 
 include hφ hS
 
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 /-- A family `φ i` of continuous maps `C(S i, β)`, where the domains `S i` contain a neighbourhood
 of each point in `α` and the functions `φ i` agree pairwise on intersections, can be glued to
 construct a continuous map in `C(α, β)`. -/
@@ -621,17 +396,11 @@ noncomputable def liftCover : C(α, β) :=
 
 variable {S φ hφ hS}
 
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 @[simp]
 theorem liftCover_coe {i : ι} (x : S i) : liftCover S φ hφ hS x = φ i x :=
   Set.liftCover_coe _
 #align continuous_map.lift_cover_coe ContinuousMap.liftCover_coe
 
-/- warning: continuous_map.lift_cover_restrict -> ContinuousMap.liftCover_restrict is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_map.lift_cover_restrict ContinuousMap.liftCover_restrictₓ'. -/
 @[simp]
 theorem liftCover_restrict {i : ι} : (liftCover S φ hφ hS).restrict (S i) = φ i :=
   ext <| liftCover_coe
@@ -647,9 +416,6 @@ variable (A : Set (Set α)) (F : ∀ (s : Set α) (hi : s ∈ A), C(s, β))
 
 include hF hA
 
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 /-- A family `F s` of continuous maps `C(s, β)`, where (1) the domains `s` are taken from a set `A`
 of sets in `α` which contain a neighbourhood of each point in `α` and (2) the functions `F s` agree
 pairwise on intersections, can be glued to construct a continuous map in `C(α, β)`. -/
@@ -665,18 +431,12 @@ noncomputable def liftCover' : C(α, β) :=
 
 variable {A F hF hA}
 
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-<too large>
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 @[simp]
 theorem liftCover_coe' {s : Set α} {hs : s ∈ A} (x : s) : liftCover' A F hF hA x = F s hs x :=
   let x' : (coe : A → Set α) ⟨s, hs⟩ := x
   liftCover_coe x'
 #align continuous_map.lift_cover_coe' ContinuousMap.liftCover_coe'
 
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 @[simp]
 theorem liftCover_restrict' {s : Set α} {hs : s ∈ A} : (liftCover' A F hF hA).restrict s = F s hs :=
   ext <| liftCover_coe'
@@ -705,11 +465,6 @@ instance : Coe (α ≃ₜ β) C(α, β) :=
   ⟨Homeomorph.toContinuousMap⟩
 
 /- warning: homeomorph.to_continuous_map_as_coe clashes with [anonymous] -> [anonymous]
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 theorem [anonymous] : f.toContinuousMap = f :=
   rfl
@@ -722,23 +477,11 @@ theorem coe_refl : (Homeomorph.refl α : C(α, α)) = ContinuousMap.id α :=
 #align homeomorph.coe_refl Homeomorph.coe_refl
 -/
 
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 @[simp]
 theorem coe_trans : (f.trans g : C(α, γ)) = (g : C(β, γ)).comp f :=
   rfl
 #align homeomorph.coe_trans Homeomorph.coe_trans
 
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 /-- Left inverse to a continuous map from a homeomorphism, mirroring `equiv.symm_comp_self`. -/
 @[simp]
 theorem symm_comp_toContinuousMap : (f.symm : C(β, α)).comp (f : C(α, β)) = ContinuousMap.id α := by

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

@@ -282,11 +282,7 @@ The continuous functions from `α` to `β` are the same as the plain functions w
 -/
 @[simps]
 def equivFnOfDiscrete [DiscreteTopology α] : C(α, β) ≃ (α → β) :=
-  ⟨fun f => f, fun f => ⟨f, continuous_of_discreteTopology⟩, fun f =>
-    by
-    ext
-    rfl, fun f => by
-    ext
+  ⟨fun f => f, fun f => ⟨f, continuous_of_discreteTopology⟩, fun f => by ext; rfl, fun f => by ext;
     rfl⟩
 #align continuous_map.equiv_fn_of_discrete ContinuousMap.equivFnOfDiscrete
 -/

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

@@ -605,10 +605,7 @@ variable {ι : Type _} (S : ι → Set α) (φ : ∀ i : ι, C(S i, β))
 include hφ hS
 
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 Case conversion may be inaccurate. Consider using '#align continuous_map.lift_cover ContinuousMap.liftCoverₓ'. -/
 /-- A family `φ i` of continuous maps `C(S i, β)`, where the domains `S i` contain a neighbourhood
 of each point in `α` and the functions `φ i` agree pairwise on intersections, can be glued to
@@ -629,10 +626,7 @@ noncomputable def liftCover : C(α, β) :=
 variable {S φ hφ hS}
 
 /- warning: continuous_map.lift_cover_coe -> ContinuousMap.liftCover_coe is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align continuous_map.lift_cover_coe ContinuousMap.liftCover_coeₓ'. -/
 @[simp]
 theorem liftCover_coe {i : ι} (x : S i) : liftCover S φ hφ hS x = φ i x :=
@@ -640,10 +634,7 @@ theorem liftCover_coe {i : ι} (x : S i) : liftCover S φ hφ hS x = φ i x :=
 #align continuous_map.lift_cover_coe ContinuousMap.liftCover_coe
 
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 Case conversion may be inaccurate. Consider using '#align continuous_map.lift_cover_restrict ContinuousMap.liftCover_restrictₓ'. -/
 @[simp]
 theorem liftCover_restrict {i : ι} : (liftCover S φ hφ hS).restrict (S i) = φ i :=
@@ -661,10 +652,7 @@ variable (A : Set (Set α)) (F : ∀ (s : Set α) (hi : s ∈ A), C(s, β))
 include hF hA
 
 /- warning: continuous_map.lift_cover' -> ContinuousMap.liftCover' is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align continuous_map.lift_cover' ContinuousMap.liftCover'ₓ'. -/
 /-- A family `F s` of continuous maps `C(s, β)`, where (1) the domains `s` are taken from a set `A`
 of sets in `α` which contain a neighbourhood of each point in `α` and (2) the functions `F s` agree
@@ -682,10 +670,7 @@ noncomputable def liftCover' : C(α, β) :=
 variable {A F hF hA}
 
 /- warning: continuous_map.lift_cover_coe' -> ContinuousMap.liftCover_coe' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align continuous_map.lift_cover_coe' ContinuousMap.liftCover_coe'ₓ'. -/
 @[simp]
 theorem liftCover_coe' {s : Set α} {hs : s ∈ A} (x : s) : liftCover' A F hF hA x = F s hs x :=
@@ -694,10 +679,7 @@ theorem liftCover_coe' {s : Set α} {hs : s ∈ A} (x : s) : liftCover' A F hF h
 #align continuous_map.lift_cover_coe' ContinuousMap.liftCover_coe'
 
 /- warning: continuous_map.lift_cover_restrict' -> ContinuousMap.liftCover_restrict' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align continuous_map.lift_cover_restrict' ContinuousMap.liftCover_restrict'ₓ'. -/
 @[simp]
 theorem liftCover_restrict' {s : Set α} {hs : s ∈ A} : (liftCover' A F hF hA).restrict s = F s hs :=

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

@@ -618,7 +618,7 @@ noncomputable def liftCover : C(α, β) :=
   have H : (⋃ i, S i) = Set.univ := by
     rw [Set.eq_univ_iff_forall]
     intro x
-    rw [Set.mem_unionᵢ]
+    rw [Set.mem_iUnion]
     obtain ⟨i, hi⟩ := hS x
     exact ⟨i, mem_of_mem_nhds hi⟩
   refine' ⟨Set.liftCover S (fun i => φ i) hφ H, continuous_of_cover_nhds hS fun i => _⟩

mathlib commit https://github.com/leanprover-community/mathlib/commit/55d771df074d0dd020139ee1cd4b95521422df9f

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Nicolò Cavalleri
 
 ! This file was ported from Lean 3 source module topology.continuous_function.basic
-! leanprover-community/mathlib commit 6efec6bb9fcaed3cf1baaddb2eaadd8a2a06679c
+! leanprover-community/mathlib commit 55d771df074d0dd020139ee1cd4b95521422df9f
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -621,11 +621,9 @@ noncomputable def liftCover : C(α, β) :=
     rw [Set.mem_unionᵢ]
     obtain ⟨i, hi⟩ := hS x
     exact ⟨i, mem_of_mem_nhds hi⟩
-  refine' ⟨Set.liftCover S (fun i => φ i) hφ H, continuous_subtype_nhds_cover hS _⟩
-  intro i
-  convert(φ i).Continuous
-  ext x
-  exact Set.liftCover_coe x
+  refine' ⟨Set.liftCover S (fun i => φ i) hφ H, continuous_of_cover_nhds hS fun i => _⟩
+  rw [continuousOn_iff_continuous_restrict]
+  simpa only [Set.restrict, Set.liftCover_coe] using (φ i).Continuous
 #align continuous_map.lift_cover ContinuousMap.liftCover
 
 variable {S φ hφ hS}

mathlib commit https://github.com/leanprover-community/mathlib/commit/290a7ba01fbcab1b64757bdaa270d28f4dcede35

@@ -559,11 +559,23 @@ theorem coe_restrict (f : C(α, β)) : ⇑(f.restrict s) = f ∘ coe :=
   rfl
 #align continuous_map.coe_restrict ContinuousMap.coe_restrict
 
+/- warning: continuous_map.restrict_apply -> ContinuousMap.restrict_apply is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : TopologicalSpace.{u2} β] (f : ContinuousMap.{u1, u2} α β _inst_1 _inst_2) (s : Set.{u1} α) (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) β (Subtype.topologicalSpace.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) _inst_1) _inst_2) (fun (_x : ContinuousMap.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) β (Subtype.topologicalSpace.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) _inst_1) _inst_2) => (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) -> β) (ContinuousMap.hasCoeToFun.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) β (Subtype.topologicalSpace.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) _inst_1) _inst_2) (ContinuousMap.restrict.{u1, u2} α β _inst_1 _inst_2 s f) x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} α β _inst_1 _inst_2) (fun (_x : ContinuousMap.{u1, u2} α β _inst_1 _inst_2) => α -> β) (ContinuousMap.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))))) x))
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+Case conversion may be inaccurate. Consider using '#align continuous_map.restrict_apply ContinuousMap.restrict_applyₓ'. -/
 @[simp]
 theorem restrict_apply (f : C(α, β)) (s : Set α) (x : s) : f.restrict s x = f x :=
   rfl
 #align continuous_map.restrict_apply ContinuousMap.restrict_apply
 
+/- warning: continuous_map.restrict_apply_mk -> ContinuousMap.restrict_apply_mk is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : TopologicalSpace.{u2} β] (f : ContinuousMap.{u1, u2} α β _inst_1 _inst_2) (s : Set.{u1} α) (x : α) (hx : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) β (Subtype.topologicalSpace.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) _inst_1) _inst_2) (fun (_x : ContinuousMap.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) β (Subtype.topologicalSpace.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) _inst_1) _inst_2) => (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) -> β) (ContinuousMap.hasCoeToFun.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) β (Subtype.topologicalSpace.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) _inst_1) _inst_2) (ContinuousMap.restrict.{u1, u2} α β _inst_1 _inst_2 s f) (Subtype.mk.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) x hx)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} α β _inst_1 _inst_2) (fun (_x : ContinuousMap.{u1, u2} α β _inst_1 _inst_2) => α -> β) (ContinuousMap.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) f x)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align continuous_map.restrict_apply_mk ContinuousMap.restrict_apply_mkₓ'. -/
 @[simp]
 theorem restrict_apply_mk (f : C(α, β)) (s : Set α) (x : α) (hx : x ∈ s) :
     f.restrict s ⟨x, hx⟩ = f x :=

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

@@ -611,7 +611,7 @@ noncomputable def liftCover : C(α, β) :=
     exact ⟨i, mem_of_mem_nhds hi⟩
   refine' ⟨Set.liftCover S (fun i => φ i) hφ H, continuous_subtype_nhds_cover hS _⟩
   intro i
-  convert (φ i).Continuous
+  convert(φ i).Continuous
   ext x
   exact Set.liftCover_coe x
 #align continuous_map.lift_cover ContinuousMap.liftCover

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

@@ -745,24 +745,24 @@ theorem coe_trans : (f.trans g : C(α, γ)) = (g : C(β, γ)).comp f :=
   rfl
 #align homeomorph.coe_trans Homeomorph.coe_trans
 
-/- warning: homeomorph.symm_comp_to_continuous_map -> Homeomorph.symm_comp_to_continuousMap is a dubious translation:
+/- warning: homeomorph.symm_comp_to_continuous_map -> Homeomorph.symm_comp_toContinuousMap is a dubious translation:
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : TopologicalSpace.{u2} β] (f : Homeomorph.{u1, u2} α β _inst_1 _inst_2), Eq.{succ u1} (ContinuousMap.{u1, u1} α α _inst_1 _inst_1) (ContinuousMap.comp.{u1, u2, u1} α β α _inst_1 _inst_2 _inst_1 ((fun (a : Sort.{max (succ u2) (succ u1)}) (b : Sort.{max (succ u2) (succ u1)}) [self : HasLiftT.{max (succ u2) (succ u1), max (succ u2) (succ u1)} a b] => self.0) (Homeomorph.{u2, u1} β α _inst_2 _inst_1) (ContinuousMap.{u2, u1} β α _inst_2 _inst_1) (HasLiftT.mk.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Homeomorph.{u2, u1} β α _inst_2 _inst_1) (ContinuousMap.{u2, u1} β α _inst_2 _inst_1) (CoeTCₓ.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Homeomorph.{u2, u1} β α _inst_2 _inst_1) (ContinuousMap.{u2, u1} β α _inst_2 _inst_1) (coeBase.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Homeomorph.{u2, u1} β α _inst_2 _inst_1) (ContinuousMap.{u2, u1} β α _inst_2 _inst_1) (Homeomorph.ContinuousMap.hasCoe.{u2, u1} β α _inst_2 _inst_1)))) (Homeomorph.symm.{u1, u2} α β _inst_1 _inst_2 f)) ((fun (a : Sort.{max (succ u1) (succ u2)}) (b : Sort.{max (succ u1) (succ u2)}) [self : HasLiftT.{max (succ u1) (succ u2), max (succ u1) (succ u2)} a b] => self.0) (Homeomorph.{u1, u2} α β _inst_1 _inst_2) (ContinuousMap.{u1, u2} α β _inst_1 _inst_2) (HasLiftT.mk.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Homeomorph.{u1, u2} α β _inst_1 _inst_2) (ContinuousMap.{u1, u2} α β _inst_1 _inst_2) (CoeTCₓ.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Homeomorph.{u1, u2} α β _inst_1 _inst_2) (ContinuousMap.{u1, u2} α β _inst_1 _inst_2) (coeBase.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Homeomorph.{u1, u2} α β _inst_1 _inst_2) (ContinuousMap.{u1, u2} α β _inst_1 _inst_2) (Homeomorph.ContinuousMap.hasCoe.{u1, u2} α β _inst_1 _inst_2)))) f)) (ContinuousMap.id.{u1} α _inst_1)
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : TopologicalSpace.{u1} β] (f : Homeomorph.{u2, u1} α β _inst_1 _inst_2), Eq.{succ u2} (ContinuousMap.{u2, u2} α α _inst_1 _inst_1) (ContinuousMap.comp.{u2, u1, u2} α β α _inst_1 _inst_2 _inst_1 (Homeomorph.toContinuousMap.{u1, u2} β α _inst_2 _inst_1 (Homeomorph.symm.{u2, u1} α β _inst_1 _inst_2 f)) (Homeomorph.toContinuousMap.{u2, u1} α β _inst_1 _inst_2 f)) (ContinuousMap.id.{u2} α _inst_1)
-Case conversion may be inaccurate. Consider using '#align homeomorph.symm_comp_to_continuous_map Homeomorph.symm_comp_to_continuousMapₓ'. -/
+Case conversion may be inaccurate. Consider using '#align homeomorph.symm_comp_to_continuous_map Homeomorph.symm_comp_toContinuousMapₓ'. -/
 /-- Left inverse to a continuous map from a homeomorphism, mirroring `equiv.symm_comp_self`. -/
 @[simp]
-theorem symm_comp_to_continuousMap : (f.symm : C(β, α)).comp (f : C(α, β)) = ContinuousMap.id α :=
-  by rw [← coeTrans, self_trans_symm, coe_refl]
-#align homeomorph.symm_comp_to_continuous_map Homeomorph.symm_comp_to_continuousMap
+theorem symm_comp_toContinuousMap : (f.symm : C(β, α)).comp (f : C(α, β)) = ContinuousMap.id α := by
+  rw [← coeTrans, self_trans_symm, coe_refl]
+#align homeomorph.symm_comp_to_continuous_map Homeomorph.symm_comp_toContinuousMap
 
-#print Homeomorph.to_continuousMap_comp_symm /-
+#print Homeomorph.toContinuousMap_comp_symm /-
 /-- Right inverse to a continuous map from a homeomorphism, mirroring `equiv.self_comp_symm`. -/
 @[simp]
-theorem to_continuousMap_comp_symm : (f : C(α, β)).comp (f.symm : C(β, α)) = ContinuousMap.id β :=
-  by rw [← coeTrans, symm_trans_self, coe_refl]
-#align homeomorph.to_continuous_map_comp_symm Homeomorph.to_continuousMap_comp_symm
+theorem toContinuousMap_comp_symm : (f : C(α, β)).comp (f.symm : C(β, α)) = ContinuousMap.id β := by
+  rw [← coeTrans, symm_trans_self, coe_refl]
+#align homeomorph.to_continuous_map_comp_symm Homeomorph.toContinuousMap_comp_symm
 -/
 
 end Homeomorph

mathlib commit https://github.com/leanprover-community/mathlib/commit/22131150f88a2d125713ffa0f4693e3355b1eb49

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Nicolò Cavalleri
 
 ! This file was ported from Lean 3 source module topology.continuous_function.basic
-! leanprover-community/mathlib commit 50832daea47b195a48b5b33b1c8b2162c48c3afc
+! leanprover-community/mathlib commit 6efec6bb9fcaed3cf1baaddb2eaadd8a2a06679c
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -559,13 +559,24 @@ theorem coe_restrict (f : C(α, β)) : ⇑(f.restrict s) = f ∘ coe :=
   rfl
 #align continuous_map.coe_restrict ContinuousMap.coe_restrict
 
+@[simp]
+theorem restrict_apply (f : C(α, β)) (s : Set α) (x : s) : f.restrict s x = f x :=
+  rfl
+#align continuous_map.restrict_apply ContinuousMap.restrict_apply
+
+@[simp]
+theorem restrict_apply_mk (f : C(α, β)) (s : Set α) (x : α) (hx : x ∈ s) :
+    f.restrict s ⟨x, hx⟩ = f x :=
+  rfl
+#align continuous_map.restrict_apply_mk ContinuousMap.restrict_apply_mk
+
 /- warning: continuous_map.restrict_preimage -> ContinuousMap.restrictPreimage is a dubious translation:
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : TopologicalSpace.{u2} β] (f : ContinuousMap.{u1, u2} α β _inst_1 _inst_2) (s : Set.{u2} β), ContinuousMap.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.preimage.{u1, u2} α β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} α β _inst_1 _inst_2) (fun (_x : ContinuousMap.{u1, u2} α β _inst_1 _inst_2) => α -> β) (ContinuousMap.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) f) s)) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) (Subtype.topologicalSpace.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.preimage.{u1, u2} α β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} α β _inst_1 _inst_2) (fun (_x : ContinuousMap.{u1, u2} α β _inst_1 _inst_2) => α -> β) (ContinuousMap.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) f) s)) _inst_1) (Subtype.topologicalSpace.{u2} β (fun (x : β) => Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) _inst_2)
 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align continuous_map.restrict_preimage ContinuousMap.restrictPreimageₓ'. -/
-/-- The restriction of a continuous map onto the preimage of a set. -/
+/-- The restriction of a continuous map to the preimage of a set. -/
 @[simps]
 def restrictPreimage (f : C(α, β)) (s : Set β) : C(f ⁻¹' s, s) :=
   ⟨s.restrictPreimage f, continuous_iff_continuousAt.mpr fun x => f.2.ContinuousAt.restrictPreimage⟩

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

Also do the same for "/-A". This is a purely aesthetic change (and exhaustive).

@@ -594,7 +594,7 @@ instance : Coe (α ≃ₜ β) C(α, β) :=
   ⟨Homeomorph.toContinuousMap⟩
 
 -- Porting note: Syntactic tautology
-/-theorem toContinuousMap_as_coe : f.toContinuousMap = f :=
+/- theorem toContinuousMap_as_coe : f.toContinuousMap = f :=
   rfl
 -/
 #noalign homeomorph.to_continuous_map_as_coe

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)

@@ -580,7 +580,6 @@ end Lift
 namespace Homeomorph
 
 variable {α β γ : Type*} [TopologicalSpace α] [TopologicalSpace β] [TopologicalSpace γ]
-
 variable (f : α ≃ₜ β) (g : β ≃ₜ γ)
 
 /-- The forward direction of a homeomorphism, as a bundled continuous map. -/

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".

@@ -487,7 +487,7 @@ noncomputable def liftCover' : C(α, β) := by
 
 variable {A F hF hA}
 
--- porting note: did not need `by delta liftCover'; exact` in mathlib3; goal was
+-- Porting note: did not need `by delta liftCover'; exact` in mathlib3; goal was
 -- closed by `liftCover_coe x'`
 -- Might be something to do with the `let`s in the definition of `liftCover'`?
 @[simp]
@@ -496,7 +496,7 @@ theorem liftCover_coe' {s : Set α} {hs : s ∈ A} (x : s) : liftCover' A F hF h
   by delta liftCover'; exact liftCover_coe x'
 #align continuous_map.lift_cover_coe' ContinuousMap.liftCover_coe'
 
--- porting note: porting program suggested `ext <| liftCover_coe'`
+-- Porting note: porting program suggested `ext <| liftCover_coe'`
 @[simp]
 theorem liftCover_restrict' {s : Set α} {hs : s ∈ A} :
     (liftCover' A F hF hA).restrict s = F s hs := ext <| liftCover_coe' (hF := hF) (hA := hA)

Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>

@@ -52,7 +52,7 @@ end
 
 export ContinuousMapClass (map_continuous)
 
-attribute [continuity] map_continuous
+attribute [continuity, fun_prop] map_continuous
 
 section ContinuousMapClass
 

Also fix GeneralizedContinuedFraction.of_convergence: it worked for the Preorder.topology only.

@@ -19,6 +19,7 @@ be satisfied by itself and all stricter types.
 
 
 open Function
+open scoped Topology
 
 /-- The type of continuous maps from `α` to `β`.
 
@@ -440,7 +441,7 @@ section Gluing
 
 variable {ι : Type*} (S : ι → Set α) (φ : ∀ i : ι, C(S i, β))
   (hφ : ∀ (i j) (x : α) (hxi : x ∈ S i) (hxj : x ∈ S j), φ i ⟨x, hxi⟩ = φ j ⟨x, hxj⟩)
-  (hS : ∀ x : α, ∃ i, S i ∈ nhds x)
+  (hS : ∀ x : α, ∃ i, S i ∈ 𝓝 x)
 
 /-- A family `φ i` of continuous maps `C(S i, β)`, where the domains `S i` contain a neighbourhood
 of each point in `α` and the functions `φ i` agree pairwise on intersections, can be glued to
@@ -470,7 +471,7 @@ theorem liftCover_restrict {i : ι} : (liftCover S φ hφ hS).restrict (S i) = 
 variable (A : Set (Set α)) (F : ∀ s ∈ A, C(s, β))
   (hF : ∀ (s) (hs : s ∈ A) (t) (ht : t ∈ A) (x : α) (hxi : x ∈ s) (hxj : x ∈ t),
     F s hs ⟨x, hxi⟩ = F t ht ⟨x, hxj⟩)
-  (hA : ∀ x : α, ∃ i ∈ A, i ∈ nhds x)
+  (hA : ∀ x : α, ∃ i ∈ A, i ∈ 𝓝 x)
 
 /-- A family `F s` of continuous maps `C(s, β)`, where (1) the domains `s` are taken from a set `A`
 of sets in `α` which contain a neighbourhood of each point in `α` and (2) the functions `F s` agree

The FunLike hierarchy is very big and gets scanned through each time we need a coercion (via the CoeFun instance). It looks like unbundled inheritance suits Lean 4 better here. The only class that still extends FunLike is EquivLike, since that has a custom coe_injective' field that is easier to implement. All other classes should take FunLike or EquivLike as a parameter.

Zulip thread

Important changes

Previously, morphism classes would be Type-valued and extend FunLike:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  extends FunLike F A B :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

After this PR, they should be Prop-valued and take FunLike as a parameter:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  [FunLike F A B] : Prop :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

(Note that A B stay marked as outParam even though they are not purely required to be so due to the FunLike parameter already filling them in. This is required to see through type synonyms, which is important in the category theory library. Also, I think keeping them as outParam is slightly faster.)

Similarly, MyEquivClass should take EquivLike as a parameter.

As a result, every mention of [MyHomClass F A B] should become [FunLike F A B] [MyHomClass F A B].

Remaining issues

Slower (failing) search

While overall this gives some great speedups, there are some cases that are noticeably slower. In particular, a failing application of a lemma such as map_mul is more expensive. This is due to suboptimal processing of arguments. For example:

variable [FunLike F M N] [Mul M] [Mul N] (f : F) (x : M) (y : M)

theorem map_mul [MulHomClass F M N] : f (x * y) = f x * f y

example [AddHomClass F A B] : f (x * y) = f x * f y := map_mul f _ _

Before this PR, applying map_mul f gives the goals [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Since M and N are out_params, [MulHomClass F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found.

After this PR, the goals become [FunLike F ?M ?N] [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Now [FunLike F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found, before trying MulHomClass F M N which fails. Since the Mul hierarchy is very big, this can be slow to fail, especially when there is no such Mul instance.

A long-term but harder to achieve solution would be to specify the order in which instance goals get solved. For example, we'd like to change the arguments to map_mul to look like [FunLike F M N] [Mul M] [Mul N] [highPriority <| MulHomClass F M N] because MulHomClass fails or succeeds much faster than the others.

As a consequence, the simpNF linter is much slower since by design it tries and fails to apply many map_ lemmas. The same issue occurs a few times in existing calls to simp [map_mul], where map_mul is tried "too soon" and fails. Thanks to the speedup of leanprover/lean4#2478 the impact is very limited, only in files that already were close to the timeout.

simp not firing sometimes

This affects map_smulₛₗ and related definitions. For simp lemmas Lean apparently uses a slightly different mechanism to find instances, so that rw can find every argument to map_smulₛₗ successfully but simp can't: leanprover/lean4#3701.

Missing instances due to unification failing

Especially in the category theory library, we might sometimes have a type A which is also accessible as a synonym (Bundled A hA).1. Instance synthesis doesn't always work if we have f : A →* B but x * y : (Bundled A hA).1 or vice versa. This seems to be mostly fixed by keeping A B as outParams in MulHomClass F A B. (Presumably because Lean will do a definitional check A =?= (Bundled A hA).1 instead of using the syntax in the discrimination tree.)

Workaround for issues

The timeouts can be worked around for now by specifying which map_mul we mean, either as map_mul f for some explicit f, or as e.g. MonoidHomClass.map_mul.

map_smulₛₗ not firing as simp lemma can be worked around by going back to the pre-FunLike situation and making LinearMap.map_smulₛₗ a simp lemma instead of the generic map_smulₛₗ. Writing simp [map_smulₛₗ _] also works.

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott@tqft.net> Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

@@ -41,8 +41,8 @@ section
 /-- `ContinuousMapClass F α β` states that `F` is a type of continuous maps.
 
 You should extend this class when you extend `ContinuousMap`. -/
-class ContinuousMapClass (F : Type*) (α β : outParam <| Type*) [TopologicalSpace α]
-  [TopologicalSpace β] extends DFunLike F α (fun _ => β) where
+class ContinuousMapClass (F α β : Type*) [TopologicalSpace α] [TopologicalSpace β]
+    [FunLike F α β] : Prop where
   /-- Continuity -/
   map_continuous (f : F) : Continuous f
 #align continuous_map_class ContinuousMapClass
@@ -55,7 +55,8 @@ attribute [continuity] map_continuous
 
 section ContinuousMapClass
 
-variable {F α β : Type*} [TopologicalSpace α] [TopologicalSpace β] [ContinuousMapClass F α β]
+variable {F α β : Type*} [TopologicalSpace α] [TopologicalSpace β] [FunLike F α β]
+variable [ContinuousMapClass F α β]
 
 theorem map_continuousAt (f : F) (a : α) : ContinuousAt f a :=
   (map_continuous f).continuousAt
@@ -80,16 +81,12 @@ namespace ContinuousMap
 variable {α β γ δ : Type*} [TopologicalSpace α] [TopologicalSpace β] [TopologicalSpace γ]
   [TopologicalSpace δ]
 
-instance toContinuousMapClass : ContinuousMapClass C(α, β) α β where
+instance funLike : FunLike C(α, β) α β where
   coe := ContinuousMap.toFun
   coe_injective' f g h := by cases f; cases g; congr
-  map_continuous := ContinuousMap.continuous_toFun
 
-/- Porting note: Probably not needed anymore
-/-- Helper instance for when there's too many metavariables to apply `DFunLike.hasCoeToFun`
-directly. -/
-instance : CoeFun C(α, β) fun _ => α → β :=
-  DFunLike.hasCoeToFun-/
+instance toContinuousMapClass : ContinuousMapClass C(α, β) α β where
+  map_continuous := ContinuousMap.continuous_toFun
 
 @[simp]
 theorem toFun_eq_coe {f : C(α, β)} : f.toFun = (f : α → β) :=
@@ -105,7 +102,8 @@ def Simps.apply (f : C(α, β)) : α → β := f
 initialize_simps_projections ContinuousMap (toFun → apply)
 
 @[simp] -- Porting note: removed `norm_cast` attribute
-protected theorem coe_coe {F : Type*} [ContinuousMapClass F α β] (f : F) : ⇑(f : C(α, β)) = f :=
+protected theorem coe_coe {F : Type*} [FunLike F α β] [ContinuousMapClass F α β] (f : F) :
+    ⇑(f : C(α, β)) = f :=
   rfl
 #align continuous_map.coe_coe ContinuousMap.coe_coe
 

This follows up from #9785, which renamed FunLike to DFunLike, by introducing a new abbreviation FunLike F α β := DFunLike F α (fun _ => β), to make the non-dependent use of FunLike easier.

I searched for the pattern DFunLike.*fun and DFunLike.*λ in all files to replace expressions of the form DFunLike F α (fun _ => β) with FunLike F α β. I did this everywhere except for extends clauses for two reasons: it would conflict with #8386, and more importantly extends must directly refer to a structure with no unfolding of defs or abbrevs.

@@ -42,7 +42,7 @@ section
 
 You should extend this class when you extend `ContinuousMap`. -/
 class ContinuousMapClass (F : Type*) (α β : outParam <| Type*) [TopologicalSpace α]
-  [TopologicalSpace β] extends DFunLike F α fun _ => β where
+  [TopologicalSpace β] extends DFunLike F α (fun _ => β) where
   /-- Continuity -/
   map_continuous (f : F) : Continuous f
 #align continuous_map_class ContinuousMapClass

This prepares for the introduction of a non-dependent synonym of FunLike, which helps a lot with keeping #8386 readable.

This is entirely search-and-replace in 680197f combined with manual fixes in 4145626, e900597 and b8428f8. The commands that generated this change:

sed -i 's/\bFunLike\b/DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoFunLike\b/toDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/import Mathlib.Data.DFunLike/import Mathlib.Data.FunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bHom_FunLike\b/Hom_DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean     
sed -i 's/\binstFunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bfunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoo many metavariables to apply `fun_like.has_coe_to_fun`/too many metavariables to apply `DFunLike.hasCoeToFun`/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean

Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

@@ -13,7 +13,7 @@ import Mathlib.Topology.Homeomorph
 
 In this file we define the type `ContinuousMap` of continuous bundled maps.
 
-We use the `FunLike` design, so each type of morphisms has a companion typeclass which is meant to
+We use the `DFunLike` design, so each type of morphisms has a companion typeclass which is meant to
 be satisfied by itself and all stricter types.
 -/
 
@@ -42,7 +42,7 @@ section
 
 You should extend this class when you extend `ContinuousMap`. -/
 class ContinuousMapClass (F : Type*) (α β : outParam <| Type*) [TopologicalSpace α]
-  [TopologicalSpace β] extends FunLike F α fun _ => β where
+  [TopologicalSpace β] extends DFunLike F α fun _ => β where
   /-- Continuity -/
   map_continuous (f : F) : Continuous f
 #align continuous_map_class ContinuousMapClass
@@ -86,17 +86,17 @@ instance toContinuousMapClass : ContinuousMapClass C(α, β) α β where
   map_continuous := ContinuousMap.continuous_toFun
 
 /- Porting note: Probably not needed anymore
-/-- Helper instance for when there's too many metavariables to apply `fun_like.has_coe_to_fun`
+/-- Helper instance for when there's too many metavariables to apply `DFunLike.hasCoeToFun`
 directly. -/
 instance : CoeFun C(α, β) fun _ => α → β :=
-  FunLike.hasCoeToFun-/
+  DFunLike.hasCoeToFun-/
 
 @[simp]
 theorem toFun_eq_coe {f : C(α, β)} : f.toFun = (f : α → β) :=
   rfl
 #align continuous_map.to_fun_eq_coe ContinuousMap.toFun_eq_coe
 
-instance : CanLift (α → β) C(α, β) FunLike.coe Continuous := ⟨fun f hf ↦ ⟨⟨f, hf⟩, rfl⟩⟩
+instance : CanLift (α → β) C(α, β) DFunLike.coe Continuous := ⟨fun f hf ↦ ⟨⟨f, hf⟩, rfl⟩⟩
 
 /-- See note [custom simps projection]. -/
 def Simps.apply (f : C(α, β)) : α → β := f
@@ -111,7 +111,7 @@ protected theorem coe_coe {F : Type*} [ContinuousMapClass F α β] (f : F) : ⇑
 
 @[ext]
 theorem ext {f g : C(α, β)} (h : ∀ a, f a = g a) : f = g :=
-  FunLike.ext _ _ h
+  DFunLike.ext _ _ h
 #align continuous_map.ext ContinuousMap.ext
 
 /-- Copy of a `ContinuousMap` with a new `toFun` equal to the old one. Useful to fix definitional
@@ -127,7 +127,7 @@ theorem coe_copy (f : C(α, β)) (f' : α → β) (h : f' = f) : ⇑(f.copy f' h
 #align continuous_map.coe_copy ContinuousMap.coe_copy
 
 theorem copy_eq (f : C(α, β)) (f' : α → β) (h : f' = f) : f.copy f' h = f :=
-  FunLike.ext' h
+  DFunLike.ext' h
 #align continuous_map.copy_eq ContinuousMap.copy_eq
 
 variable {f g : C(α, β)}
@@ -147,12 +147,12 @@ protected theorem continuousAt (f : C(α, β)) (x : α) : ContinuousAt f x :=
   f.continuous.continuousAt
 #align continuous_map.continuous_at ContinuousMap.continuousAt
 
-/-- Deprecated. Use `FunLike.congr_fun` instead. -/
+/-- Deprecated. Use `DFunLike.congr_fun` instead. -/
 protected theorem congr_fun {f g : C(α, β)} (H : f = g) (x : α) : f x = g x :=
   H ▸ rfl
 #align continuous_map.congr_fun ContinuousMap.congr_fun
 
-/-- Deprecated. Use `FunLike.congr_arg` instead. -/
+/-- Deprecated. Use `DFunLike.congr_arg` instead. -/
 protected theorem congr_arg (f : C(α, β)) {x y : α} (h : x = y) : f x = f y :=
   h ▸ rfl
 #align continuous_map.congr_arg ContinuousMap.congr_arg
@@ -273,7 +273,7 @@ theorem comp_const (f : C(β, γ)) (b : β) : f.comp (const α b) = const α (f
 @[simp]
 theorem cancel_right {f₁ f₂ : C(β, γ)} {g : C(α, β)} (hg : Surjective g) :
     f₁.comp g = f₂.comp g ↔ f₁ = f₂ :=
-  ⟨fun h => ext <| hg.forall.2 <| FunLike.ext_iff.1 h, congr_arg (ContinuousMap.comp · g)⟩
+  ⟨fun h => ext <| hg.forall.2 <| DFunLike.ext_iff.1 h, congr_arg (ContinuousMap.comp · g)⟩
 #align continuous_map.cancel_right ContinuousMap.cancel_right
 
 @[simp]
@@ -284,7 +284,7 @@ theorem cancel_left {f : C(β, γ)} {g₁ g₂ : C(α, β)} (hf : Injective f) :
 
 instance [Nonempty α] [Nontrivial β] : Nontrivial C(α, β) :=
   ⟨let ⟨b₁, b₂, hb⟩ := exists_pair_ne β
-  ⟨const _ b₁, const _ b₂, fun h => hb <| FunLike.congr_fun h <| Classical.arbitrary α⟩⟩
+  ⟨const _ b₁, const _ b₂, fun h => hb <| DFunLike.congr_fun h <| Classical.arbitrary α⟩⟩
 
 section Prod
 
@@ -427,8 +427,8 @@ theorem restrict_apply_mk (f : C(α, β)) (s : Set α) (x : α) (hx : x ∈ s) :
 
 theorem injective_restrict [T2Space β] {s : Set α} (hs : Dense s) :
     Injective (restrict s : C(α, β) → C(s, β)) := fun f g h ↦
-  FunLike.ext' <| f.continuous.ext_on hs g.continuous <| Set.restrict_eq_restrict_iff.1 <|
-    congr_arg FunLike.coe h
+  DFunLike.ext' <| f.continuous.ext_on hs g.continuous <| Set.restrict_eq_restrict_iff.1 <|
+    congr_arg DFunLike.coe h
 
 /-- The restriction of a continuous map to the preimage of a set. -/
 @[simps]

PR contents

This is the supremum of

• #8284
• #8056
• #8023
• #8332
• #8226 (already approved)
• #7834 (already approved)

along with some minor fixes from failures on nightly-testing as Mathlib master is merged into it.

Note that some PRs for changes that are already compatible with the current toolchain and will be necessary have already been split out: #8380.

I am hopeful that in future we will be able to progressively merge adaptation PRs into a bump/v4.X.0 branch, so we never end up with a "big merge" like this. However one of these adaptation PRs (#8056) predates my new scheme for combined CI, and it wasn't possible to keep that PR viable in the meantime.

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

• leanprover/lean4#2778
• leanprover/lean4#2790
• leanprover/lean4#2783
• leanprover/lean4#2825
• leanprover/lean4#2722

leanprover/lean4#2778

We can get rid of all the

local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue [lean4#2220](https://github.com/leanprover/lean4/pull/2220)

macros across Mathlib (and in any projects that want to write natural number powers of reals).

leanprover/lean4#2722

Changes the default behaviour of simp to (config := {decide := false}). This makes simp (and consequentially norm_num) less powerful, but also more consistent, and less likely to blow up in long failures. This requires a variety of changes: changing some previously by simp or norm_num to decide or rfl, or adding (config := {decide := true}).

leanprover/lean4#2783

This changed the behaviour of simp so that simp [f] will only unfold "fully applied" occurrences of f. The old behaviour can be recovered with simp (config := { unfoldPartialApp := true }). We may in future add a syntax for this, e.g. simp [!f]; please provide feedback! In the meantime, we have made the following changes:

• switching to using explicit lemmas that have the intended level of application
• (config := { unfoldPartialApp := true }) in some places, to recover the old behaviour
• Using @[eqns] to manually adjust the equation lemmas for a particular definition, recovering the old behaviour just for that definition. See #8371, where we do this for Function.comp and Function.flip.

This change in Lean may require further changes down the line (e.g. adding the !f syntax, and/or upstreaming the special treatment for Function.comp and Function.flip, and/or removing this special treatment). Please keep an open and skeptical mind about these changes!

Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Mauricio Collares <mauricio@collares.org>

@@ -452,7 +452,8 @@ noncomputable def liftCover : C(α, β) :=
     Set.iUnion_eq_univ_iff.2 fun x ↦ (hS x).imp fun _ ↦ mem_of_mem_nhds
   mk (Set.liftCover S (fun i ↦ φ i) hφ H) <| continuous_of_cover_nhds hS fun i ↦ by
     rw [continuousOn_iff_continuous_restrict]
-    simpa only [Set.restrict, Set.liftCover_coe] using (φ i).continuous
+    simpa (config := { unfoldPartialApp := true }) only [Set.restrict, Set.liftCover_coe] using
+      (φ i).continuous
 #align continuous_map.lift_cover ContinuousMap.liftCover
 
 variable {S φ hφ hS}

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -612,14 +612,16 @@ theorem coe_trans : (f.trans g : C(α, γ)) = (g : C(β, γ)).comp f :=
 
 /-- Left inverse to a continuous map from a homeomorphism, mirroring `Equiv.symm_comp_self`. -/
 @[simp]
-theorem symm_comp_toContinuousMap : (f.symm : C(β, α)).comp (f : C(α, β)) = ContinuousMap.id α :=
-  by rw [← coe_trans, self_trans_symm, coe_refl]
+theorem symm_comp_toContinuousMap :
+    (f.symm : C(β, α)).comp (f : C(α, β)) = ContinuousMap.id α := by
+  rw [← coe_trans, self_trans_symm, coe_refl]
 #align homeomorph.symm_comp_to_continuous_map Homeomorph.symm_comp_toContinuousMap
 
 /-- Right inverse to a continuous map from a homeomorphism, mirroring `Equiv.self_comp_symm`. -/
 @[simp]
-theorem toContinuousMap_comp_symm : (f : C(α, β)).comp (f.symm : C(β, α)) = ContinuousMap.id β :=
-  by rw [← coe_trans, symm_trans_self, coe_refl]
+theorem toContinuousMap_comp_symm :
+    (f : C(α, β)).comp (f.symm : C(β, α)) = ContinuousMap.id β := by
+  rw [← coe_trans, symm_trans_self, coe_refl]
 #align homeomorph.to_continuous_map_comp_symm Homeomorph.toContinuousMap_comp_symm
 
 end Homeomorph

We'll need to do this step anyway when it is time to remove them all.

(See #8214 where I'm benchmarking the removal.)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -597,7 +597,7 @@ instance : Coe (α ≃ₜ β) C(α, β) :=
 -- Porting note: Syntactic tautology
 /-theorem toContinuousMap_as_coe : f.toContinuousMap = f :=
   rfl
-#align homeomorph.to_continuous_map_as_coe Homeomorph.toContinuousMap_as_coe-/
+-/
 #noalign homeomorph.to_continuous_map_as_coe
 
 @[simp]

This was done for profinite sets in LTE.

We give a homeomorphism from the quotient of a quotient map to its codomain, and prove that a continuous map which is constant on the fibres of a quotient map can be descended along the quotient map.

@@ -506,6 +506,77 @@ end Gluing
 
 end ContinuousMap
 
+section Lift
+
+variable {X Y Z : Type*} [TopologicalSpace X] [TopologicalSpace Y] [TopologicalSpace Z]
+    {f : C(X, Y)}
+
+/-- `Setoid.quotientKerEquivOfRightInverse` as a homeomorphism. -/
+@[simps!]
+def Function.RightInverse.homeomorph {f' : C(Y, X)} (hf : Function.RightInverse f' f) :
+    Quotient (Setoid.ker f) ≃ₜ Y where
+  toEquiv := Setoid.quotientKerEquivOfRightInverse _ _ hf
+  continuous_toFun := quotientMap_quot_mk.continuous_iff.mpr f.continuous
+  continuous_invFun := continuous_quotient_mk'.comp f'.continuous
+
+namespace QuotientMap
+
+/--
+The homeomorphism from the quotient of a quotient map to its codomain. This is
+`Setoid.quotientKerEquivOfSurjective` as a homeomorphism.
+-/
+@[simps!]
+noncomputable def homeomorph (hf : QuotientMap f) : Quotient (Setoid.ker f) ≃ₜ Y where
+  toEquiv := Setoid.quotientKerEquivOfSurjective _ hf.surjective
+  continuous_toFun := quotientMap_quot_mk.continuous_iff.mpr hf.continuous
+  continuous_invFun := by
+    rw [hf.continuous_iff]
+    convert continuous_quotient_mk'
+    ext
+    simp only [Equiv.invFun_as_coe, Function.comp_apply,
+      (Setoid.quotientKerEquivOfSurjective f hf.surjective).symm_apply_eq]
+    rfl
+
+variable (hf : QuotientMap f) (g : C(X, Z)) (h : Function.FactorsThrough g f)
+
+/-- Descend a continuous map, which is constant on the fibres, along a quotient map. -/
+@[simps]
+noncomputable def lift : C(Y, Z) where
+  toFun := ((fun i ↦ Quotient.liftOn' i g (fun _ _ (hab : f _ = f _) ↦ h hab)) :
+    Quotient (Setoid.ker f) → Z) ∘ hf.homeomorph.symm
+  continuous_toFun := Continuous.comp (continuous_quot_lift _ g.2) (Homeomorph.continuous _)
+
+/--
+The obvious triangle induced by `QuotientMap.lift` commutes:
+```
+     g
+  X --→ Z
+  |   ↗
+f |  / hf.lift g h
+  v /
+  Y
+```
+-/
+@[simp]
+theorem lift_comp : (hf.lift g h).comp f = g := by
+  ext
+  simpa using h (Function.rightInverse_surjInv _ _)
+
+/-- `QuotientMap.lift` as an equivalence. -/
+@[simps]
+noncomputable def liftEquiv : { g : C(X, Z) // Function.FactorsThrough g f} ≃ C(Y, Z) where
+  toFun g := hf.lift g g.prop
+  invFun g := ⟨g.comp f, fun _ _ h ↦ by simp only [ContinuousMap.comp_apply]; rw [h]⟩
+  left_inv := by intro; simp
+  right_inv := by
+    intro g
+    ext a
+    simpa using congrArg g (Function.rightInverse_surjInv hf.surjective a)
+
+end QuotientMap
+
+end Lift
+
 namespace Homeomorph
 
 variable {α β γ : Type*} [TopologicalSpace α] [TopologicalSpace β] [TopologicalSpace γ]

@@ -325,12 +325,37 @@ def prodSwap : C(α × β, β × α) := .prodMk .snd .fst
 
 end Prod
 
+section Sigma
+
+variable {I A : Type*} {X : I → Type*} [TopologicalSpace A] [∀ i, TopologicalSpace (X i)]
+
 /-- `Sigma.mk i` as a bundled continuous map. -/
 @[simps apply]
-def sigmaMk {ι : Type*} {Y : ι → Type*} [∀ i, TopologicalSpace (Y i)] (i : ι) :
-    C(Y i, Σ i, Y i) where
+def sigmaMk (i : I) : C(X i, Σ i, X i) where
   toFun := Sigma.mk i
 
+/--
+To give a continuous map out of a disjoint union, it suffices to give a continuous map out of
+each term. This is `Sigma.uncurry` for continuous maps.
+-/
+@[simps]
+def sigma (f : ∀ i, C(X i, A)) : C((Σ i, X i), A) where
+  toFun ig := f ig.fst ig.snd
+
+variable (A X) in
+/--
+Giving a continuous map out of a disjoint union is the same as giving a continuous map out of
+each term. This is a version of `Equiv.piCurry` for continuous maps.
+-/
+@[simps]
+def sigmaEquiv : (∀ i, C(X i, A)) ≃ C((Σ i, X i), A) where
+  toFun := sigma
+  invFun f i := f.comp (sigmaMk i)
+  left_inv := by intro; ext; simp
+  right_inv := by intro; ext; simp
+
+end Sigma
+
 section Pi
 
 variable {I A : Type*} {X Y : I → Type*} [TopologicalSpace A] [∀ i, TopologicalSpace (X i)]
@@ -351,6 +376,18 @@ theorem pi_eval (f : ∀ i, C(A, X i)) (a : A) : (pi f) a = fun i : I => (f i) a
 def eval (i : I) : C(∀ j, X j, X i) where
   toFun := Function.eval i
 
+variable (A X) in
+/--
+Giving a continuous map out of a disjoint union is the same as giving a continuous map out of
+each term
+-/
+@[simps]
+def piEquiv : (∀ i, C(A, X i)) ≃ C(A, ∀ i, X i) where
+  toFun := pi
+  invFun f i := (eval i).comp f
+  left_inv := by intro; ext; simp [pi]
+  right_inv := by intro; ext; simp [pi]
+
 /-- Combine a collection of bundled continuous maps `C(X i, Y i)` into a bundled continuous map
 `C(∀ i, X i, ∀ i, Y i)`. -/
 @[simps!]

We exhibit a compact subset in a product of totally disconnected Hausdorff spaces as a limit of its projections to finite subsets of the indexing set, in the category Profinite. The proof is structured in the same way as Profinite.isIso_asLimitCone_lift and DiscreteQuotient.exists_of_compat.

@@ -357,6 +357,10 @@ def eval (i : I) : C(∀ j, X j, X i) where
 def piMap (f : ∀ i, C(X i, Y i)) : C((i : I) → X i, (i : I) → Y i) :=
   .pi fun i ↦ (f i).comp (eval i)
 
+/-- "Precomposition" as a continuous map between dependent types. -/
+def precomp {ι : Type*} (φ : ι → I) : C((i : I) → X i, (i : ι) → X (φ i)) :=
+  ⟨_, Pi.continuous_precomp' φ⟩
+
 end Pi
 
 section Restrict

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -270,11 +270,13 @@ theorem comp_const (f : C(β, γ)) (b : β) : f.comp (const α b) = const α (f
   ext fun _ => rfl
 #align continuous_map.comp_const ContinuousMap.comp_const
 
+@[simp]
 theorem cancel_right {f₁ f₂ : C(β, γ)} {g : C(α, β)} (hg : Surjective g) :
     f₁.comp g = f₂.comp g ↔ f₁ = f₂ :=
   ⟨fun h => ext <| hg.forall.2 <| FunLike.ext_iff.1 h, congr_arg (ContinuousMap.comp · g)⟩
 #align continuous_map.cancel_right ContinuousMap.cancel_right
 
+@[simp]
 theorem cancel_left {f : C(β, γ)} {g₁ g₂ : C(α, β)} (hf : Injective f) :
     f.comp g₁ = f.comp g₂ ↔ g₁ = g₂ :=
   ⟨fun h => ext fun a => hf <| by rw [← comp_apply, h, comp_apply], congr_arg _⟩

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

This has nice performance benefits.

@@ -26,7 +26,7 @@ When possible, instead of parametrizing results over `(f : C(α, β))`,
 you should parametrize over `{F : Type*} [ContinuousMapClass F α β] (f : F)`.
 
 When you extend this structure, make sure to extend `ContinuousMapClass`. -/
-structure ContinuousMap (α β : Type _) [TopologicalSpace α] [TopologicalSpace β] where
+structure ContinuousMap (α β : Type*) [TopologicalSpace α] [TopologicalSpace β] where
   /-- The function `α → β` -/
   protected toFun : α → β
   /-- Proposition that `toFun` is continuous -/
@@ -41,7 +41,7 @@ section
 /-- `ContinuousMapClass F α β` states that `F` is a type of continuous maps.
 
 You should extend this class when you extend `ContinuousMap`. -/
-class ContinuousMapClass (F : Type _) (α β : outParam <| Type _) [TopologicalSpace α]
+class ContinuousMapClass (F : Type*) (α β : outParam <| Type*) [TopologicalSpace α]
   [TopologicalSpace β] extends FunLike F α fun _ => β where
   /-- Continuity -/
   map_continuous (f : F) : Continuous f
@@ -55,7 +55,7 @@ attribute [continuity] map_continuous
 
 section ContinuousMapClass
 
-variable {F α β : Type _} [TopologicalSpace α] [TopologicalSpace β] [ContinuousMapClass F α β]
+variable {F α β : Type*} [TopologicalSpace α] [TopologicalSpace β] [ContinuousMapClass F α β]
 
 theorem map_continuousAt (f : F) (a : α) : ContinuousAt f a :=
   (map_continuous f).continuousAt
@@ -77,7 +77,7 @@ end ContinuousMapClass
 
 namespace ContinuousMap
 
-variable {α β γ δ : Type _} [TopologicalSpace α] [TopologicalSpace β] [TopologicalSpace γ]
+variable {α β γ δ : Type*} [TopologicalSpace α] [TopologicalSpace β] [TopologicalSpace γ]
   [TopologicalSpace δ]
 
 instance toContinuousMapClass : ContinuousMapClass C(α, β) α β where
@@ -105,7 +105,7 @@ def Simps.apply (f : C(α, β)) : α → β := f
 initialize_simps_projections ContinuousMap (toFun → apply)
 
 @[simp] -- Porting note: removed `norm_cast` attribute
-protected theorem coe_coe {F : Type _} [ContinuousMapClass F α β] (f : F) : ⇑(f : C(α, β)) = f :=
+protected theorem coe_coe {F : Type*} [ContinuousMapClass F α β] (f : F) : ⇑(f : C(α, β)) = f :=
   rfl
 #align continuous_map.coe_coe ContinuousMap.coe_coe
 
@@ -286,7 +286,7 @@ instance [Nonempty α] [Nontrivial β] : Nontrivial C(α, β) :=
 
 section Prod
 
-variable {α₁ α₂ β₁ β₂ : Type _} [TopologicalSpace α₁] [TopologicalSpace α₂] [TopologicalSpace β₁]
+variable {α₁ α₂ β₁ β₂ : Type*} [TopologicalSpace α₁] [TopologicalSpace α₂] [TopologicalSpace β₁]
   [TopologicalSpace β₂]
 
 /-- `Prod.fst : (x, y) ↦ x` as a bundled continuous map. -/
@@ -325,13 +325,13 @@ end Prod
 
 /-- `Sigma.mk i` as a bundled continuous map. -/
 @[simps apply]
-def sigmaMk {ι : Type _} {Y : ι → Type _} [∀ i, TopologicalSpace (Y i)] (i : ι) :
+def sigmaMk {ι : Type*} {Y : ι → Type*} [∀ i, TopologicalSpace (Y i)] (i : ι) :
     C(Y i, Σ i, Y i) where
   toFun := Sigma.mk i
 
 section Pi
 
-variable {I A : Type _} {X Y : I → Type _} [TopologicalSpace A] [∀ i, TopologicalSpace (X i)]
+variable {I A : Type*} {X Y : I → Type*} [TopologicalSpace A] [∀ i, TopologicalSpace (X i)]
   [∀ i, TopologicalSpace (Y i)]
 
 /-- Abbreviation for product of continuous maps, which is continuous -/
@@ -397,7 +397,7 @@ end Restrict
 
 section Gluing
 
-variable {ι : Type _} (S : ι → Set α) (φ : ∀ i : ι, C(S i, β))
+variable {ι : Type*} (S : ι → Set α) (φ : ∀ i : ι, C(S i, β))
   (hφ : ∀ (i j) (x : α) (hxi : x ∈ S i) (hxj : x ∈ S j), φ i ⟨x, hxi⟩ = φ j ⟨x, hxj⟩)
   (hS : ∀ x : α, ∃ i, S i ∈ nhds x)
 
@@ -465,7 +465,7 @@ end ContinuousMap
 
 namespace Homeomorph
 
-variable {α β γ : Type _} [TopologicalSpace α] [TopologicalSpace β] [TopologicalSpace γ]
+variable {α β γ : Type*} [TopologicalSpace α] [TopologicalSpace β] [TopologicalSpace γ]
 
 variable (f : α ≃ₜ β) (g : β ≃ₜ γ)
 

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright © 2020 Nicolò Cavalleri. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Nicolò Cavalleri
-
-! This file was ported from Lean 3 source module topology.continuous_function.basic
-! leanprover-community/mathlib commit 55d771df074d0dd020139ee1cd4b95521422df9f
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Set.UnionLift
 import Mathlib.Topology.Homeomorph
 
+#align_import topology.continuous_function.basic from "leanprover-community/mathlib"@"55d771df074d0dd020139ee1cd4b95521422df9f"
+
 /-!
 # Continuous bundled maps
 

@@ -99,6 +99,8 @@ theorem toFun_eq_coe {f : C(α, β)} : f.toFun = (f : α → β) :=
   rfl
 #align continuous_map.to_fun_eq_coe ContinuousMap.toFun_eq_coe
 
+instance : CanLift (α → β) C(α, β) FunLike.coe Continuous := ⟨fun f hf ↦ ⟨⟨f, hf⟩, rfl⟩⟩
+
 /-- See note [custom simps projection]. -/
 def Simps.apply (f : C(α, β)) : α → β := f
 
@@ -383,6 +385,11 @@ theorem restrict_apply_mk (f : C(α, β)) (s : Set α) (x : α) (hx : x ∈ s) :
   rfl
 #align continuous_map.restrict_apply_mk ContinuousMap.restrict_apply_mk
 
+theorem injective_restrict [T2Space β] {s : Set α} (hs : Dense s) :
+    Injective (restrict s : C(α, β) → C(s, β)) := fun f g h ↦
+  FunLike.ext' <| f.continuous.ext_on hs g.continuous <| Set.restrict_eq_restrict_iff.1 <|
+    congr_arg FunLike.coe h
+
 /-- The restriction of a continuous map to the preimage of a set. -/
 @[simps]
 def restrictPreimage (f : C(α, β)) (s : Set β) : C(f ⁻¹' s, s) :=

Grepping for [^ .:{-] [^ :] and reviewing the results. Once I started I couldn't stop. :-)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -402,7 +402,7 @@ of each point in `α` and the functions `φ i` agree pairwise on intersections,
 construct a continuous map in `C(α, β)`. -/
 noncomputable def liftCover : C(α, β) :=
   haveI H : ⋃ i, S i = Set.univ :=
-    Set.iUnion_eq_univ_iff.2 fun x ↦ (hS x).imp fun _  ↦ mem_of_mem_nhds
+    Set.iUnion_eq_univ_iff.2 fun x ↦ (hS x).imp fun _ ↦ mem_of_mem_nhds
   mk (Set.liftCover S (fun i ↦ φ i) hφ H) <| continuous_of_cover_nhds hS fun i ↦ by
     rw [continuousOn_iff_continuous_restrict]
     simpa only [Set.restrict, Set.liftCover_coe] using (φ i).continuous

This is a follow-up to #4325.

@@ -324,6 +324,12 @@ def prodSwap : C(α × β, β × α) := .prodMk .snd .fst
 
 end Prod
 
+/-- `Sigma.mk i` as a bundled continuous map. -/
+@[simps apply]
+def sigmaMk {ι : Type _} {Y : ι → Type _} [∀ i, TopologicalSpace (Y i)] (i : ι) :
+    C(Y i, Σ i, Y i) where
+  toFun := Sigma.mk i
+
 section Pi
 
 variable {I A : Type _} {X Y : I → Type _} [TopologicalSpace A] [∀ i, TopologicalSpace (X i)]

@@ -395,7 +395,7 @@ variable {ι : Type _} (S : ι → Set α) (φ : ∀ i : ι, C(S i, β))
 of each point in `α` and the functions `φ i` agree pairwise on intersections, can be glued to
 construct a continuous map in `C(α, β)`. -/
 noncomputable def liftCover : C(α, β) :=
-  haveI H : (⋃ i, S i) = Set.univ :=
+  haveI H : ⋃ i, S i = Set.univ :=
     Set.iUnion_eq_univ_iff.2 fun x ↦ (hS x).imp fun _  ↦ mem_of_mem_nhds
   mk (Set.liftCover S (fun i ↦ φ i) hφ H) <| continuous_of_cover_nhds hS fun i ↦ by
     rw [continuousOn_iff_continuous_restrict]

@@ -68,10 +68,10 @@ theorem map_continuousWithinAt (f : F) (s : Set α) (a : α) : ContinuousWithinA
   (map_continuous f).continuousWithinAt
 #align map_continuous_within_at map_continuousWithinAt
 
-instance : CoeTC F C(α, β) :=
-  ⟨fun f =>
-    { toFun := f
-      continuous_toFun := map_continuous f }⟩
+/-- Coerce a bundled morphism with a `ContinuousMapClass` instance to a `ContinuousMap`. -/
+@[coe] def toContinuousMap (f : F) : C(α, β) := ⟨f, map_continuous f⟩
+
+instance : CoeTC F C(α, β) := ⟨toContinuousMap⟩
 
 end ContinuousMapClass
 
@@ -88,7 +88,6 @@ instance toContinuousMapClass : ContinuousMapClass C(α, β) α β where
   coe_injective' f g h := by cases f; cases g; congr
   map_continuous := ContinuousMap.continuous_toFun
 
-
 /- Porting note: Probably not needed anymore
 /-- Helper instance for when there's too many metavariables to apply `fun_like.has_coe_to_fun`
 directly. -/

Co-authored-by: Scott Morrison <scott@tqft.net> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: adomani <adomani@gmail.com>

@@ -83,7 +83,7 @@ namespace ContinuousMap
 variable {α β γ δ : Type _} [TopologicalSpace α] [TopologicalSpace β] [TopologicalSpace γ]
   [TopologicalSpace δ]
 
-instance : ContinuousMapClass C(α, β) α β where
+instance toContinuousMapClass : ContinuousMapClass C(α, β) α β where
   coe := ContinuousMap.toFun
   coe_injective' f g h := by cases f; cases g; congr
   map_continuous := ContinuousMap.continuous_toFun

Removed diagonal stuff which is no longer needed.

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

@@ -465,6 +465,7 @@ variable (f : α ≃ₜ β) (g : β ≃ₜ γ)
 def toContinuousMap (e : α ≃ₜ β) : C(α, β) :=
   ⟨e, e.continuous_toFun⟩
 #align homeomorph.to_continuous_map Homeomorph.toContinuousMap
+#align homeomorph.to_continuous_map_apply Homeomorph.toContinuousMap_apply
 
 /-- `Homeomorph.toContinuousMap` as a coercion. -/
 instance : Coe (α ≃ₜ β) C(α, β) :=

@@ -211,6 +211,11 @@ theorem coe_const (b : β) : ⇑(const α b) = Function.const α b :=
   rfl
 #align continuous_map.coe_const ContinuousMap.coe_const
 
+/-- `Function.const α b` as a bundled continuous function of `b`. -/
+@[simps (config := .asFn)]
+def constPi : C(β, α → β) where
+  toFun b := Function.const α b
+
 instance [Inhabited β] : Inhabited C(α, β) :=
   ⟨const α default⟩
 
@@ -314,6 +319,10 @@ theorem prod_eval (f : C(α, β₁)) (g : C(α, β₂)) (a : α) : (prodMk f g)
   rfl
 #align continuous_map.prod_eval ContinuousMap.prod_eval
 
+/-- `Prod.swap` bundled as a `ContinuousMap`. -/
+@[simps!]
+def prodSwap : C(α × β, β × α) := .prodMk .snd .fst
+
 end Prod
 
 section Pi

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -29,12 +29,11 @@ When possible, instead of parametrizing results over `(f : C(α, β))`,
 you should parametrize over `{F : Type*} [ContinuousMapClass F α β] (f : F)`.
 
 When you extend this structure, make sure to extend `ContinuousMapClass`. -/
---@[protect_proj] -- Porting note: missing attribute?
 structure ContinuousMap (α β : Type _) [TopologicalSpace α] [TopologicalSpace β] where
   /-- The function `α → β` -/
-  toFun : α → β
+  protected toFun : α → β
   /-- Proposition that `toFun` is continuous -/
-  continuous_toFun : Continuous toFun := by continuity
+  protected continuous_toFun : Continuous toFun := by continuity
 #align continuous_map ContinuousMap
 
 /-- The type of continuous maps from `α` to `β`. -/

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>

@@ -389,7 +389,7 @@ of each point in `α` and the functions `φ i` agree pairwise on intersections,
 construct a continuous map in `C(α, β)`. -/
 noncomputable def liftCover : C(α, β) :=
   haveI H : (⋃ i, S i) = Set.univ :=
-    Set.unionᵢ_eq_univ_iff.2 fun x ↦ (hS x).imp fun _  ↦ mem_of_mem_nhds
+    Set.iUnion_eq_univ_iff.2 fun x ↦ (hS x).imp fun _  ↦ mem_of_mem_nhds
   mk (Set.liftCover S (fun i ↦ φ i) hφ H) <| continuous_of_cover_nhds hS fun i ↦ by
     rw [continuousOn_iff_continuous_restrict]
     simpa only [Set.restrict, Set.liftCover_coe] using (φ i).continuous

• Add ContinuousMap.fst, ContinuousMap.snd, ContinuousMap.eval, and ContinuousMap.piMap.

• Add ContinuousMap.Homotopy.prodMk, ContinuousMap.Homotopy.prodMap, ContinuousMap.Homotopy.pi, ContinuousMap.Homotopy.piMap.

• Add ContinuousMap.Homotopic.prodMk, ContinuousMap.Homotopic.prodMap, ContinuousMap.Homotopic.pi, ContinuousMap.Homotopic.piMap.

• Add ContinuousMap.HomotopyEquiv.prodCongr and ContinuousMap.HomotopyEquiv.piCongrRight.

@@ -287,6 +287,16 @@ section Prod
 variable {α₁ α₂ β₁ β₂ : Type _} [TopologicalSpace α₁] [TopologicalSpace α₂] [TopologicalSpace β₁]
   [TopologicalSpace β₂]
 
+/-- `Prod.fst : (x, y) ↦ x` as a bundled continuous map. -/
+@[simps (config := .asFn)]
+def fst : C(α × β, α) where
+  toFun := Prod.fst
+
+/-- `Prod.snd : (x, y) ↦ y` as a bundled continuous map. -/
+@[simps (config := .asFn)]
+def snd : C(α × β, β) where
+  toFun := Prod.snd
+
 /-- Given two continuous maps `f` and `g`, this is the continuous map `x ↦ (f x, g x)`. -/
 def prodMk (f : C(α, β₁)) (g : C(α, β₂)) : C(α, β₁ × β₂) where
   toFun x := (f x, g x)
@@ -309,7 +319,8 @@ end Prod
 
 section Pi
 
-variable {I A : Type _} {X : I → Type _} [TopologicalSpace A] [∀ i, TopologicalSpace (X i)]
+variable {I A : Type _} {X Y : I → Type _} [TopologicalSpace A] [∀ i, TopologicalSpace (X i)]
+  [∀ i, TopologicalSpace (Y i)]
 
 /-- Abbreviation for product of continuous maps, which is continuous -/
 def pi (f : ∀ i, C(A, X i)) : C(A, ∀ i, X i) where
@@ -321,6 +332,17 @@ theorem pi_eval (f : ∀ i, C(A, X i)) (a : A) : (pi f) a = fun i : I => (f i) a
   rfl
 #align continuous_map.pi_eval ContinuousMap.pi_eval
 
+/-- Evaluation at point as a bundled continuous map. -/
+@[simps (config := .asFn)]
+def eval (i : I) : C(∀ j, X j, X i) where
+  toFun := Function.eval i
+
+/-- Combine a collection of bundled continuous maps `C(X i, Y i)` into a bundled continuous map
+`C(∀ i, X i, ∀ i, Y i)`. -/
+@[simps!]
+def piMap (f : ∀ i, C(X i, Y i)) : C((i : I) → X i, (i : I) → Y i) :=
+  .pi fun i ↦ (f i).comp (eval i)
+
 end Pi
 
 section Restrict

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Nicolò Cavalleri
 
 ! This file was ported from Lean 3 source module topology.continuous_function.basic
-! leanprover-community/mathlib commit 6efec6bb9fcaed3cf1baaddb2eaadd8a2a06679c
+! leanprover-community/mathlib commit 55d771df074d0dd020139ee1cd4b95521422df9f
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -365,17 +365,12 @@ variable {ι : Type _} (S : ι → Set α) (φ : ∀ i : ι, C(S i, β))
 /-- A family `φ i` of continuous maps `C(S i, β)`, where the domains `S i` contain a neighbourhood
 of each point in `α` and the functions `φ i` agree pairwise on intersections, can be glued to
 construct a continuous map in `C(α, β)`. -/
-noncomputable def liftCover : C(α, β) := by
-  have H : (⋃ i, S i) = Set.univ := by
-    rw [Set.eq_univ_iff_forall]
-    intro x
-    rw [Set.mem_unionᵢ]
-    obtain ⟨i, hi⟩ := hS x
-    exact ⟨i, mem_of_mem_nhds hi⟩
-  refine' ⟨Set.liftCover S (fun i => φ i) hφ H, continuous_subtype_nhds_cover hS _⟩
-  intro i
-  convert (φ i).continuous
-  apply Set.liftCover_coe
+noncomputable def liftCover : C(α, β) :=
+  haveI H : (⋃ i, S i) = Set.univ :=
+    Set.unionᵢ_eq_univ_iff.2 fun x ↦ (hS x).imp fun _  ↦ mem_of_mem_nhds
+  mk (Set.liftCover S (fun i ↦ φ i) hφ H) <| continuous_of_cover_nhds hS fun i ↦ by
+    rw [continuousOn_iff_continuous_restrict]
+    simpa only [Set.restrict, Set.liftCover_coe] using (φ i).continuous
 #align continuous_map.lift_cover ContinuousMap.liftCover
 
 variable {S φ hφ hS}

Forward-port of changes to already-ported files topology.algebra.monoid and topology.continuous_map.basic made in mathlib3 PR [#18465](https://github.com/leanprover-community/mathlib/pull/18465)

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Nicolò Cavalleri
 
 ! This file was ported from Lean 3 source module topology.continuous_function.basic
-! leanprover-community/mathlib commit b363547b3113d350d053abdf2884e9850a56b205
+! leanprover-community/mathlib commit 6efec6bb9fcaed3cf1baaddb2eaadd8a2a06679c
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -337,7 +337,18 @@ theorem coe_restrict (f : C(α, β)) : ⇑(f.restrict s) = f ∘ ((↑) : s →
   rfl
 #align continuous_map.coe_restrict ContinuousMap.coe_restrict
 
-/-- The restriction of a continuous map onto the preimage of a set. -/
+@[simp]
+theorem restrict_apply (f : C(α, β)) (s : Set α) (x : s) : f.restrict s x = f x :=
+  rfl
+#align continuous_map.restrict_apply ContinuousMap.restrict_apply
+
+@[simp]
+theorem restrict_apply_mk (f : C(α, β)) (s : Set α) (x : α) (hx : x ∈ s) :
+    f.restrict s ⟨x, hx⟩ = f x :=
+  rfl
+#align continuous_map.restrict_apply_mk ContinuousMap.restrict_apply_mk
+
+/-- The restriction of a continuous map to the preimage of a set. -/
 @[simps]
 def restrictPreimage (f : C(α, β)) (s : Set β) : C(f ⁻¹' s, s) :=
   ⟨s.restrictPreimage f, continuous_iff_continuousAt.mpr fun _ => f.2.continuousAt.restrictPreimage⟩

Misc changes:

• rename Homeomorph.symm_comp_to_continuousMap to Homeomorph.symm_comp_toContinuousMap;
• rename Homeomorph.to_continuousMap_comp_symm to Homeomorph.toContinuousMap_comp_symm;
• add CoeFun instance for Homeomorph; otherwise, toFun_eq_coe was stuck trying to coerce h to a function.

@@ -452,14 +452,14 @@ theorem coe_trans : (f.trans g : C(α, γ)) = (g : C(β, γ)).comp f :=
 
 /-- Left inverse to a continuous map from a homeomorphism, mirroring `Equiv.symm_comp_self`. -/
 @[simp]
-theorem symm_comp_to_continuousMap : (f.symm : C(β, α)).comp (f : C(α, β)) = ContinuousMap.id α :=
+theorem symm_comp_toContinuousMap : (f.symm : C(β, α)).comp (f : C(α, β)) = ContinuousMap.id α :=
   by rw [← coe_trans, self_trans_symm, coe_refl]
-#align homeomorph.symm_comp_to_continuous_map Homeomorph.symm_comp_to_continuousMap
+#align homeomorph.symm_comp_to_continuous_map Homeomorph.symm_comp_toContinuousMap
 
 /-- Right inverse to a continuous map from a homeomorphism, mirroring `Equiv.self_comp_symm`. -/
 @[simp]
-theorem to_continuousMap_comp_symm : (f : C(α, β)).comp (f.symm : C(β, α)) = ContinuousMap.id β :=
+theorem toContinuousMap_comp_symm : (f : C(α, β)).comp (f.symm : C(β, α)) = ContinuousMap.id β :=
   by rw [← coe_trans, symm_trans_self, coe_refl]
-#align homeomorph.to_continuous_map_comp_symm Homeomorph.to_continuousMap_comp_symm
+#align homeomorph.to_continuous_map_comp_symm Homeomorph.toContinuousMap_comp_symm
 
 end Homeomorph

@@ -84,8 +84,7 @@ namespace ContinuousMap
 variable {α β γ δ : Type _} [TopologicalSpace α] [TopologicalSpace β] [TopologicalSpace γ]
   [TopologicalSpace δ]
 
-instance : ContinuousMapClass C(α, β) α β
-    where
+instance : ContinuousMapClass C(α, β) α β where
   coe := ContinuousMap.toFun
   coe_injective' f g h := by cases f; cases g; congr
   map_continuous := ContinuousMap.continuous_toFun
@@ -102,6 +101,9 @@ theorem toFun_eq_coe {f : C(α, β)} : f.toFun = (f : α → β) :=
   rfl
 #align continuous_map.to_fun_eq_coe ContinuousMap.toFun_eq_coe
 
+/-- See note [custom simps projection]. -/
+def Simps.apply (f : C(α, β)) : α → β := f
+
 -- this must come after the coe_to_fun definition
 initialize_simps_projections ContinuousMap (toFun → apply)
 
@@ -117,8 +119,7 @@ theorem ext {f g : C(α, β)} (h : ∀ a, f a = g a) : f = g :=
 
 /-- Copy of a `ContinuousMap` with a new `toFun` equal to the old one. Useful to fix definitional
 equalities. -/
-protected def copy (f : C(α, β)) (f' : α → β) (h : f' = f) : C(α, β)
-    where
+protected def copy (f : C(α, β)) (f' : α → β) (h : f' = f) : C(α, β) where
   toFun := f'
   continuous_toFun := h.symm ▸ f.continuous_toFun
 #align continuous_map.copy ContinuousMap.copy
@@ -379,10 +380,9 @@ theorem liftCover_restrict {i : ι} : (liftCover S φ hφ hS).restrict (S i) = 
   simp only [coe_restrict, Function.comp_apply, liftCover_coe]
 #align continuous_map.lift_cover_restrict ContinuousMap.liftCover_restrict
 
-variable (A : Set (Set α)) (F : ∀ (s : Set α) (_ : s ∈ A), C(s, β))
-  (hF :
-    ∀ (s) (hs : s ∈ A) (t) (ht : t ∈ A) (x : α) (hxi : x ∈ s) (hxj : x ∈ t),
-      F s hs ⟨x, hxi⟩ = F t ht ⟨x, hxj⟩)
+variable (A : Set (Set α)) (F : ∀ s ∈ A, C(s, β))
+  (hF : ∀ (s) (hs : s ∈ A) (t) (ht : t ∈ A) (x : α) (hxi : x ∈ s) (hxj : x ∈ t),
+    F s hs ⟨x, hxi⟩ = F t ht ⟨x, hxj⟩)
   (hA : ∀ x : α, ∃ i ∈ A, i ∈ nhds x)
 
 /-- A family `F s` of continuous maps `C(s, β)`, where (1) the domains `s` are taken from a set `A`

This introduces a tactic congr! that is an analogue to mathlib 3's congr'. It is a more insistent version of congr that makes use of more congruence lemmas (including user congruence lemmas), propext, funext, and Subsingleton instances. It also has a feature to lift reflexive relations to equalities. Along with funext, the tactic does intros, allowing congr! to get access to function bodies; the introduced variables can be named using rename_i if needed.

This also modifies convert to use congr! rather than congr, which makes it work more like the mathlib3 version of the tactic.

@@ -363,8 +363,7 @@ noncomputable def liftCover : C(α, β) := by
   refine' ⟨Set.liftCover S (fun i => φ i) hφ H, continuous_subtype_nhds_cover hS _⟩
   intro i
   convert (φ i).continuous
-  ext x
-  exact Set.liftCover_coe x
+  apply Set.liftCover_coe
 #align continuous_map.lift_cover ContinuousMap.liftCover
 
 variable {S φ hφ hS}

We implement the continuity tactic using aesop, this makes it more robust and reduces the code to trivial macros.

@@ -34,7 +34,7 @@ structure ContinuousMap (α β : Type _) [TopologicalSpace α] [TopologicalSpace
   /-- The function `α → β` -/
   toFun : α → β
   /-- Proposition that `toFun` is continuous -/
-  continuous_toFun : Continuous toFun --:= by continuity -- Porting note: need tactic
+  continuous_toFun : Continuous toFun := by continuity
 #align continuous_map ContinuousMap
 
 /-- The type of continuous maps from `α` to `β`. -/
@@ -55,7 +55,7 @@ end
 
 export ContinuousMapClass (map_continuous)
 
---attribute [continuity] map_continuous -- Porting note: need tactic
+attribute [continuity] map_continuous
 
 section ContinuousMapClass
 
@@ -139,7 +139,7 @@ protected theorem continuous (f : C(α, β)) : Continuous f :=
   f.continuous_toFun
 #align continuous_map.continuous ContinuousMap.continuous
 
---porting note: todo: restore @[continuity]
+@[continuity]
 theorem continuous_set_coe (s : Set C(α, β)) (f : s) : Continuous (f : α → β) :=
   f.1.continuous
 #align continuous_map.continuous_set_coe ContinuousMap.continuous_set_coe
@@ -192,9 +192,8 @@ end
 variable (α)
 
 /-- The identity as a continuous map. -/
-protected def id : C(α, α) :=
-  ⟨id, continuous_id⟩
-  -- Porting note: proof was `continuity`
+protected def id : C(α, α) where
+  toFun := id
 #align continuous_map.id ContinuousMap.id
 
 @[simp]
@@ -203,9 +202,8 @@ theorem coe_id : ⇑(ContinuousMap.id α) = id :=
 #align continuous_map.coe_id ContinuousMap.coe_id
 
 /-- The constant map as a continuous map. -/
-def const (b : β) : C(α, β) :=
-  ⟨fun _ : α => b, continuous_const⟩
-  -- Porting note: proof was `continuity`
+def const (b : β) : C(α, β) where
+  toFun := fun _ : α => b
 #align continuous_map.const ContinuousMap.const
 
 @[simp]
@@ -229,9 +227,8 @@ theorem const_apply (b : β) (a : α) : const α b a = b :=
 #align continuous_map.const_apply ContinuousMap.const_apply
 
 /-- The composition of continuous maps, as a continuous map. -/
-def comp (f : C(β, γ)) (g : C(α, β)) : C(α, γ) :=
-  ⟨f ∘ g, f.continuous.comp g.continuous⟩
-  -- Porting note: proof was `continuity`
+def comp (f : C(β, γ)) (g : C(α, β)) : C(α, γ) where
+  toFun := f ∘ g
 #align continuous_map.comp ContinuousMap.comp
 
 @[simp]
@@ -290,17 +287,13 @@ variable {α₁ α₂ β₁ β₂ : Type _} [TopologicalSpace α₁] [Topologica
   [TopologicalSpace β₂]
 
 /-- Given two continuous maps `f` and `g`, this is the continuous map `x ↦ (f x, g x)`. -/
-def prodMk (f : C(α, β₁)) (g : C(α, β₂)) : C(α, β₁ × β₂)
-    where
+def prodMk (f : C(α, β₁)) (g : C(α, β₂)) : C(α, β₁ × β₂) where
   toFun x := (f x, g x)
-  continuous_toFun := f.continuous.prod_mk g.continuous
-  -- Porting note: proof was `continuity`
 #align continuous_map.prod_mk ContinuousMap.prodMk
 
 /-- Given two continuous maps `f` and `g`, this is the continuous map `(x, y) ↦ (f x, g y)`. -/
 @[simps]
-def prodMap (f : C(α₁, α₂)) (g : C(β₁, β₂)) : C(α₁ × β₁, α₂ × β₂)
-    where
+def prodMap (f : C(α₁, α₂)) (g : C(β₁, β₂)) : C(α₁ × β₁, α₂ × β₂) where
   toFun := Prod.map f g
   continuous_toFun := f.continuous.prod_map g.continuous
   -- Porting note: proof was `continuity`
@@ -320,8 +313,6 @@ variable {I A : Type _} {X : I → Type _} [TopologicalSpace A] [∀ i, Topologi
 /-- Abbreviation for product of continuous maps, which is continuous -/
 def pi (f : ∀ i, C(A, X i)) : C(A, ∀ i, X i) where
   toFun (a : A) (i : I) := f i a
-  continuous_toFun := continuous_pi (fun i => (f i).continuous)
-  -- Porting note: proof was `continuity`
 #align continuous_map.pi ContinuousMap.pi
 
 @[simp]
@@ -336,9 +327,8 @@ section Restrict
 variable (s : Set α)
 
 /-- The restriction of a continuous function `α → β` to a subset `s` of `α`. -/
-def restrict (f : C(α, β)) : C(s, β) :=
-  ⟨f ∘ ((↑) : s → α), f.continuous.comp continuous_subtype_val⟩
-  -- Porting note: proof was `continuity`
+def restrict (f : C(α, β)) : C(s, β) where
+  toFun := f ∘ ((↑) : s → α)
 #align continuous_map.restrict ContinuousMap.restrict
 
 @[simp]

Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Kevin Buzzard <k.buzzard@imperial.ac.uk>