topology.homotopy.basic | Mathlib porting status

Changes since the initial port

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

Changes in mathlib3

11c53f17

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

10bf4f82

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2021 Shing Tak Lam. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Shing Tak Lam
 -/
-import Topology.Algebra.Order.ProjIcc
+import Topology.Order.ProjIcc
 import Topology.ContinuousFunction.Ordered
 import Topology.CompactOpen
 import Topology.UnitInterval

10bf4f82

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -305,8 +305,8 @@ theorem symm_trans {f₀ f₁ f₂ : C(X, Y)} (F : Homotopy f₀ f₁) (G : Homo
   ext x
   simp only [symm_apply, trans_apply]
   split_ifs with h₁ h₂
-  · change (x.1 : ℝ) ≤ _ at h₂ 
-    change (1 : ℝ) - x.1 ≤ _ at h₁ 
+  · change (x.1 : ℝ) ≤ _ at h₂
+    change (1 : ℝ) - x.1 ≤ _ at h₁
     have ht : (x.1 : ℝ) = 1 / 2 := by linarith
     norm_num [ht]
   · congr 2
@@ -317,8 +317,8 @@ theorem symm_trans {f₀ f₁ f₂ : C(X, Y)} (F : Homotopy f₀ f₁) (G : Homo
     apply Subtype.ext
     simp only [unitInterval.coe_symm_eq, Subtype.coe_mk]
     linarith
-  · change ¬(x.1 : ℝ) ≤ _ at h 
-    change ¬(1 : ℝ) - x.1 ≤ _ at h₁ 
+  · change ¬(x.1 : ℝ) ≤ _ at h
+    change ¬(1 : ℝ) - x.1 ≤ _ at h₁
     exfalso; linarith
 #align continuous_map.homotopy.symm_trans ContinuousMap.Homotopy.symm_trans
 -/

10bf4f82

bump to nightly-2024-01-19-06

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

33b57512

Diff

@@ -119,12 +119,12 @@ instance : HomotopyLike (Homotopy f₀ f₁) f₀ f₁
 /-- Helper instance for when there's too many metavariables to apply `fun_like.has_coe_to_fun`
 directly. -/
 instance : CoeFun (Homotopy f₀ f₁) fun _ => I × X → Y :=
-  FunLike.hasCoeToFun
+  DFunLike.hasCoeToFun
 
 #print ContinuousMap.Homotopy.ext /-
 @[ext]
 theorem ext {F G : Homotopy f₀ f₁} (h : ∀ x, F x = G x) : F = G :=
-  FunLike.ext _ _ h
+  DFunLike.ext _ _ h
 #align continuous_map.homotopy.ext ContinuousMap.Homotopy.ext
 -/

10bf4f82

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,10 +3,10 @@ Copyright (c) 2021 Shing Tak Lam. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Shing Tak Lam
 -/
-import Mathbin.Topology.Algebra.Order.ProjIcc
-import Mathbin.Topology.ContinuousFunction.Ordered
-import Mathbin.Topology.CompactOpen
-import Mathbin.Topology.UnitInterval
+import Topology.Algebra.Order.ProjIcc
+import Topology.ContinuousFunction.Ordered
+import Topology.CompactOpen
+import Topology.UnitInterval
 
 #align_import topology.homotopy.basic from "leanprover-community/mathlib"@"10bf4f825ad729c5653adc039dafa3622e7f93c9"

10bf4f82

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,17 +2,14 @@
 Copyright (c) 2021 Shing Tak Lam. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Shing Tak Lam
-
-! This file was ported from Lean 3 source module topology.homotopy.basic
-! leanprover-community/mathlib commit 10bf4f825ad729c5653adc039dafa3622e7f93c9
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Topology.Algebra.Order.ProjIcc
 import Mathbin.Topology.ContinuousFunction.Ordered
 import Mathbin.Topology.CompactOpen
 import Mathbin.Topology.UnitInterval
 
+#align_import topology.homotopy.basic from "leanprover-community/mathlib"@"10bf4f825ad729c5653adc039dafa3622e7f93c9"
+
 /-!
 # Homotopy between functions

10bf4f82

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -124,10 +124,12 @@ directly. -/
 instance : CoeFun (Homotopy f₀ f₁) fun _ => I × X → Y :=
   FunLike.hasCoeToFun
 
+#print ContinuousMap.Homotopy.ext /-
 @[ext]
 theorem ext {F G : Homotopy f₀ f₁} (h : ∀ x, F x = G x) : F = G :=
   FunLike.ext _ _ h
 #align continuous_map.homotopy.ext ContinuousMap.Homotopy.ext
+-/
 
 #print ContinuousMap.Homotopy.Simps.apply /-
 /-- See Note [custom simps projection]. We need to specify this projection explicitly in this case,
@@ -139,25 +141,33 @@ def Simps.apply (F : Homotopy f₀ f₁) : I × X → Y :=
 
 initialize_simps_projections Homotopy (to_continuous_map_to_fun → apply, -toContinuousMap)
 
+#print ContinuousMap.Homotopy.continuous /-
 /-- Deprecated. Use `map_continuous` instead. -/
 protected theorem continuous (F : Homotopy f₀ f₁) : Continuous F :=
   F.continuous_toFun
 #align continuous_map.homotopy.continuous ContinuousMap.Homotopy.continuous
+-/
 
+#print ContinuousMap.Homotopy.apply_zero /-
 @[simp]
 theorem apply_zero (F : Homotopy f₀ f₁) (x : X) : F (0, x) = f₀ x :=
   F.map_zero_left' x
 #align continuous_map.homotopy.apply_zero ContinuousMap.Homotopy.apply_zero
+-/
 
+#print ContinuousMap.Homotopy.apply_one /-
 @[simp]
 theorem apply_one (F : Homotopy f₀ f₁) (x : X) : F (1, x) = f₁ x :=
   F.map_one_left' x
 #align continuous_map.homotopy.apply_one ContinuousMap.Homotopy.apply_one
+-/
 
+#print ContinuousMap.Homotopy.coe_toContinuousMap /-
 @[simp]
 theorem coe_toContinuousMap (F : Homotopy f₀ f₁) : ⇑F.toContinuousMap = F :=
   rfl
 #align continuous_map.homotopy.coe_to_continuous_map ContinuousMap.Homotopy.coe_toContinuousMap
+-/
 
 #print ContinuousMap.Homotopy.curry /-
 /-- Currying a homotopy to a continuous function fron `I` to `C(X, Y)`.
@@ -167,10 +177,12 @@ def curry (F : Homotopy f₀ f₁) : C(I, C(X, Y)) :=
 #align continuous_map.homotopy.curry ContinuousMap.Homotopy.curry
 -/
 
+#print ContinuousMap.Homotopy.curry_apply /-
 @[simp]
 theorem curry_apply (F : Homotopy f₀ f₁) (t : I) (x : X) : F.curry t x = F (t, x) :=
   rfl
 #align continuous_map.homotopy.curry_apply ContinuousMap.Homotopy.curry_apply
+-/
 
 #print ContinuousMap.Homotopy.extend /-
 /-- Continuously extending a curried homotopy to a function from `ℝ` to `C(X, Y)`.
@@ -180,36 +192,48 @@ def extend (F : Homotopy f₀ f₁) : C(ℝ, C(X, Y)) :=
 #align continuous_map.homotopy.extend ContinuousMap.Homotopy.extend
 -/
 
+#print ContinuousMap.Homotopy.extend_apply_of_le_zero /-
 theorem extend_apply_of_le_zero (F : Homotopy f₀ f₁) {t : ℝ} (ht : t ≤ 0) (x : X) :
     F.extend t x = f₀ x := by
   rw [← F.apply_zero]
   exact ContinuousMap.congr_fun (Set.IccExtend_of_le_left (zero_le_one' ℝ) F.curry ht) x
 #align continuous_map.homotopy.extend_apply_of_le_zero ContinuousMap.Homotopy.extend_apply_of_le_zero
+-/
 
+#print ContinuousMap.Homotopy.extend_apply_of_one_le /-
 theorem extend_apply_of_one_le (F : Homotopy f₀ f₁) {t : ℝ} (ht : 1 ≤ t) (x : X) :
     F.extend t x = f₁ x := by
   rw [← F.apply_one]
   exact ContinuousMap.congr_fun (Set.IccExtend_of_right_le (zero_le_one' ℝ) F.curry ht) x
 #align continuous_map.homotopy.extend_apply_of_one_le ContinuousMap.Homotopy.extend_apply_of_one_le
+-/
 
+#print ContinuousMap.Homotopy.extend_apply_coe /-
 @[simp]
 theorem extend_apply_coe (F : Homotopy f₀ f₁) (t : I) (x : X) : F.extend t x = F (t, x) :=
   ContinuousMap.congr_fun (Set.IccExtend_val (zero_le_one' ℝ) F.curry t) x
 #align continuous_map.homotopy.extend_apply_coe ContinuousMap.Homotopy.extend_apply_coe
+-/
 
+#print ContinuousMap.Homotopy.extend_apply_of_mem_I /-
 @[simp]
 theorem extend_apply_of_mem_I (F : Homotopy f₀ f₁) {t : ℝ} (ht : t ∈ I) (x : X) :
     F.extend t x = F (⟨t, ht⟩, x) :=
   ContinuousMap.congr_fun (Set.IccExtend_of_mem (zero_le_one' ℝ) F.curry ht) x
 #align continuous_map.homotopy.extend_apply_of_mem_I ContinuousMap.Homotopy.extend_apply_of_mem_I
+-/
 
+#print ContinuousMap.Homotopy.congr_fun /-
 theorem congr_fun {F G : Homotopy f₀ f₁} (h : F = G) (x : I × X) : F x = G x :=
   ContinuousMap.congr_fun (congr_arg _ h) x
 #align continuous_map.homotopy.congr_fun ContinuousMap.Homotopy.congr_fun
+-/
 
+#print ContinuousMap.Homotopy.congr_arg /-
 theorem congr_arg (F : Homotopy f₀ f₁) {x y : I × X} (h : x = y) : F x = F y :=
   F.toContinuousMap.congr_arg h
 #align continuous_map.homotopy.congr_arg ContinuousMap.Homotopy.congr_arg
+-/
 
 end
 
@@ -266,6 +290,7 @@ def trans {f₀ f₁ f₂ : C(X, Y)} (F : Homotopy f₀ f₁) (G : Homotopy f₁
 #align continuous_map.homotopy.trans ContinuousMap.Homotopy.trans
 -/
 
+#print ContinuousMap.Homotopy.trans_apply /-
 theorem trans_apply {f₀ f₁ f₂ : C(X, Y)} (F : Homotopy f₀ f₁) (G : Homotopy f₁ f₂) (x : I × X) :
     (F.trans G) x =
       if h : (x.1 : ℝ) ≤ 1 / 2 then
@@ -275,6 +300,7 @@ theorem trans_apply {f₀ f₁ f₂ : C(X, Y)} (F : Homotopy f₀ f₁) (G : Hom
   show ite _ _ _ = _ by
     split_ifs <;> · rw [extend, ContinuousMap.coe_IccExtend, Set.IccExtend_of_mem]; rfl
 #align continuous_map.homotopy.trans_apply ContinuousMap.Homotopy.trans_apply
+-/
 
 #print ContinuousMap.Homotopy.symm_trans /-
 theorem symm_trans {f₀ f₁ f₂ : C(X, Y)} (F : Homotopy f₀ f₁) (G : Homotopy f₁ f₂) :
@@ -398,16 +424,20 @@ variable {f₀ f₁ : C(X, Y)} {P : C(X, Y) → Prop}
 instance : CoeFun (HomotopyWith f₀ f₁ P) fun _ => I × X → Y :=
   ⟨fun F => F.toFun⟩
 
+#print ContinuousMap.HomotopyWith.coeFn_injective /-
 theorem coeFn_injective : @Function.Injective (HomotopyWith f₀ f₁ P) (I × X → Y) coeFn :=
   by
   rintro ⟨⟨⟨F, _⟩, _⟩, _⟩ ⟨⟨⟨G, _⟩, _⟩, _⟩ h
   congr 3
 #align continuous_map.homotopy_with.coe_fn_injective ContinuousMap.HomotopyWith.coeFn_injective
+-/
 
+#print ContinuousMap.HomotopyWith.ext /-
 @[ext]
 theorem ext {F G : HomotopyWith f₀ f₁ P} (h : ∀ x, F x = G x) : F = G :=
   coeFn_injective <| funext h
 #align continuous_map.homotopy_with.ext ContinuousMap.HomotopyWith.ext
+-/
 
 #print ContinuousMap.HomotopyWith.Simps.apply /-
 /-- See Note [custom simps projection]. We need to specify this projection explicitly in this case,
@@ -420,35 +450,48 @@ def Simps.apply (F : HomotopyWith f₀ f₁ P) : I × X → Y :=
 initialize_simps_projections HomotopyWith (to_homotopy_to_continuous_map_to_fun → apply,
   -to_homotopy_to_continuous_map)
 
+#print ContinuousMap.HomotopyWith.continuous /-
 @[continuity]
 protected theorem continuous (F : HomotopyWith f₀ f₁ P) : Continuous F :=
   F.continuous_toFun
 #align continuous_map.homotopy_with.continuous ContinuousMap.HomotopyWith.continuous
+-/
 
+#print ContinuousMap.HomotopyWith.apply_zero /-
 @[simp]
 theorem apply_zero (F : HomotopyWith f₀ f₁ P) (x : X) : F (0, x) = f₀ x :=
   F.map_zero_left' x
 #align continuous_map.homotopy_with.apply_zero ContinuousMap.HomotopyWith.apply_zero
+-/
 
+#print ContinuousMap.HomotopyWith.apply_one /-
 @[simp]
 theorem apply_one (F : HomotopyWith f₀ f₁ P) (x : X) : F (1, x) = f₁ x :=
   F.map_one_left' x
 #align continuous_map.homotopy_with.apply_one ContinuousMap.HomotopyWith.apply_one
+-/
 
+#print ContinuousMap.HomotopyWith.coe_toContinuousMap /-
 @[simp]
 theorem coe_toContinuousMap (F : HomotopyWith f₀ f₁ P) : ⇑F.toContinuousMap = F :=
   rfl
 #align continuous_map.homotopy_with.coe_to_continuous_map ContinuousMap.HomotopyWith.coe_toContinuousMap
+-/
 
+#print ContinuousMap.HomotopyWith.coe_toHomotopy /-
 @[simp]
 theorem coe_toHomotopy (F : HomotopyWith f₀ f₁ P) : ⇑F.toHomotopy = F :=
   rfl
 #align continuous_map.homotopy_with.coe_to_homotopy ContinuousMap.HomotopyWith.coe_toHomotopy
+-/
 
+#print ContinuousMap.HomotopyWith.prop /-
 theorem prop (F : HomotopyWith f₀ f₁ P) (t : I) : P (F.toHomotopy.curry t) :=
   F.prop' t
 #align continuous_map.homotopy_with.prop ContinuousMap.HomotopyWith.prop
+-/
 
+#print ContinuousMap.HomotopyWith.extendProp /-
 theorem extendProp (F : HomotopyWith f₀ f₁ P) (t : ℝ) : P (F.toHomotopy.extend t) :=
   by
   by_cases ht₀ : 0 ≤ t
@@ -465,6 +508,7 @@ theorem extendProp (F : HomotopyWith f₀ f₁ P) (t : ℝ) : P (F.toHomotopy.ex
     rw [F.to_homotopy.extend_apply_of_le_zero (le_of_not_le ht₀), F.to_homotopy.curry_apply,
       F.to_homotopy.apply_zero]
 #align continuous_map.homotopy_with.extend_prop ContinuousMap.HomotopyWith.extendProp
+-/
 
 end
 
@@ -517,6 +561,7 @@ def trans {f₀ f₁ f₂ : C(X, Y)} (F : HomotopyWith f₀ f₁ P) (G : Homotop
 #align continuous_map.homotopy_with.trans ContinuousMap.HomotopyWith.trans
 -/
 
+#print ContinuousMap.HomotopyWith.trans_apply /-
 theorem trans_apply {f₀ f₁ f₂ : C(X, Y)} (F : HomotopyWith f₀ f₁ P) (G : HomotopyWith f₁ f₂ P)
     (x : I × X) :
     (F.trans G) x =
@@ -526,6 +571,7 @@ theorem trans_apply {f₀ f₁ f₂ : C(X, Y)} (F : HomotopyWith f₀ f₁ P) (G
         G (⟨2 * x.1 - 1, unitInterval.two_mul_sub_one_mem_iff.2 ⟨(not_le.1 h).le, x.1.2.2⟩⟩, x.2) :=
   Homotopy.trans_apply _ _ _
 #align continuous_map.homotopy_with.trans_apply ContinuousMap.HomotopyWith.trans_apply
+-/
 
 #print ContinuousMap.HomotopyWith.symm_trans /-
 theorem symm_trans {f₀ f₁ f₂ : C(X, Y)} (F : HomotopyWith f₀ f₁ P) (G : HomotopyWith f₁ f₂ P) :
@@ -598,17 +644,23 @@ section
 
 variable {f₀ f₁ : C(X, Y)} {S : Set X}
 
+#print ContinuousMap.HomotopyRel.eq_fst /-
 theorem eq_fst (F : HomotopyRel f₀ f₁ S) (t : I) {x : X} (hx : x ∈ S) : F (t, x) = f₀ x :=
   (F.Prop t x hx).1
 #align continuous_map.homotopy_rel.eq_fst ContinuousMap.HomotopyRel.eq_fst
+-/
 
+#print ContinuousMap.HomotopyRel.eq_snd /-
 theorem eq_snd (F : HomotopyRel f₀ f₁ S) (t : I) {x : X} (hx : x ∈ S) : F (t, x) = f₁ x :=
   (F.Prop t x hx).2
 #align continuous_map.homotopy_rel.eq_snd ContinuousMap.HomotopyRel.eq_snd
+-/
 
+#print ContinuousMap.HomotopyRel.fst_eq_snd /-
 theorem fst_eq_snd (F : HomotopyRel f₀ f₁ S) {x : X} (hx : x ∈ S) : f₀ x = f₁ x :=
   F.eq_fst 0 hx ▸ F.eq_snd 0 hx
 #align continuous_map.homotopy_rel.fst_eq_snd ContinuousMap.HomotopyRel.fst_eq_snd
+-/
 
 end
 
@@ -658,6 +710,7 @@ def trans (F : HomotopyRel f₀ f₁ S) (G : HomotopyRel f₁ f₂ S) : Homotopy
 #align continuous_map.homotopy_rel.trans ContinuousMap.HomotopyRel.trans
 -/
 
+#print ContinuousMap.HomotopyRel.trans_apply /-
 theorem trans_apply (F : HomotopyRel f₀ f₁ S) (G : HomotopyRel f₁ f₂ S) (x : I × X) :
     (F.trans G) x =
       if h : (x.1 : ℝ) ≤ 1 / 2 then
@@ -666,6 +719,7 @@ theorem trans_apply (F : HomotopyRel f₀ f₁ S) (G : HomotopyRel f₁ f₂ S)
         G (⟨2 * x.1 - 1, unitInterval.two_mul_sub_one_mem_iff.2 ⟨(not_le.1 h).le, x.1.2.2⟩⟩, x.2) :=
   Homotopy.trans_apply _ _ _
 #align continuous_map.homotopy_rel.trans_apply ContinuousMap.HomotopyRel.trans_apply
+-/
 
 #print ContinuousMap.HomotopyRel.symm_trans /-
 theorem symm_trans (F : HomotopyRel f₀ f₁ S) (G : HomotopyRel f₁ f₂ S) :

10bf4f82

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -94,7 +94,7 @@ section
 
 You should extend this class when you extend `continuous_map.homotopy`. -/
 class HomotopyLike (F : Type _) (f₀ f₁ : outParam <| C(X, Y)) extends
-  ContinuousMapClass F (I × X) Y where
+    ContinuousMapClass F (I × X) Y where
   map_zero_left (f : F) : ∀ x, f (0, x) = f₀ x
   map_one_left (f : F) : ∀ x, f (1, x) = f₁ x
 #align continuous_map.homotopy_like ContinuousMap.HomotopyLike
@@ -282,8 +282,8 @@ theorem symm_trans {f₀ f₁ f₂ : C(X, Y)} (F : Homotopy f₀ f₁) (G : Homo
   ext x
   simp only [symm_apply, trans_apply]
   split_ifs with h₁ h₂
-  · change (x.1 : ℝ) ≤ _ at h₂
-    change (1 : ℝ) - x.1 ≤ _ at h₁
+  · change (x.1 : ℝ) ≤ _ at h₂ 
+    change (1 : ℝ) - x.1 ≤ _ at h₁ 
     have ht : (x.1 : ℝ) = 1 / 2 := by linarith
     norm_num [ht]
   · congr 2
@@ -294,8 +294,8 @@ theorem symm_trans {f₀ f₁ f₂ : C(X, Y)} (F : Homotopy f₀ f₁) (G : Homo
     apply Subtype.ext
     simp only [unitInterval.coe_symm_eq, Subtype.coe_mk]
     linarith
-  · change ¬(x.1 : ℝ) ≤ _ at h
-    change ¬(1 : ℝ) - x.1 ≤ _ at h₁
+  · change ¬(x.1 : ℝ) ≤ _ at h 
+    change ¬(1 : ℝ) - x.1 ≤ _ at h₁ 
     exfalso; linarith
 #align continuous_map.homotopy.symm_trans ContinuousMap.Homotopy.symm_trans
 -/

10bf4f82

bump to nightly-2023-05-29-00

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

f7040f5d

Diff

@@ -194,7 +194,7 @@ theorem extend_apply_of_one_le (F : Homotopy f₀ f₁) {t : ℝ} (ht : 1 ≤ t)
 
 @[simp]
 theorem extend_apply_coe (F : Homotopy f₀ f₁) (t : I) (x : X) : F.extend t x = F (t, x) :=
-  ContinuousMap.congr_fun (Set.Icc_extend_coe (zero_le_one' ℝ) F.curry t) x
+  ContinuousMap.congr_fun (Set.IccExtend_val (zero_le_one' ℝ) F.curry t) x
 #align continuous_map.homotopy.extend_apply_coe ContinuousMap.Homotopy.extend_apply_coe
 
 @[simp]

10bf4f82

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -69,7 +69,7 @@ variable {F : Type _} {X : Type u} {Y : Type v} {Z : Type w}
 
 variable [TopologicalSpace X] [TopologicalSpace Y] [TopologicalSpace Z]
 
-open unitInterval
+open scoped unitInterval
 
 namespace ContinuousMap

10bf4f82

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -124,12 +124,6 @@ directly. -/
 instance : CoeFun (Homotopy f₀ f₁) fun _ => I × X → Y :=
   FunLike.hasCoeToFun
 
-/- warning: continuous_map.homotopy.ext -> ContinuousMap.Homotopy.ext is a dubious translation:
-lean 3 declaration is
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 @[ext]
 theorem ext {F G : Homotopy f₀ f₁} (h : ∀ x, F x = G x) : F = G :=
   FunLike.ext _ _ h
@@ -145,45 +139,21 @@ def Simps.apply (F : Homotopy f₀ f₁) : I × X → Y :=
 
 initialize_simps_projections Homotopy (to_continuous_map_to_fun → apply, -toContinuousMap)
 
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 /-- Deprecated. Use `map_continuous` instead. -/
 protected theorem continuous (F : Homotopy f₀ f₁) : Continuous F :=
   F.continuous_toFun
 #align continuous_map.homotopy.continuous ContinuousMap.Homotopy.continuous
 
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 @[simp]
 theorem apply_zero (F : Homotopy f₀ f₁) (x : X) : F (0, x) = f₀ x :=
   F.map_zero_left' x
 #align continuous_map.homotopy.apply_zero ContinuousMap.Homotopy.apply_zero
 
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 @[simp]
 theorem apply_one (F : Homotopy f₀ f₁) (x : X) : F (1, x) = f₁ x :=
   F.map_one_left' x
 #align continuous_map.homotopy.apply_one ContinuousMap.Homotopy.apply_one
 
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 @[simp]
 theorem coe_toContinuousMap (F : Homotopy f₀ f₁) : ⇑F.toContinuousMap = F :=
   rfl
@@ -197,9 +167,6 @@ def curry (F : Homotopy f₀ f₁) : C(I, C(X, Y)) :=
 #align continuous_map.homotopy.curry ContinuousMap.Homotopy.curry
 -/
 
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-<too large>
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 @[simp]
 theorem curry_apply (F : Homotopy f₀ f₁) (t : I) (x : X) : F.curry t x = F (t, x) :=
   rfl
@@ -213,69 +180,33 @@ def extend (F : Homotopy f₀ f₁) : C(ℝ, C(X, Y)) :=
 #align continuous_map.homotopy.extend ContinuousMap.Homotopy.extend
 -/
 
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 theorem extend_apply_of_le_zero (F : Homotopy f₀ f₁) {t : ℝ} (ht : t ≤ 0) (x : X) :
     F.extend t x = f₀ x := by
   rw [← F.apply_zero]
   exact ContinuousMap.congr_fun (Set.IccExtend_of_le_left (zero_le_one' ℝ) F.curry ht) x
 #align continuous_map.homotopy.extend_apply_of_le_zero ContinuousMap.Homotopy.extend_apply_of_le_zero
 
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 theorem extend_apply_of_one_le (F : Homotopy f₀ f₁) {t : ℝ} (ht : 1 ≤ t) (x : X) :
     F.extend t x = f₁ x := by
   rw [← F.apply_one]
   exact ContinuousMap.congr_fun (Set.IccExtend_of_right_le (zero_le_one' ℝ) F.curry ht) x
 #align continuous_map.homotopy.extend_apply_of_one_le ContinuousMap.Homotopy.extend_apply_of_one_le
 
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 @[simp]
 theorem extend_apply_coe (F : Homotopy f₀ f₁) (t : I) (x : X) : F.extend t x = F (t, x) :=
   ContinuousMap.congr_fun (Set.Icc_extend_coe (zero_le_one' ℝ) F.curry t) x
 #align continuous_map.homotopy.extend_apply_coe ContinuousMap.Homotopy.extend_apply_coe
 
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 @[simp]
 theorem extend_apply_of_mem_I (F : Homotopy f₀ f₁) {t : ℝ} (ht : t ∈ I) (x : X) :
     F.extend t x = F (⟨t, ht⟩, x) :=
   ContinuousMap.congr_fun (Set.IccExtend_of_mem (zero_le_one' ℝ) F.curry ht) x
 #align continuous_map.homotopy.extend_apply_of_mem_I ContinuousMap.Homotopy.extend_apply_of_mem_I
 
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 theorem congr_fun {F G : Homotopy f₀ f₁} (h : F = G) (x : I × X) : F x = G x :=
   ContinuousMap.congr_fun (congr_arg _ h) x
 #align continuous_map.homotopy.congr_fun ContinuousMap.Homotopy.congr_fun
 
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 theorem congr_arg (F : Homotopy f₀ f₁) {x y : I × X} (h : x = y) : F x = F y :=
   F.toContinuousMap.congr_arg h
 #align continuous_map.homotopy.congr_arg ContinuousMap.Homotopy.congr_arg
@@ -335,9 +266,6 @@ def trans {f₀ f₁ f₂ : C(X, Y)} (F : Homotopy f₀ f₁) (G : Homotopy f₁
 #align continuous_map.homotopy.trans ContinuousMap.Homotopy.trans
 -/
 
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 theorem trans_apply {f₀ f₁ f₂ : C(X, Y)} (F : Homotopy f₀ f₁) (G : Homotopy f₁ f₂) (x : I × X) :
     (F.trans G) x =
       if h : (x.1 : ℝ) ≤ 1 / 2 then
@@ -470,24 +398,12 @@ variable {f₀ f₁ : C(X, Y)} {P : C(X, Y) → Prop}
 instance : CoeFun (HomotopyWith f₀ f₁ P) fun _ => I × X → Y :=
   ⟨fun F => F.toFun⟩
 
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 theorem coeFn_injective : @Function.Injective (HomotopyWith f₀ f₁ P) (I × X → Y) coeFn :=
   by
   rintro ⟨⟨⟨F, _⟩, _⟩, _⟩ ⟨⟨⟨G, _⟩, _⟩, _⟩ h
   congr 3
 #align continuous_map.homotopy_with.coe_fn_injective ContinuousMap.HomotopyWith.coeFn_injective
 
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 @[ext]
 theorem ext {F G : HomotopyWith f₀ f₁ P} (h : ∀ x, F x = G x) : F = G :=
   coeFn_injective <| funext h
@@ -504,77 +420,35 @@ def Simps.apply (F : HomotopyWith f₀ f₁ P) : I × X → Y :=
 initialize_simps_projections HomotopyWith (to_homotopy_to_continuous_map_to_fun → apply,
   -to_homotopy_to_continuous_map)
 
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 @[continuity]
 protected theorem continuous (F : HomotopyWith f₀ f₁ P) : Continuous F :=
   F.continuous_toFun
 #align continuous_map.homotopy_with.continuous ContinuousMap.HomotopyWith.continuous
 
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 @[simp]
 theorem apply_zero (F : HomotopyWith f₀ f₁ P) (x : X) : F (0, x) = f₀ x :=
   F.map_zero_left' x
 #align continuous_map.homotopy_with.apply_zero ContinuousMap.HomotopyWith.apply_zero
 
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 @[simp]
 theorem apply_one (F : HomotopyWith f₀ f₁ P) (x : X) : F (1, x) = f₁ x :=
   F.map_one_left' x
 #align continuous_map.homotopy_with.apply_one ContinuousMap.HomotopyWith.apply_one
 
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 @[simp]
 theorem coe_toContinuousMap (F : HomotopyWith f₀ f₁ P) : ⇑F.toContinuousMap = F :=
   rfl
 #align continuous_map.homotopy_with.coe_to_continuous_map ContinuousMap.HomotopyWith.coe_toContinuousMap
 
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 @[simp]
 theorem coe_toHomotopy (F : HomotopyWith f₀ f₁ P) : ⇑F.toHomotopy = F :=
   rfl
 #align continuous_map.homotopy_with.coe_to_homotopy ContinuousMap.HomotopyWith.coe_toHomotopy
 
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 theorem prop (F : HomotopyWith f₀ f₁ P) (t : I) : P (F.toHomotopy.curry t) :=
   F.prop' t
 #align continuous_map.homotopy_with.prop ContinuousMap.HomotopyWith.prop
 
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 theorem extendProp (F : HomotopyWith f₀ f₁ P) (t : ℝ) : P (F.toHomotopy.extend t) :=
   by
   by_cases ht₀ : 0 ≤ t
@@ -643,9 +517,6 @@ def trans {f₀ f₁ f₂ : C(X, Y)} (F : HomotopyWith f₀ f₁ P) (G : Homotop
 #align continuous_map.homotopy_with.trans ContinuousMap.HomotopyWith.trans
 -/
 
-/- warning: continuous_map.homotopy_with.trans_apply -> ContinuousMap.HomotopyWith.trans_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy_with.trans_apply ContinuousMap.HomotopyWith.trans_applyₓ'. -/
 theorem trans_apply {f₀ f₁ f₂ : C(X, Y)} (F : HomotopyWith f₀ f₁ P) (G : HomotopyWith f₁ f₂ P)
     (x : I × X) :
     (F.trans G) x =
@@ -727,26 +598,14 @@ section
 
 variable {f₀ f₁ : C(X, Y)} {S : Set X}
 
-/- warning: continuous_map.homotopy_rel.eq_fst -> ContinuousMap.HomotopyRel.eq_fst is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy_rel.eq_fst ContinuousMap.HomotopyRel.eq_fstₓ'. -/
 theorem eq_fst (F : HomotopyRel f₀ f₁ S) (t : I) {x : X} (hx : x ∈ S) : F (t, x) = f₀ x :=
   (F.Prop t x hx).1
 #align continuous_map.homotopy_rel.eq_fst ContinuousMap.HomotopyRel.eq_fst
 
-/- warning: continuous_map.homotopy_rel.eq_snd -> ContinuousMap.HomotopyRel.eq_snd is a dubious translation:
-<too large>
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 theorem eq_snd (F : HomotopyRel f₀ f₁ S) (t : I) {x : X} (hx : x ∈ S) : F (t, x) = f₁ x :=
   (F.Prop t x hx).2
 #align continuous_map.homotopy_rel.eq_snd ContinuousMap.HomotopyRel.eq_snd
 
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 theorem fst_eq_snd (F : HomotopyRel f₀ f₁ S) {x : X} (hx : x ∈ S) : f₀ x = f₁ x :=
   F.eq_fst 0 hx ▸ F.eq_snd 0 hx
 #align continuous_map.homotopy_rel.fst_eq_snd ContinuousMap.HomotopyRel.fst_eq_snd
@@ -799,9 +658,6 @@ def trans (F : HomotopyRel f₀ f₁ S) (G : HomotopyRel f₁ f₂ S) : Homotopy
 #align continuous_map.homotopy_rel.trans ContinuousMap.HomotopyRel.trans
 -/
 
-/- warning: continuous_map.homotopy_rel.trans_apply -> ContinuousMap.HomotopyRel.trans_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy_rel.trans_apply ContinuousMap.HomotopyRel.trans_applyₓ'. -/
 theorem trans_apply (F : HomotopyRel f₀ f₁ S) (G : HomotopyRel f₁ f₂ S) (x : I × X) :
     (F.trans G) x =
       if h : (x.1 : ℝ) ≤ 1 / 2 then

10bf4f82

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -114,10 +114,7 @@ variable {f₀ f₁ : C(X, Y)}
 instance : HomotopyLike (Homotopy f₀ f₁) f₀ f₁
     where
   coe f := f.toFun
-  coe_injective' f g h := by
-    obtain ⟨⟨_, _⟩, _⟩ := f
-    obtain ⟨⟨_, _⟩, _⟩ := g
-    congr
+  coe_injective' f g h := by obtain ⟨⟨_, _⟩, _⟩ := f; obtain ⟨⟨_, _⟩, _⟩ := g; congr
   map_continuous f := f.continuous_toFun
   map_zero_left f := f.map_zero_left'
   map_one_left f := f.map_one_left'
@@ -313,10 +310,7 @@ def symm {f₀ f₁ : C(X, Y)} (F : Homotopy f₀ f₁) : Homotopy f₁ f₀
 
 #print ContinuousMap.Homotopy.symm_symm /-
 @[simp]
-theorem symm_symm {f₀ f₁ : C(X, Y)} (F : Homotopy f₀ f₁) : F.symm.symm = F :=
-  by
-  ext
-  simp
+theorem symm_symm {f₀ f₁ : C(X, Y)} (F : Homotopy f₀ f₁) : F.symm.symm = F := by ext; simp
 #align continuous_map.homotopy.symm_symm ContinuousMap.Homotopy.symm_symm
 -/
 
@@ -351,9 +345,7 @@ theorem trans_apply {f₀ f₁ f₂ : C(X, Y)} (F : Homotopy f₀ f₁) (G : Hom
       else
         G (⟨2 * x.1 - 1, unitInterval.two_mul_sub_one_mem_iff.2 ⟨(not_le.1 h).le, x.1.2.2⟩⟩, x.2) :=
   show ite _ _ _ = _ by
-    split_ifs <;>
-      · rw [extend, ContinuousMap.coe_IccExtend, Set.IccExtend_of_mem]
-        rfl
+    split_ifs <;> · rw [extend, ContinuousMap.coe_IccExtend, Set.IccExtend_of_mem]; rfl
 #align continuous_map.homotopy.trans_apply ContinuousMap.Homotopy.trans_apply
 
 #print ContinuousMap.Homotopy.symm_trans /-
@@ -376,8 +368,7 @@ theorem symm_trans {f₀ f₁ f₂ : C(X, Y)} (F : Homotopy f₀ f₁) (G : Homo
     linarith
   · change ¬(x.1 : ℝ) ≤ _ at h
     change ¬(1 : ℝ) - x.1 ≤ _ at h₁
-    exfalso
-    linarith
+    exfalso; linarith
 #align continuous_map.homotopy.symm_trans ContinuousMap.Homotopy.symm_trans
 -/
 
@@ -611,11 +602,7 @@ variable {P : C(X, Y) → Prop}
 -/
 @[simps]
 def refl (f : C(X, Y)) (hf : P f) : HomotopyWith f f P :=
-  { Homotopy.refl f with
-    prop' := fun t => by
-      convert hf
-      cases f
-      rfl }
+  { Homotopy.refl f with prop' := fun t => by convert hf; cases f; rfl }
 #align continuous_map.homotopy_with.refl ContinuousMap.HomotopyWith.refl
 -/

10bf4f82

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -201,10 +201,7 @@ def curry (F : Homotopy f₀ f₁) : C(I, C(X, Y)) :=
 -/
 
 /- warning: continuous_map.homotopy.curry_apply -> ContinuousMap.Homotopy.curry_apply is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy.curry_apply ContinuousMap.Homotopy.curry_applyₓ'. -/
 @[simp]
 theorem curry_apply (F : Homotopy f₀ f₁) (t : I) (x : X) : F.curry t x = F (t, x) :=
@@ -345,10 +342,7 @@ def trans {f₀ f₁ f₂ : C(X, Y)} (F : Homotopy f₀ f₁) (G : Homotopy f₁
 -/
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy.trans_apply ContinuousMap.Homotopy.trans_applyₓ'. -/
 theorem trans_apply {f₀ f₁ f₂ : C(X, Y)} (F : Homotopy f₀ f₁) (G : Homotopy f₁ f₂) (x : I × X) :
     (F.trans G) x =
@@ -663,10 +657,7 @@ def trans {f₀ f₁ f₂ : C(X, Y)} (F : HomotopyWith f₀ f₁ P) (G : Homotop
 -/
 
 /- warning: continuous_map.homotopy_with.trans_apply -> ContinuousMap.HomotopyWith.trans_apply is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy_with.trans_apply ContinuousMap.HomotopyWith.trans_applyₓ'. -/
 theorem trans_apply {f₀ f₁ f₂ : C(X, Y)} (F : HomotopyWith f₀ f₁ P) (G : HomotopyWith f₁ f₂ P)
     (x : I × X) :
@@ -750,20 +741,14 @@ section
 variable {f₀ f₁ : C(X, Y)} {S : Set X}
 
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 Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy_rel.eq_fst ContinuousMap.HomotopyRel.eq_fstₓ'. -/
 theorem eq_fst (F : HomotopyRel f₀ f₁ S) (t : I) {x : X} (hx : x ∈ S) : F (t, x) = f₀ x :=
   (F.Prop t x hx).1
 #align continuous_map.homotopy_rel.eq_fst ContinuousMap.HomotopyRel.eq_fst
 
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 Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy_rel.eq_snd ContinuousMap.HomotopyRel.eq_sndₓ'. -/
 theorem eq_snd (F : HomotopyRel f₀ f₁ S) (t : I) {x : X} (hx : x ∈ S) : F (t, x) = f₁ x :=
   (F.Prop t x hx).2
@@ -828,10 +813,7 @@ def trans (F : HomotopyRel f₀ f₁ S) (G : HomotopyRel f₁ f₂ S) : Homotopy
 -/
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy_rel.trans_apply ContinuousMap.HomotopyRel.trans_applyₓ'. -/
 theorem trans_apply (F : HomotopyRel f₀ f₁ S) (G : HomotopyRel f₁ f₂ S) (x : I × X) :
     (F.trans G) x =

10bf4f82

bump to nightly-2023-05-16-16

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

9cb92e8c

Diff

@@ -346,7 +346,7 @@ def trans {f₀ f₁ f₂ : C(X, Y)} (F : Homotopy f₀ f₁) (G : Homotopy f₁
 
 /- warning: continuous_map.homotopy.trans_apply -> ContinuousMap.Homotopy.trans_apply is a dubious translation:
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 but is expected to have type
   forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f₀ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₁ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₂ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} (F : ContinuousMap.Homotopy.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁) (G : ContinuousMap.Homotopy.{u1, u2} X Y _inst_1 _inst_2 f₁ f₂) (x : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X), Eq.{succ u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => Y) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.Homotopy.{u1, u2} X Y _inst_1 _inst_2 f₀ f₂) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) (fun (_x : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => Y) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} 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 Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy.trans_apply ContinuousMap.Homotopy.trans_applyₓ'. -/
@@ -664,7 +664,7 @@ def trans {f₀ f₁ f₂ : C(X, Y)} (F : HomotopyWith f₀ f₁ P) (G : Homotop
 
 /- warning: continuous_map.homotopy_with.trans_apply -> ContinuousMap.HomotopyWith.trans_apply is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
   forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {P : (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) -> Prop} {f₀ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₁ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₂ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} (F : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (G : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₁ f₂ P) (x : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X), Eq.{succ u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => Y) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₂ P) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) (fun (_x : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) 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(ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2 (ContinuousMap.HomotopyLike.toContinuousMapClass.{u1, u2, max u1 u2} X Y _inst_1 _inst_2 (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) f₀ f₁ (ContinuousMap.HomotopyWith.instHomotopyLikeHomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P))) F (Prod.mk.{0, u1} (Set.Elem.{0} Real unitInterval) X (Subtype.mk.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 (AddMonoidWithOne.toNatCast.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x))) (Iff.mpr (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 (AddMonoidWithOne.toNatCast.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x 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(AddMonoidWithOne.toNatCast.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (zero_lt_two.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal)) Real.partialOrder (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring) (NeZero.one.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real.nontrivial) (OrderedAddCommGroup.to_covariantClass_left_le.{0} Real Real.orderedAddCommGroup))) (And.intro (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Subtype.val.{1} Real 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 Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy_with.trans_apply ContinuousMap.HomotopyWith.trans_applyₓ'. -/
@@ -829,7 +829,7 @@ def trans (F : HomotopyRel f₀ f₁ S) (G : HomotopyRel f₁ f₂ S) : Homotopy
 
 /- warning: continuous_map.homotopy_rel.trans_apply -> ContinuousMap.HomotopyRel.trans_apply is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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(instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) h)) (And.right (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x))) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (Subtype.property.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)))))) (Prod.snd.{0, u1} (Set.Elem.{0} Real unitInterval) X x))))
 Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy_rel.trans_apply ContinuousMap.HomotopyRel.trans_applyₓ'. -/

10bf4f82

bump to nightly-2023-05-08-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/08e1d8d4d989df3a6df86f385e9053ec8a372cc1

63e712c6

Diff

@@ -348,7 +348,7 @@ def trans {f₀ f₁ f₂ : C(X, Y)} (F : Homotopy f₀ f₁) (G : Homotopy f₁
 lean 3 declaration is
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 but is expected to have type
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u1} (Set.Elem.{0} Real unitInterval) X x)))))) (Prod.snd.{0, u1} (Set.Elem.{0} Real unitInterval) X x))))
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f₀ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₁ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₂ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} (F : ContinuousMap.Homotopy.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁) (G : ContinuousMap.Homotopy.{u1, u2} X Y _inst_1 _inst_2 f₁ f₂) (x : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X), Eq.{succ u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => Y) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.Homotopy.{u1, u2} X Y _inst_1 _inst_2 f₀ f₂) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) (fun (_x : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => Y) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} 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(Set.{0} Real) (Set.instMembershipSet.{0} Real) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 (AddMonoidWithOne.toNatCast.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (unitInterval.mul_pos_mem_iff (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 (AddMonoidWithOne.toNatCast.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real 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(Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x))) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 (AddMonoidWithOne.toNatCast.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (And.left (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x))) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (Subtype.property.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x))) h))) (Prod.snd.{0, u1} (Set.Elem.{0} Real unitInterval) X x))) (fun (h : Not (LE.le.{0} Real Real.instLEReal (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) => FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.Homotopy.{u1, u2} X Y _inst_1 _inst_2 f₁ f₂) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) (fun (_x : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => Y) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousMap.Homotopy.{u1, u2} X Y _inst_1 _inst_2 f₁ f₂) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2 (ContinuousMap.HomotopyLike.toContinuousMapClass.{u1, u2, max u1 u2} X Y _inst_1 _inst_2 (ContinuousMap.Homotopy.{u1, u2} X Y _inst_1 _inst_2 f₁ f₂) f₁ f₂ (ContinuousMap.Homotopy.instHomotopyLikeHomotopy.{u1, u2} X Y _inst_1 _inst_2 f₁ f₂))) G (Prod.mk.{0, u1} (Set.Elem.{0} Real unitInterval) X (Subtype.mk.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (Iff.mpr (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) unitInterval) (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) 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(OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (Iff.mp (Not (LE.le.{0} Real (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (LinearOrder.toPartialOrder.{0} Real Real.linearOrder))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (LT.lt.{0} Real (Preorder.toLT.{0} Real (PartialOrder.toPreorder.{0} Real (LinearOrder.toPartialOrder.{0} Real Real.linearOrder))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x))) (not_le.{0} Real Real.linearOrder (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) h)) (And.right (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x))) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (Subtype.property.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)))))) (Prod.snd.{0, u1} (Set.Elem.{0} Real unitInterval) X x))))
 Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy.trans_apply ContinuousMap.Homotopy.trans_applyₓ'. -/
 theorem trans_apply {f₀ f₁ f₂ : C(X, Y)} (F : Homotopy f₀ f₁) (G : Homotopy f₁ f₂) (x : I × X) :
     (F.trans G) x =
@@ -666,7 +666,7 @@ def trans {f₀ f₁ f₂ : C(X, Y)} (F : HomotopyWith f₀ f₁ P) (G : Homotop
 lean 3 declaration is
   forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {P : (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) -> Prop} {f₀ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₁ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₂ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} (F : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (G : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₁ f₂ P) (x : Prod.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X), Eq.{succ u2} Y (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₂ P) (fun (_x : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₂ P) => (Prod.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X) -> Y) (ContinuousMap.HomotopyWith.hasCoeToFun.{u1, u2} X Y _inst_1 _inst_2 f₀ f₂ P) (ContinuousMap.HomotopyWith.trans.{u1, 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Real.hasAdd (One.one.{0} Real Real.hasOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval))))) (Prod.fst.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X x))) (not_le.{0} Real Real.linearOrder ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) 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(Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (Prod.fst.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X x))) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.preorder) (Subtype.val.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (Prod.fst.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X x)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (Subtype.property.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (Prod.fst.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X x)))))) (Prod.snd.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X x))))
 but is expected to have type
-  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {P : (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) -> Prop} {f₀ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₁ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₂ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} (F : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (G : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₁ f₂ P) (x : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X), Eq.{succ u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => Y) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₂ P) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) (fun (_x : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) 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(h : LE.le.{0} Real Real.instLEReal (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) => FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) (fun (_x : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => Y) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2 (ContinuousMap.HomotopyLike.toContinuousMapClass.{u1, u2, max u1 u2} X Y _inst_1 _inst_2 (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) f₀ f₁ (ContinuousMap.HomotopyWith.instHomotopyLikeHomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P))) F (Prod.mk.{0, u1} (Set.Elem.{0} Real unitInterval) X (Subtype.mk.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 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+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {P : (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) -> Prop} {f₀ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₁ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₂ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} (F : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (G : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₁ f₂ P) (x : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X), Eq.{succ u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => Y) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₂ P) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) (fun (_x : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) 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 Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy_with.trans_apply ContinuousMap.HomotopyWith.trans_applyₓ'. -/
 theorem trans_apply {f₀ f₁ f₂ : C(X, Y)} (F : HomotopyWith f₀ f₁ P) (G : HomotopyWith f₁ f₂ P)
     (x : I × X) :
@@ -831,7 +831,7 @@ def trans (F : HomotopyRel f₀ f₁ S) (G : HomotopyRel f₁ f₂ S) : Homotopy
 lean 3 declaration is
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 but is expected to have type
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(ContinuousMap.instContinuousMapClassContinuousMap.{u1, u2} X Y _inst_1 _inst_2)) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) X (fun (a : X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : X) => Y) a) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) X Y _inst_1 _inst_2 (ContinuousMap.instContinuousMapClassContinuousMap.{u1, u2} X Y _inst_1 _inst_2)) f₁ x)) (Eq.{succ u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : X) => Y) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) X (fun (a : X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : X) => Y) a) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) X Y _inst_1 _inst_2 (ContinuousMap.instContinuousMapClassContinuousMap.{u1, u2} X Y _inst_1 _inst_2)) f x) (FunLike.coe.{max (succ 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(Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (Iff.mpr (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) unitInterval) (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (Set.Icc.{0} Real Real.instPreorderReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (unitInterval.two_mul_sub_one_mem_iff (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x))) (And.intro (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x))) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (LT.lt.le.{0} Real Real.instPreorderReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 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Real.linearOrder))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x))) (not_le.{0} Real Real.linearOrder (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) h)) (And.right (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x))) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (Subtype.property.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)))))) (Prod.snd.{0, u1} (Set.Elem.{0} Real unitInterval) X x))))
 Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy_rel.trans_apply ContinuousMap.HomotopyRel.trans_applyₓ'. -/
 theorem trans_apply (F : HomotopyRel f₀ f₁ S) (G : HomotopyRel f₁ f₂ S) (x : I × X) :
     (F.trans G) x =

10bf4f82

bump to nightly-2023-04-24-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/09079525fd01b3dda35e96adaa08d2f943e1648c

1d7f47bc

Diff

@@ -424,7 +424,7 @@ def Homotopic (f₀ f₁ : C(X, Y)) : Prop :=
 #align continuous_map.homotopic ContinuousMap.Homotopic
 -/
 
-namespace Homotopic
+namespace homotopic
 
 #print ContinuousMap.Homotopic.refl /-
 @[refl]
@@ -460,7 +460,7 @@ theorem equivalence : Equivalence (@Homotopic X Y _ _) :=
 #align continuous_map.homotopic.equivalence ContinuousMap.Homotopic.equivalence
 -/
 
-end Homotopic
+end homotopic
 
 #print ContinuousMap.HomotopyWith /-
 /--

10bf4f82

bump to nightly-2023-04-20-00

mathlib commit https://github.com/leanprover-community/mathlib/commit/cd8fafa2fac98e1a67097e8a91ad9901cfde48af

d6678ca6

Diff

@@ -654,7 +654,7 @@ def trans {f₀ f₁ f₂ : C(X, Y)} (F : HomotopyWith f₀ f₁ P) (G : Homotop
     HomotopyWith f₀ f₂ P :=
   { F.toHomotopy.trans G.toHomotopy with
     prop' := fun t => by
-      simp only [homotopy.trans]
+      simp only [Homotopy.trans]
       change P ⟨fun _ => ite ((t : ℝ) ≤ _) _ _, _⟩
       split_ifs
       · exact F.extend_prop _
@@ -819,7 +819,7 @@ def trans (F : HomotopyRel f₀ f₁ S) (G : HomotopyRel f₁ f₂ S) : Homotopy
   { Homotopy.trans F.toHomotopy G.toHomotopy with
     prop' := fun t => by
       intro x hx
-      simp only [homotopy.trans]
+      simp only [Homotopy.trans]
       change (⟨fun _ => ite ((t : ℝ) ≤ _) _ _, _⟩ : C(X, Y)) _ = _ ∧ _ = _
       split_ifs
       · simp [(homotopy_with.extend_prop F (2 * t) x hx).1, F.fst_eq_snd hx, G.fst_eq_snd hx]

10bf4f82

bump to nightly-2023-04-17-12

mathlib commit https://github.com/leanprover-community/mathlib/commit/17ad94b4953419f3e3ce3e77da3239c62d1d09f0

ab6befdb

Diff

@@ -489,7 +489,7 @@ instance : CoeFun (HomotopyWith f₀ f₁ P) fun _ => I × X → Y :=
 lean 3 declaration is
   forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f₀ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₁ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {P : (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) -> Prop}, Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) ((Prod.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X) -> Y) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (fun (ᾰ : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) => (Prod.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X) -> Y) (ContinuousMap.HomotopyWith.hasCoeToFun.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P))
 but is expected to have type
-  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f₀ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₁ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {P : (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) -> Prop}, Function.Injective.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) ((Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) -> Y) (fun (x : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) => ContinuousMap.toFun.{u1, u2} (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2 (ContinuousMap.Homotopy.toContinuousMap.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ (ContinuousMap.HomotopyWith.toHomotopy.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P x)))
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f₀ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₁ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {P : (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) -> Prop}, Function.Injective.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) ((Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) -> Y) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) (fun (ᾰ : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => Y) ᾰ) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2 (ContinuousMap.HomotopyLike.toContinuousMapClass.{u1, u2, max u1 u2} X Y _inst_1 _inst_2 (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) f₀ f₁ (ContinuousMap.HomotopyWith.instHomotopyLikeHomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P))))
 Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy_with.coe_fn_injective ContinuousMap.HomotopyWith.coeFn_injectiveₓ'. -/
 theorem coeFn_injective : @Function.Injective (HomotopyWith f₀ f₁ P) (I × X → Y) coeFn :=
   by
@@ -501,7 +501,7 @@ theorem coeFn_injective : @Function.Injective (HomotopyWith f₀ f₁ P) (I × X
 lean 3 declaration is
   forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f₀ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₁ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {P : (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) -> Prop} {F : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P} {G : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P}, (forall (x : Prod.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X), Eq.{succ u2} Y (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (fun (_x : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) => (Prod.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X) -> Y) (ContinuousMap.HomotopyWith.hasCoeToFun.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) F x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (fun (_x : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) => (Prod.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X) -> Y) (ContinuousMap.HomotopyWith.hasCoeToFun.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) G x)) -> (Eq.{max (succ u1) (succ u2)} (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) F G)
 but is expected to have type
-  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f₀ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₁ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {P : (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) -> Prop} {F : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P} {G : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P}, (forall (x : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X), Eq.{succ u2} Y (ContinuousMap.toFun.{u1, u2} (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2 (ContinuousMap.Homotopy.toContinuousMap.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ (ContinuousMap.HomotopyWith.toHomotopy.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P F)) x) (ContinuousMap.toFun.{u1, u2} (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2 (ContinuousMap.Homotopy.toContinuousMap.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ (ContinuousMap.HomotopyWith.toHomotopy.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P G)) x)) -> (Eq.{max (succ u1) (succ u2)} (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) F G)
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f₀ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₁ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {P : (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) -> Prop} {F : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P} {G : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P}, (forall (x : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X), Eq.{succ u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => Y) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) (fun (_x : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => Y) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2 (ContinuousMap.HomotopyLike.toContinuousMapClass.{u1, u2, max u1 u2} X Y _inst_1 _inst_2 (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) f₀ f₁ (ContinuousMap.HomotopyWith.instHomotopyLikeHomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P))) F x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) (fun (_x : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => Y) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2 (ContinuousMap.HomotopyLike.toContinuousMapClass.{u1, u2, max u1 u2} X Y _inst_1 _inst_2 (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) f₀ f₁ (ContinuousMap.HomotopyWith.instHomotopyLikeHomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P))) G x)) -> (Eq.{max (succ u1) (succ u2)} (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) F G)
 Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy_with.ext ContinuousMap.HomotopyWith.extₓ'. -/
 @[ext]
 theorem ext {F G : HomotopyWith f₀ f₁ P} (h : ∀ x, F x = G x) : F = G :=
@@ -523,7 +523,7 @@ initialize_simps_projections HomotopyWith (to_homotopy_to_continuous_map_to_fun
 lean 3 declaration is
   forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f₀ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₁ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {P : (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) -> Prop} (F : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P), Continuous.{u1, u2} (Prod.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X) Y (Prod.topologicalSpace.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2 (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (fun (_x : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) => (Prod.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X) -> Y) (ContinuousMap.HomotopyWith.hasCoeToFun.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) F)
 but is expected to have type
-  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f₀ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₁ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {P : (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) -> Prop} (F : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P), Continuous.{u1, u2} (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2 (ContinuousMap.toFun.{u1, u2} (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2 (ContinuousMap.Homotopy.toContinuousMap.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ (ContinuousMap.HomotopyWith.toHomotopy.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P F)))
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f₀ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₁ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {P : (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) -> Prop} (F : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P), Continuous.{u1, u2} (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2 (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) (fun (_x : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => Y) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2 (ContinuousMap.HomotopyLike.toContinuousMapClass.{u1, u2, max u1 u2} X Y _inst_1 _inst_2 (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) f₀ f₁ (ContinuousMap.HomotopyWith.instHomotopyLikeHomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P))) F)
 Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy_with.continuous ContinuousMap.HomotopyWith.continuousₓ'. -/
 @[continuity]
 protected theorem continuous (F : HomotopyWith f₀ f₁ P) : Continuous F :=
@@ -534,7 +534,7 @@ protected theorem continuous (F : HomotopyWith f₀ f₁ P) : Continuous F :=
 lean 3 declaration is
   forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f₀ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₁ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {P : (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) -> Prop} (F : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (x : X), Eq.{succ u2} Y (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (fun (_x : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) => (Prod.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X) -> Y) (ContinuousMap.HomotopyWith.hasCoeToFun.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) F (Prod.mk.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X (OfNat.ofNat.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) 0 (OfNat.mk.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) 0 (Zero.zero.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) unitInterval.hasZero))) x)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) (fun (_x : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) => X -> Y) (ContinuousMap.hasCoeToFun.{u1, u2} X Y _inst_1 _inst_2) f₀ x)
 but is expected to have type
-  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f₀ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₁ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {P : (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) -> Prop} (F : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (x : X), Eq.{succ u2} Y (ContinuousMap.toFun.{u1, u2} (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2 (ContinuousMap.Homotopy.toContinuousMap.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ (ContinuousMap.HomotopyWith.toHomotopy.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P F)) (Prod.mk.{0, u1} (Set.Elem.{0} Real unitInterval) X (OfNat.ofNat.{0} (Set.Elem.{0} Real unitInterval) 0 (Zero.toOfNat0.{0} (Set.Elem.{0} Real unitInterval) unitInterval.hasZero)) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) X (fun (_x : X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : X) => Y) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) X Y _inst_1 _inst_2 (ContinuousMap.instContinuousMapClassContinuousMap.{u1, u2} X Y _inst_1 _inst_2)) f₀ x)
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f₀ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₁ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {P : (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) -> Prop} (F : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (x : X), Eq.{succ u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => Y) (Prod.mk.{0, u1} (Set.Elem.{0} Real unitInterval) X (OfNat.ofNat.{0} (Set.Elem.{0} Real unitInterval) 0 (Zero.toOfNat0.{0} (Set.Elem.{0} Real unitInterval) unitInterval.hasZero)) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) (fun (_x : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => Y) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2 (ContinuousMap.HomotopyLike.toContinuousMapClass.{u1, u2, max u1 u2} X Y _inst_1 _inst_2 (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) f₀ f₁ (ContinuousMap.HomotopyWith.instHomotopyLikeHomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P))) F (Prod.mk.{0, u1} (Set.Elem.{0} Real unitInterval) X (OfNat.ofNat.{0} (Set.Elem.{0} Real unitInterval) 0 (Zero.toOfNat0.{0} (Set.Elem.{0} Real unitInterval) unitInterval.hasZero)) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) X (fun (_x : X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : X) => Y) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) X Y _inst_1 _inst_2 (ContinuousMap.instContinuousMapClassContinuousMap.{u1, u2} X Y _inst_1 _inst_2)) f₀ x)
 Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy_with.apply_zero ContinuousMap.HomotopyWith.apply_zeroₓ'. -/
 @[simp]
 theorem apply_zero (F : HomotopyWith f₀ f₁ P) (x : X) : F (0, x) = f₀ x :=
@@ -545,7 +545,7 @@ theorem apply_zero (F : HomotopyWith f₀ f₁ P) (x : X) : F (0, x) = f₀ x :=
 lean 3 declaration is
   forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f₀ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₁ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {P : (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) -> Prop} (F : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (x : X), Eq.{succ u2} Y (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (fun (_x : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) => (Prod.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X) -> Y) (ContinuousMap.HomotopyWith.hasCoeToFun.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) F (Prod.mk.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X (OfNat.ofNat.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) 1 (OfNat.mk.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) 1 (One.one.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) unitInterval.hasOne))) x)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) (fun (_x : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) => X -> Y) (ContinuousMap.hasCoeToFun.{u1, u2} X Y _inst_1 _inst_2) f₁ x)
 but is expected to have type
-  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f₀ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₁ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {P : (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) -> Prop} (F : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (x : X), Eq.{succ u2} Y (ContinuousMap.toFun.{u1, u2} (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2 (ContinuousMap.Homotopy.toContinuousMap.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ (ContinuousMap.HomotopyWith.toHomotopy.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P F)) (Prod.mk.{0, u1} (Set.Elem.{0} Real unitInterval) X (OfNat.ofNat.{0} (Set.Elem.{0} Real unitInterval) 1 (One.toOfNat1.{0} (Set.Elem.{0} Real unitInterval) unitInterval.hasOne)) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) X (fun (_x : X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : X) => Y) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) X Y _inst_1 _inst_2 (ContinuousMap.instContinuousMapClassContinuousMap.{u1, u2} X Y _inst_1 _inst_2)) f₁ x)
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f₀ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₁ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {P : (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) -> Prop} (F : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (x : X), Eq.{succ u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => Y) (Prod.mk.{0, u1} (Set.Elem.{0} Real unitInterval) X (OfNat.ofNat.{0} (Set.Elem.{0} Real unitInterval) 1 (One.toOfNat1.{0} (Set.Elem.{0} Real unitInterval) unitInterval.hasOne)) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) (fun (_x : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => Y) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2 (ContinuousMap.HomotopyLike.toContinuousMapClass.{u1, u2, max u1 u2} X Y _inst_1 _inst_2 (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) f₀ f₁ (ContinuousMap.HomotopyWith.instHomotopyLikeHomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P))) F (Prod.mk.{0, u1} (Set.Elem.{0} Real unitInterval) X (OfNat.ofNat.{0} (Set.Elem.{0} Real unitInterval) 1 (One.toOfNat1.{0} (Set.Elem.{0} Real unitInterval) unitInterval.hasOne)) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) X (fun (_x : X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : X) => Y) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) X Y _inst_1 _inst_2 (ContinuousMap.instContinuousMapClassContinuousMap.{u1, u2} X Y _inst_1 _inst_2)) f₁ x)
 Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy_with.apply_one ContinuousMap.HomotopyWith.apply_oneₓ'. -/
 @[simp]
 theorem apply_one (F : HomotopyWith f₀ f₁ P) (x : X) : F (1, x) = f₁ x :=
@@ -556,7 +556,7 @@ theorem apply_one (F : HomotopyWith f₀ f₁ P) (x : X) : F (1, x) = f₁ x :=
 lean 3 declaration is
   forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f₀ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₁ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {P : (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) -> Prop} (F : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P), Eq.{max (succ u1) (succ u2)} ((Prod.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X) -> Y) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} (Prod.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X) Y (Prod.topologicalSpace.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2) (fun (_x : ContinuousMap.{u1, u2} (Prod.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X) Y (Prod.topologicalSpace.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2) => (Prod.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X) -> Y) (ContinuousMap.hasCoeToFun.{u1, u2} (Prod.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X) Y (Prod.topologicalSpace.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2) (ContinuousMap.Homotopy.toContinuousMap.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ (ContinuousMap.HomotopyWith.toHomotopy.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P F))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (fun (_x : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) => (Prod.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X) -> Y) (ContinuousMap.HomotopyWith.hasCoeToFun.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) F)
 but is expected to have type
-  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f₀ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₁ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {P : (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) -> Prop} (F : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P), Eq.{max (succ u1) (succ u2)} (forall (ᾰ : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => Y) ᾰ) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.{u1, u2} (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) (fun (_x : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => Y) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousMap.{u1, u2} (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2 (ContinuousMap.instContinuousMapClassContinuousMap.{u1, u2} (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2)) (ContinuousMap.Homotopy.toContinuousMap.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ (ContinuousMap.HomotopyWith.toHomotopy.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P F))) (ContinuousMap.toFun.{u1, u2} (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2 (ContinuousMap.Homotopy.toContinuousMap.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ (ContinuousMap.HomotopyWith.toHomotopy.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P F)))
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f₀ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₁ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {P : (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) -> Prop} (F : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P), Eq.{max (succ u1) (succ u2)} (forall (ᾰ : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => Y) ᾰ) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.{u1, u2} (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) (fun (_x : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => Y) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousMap.{u1, u2} (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2 (ContinuousMap.instContinuousMapClassContinuousMap.{u1, u2} (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2)) (ContinuousMap.Homotopy.toContinuousMap.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ (ContinuousMap.HomotopyWith.toHomotopy.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P F))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) (fun (_x : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => Y) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2 (ContinuousMap.HomotopyLike.toContinuousMapClass.{u1, u2, max u1 u2} X Y _inst_1 _inst_2 (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) f₀ f₁ (ContinuousMap.HomotopyWith.instHomotopyLikeHomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P))) F)
 Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy_with.coe_to_continuous_map ContinuousMap.HomotopyWith.coe_toContinuousMapₓ'. -/
 @[simp]
 theorem coe_toContinuousMap (F : HomotopyWith f₀ f₁ P) : ⇑F.toContinuousMap = F :=
@@ -567,7 +567,7 @@ theorem coe_toContinuousMap (F : HomotopyWith f₀ f₁ P) : ⇑F.toContinuousMa
 lean 3 declaration is
   forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f₀ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₁ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {P : (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) -> Prop} (F : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P), Eq.{max (succ u1) (succ u2)} ((Prod.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X) -> Y) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.Homotopy.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁) (fun (_x : ContinuousMap.Homotopy.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁) => (Prod.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X) -> Y) (ContinuousMap.Homotopy.hasCoeToFun.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁) (ContinuousMap.HomotopyWith.toHomotopy.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P F)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (fun (_x : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) => (Prod.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X) -> Y) (ContinuousMap.HomotopyWith.hasCoeToFun.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) F)
 but is expected to have type
-  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f₀ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₁ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {P : (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) -> Prop} (F : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P), Eq.{max (succ u1) (succ u2)} (forall (ᾰ : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => Y) ᾰ) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.Homotopy.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) (fun (_x : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => Y) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousMap.Homotopy.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2 (ContinuousMap.HomotopyLike.toContinuousMapClass.{u1, u2, max u1 u2} X Y _inst_1 _inst_2 (ContinuousMap.Homotopy.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁) f₀ f₁ (ContinuousMap.Homotopy.instHomotopyLikeHomotopy.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁))) (ContinuousMap.HomotopyWith.toHomotopy.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P F)) (ContinuousMap.toFun.{u1, u2} (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2 (ContinuousMap.Homotopy.toContinuousMap.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ (ContinuousMap.HomotopyWith.toHomotopy.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P F)))
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f₀ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₁ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {P : (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) -> Prop} (F : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P), Eq.{max (succ u1) (succ u2)} (forall (ᾰ : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => Y) ᾰ) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.Homotopy.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) (fun (_x : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => Y) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousMap.Homotopy.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2 (ContinuousMap.HomotopyLike.toContinuousMapClass.{u1, u2, max u1 u2} X Y _inst_1 _inst_2 (ContinuousMap.Homotopy.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁) f₀ f₁ (ContinuousMap.Homotopy.instHomotopyLikeHomotopy.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁))) (ContinuousMap.HomotopyWith.toHomotopy.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P F)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) (fun (_x : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => Y) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2 (ContinuousMap.HomotopyLike.toContinuousMapClass.{u1, u2, max u1 u2} X Y _inst_1 _inst_2 (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) f₀ f₁ (ContinuousMap.HomotopyWith.instHomotopyLikeHomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P))) F)
 Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy_with.coe_to_homotopy ContinuousMap.HomotopyWith.coe_toHomotopyₓ'. -/
 @[simp]
 theorem coe_toHomotopy (F : HomotopyWith f₀ f₁ P) : ⇑F.toHomotopy = F :=
@@ -666,7 +666,7 @@ def trans {f₀ f₁ f₂ : C(X, Y)} (F : HomotopyWith f₀ f₁ P) (G : Homotop
 lean 3 declaration is
   forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {P : (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) -> Prop} {f₀ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₁ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₂ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} (F : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (G : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₁ f₂ P) (x : Prod.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X), Eq.{succ u2} Y (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₂ P) (fun (_x : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₂ P) => (Prod.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X) -> Y) (ContinuousMap.HomotopyWith.hasCoeToFun.{u1, u2} X Y _inst_1 _inst_2 f₀ f₂ P) (ContinuousMap.HomotopyWith.trans.{u1, 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(HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval))))) (Prod.fst.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X x))) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.preorder) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval))))) (Prod.fst.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X x)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (LT.lt.le.{0} Real Real.preorder (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval))))) (Prod.fst.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X x)) (Iff.mp (Not (LE.le.{0} Real (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (LinearOrder.toPartialOrder.{0} Real Real.linearOrder))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval))))) (Prod.fst.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X x)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) (LT.lt.{0} Real (Preorder.toLT.{0} Real (PartialOrder.toPreorder.{0} Real (LinearOrder.toPartialOrder.{0} Real Real.linearOrder))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval))))) (Prod.fst.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X x))) (not_le.{0} Real Real.linearOrder ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval))))) (Prod.fst.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X x)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) h)) (And.right (LE.le.{0} Real (Preorder.toLE.{0} Real Real.preorder) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Subtype.val.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (Prod.fst.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X x))) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.preorder) (Subtype.val.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (Prod.fst.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X x)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (Subtype.property.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (Prod.fst.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X x)))))) (Prod.snd.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X x))))
 but is expected to have type
-  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {P : (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) -> Prop} {f₀ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₁ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₂ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} (F : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (G : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₁ f₂ P) (x : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X), Eq.{succ u2} Y (ContinuousMap.toFun.{u1, u2} (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2 (ContinuousMap.Homotopy.toContinuousMap.{u1, u2} X Y _inst_1 _inst_2 f₀ f₂ (ContinuousMap.HomotopyWith.toHomotopy.{u1, u2} X Y _inst_1 _inst_2 f₀ f₂ P (ContinuousMap.HomotopyWith.trans.{u1, u2} X Y _inst_1 _inst_2 P f₀ f₁ f₂ F G))) x) (dite.{succ u2} Y (LE.le.{0} Real Real.instLEReal (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (Real.decidableLE (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (fun (h : LE.le.{0} Real Real.instLEReal (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) => ContinuousMap.toFun.{u1, u2} (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2 (ContinuousMap.Homotopy.toContinuousMap.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ (ContinuousMap.HomotopyWith.toHomotopy.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P F)) (Prod.mk.{0, u1} (Set.Elem.{0} Real unitInterval) X (Subtype.mk.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 (AddMonoidWithOne.toNatCast.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x))) (Iff.mpr (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 (AddMonoidWithOne.toNatCast.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x))) unitInterval) (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 (AddMonoidWithOne.toNatCast.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (unitInterval.mul_pos_mem_iff (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 (AddMonoidWithOne.toNatCast.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (zero_lt_two.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal)) Real.partialOrder (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring) (NeZero.one.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) Real.nontrivial) (OrderedAddCommGroup.to_covariantClass_left_le.{0} Real Real.orderedAddCommGroup))) (And.intro (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x 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(LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) => ContinuousMap.toFun.{u1, u2} (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2 (ContinuousMap.Homotopy.toContinuousMap.{u1, u2} X Y _inst_1 _inst_2 f₁ f₂ (ContinuousMap.HomotopyWith.toHomotopy.{u1, u2} X Y _inst_1 _inst_2 f₁ f₂ P G)) (Prod.mk.{0, u1} (Set.Elem.{0} Real unitInterval) X (Subtype.mk.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} 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+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {P : (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) -> Prop} {f₀ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₁ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₂ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} (F : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (G : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₁ f₂ P) (x : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X), Eq.{succ u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => Y) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₂ P) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) (fun (_x : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) 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(h : LE.le.{0} Real Real.instLEReal (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) => FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) (fun (_x : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => Y) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2 (ContinuousMap.HomotopyLike.toContinuousMapClass.{u1, u2, max u1 u2} X Y _inst_1 _inst_2 (ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) f₀ f₁ (ContinuousMap.HomotopyWith.instHomotopyLikeHomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P))) F (Prod.mk.{0, u1} (Set.Elem.{0} Real unitInterval) X (Subtype.mk.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 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Real.instZeroReal)) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x))) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 (AddMonoidWithOne.toNatCast.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (And.left (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x))) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (Subtype.property.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x))) h))) (Prod.snd.{0, u1} (Set.Elem.{0} Real unitInterval) X x))) (fun (h : Not (LE.le.{0} Real Real.instLEReal (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x 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(OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (Iff.mp (Not (LE.le.{0} Real (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (LinearOrder.toPartialOrder.{0} Real Real.linearOrder))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (LT.lt.{0} Real (Preorder.toLT.{0} Real (PartialOrder.toPreorder.{0} Real (LinearOrder.toPartialOrder.{0} Real Real.linearOrder))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x))) (not_le.{0} Real Real.linearOrder (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) h)) (And.right (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x))) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (Subtype.property.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)))))) (Prod.snd.{0, u1} (Set.Elem.{0} Real unitInterval) X x))))
 Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy_with.trans_apply ContinuousMap.HomotopyWith.trans_applyₓ'. -/
 theorem trans_apply {f₀ f₁ f₂ : C(X, Y)} (F : HomotopyWith f₀ f₁ P) (G : HomotopyWith f₁ f₂ P)
     (x : I × X) :
@@ -753,7 +753,7 @@ variable {f₀ f₁ : C(X, Y)} {S : Set X}
 lean 3 declaration is
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 but is expected to have type
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+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f₀ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₁ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {S : Set.{u1} X} (F : ContinuousMap.HomotopyRel.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ S) (t : Set.Elem.{0} Real unitInterval) {x : X}, (Membership.mem.{u1, u1} X (Set.{u1} X) (Set.instMembershipSet.{u1} X) x S) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => Y) (Prod.mk.{0, u1} (Set.Elem.{0} Real unitInterval) X t x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.HomotopyRel.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ S) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) (fun (_x : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => Y) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousMap.HomotopyRel.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ S) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2 (ContinuousMap.HomotopyLike.toContinuousMapClass.{u1, u2, max u1 u2} X Y _inst_1 _inst_2 (ContinuousMap.HomotopyRel.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ S) f₀ f₁ (ContinuousMap.HomotopyWith.instHomotopyLikeHomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ (fun (f : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) => forall (x : X), (Membership.mem.{u1, u1} X (Set.{u1} X) (Set.instMembershipSet.{u1} X) x S) -> (And (Eq.{succ u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : X) => Y) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) X (fun (a : X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : X) => Y) a) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) X Y _inst_1 _inst_2 (ContinuousMap.instContinuousMapClassContinuousMap.{u1, u2} X Y _inst_1 _inst_2)) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) X (fun (a : X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : X) => Y) a) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) X Y _inst_1 _inst_2 (ContinuousMap.instContinuousMapClassContinuousMap.{u1, u2} X Y _inst_1 _inst_2)) f₀ x)) (Eq.{succ u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : X) => Y) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) X (fun (a : X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : X) => Y) a) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) X Y _inst_1 _inst_2 (ContinuousMap.instContinuousMapClassContinuousMap.{u1, u2} X Y _inst_1 _inst_2)) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) X (fun (a : X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : X) => Y) a) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) X Y _inst_1 _inst_2 (ContinuousMap.instContinuousMapClassContinuousMap.{u1, u2} X Y _inst_1 _inst_2)) f₁ x))))))) F (Prod.mk.{0, u1} (Set.Elem.{0} Real unitInterval) X t x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) X (fun (_x : X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : X) => Y) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) X Y _inst_1 _inst_2 (ContinuousMap.instContinuousMapClassContinuousMap.{u1, u2} X Y _inst_1 _inst_2)) f₀ x))
 Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy_rel.eq_fst ContinuousMap.HomotopyRel.eq_fstₓ'. -/
 theorem eq_fst (F : HomotopyRel f₀ f₁ S) (t : I) {x : X} (hx : x ∈ S) : F (t, x) = f₀ x :=
   (F.Prop t x hx).1
@@ -763,7 +763,7 @@ theorem eq_fst (F : HomotopyRel f₀ f₁ S) (t : I) {x : X} (hx : x ∈ S) : F
 lean 3 declaration is
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 but is expected to have type
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+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f₀ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₁ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {S : Set.{u1} X} (F : ContinuousMap.HomotopyRel.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ S) (t : Set.Elem.{0} Real unitInterval) {x : X}, (Membership.mem.{u1, u1} X (Set.{u1} X) (Set.instMembershipSet.{u1} X) x S) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => Y) (Prod.mk.{0, u1} (Set.Elem.{0} Real unitInterval) X t x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.HomotopyRel.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ S) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) (fun (_x : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => Y) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousMap.HomotopyRel.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ S) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2 (ContinuousMap.HomotopyLike.toContinuousMapClass.{u1, u2, max u1 u2} X Y _inst_1 _inst_2 (ContinuousMap.HomotopyRel.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ S) f₀ f₁ (ContinuousMap.HomotopyWith.instHomotopyLikeHomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ (fun (f : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) => forall (x : X), (Membership.mem.{u1, u1} X (Set.{u1} X) (Set.instMembershipSet.{u1} X) x S) -> (And (Eq.{succ u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : X) => Y) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) X (fun (a : X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : X) => Y) a) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) X Y _inst_1 _inst_2 (ContinuousMap.instContinuousMapClassContinuousMap.{u1, u2} X Y _inst_1 _inst_2)) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) X (fun (a : X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : X) => Y) a) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) X Y _inst_1 _inst_2 (ContinuousMap.instContinuousMapClassContinuousMap.{u1, u2} X Y _inst_1 _inst_2)) f₀ x)) (Eq.{succ u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : X) => Y) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) X (fun (a : X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : X) => Y) a) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) X Y _inst_1 _inst_2 (ContinuousMap.instContinuousMapClassContinuousMap.{u1, u2} X Y _inst_1 _inst_2)) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) X (fun (a : X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : X) => Y) a) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) X Y _inst_1 _inst_2 (ContinuousMap.instContinuousMapClassContinuousMap.{u1, u2} X Y _inst_1 _inst_2)) f₁ x))))))) F (Prod.mk.{0, u1} (Set.Elem.{0} Real unitInterval) X t x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) X (fun (_x : X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : X) => Y) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) X Y _inst_1 _inst_2 (ContinuousMap.instContinuousMapClassContinuousMap.{u1, u2} X Y _inst_1 _inst_2)) f₁ x))
 Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy_rel.eq_snd ContinuousMap.HomotopyRel.eq_sndₓ'. -/
 theorem eq_snd (F : HomotopyRel f₀ f₁ S) (t : I) {x : X} (hx : x ∈ S) : F (t, x) = f₁ x :=
   (F.Prop t x hx).2
@@ -831,7 +831,7 @@ def trans (F : HomotopyRel f₀ f₁ S) (G : HomotopyRel f₁ f₂ S) : Homotopy
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy_rel.trans_apply ContinuousMap.HomotopyRel.trans_applyₓ'. -/
 theorem trans_apply (F : HomotopyRel f₀ f₁ S) (G : HomotopyRel f₁ f₂ S) (x : I × X) :
     (F.trans G) x =

10bf4f82

bump to nightly-2023-03-27-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce86f4e05e9a9b8da5e316b22c76ce76440c56a1

0e4ebd8c

Diff

@@ -346,7 +346,7 @@ def trans {f₀ f₁ f₂ : C(X, Y)} (F : Homotopy f₀ f₁) (G : Homotopy f₁
 
 /- warning: continuous_map.homotopy.trans_apply -> ContinuousMap.Homotopy.trans_apply is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
   forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f₀ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₁ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₂ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} (F : ContinuousMap.Homotopy.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁) (G : ContinuousMap.Homotopy.{u1, u2} X Y _inst_1 _inst_2 f₁ f₂) (x : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X), Eq.{succ u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => Y) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.Homotopy.{u1, u2} X Y _inst_1 _inst_2 f₀ f₂) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) (fun (_x : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => Y) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} 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 Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy.trans_apply ContinuousMap.Homotopy.trans_applyₓ'. -/
@@ -664,7 +664,7 @@ def trans {f₀ f₁ f₂ : C(X, Y)} (F : HomotopyWith f₀ f₁ P) (G : Homotop
 
 /- warning: continuous_map.homotopy_with.trans_apply -> ContinuousMap.HomotopyWith.trans_apply is a dubious translation:
 lean 3 declaration is
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(Set.hasCoeToSort.{0} Real) unitInterval) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval))))) (Prod.fst.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X x)) (Set.Icc.{0} Real Real.preorder (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (unitInterval.two_mul_sub_one_mem_iff ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) 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(HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval))))) (Prod.fst.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X x))) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.preorder) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval))))) (Prod.fst.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X x)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (LT.lt.le.{0} Real Real.preorder (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval))))) (Prod.fst.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X x)) (Iff.mp (Not (LE.le.{0} Real (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (LinearOrder.toPartialOrder.{0} Real Real.linearOrder))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval))))) (Prod.fst.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X x)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) (LT.lt.{0} Real (Preorder.toLT.{0} Real (PartialOrder.toPreorder.{0} Real (LinearOrder.toPartialOrder.{0} Real Real.linearOrder))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval))))) (Prod.fst.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X x))) (not_le.{0} Real Real.linearOrder ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval))))) (Prod.fst.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X x)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) h)) (And.right (LE.le.{0} Real (Preorder.toLE.{0} Real Real.preorder) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Subtype.val.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (Prod.fst.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X x))) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.preorder) (Subtype.val.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (Prod.fst.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X x)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (Subtype.property.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (Prod.fst.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X x)))))) (Prod.snd.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X x))))
 but is expected to have type
   forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {P : (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) -> Prop} {f₀ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₁ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₂ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} (F : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (G : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₁ f₂ P) (x : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X), Eq.{succ u2} Y (ContinuousMap.toFun.{u1, u2} (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2 (ContinuousMap.Homotopy.toContinuousMap.{u1, u2} X Y _inst_1 _inst_2 f₀ f₂ (ContinuousMap.HomotopyWith.toHomotopy.{u1, u2} X Y _inst_1 _inst_2 f₀ f₂ P (ContinuousMap.HomotopyWith.trans.{u1, u2} X Y _inst_1 _inst_2 P f₀ f₁ f₂ F G))) x) (dite.{succ u2} Y (LE.le.{0} Real Real.instLEReal (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (Real.decidableLE (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (fun (h : LE.le.{0} Real Real.instLEReal (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) => ContinuousMap.toFun.{u1, u2} (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2 (ContinuousMap.Homotopy.toContinuousMap.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ (ContinuousMap.HomotopyWith.toHomotopy.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P F)) (Prod.mk.{0, u1} (Set.Elem.{0} Real unitInterval) X (Subtype.mk.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 (AddMonoidWithOne.toNatCast.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x))) (Iff.mpr (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 (AddMonoidWithOne.toNatCast.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x))) unitInterval) (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) 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(instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (zero_lt_two.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal)) Real.partialOrder (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring) (NeZero.one.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) Real.nontrivial) (OrderedAddCommGroup.to_covariantClass_left_le.{0} Real Real.orderedAddCommGroup))) (And.intro (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x 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 Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy_with.trans_apply ContinuousMap.HomotopyWith.trans_applyₓ'. -/
@@ -829,7 +829,7 @@ def trans (F : HomotopyRel f₀ f₁ S) (G : HomotopyRel f₁ f₂ S) : Homotopy
 
 /- warning: continuous_map.homotopy_rel.trans_apply -> ContinuousMap.HomotopyRel.trans_apply is a dubious translation:
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy_rel.trans_apply ContinuousMap.HomotopyRel.trans_applyₓ'. -/

10bf4f82

bump to nightly-2023-03-16-03

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

8ae28b0b

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Shing Tak Lam
 
 ! This file was ported from Lean 3 source module topology.homotopy.basic
-! leanprover-community/mathlib commit 11c53f174270aa43140c0b26dabce5fc4a253e80
+! leanprover-community/mathlib commit 10bf4f825ad729c5653adc039dafa3622e7f93c9
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.Topology.UnitInterval
 /-!
 # Homotopy between functions
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file, we define a homotopy between two functions `f₀` and `f₁`. First we define
 `continuous_map.homotopy` between the two functions, with no restrictions on the intermediate
 maps. Then, as in the formalisation in HOL-Analysis, we define

11c53f17

bump to nightly-2023-03-13-14

mathlib commit https://github.com/leanprover-community/mathlib/commit/2af0836443b4cfb5feda0df0051acdb398304931

a0c9db6f

Diff

@@ -70,6 +70,7 @@ open unitInterval
 
 namespace ContinuousMap
 
+#print ContinuousMap.Homotopy /-
 /-- `continuous_map.homotopy f₀ f₁` is the type of homotopies from `f₀` to `f₁`.
 
 When possible, instead of parametrizing results over `(f : homotopy f₀ f₁)`,
@@ -80,9 +81,11 @@ structure Homotopy (f₀ f₁ : C(X, Y)) extends C(I × X, Y) where
   map_zero_left' : ∀ x, to_fun (0, x) = f₀ x
   map_one_left' : ∀ x, to_fun (1, x) = f₁ x
 #align continuous_map.homotopy ContinuousMap.Homotopy
+-/
 
 section
 
+#print ContinuousMap.HomotopyLike /-
 /-- `continuous_map.homotopy_like F f₀ f₁` states that `F` is a type of homotopies between `f₀` and
 `f₁`.
 
@@ -92,6 +95,7 @@ class HomotopyLike (F : Type _) (f₀ f₁ : outParam <| C(X, Y)) extends
   map_zero_left (f : F) : ∀ x, f (0, x) = f₀ x
   map_one_left (f : F) : ∀ x, f (1, x) = f₁ x
 #align continuous_map.homotopy_like ContinuousMap.HomotopyLike
+-/
 
 end
 
@@ -120,89 +124,168 @@ directly. -/
 instance : CoeFun (Homotopy f₀ f₁) fun _ => I × X → Y :=
   FunLike.hasCoeToFun
 
+/- warning: continuous_map.homotopy.ext -> ContinuousMap.Homotopy.ext is a dubious translation:
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 @[ext]
 theorem ext {F G : Homotopy f₀ f₁} (h : ∀ x, F x = G x) : F = G :=
   FunLike.ext _ _ h
 #align continuous_map.homotopy.ext ContinuousMap.Homotopy.ext
 
+#print ContinuousMap.Homotopy.Simps.apply /-
 /-- See Note [custom simps projection]. We need to specify this projection explicitly in this case,
 because it is a composition of multiple projections. -/
 def Simps.apply (F : Homotopy f₀ f₁) : I × X → Y :=
   F
 #align continuous_map.homotopy.simps.apply ContinuousMap.Homotopy.Simps.apply
+-/
 
 initialize_simps_projections Homotopy (to_continuous_map_to_fun → apply, -toContinuousMap)
 
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+Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy.continuous ContinuousMap.Homotopy.continuousₓ'. -/
 /-- Deprecated. Use `map_continuous` instead. -/
 protected theorem continuous (F : Homotopy f₀ f₁) : Continuous F :=
   F.continuous_toFun
 #align continuous_map.homotopy.continuous ContinuousMap.Homotopy.continuous
 
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 @[simp]
 theorem apply_zero (F : Homotopy f₀ f₁) (x : X) : F (0, x) = f₀ x :=
   F.map_zero_left' x
 #align continuous_map.homotopy.apply_zero ContinuousMap.Homotopy.apply_zero
 
+/- warning: continuous_map.homotopy.apply_one -> ContinuousMap.Homotopy.apply_one is a dubious translation:
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 @[simp]
 theorem apply_one (F : Homotopy f₀ f₁) (x : X) : F (1, x) = f₁ x :=
   F.map_one_left' x
 #align continuous_map.homotopy.apply_one ContinuousMap.Homotopy.apply_one
 
+/- warning: continuous_map.homotopy.coe_to_continuous_map -> ContinuousMap.Homotopy.coe_toContinuousMap is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy.coe_to_continuous_map ContinuousMap.Homotopy.coe_toContinuousMapₓ'. -/
 @[simp]
 theorem coe_toContinuousMap (F : Homotopy f₀ f₁) : ⇑F.toContinuousMap = F :=
   rfl
 #align continuous_map.homotopy.coe_to_continuous_map ContinuousMap.Homotopy.coe_toContinuousMap
 
+#print ContinuousMap.Homotopy.curry /-
 /-- Currying a homotopy to a continuous function fron `I` to `C(X, Y)`.
 -/
 def curry (F : Homotopy f₀ f₁) : C(I, C(X, Y)) :=
   F.toContinuousMap.curry
 #align continuous_map.homotopy.curry ContinuousMap.Homotopy.curry
+-/
 
+/- warning: continuous_map.homotopy.curry_apply -> ContinuousMap.Homotopy.curry_apply is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy.curry_apply ContinuousMap.Homotopy.curry_applyₓ'. -/
 @[simp]
 theorem curry_apply (F : Homotopy f₀ f₁) (t : I) (x : X) : F.curry t x = F (t, x) :=
   rfl
 #align continuous_map.homotopy.curry_apply ContinuousMap.Homotopy.curry_apply
 
+#print ContinuousMap.Homotopy.extend /-
 /-- Continuously extending a curried homotopy to a function from `ℝ` to `C(X, Y)`.
 -/
 def extend (F : Homotopy f₀ f₁) : C(ℝ, C(X, Y)) :=
   F.curry.IccExtend zero_le_one
 #align continuous_map.homotopy.extend ContinuousMap.Homotopy.extend
+-/
 
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+Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy.extend_apply_of_le_zero ContinuousMap.Homotopy.extend_apply_of_le_zeroₓ'. -/
 theorem extend_apply_of_le_zero (F : Homotopy f₀ f₁) {t : ℝ} (ht : t ≤ 0) (x : X) :
     F.extend t x = f₀ x := by
   rw [← F.apply_zero]
   exact ContinuousMap.congr_fun (Set.IccExtend_of_le_left (zero_le_one' ℝ) F.curry ht) x
 #align continuous_map.homotopy.extend_apply_of_le_zero ContinuousMap.Homotopy.extend_apply_of_le_zero
 
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+Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy.extend_apply_of_one_le ContinuousMap.Homotopy.extend_apply_of_one_leₓ'. -/
 theorem extend_apply_of_one_le (F : Homotopy f₀ f₁) {t : ℝ} (ht : 1 ≤ t) (x : X) :
     F.extend t x = f₁ x := by
   rw [← F.apply_one]
   exact ContinuousMap.congr_fun (Set.IccExtend_of_right_le (zero_le_one' ℝ) F.curry ht) x
 #align continuous_map.homotopy.extend_apply_of_one_le ContinuousMap.Homotopy.extend_apply_of_one_le
 
+/- warning: continuous_map.homotopy.extend_apply_coe -> ContinuousMap.Homotopy.extend_apply_coe is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy.extend_apply_coe ContinuousMap.Homotopy.extend_apply_coeₓ'. -/
 @[simp]
 theorem extend_apply_coe (F : Homotopy f₀ f₁) (t : I) (x : X) : F.extend t x = F (t, x) :=
   ContinuousMap.congr_fun (Set.Icc_extend_coe (zero_le_one' ℝ) F.curry t) x
 #align continuous_map.homotopy.extend_apply_coe ContinuousMap.Homotopy.extend_apply_coe
 
+/- warning: continuous_map.homotopy.extend_apply_of_mem_I -> ContinuousMap.Homotopy.extend_apply_of_mem_I is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy.extend_apply_of_mem_I ContinuousMap.Homotopy.extend_apply_of_mem_Iₓ'. -/
 @[simp]
 theorem extend_apply_of_mem_I (F : Homotopy f₀ f₁) {t : ℝ} (ht : t ∈ I) (x : X) :
     F.extend t x = F (⟨t, ht⟩, x) :=
   ContinuousMap.congr_fun (Set.IccExtend_of_mem (zero_le_one' ℝ) F.curry ht) x
 #align continuous_map.homotopy.extend_apply_of_mem_I ContinuousMap.Homotopy.extend_apply_of_mem_I
 
+/- warning: continuous_map.homotopy.congr_fun -> ContinuousMap.Homotopy.congr_fun is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy.congr_fun ContinuousMap.Homotopy.congr_funₓ'. -/
 theorem congr_fun {F G : Homotopy f₀ f₁} (h : F = G) (x : I × X) : F x = G x :=
   ContinuousMap.congr_fun (congr_arg _ h) x
 #align continuous_map.homotopy.congr_fun ContinuousMap.Homotopy.congr_fun
 
+/- warning: continuous_map.homotopy.congr_arg -> ContinuousMap.Homotopy.congr_arg is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy.congr_arg ContinuousMap.Homotopy.congr_argₓ'. -/
 theorem congr_arg (F : Homotopy f₀ f₁) {x y : I × X} (h : x = y) : F x = F y :=
   F.toContinuousMap.congr_arg h
 #align continuous_map.homotopy.congr_arg ContinuousMap.Homotopy.congr_arg
 
 end
 
+#print ContinuousMap.Homotopy.refl /-
 /-- Given a continuous function `f`, we can define a `homotopy f f` by `F (t, x) = f x`
 -/
 @[simps]
@@ -211,10 +294,12 @@ def refl (f : C(X, Y)) : Homotopy f f where
   map_zero_left' _ := rfl
   map_one_left' _ := rfl
 #align continuous_map.homotopy.refl ContinuousMap.Homotopy.refl
+-/
 
 instance : Inhabited (Homotopy (ContinuousMap.id X) (ContinuousMap.id X)) :=
   ⟨Homotopy.refl _⟩
 
+#print ContinuousMap.Homotopy.symm /-
 /-- Given a `homotopy f₀ f₁`, we can define a `homotopy f₁ f₀` by reversing the homotopy.
 -/
 @[simps]
@@ -224,14 +309,18 @@ def symm {f₀ f₁ : C(X, Y)} (F : Homotopy f₀ f₁) : Homotopy f₁ f₀
   map_zero_left' := by norm_num
   map_one_left' := by norm_num
 #align continuous_map.homotopy.symm ContinuousMap.Homotopy.symm
+-/
 
+#print ContinuousMap.Homotopy.symm_symm /-
 @[simp]
 theorem symm_symm {f₀ f₁ : C(X, Y)} (F : Homotopy f₀ f₁) : F.symm.symm = F :=
   by
   ext
   simp
 #align continuous_map.homotopy.symm_symm ContinuousMap.Homotopy.symm_symm
+-/
 
+#print ContinuousMap.Homotopy.trans /-
 /--
 Given `homotopy f₀ f₁` and `homotopy f₁ f₂`, we can define a `homotopy f₀ f₂` by putting the first
 homotopy on `[0, 1/2]` and the second on `[1/2, 1]`.
@@ -250,7 +339,14 @@ def trans {f₀ f₁ f₂ : C(X, Y)} (F : Homotopy f₀ f₁) (G : Homotopy f₁
   map_zero_left' x := by norm_num
   map_one_left' x := by norm_num
 #align continuous_map.homotopy.trans ContinuousMap.Homotopy.trans
+-/
 
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+but is expected to have type
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f₀ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₁ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₂ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} (F : ContinuousMap.Homotopy.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁) (G : ContinuousMap.Homotopy.{u1, u2} X Y _inst_1 _inst_2 f₁ f₂) (x : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X), Eq.{succ u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => Y) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.Homotopy.{u1, u2} X Y _inst_1 _inst_2 f₀ f₂) (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) (fun (_x : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) => Y) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} 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unitInterval) X x)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (Real.decidableLE (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (fun (h : LE.le.{0} Real Real.instLEReal (Subtype.val.{1} Real (fun (x : Real) => 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(Set.{0} Real) (Set.instMembershipSet.{0} Real) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 (AddMonoidWithOne.toNatCast.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (unitInterval.mul_pos_mem_iff (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 (AddMonoidWithOne.toNatCast.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real 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u1} (Set.Elem.{0} Real unitInterval) X x)))))) (Prod.snd.{0, u1} (Set.Elem.{0} Real unitInterval) X x))))
+Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy.trans_apply ContinuousMap.Homotopy.trans_applyₓ'. -/
 theorem trans_apply {f₀ f₁ f₂ : C(X, Y)} (F : Homotopy f₀ f₁) (G : Homotopy f₁ f₂) (x : I × X) :
     (F.trans G) x =
       if h : (x.1 : ℝ) ≤ 1 / 2 then
@@ -263,6 +359,7 @@ theorem trans_apply {f₀ f₁ f₂ : C(X, Y)} (F : Homotopy f₀ f₁) (G : Hom
         rfl
 #align continuous_map.homotopy.trans_apply ContinuousMap.Homotopy.trans_apply
 
+#print ContinuousMap.Homotopy.symm_trans /-
 theorem symm_trans {f₀ f₁ f₂ : C(X, Y)} (F : Homotopy f₀ f₁) (G : Homotopy f₁ f₂) :
     (F.trans G).symm = G.symm.trans F.symm := by
   ext x
@@ -285,7 +382,9 @@ theorem symm_trans {f₀ f₁ f₂ : C(X, Y)} (F : Homotopy f₀ f₁) (G : Homo
     exfalso
     linarith
 #align continuous_map.homotopy.symm_trans ContinuousMap.Homotopy.symm_trans
+-/
 
+#print ContinuousMap.Homotopy.cast /-
 /-- Casting a `homotopy f₀ f₁` to a `homotopy g₀ g₁` where `f₀ = g₀` and `f₁ = g₁`.
 -/
 @[simps]
@@ -295,7 +394,9 @@ def cast {f₀ f₁ g₀ g₁ : C(X, Y)} (F : Homotopy f₀ f₁) (h₀ : f₀ =
   map_zero_left' := by simp [← h₀]
   map_one_left' := by simp [← h₁]
 #align continuous_map.homotopy.cast ContinuousMap.Homotopy.cast
+-/
 
+#print ContinuousMap.Homotopy.hcomp /-
 /-- If we have a `homotopy f₀ f₁` and a `homotopy g₀ g₁`, then we can compose them and get a
 `homotopy (g₀.comp f₀) (g₁.comp f₁)`.
 -/
@@ -307,44 +408,58 @@ def hcomp {f₀ f₁ : C(X, Y)} {g₀ g₁ : C(Y, Z)} (F : Homotopy f₀ f₁) (
   map_zero_left' := by simp
   map_one_left' := by simp
 #align continuous_map.homotopy.hcomp ContinuousMap.Homotopy.hcomp
+-/
 
 end Homotopy
 
+#print ContinuousMap.Homotopic /-
 /-- Given continuous maps `f₀` and `f₁`, we say `f₀` and `f₁` are homotopic if there exists a
 `homotopy f₀ f₁`.
 -/
 def Homotopic (f₀ f₁ : C(X, Y)) : Prop :=
   Nonempty (Homotopy f₀ f₁)
 #align continuous_map.homotopic ContinuousMap.Homotopic
+-/
 
 namespace Homotopic
 
+#print ContinuousMap.Homotopic.refl /-
 @[refl]
 theorem refl (f : C(X, Y)) : Homotopic f f :=
   ⟨Homotopy.refl f⟩
 #align continuous_map.homotopic.refl ContinuousMap.Homotopic.refl
+-/
 
+#print ContinuousMap.Homotopic.symm /-
 @[symm]
 theorem symm ⦃f g : C(X, Y)⦄ (h : Homotopic f g) : Homotopic g f :=
   h.map Homotopy.symm
 #align continuous_map.homotopic.symm ContinuousMap.Homotopic.symm
+-/
 
+#print ContinuousMap.Homotopic.trans /-
 @[trans]
 theorem trans ⦃f g h : C(X, Y)⦄ (h₀ : Homotopic f g) (h₁ : Homotopic g h) : Homotopic f h :=
   h₀.map2 Homotopy.trans h₁
 #align continuous_map.homotopic.trans ContinuousMap.Homotopic.trans
+-/
 
+#print ContinuousMap.Homotopic.hcomp /-
 theorem hcomp {f₀ f₁ : C(X, Y)} {g₀ g₁ : C(Y, Z)} (h₀ : Homotopic f₀ f₁) (h₁ : Homotopic g₀ g₁) :
     Homotopic (g₀.comp f₀) (g₁.comp f₁) :=
   h₀.map2 Homotopy.hcomp h₁
 #align continuous_map.homotopic.hcomp ContinuousMap.Homotopic.hcomp
+-/
 
+#print ContinuousMap.Homotopic.equivalence /-
 theorem equivalence : Equivalence (@Homotopic X Y _ _) :=
   ⟨refl, symm, trans⟩
 #align continuous_map.homotopic.equivalence ContinuousMap.Homotopic.equivalence
+-/
 
 end Homotopic
 
+#print ContinuousMap.HomotopyWith /-
 /--
 The type of homotopies between `f₀ f₁ : C(X, Y)`, where the intermediate maps satisfy the predicate
 `P : C(X, Y) → Prop`
@@ -356,6 +471,7 @@ structure HomotopyWith (f₀ f₁ : C(X, Y)) (P : C(X, Y) → Prop) extends Homo
         ⟨fun x => to_fun (t, x),
           Continuous.comp continuous_to_fun (continuous_const.prod_mk continuous_id')⟩
 #align continuous_map.homotopy_with ContinuousMap.HomotopyWith
+-/
 
 namespace HomotopyWith
 
@@ -366,55 +482,111 @@ variable {f₀ f₁ : C(X, Y)} {P : C(X, Y) → Prop}
 instance : CoeFun (HomotopyWith f₀ f₁ P) fun _ => I × X → Y :=
   ⟨fun F => F.toFun⟩
 
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 theorem coeFn_injective : @Function.Injective (HomotopyWith f₀ f₁ P) (I × X → Y) coeFn :=
   by
   rintro ⟨⟨⟨F, _⟩, _⟩, _⟩ ⟨⟨⟨G, _⟩, _⟩, _⟩ h
   congr 3
 #align continuous_map.homotopy_with.coe_fn_injective ContinuousMap.HomotopyWith.coeFn_injective
 
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 @[ext]
 theorem ext {F G : HomotopyWith f₀ f₁ P} (h : ∀ x, F x = G x) : F = G :=
   coeFn_injective <| funext h
 #align continuous_map.homotopy_with.ext ContinuousMap.HomotopyWith.ext
 
+#print ContinuousMap.HomotopyWith.Simps.apply /-
 /-- See Note [custom simps projection]. We need to specify this projection explicitly in this case,
 because it is a composition of multiple projections. -/
 def Simps.apply (F : HomotopyWith f₀ f₁ P) : I × X → Y :=
   F
 #align continuous_map.homotopy_with.simps.apply ContinuousMap.HomotopyWith.Simps.apply
+-/
 
 initialize_simps_projections HomotopyWith (to_homotopy_to_continuous_map_to_fun → apply,
   -to_homotopy_to_continuous_map)
 
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 @[continuity]
 protected theorem continuous (F : HomotopyWith f₀ f₁ P) : Continuous F :=
   F.continuous_toFun
 #align continuous_map.homotopy_with.continuous ContinuousMap.HomotopyWith.continuous
 
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 @[simp]
 theorem apply_zero (F : HomotopyWith f₀ f₁ P) (x : X) : F (0, x) = f₀ x :=
   F.map_zero_left' x
 #align continuous_map.homotopy_with.apply_zero ContinuousMap.HomotopyWith.apply_zero
 
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 @[simp]
 theorem apply_one (F : HomotopyWith f₀ f₁ P) (x : X) : F (1, x) = f₁ x :=
   F.map_one_left' x
 #align continuous_map.homotopy_with.apply_one ContinuousMap.HomotopyWith.apply_one
 
+/- warning: continuous_map.homotopy_with.coe_to_continuous_map -> ContinuousMap.HomotopyWith.coe_toContinuousMap is a dubious translation:
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 @[simp]
 theorem coe_toContinuousMap (F : HomotopyWith f₀ f₁ P) : ⇑F.toContinuousMap = F :=
   rfl
 #align continuous_map.homotopy_with.coe_to_continuous_map ContinuousMap.HomotopyWith.coe_toContinuousMap
 
+/- warning: continuous_map.homotopy_with.coe_to_homotopy -> ContinuousMap.HomotopyWith.coe_toHomotopy is a dubious translation:
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 @[simp]
 theorem coe_toHomotopy (F : HomotopyWith f₀ f₁ P) : ⇑F.toHomotopy = F :=
   rfl
 #align continuous_map.homotopy_with.coe_to_homotopy ContinuousMap.HomotopyWith.coe_toHomotopy
 
+/- warning: continuous_map.homotopy_with.prop -> ContinuousMap.HomotopyWith.prop is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy_with.prop ContinuousMap.HomotopyWith.propₓ'. -/
 theorem prop (F : HomotopyWith f₀ f₁ P) (t : I) : P (F.toHomotopy.curry t) :=
   F.prop' t
 #align continuous_map.homotopy_with.prop ContinuousMap.HomotopyWith.prop
 
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+Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy_with.extend_prop ContinuousMap.HomotopyWith.extendPropₓ'. -/
 theorem extendProp (F : HomotopyWith f₀ f₁ P) (t : ℝ) : P (F.toHomotopy.extend t) :=
   by
   by_cases ht₀ : 0 ≤ t
@@ -436,6 +608,7 @@ end
 
 variable {P : C(X, Y) → Prop}
 
+#print ContinuousMap.HomotopyWith.refl /-
 /-- Given a continuous function `f`, and a proof `h : P f`, we can define a `homotopy_with f f P` by
 `F (t, x) = f x`
 -/
@@ -447,10 +620,12 @@ def refl (f : C(X, Y)) (hf : P f) : HomotopyWith f f P :=
       cases f
       rfl }
 #align continuous_map.homotopy_with.refl ContinuousMap.HomotopyWith.refl
+-/
 
 instance : Inhabited (HomotopyWith (ContinuousMap.id X) (ContinuousMap.id X) fun f => True) :=
   ⟨HomotopyWith.refl _ trivial⟩
 
+#print ContinuousMap.HomotopyWith.symm /-
 /--
 Given a `homotopy_with f₀ f₁ P`, we can define a `homotopy_with f₁ f₀ P` by reversing the homotopy.
 -/
@@ -458,12 +633,16 @@ Given a `homotopy_with f₀ f₁ P`, we can define a `homotopy_with f₁ f₀ P`
 def symm {f₀ f₁ : C(X, Y)} (F : HomotopyWith f₀ f₁ P) : HomotopyWith f₁ f₀ P :=
   { F.toHomotopy.symm with prop' := fun t => by simpa using F.prop (σ t) }
 #align continuous_map.homotopy_with.symm ContinuousMap.HomotopyWith.symm
+-/
 
+#print ContinuousMap.HomotopyWith.symm_symm /-
 @[simp]
 theorem symm_symm {f₀ f₁ : C(X, Y)} (F : HomotopyWith f₀ f₁ P) : F.symm.symm = F :=
   ext <| Homotopy.congr_fun <| Homotopy.symm_symm _
 #align continuous_map.homotopy_with.symm_symm ContinuousMap.HomotopyWith.symm_symm
+-/
 
+#print ContinuousMap.HomotopyWith.trans /-
 /--
 Given `homotopy_with f₀ f₁ P` and `homotopy_with f₁ f₂ P`, we can define a `homotopy_with f₀ f₂ P`
 by putting the first homotopy on `[0, 1/2]` and the second on `[1/2, 1]`.
@@ -478,7 +657,14 @@ def trans {f₀ f₁ f₂ : C(X, Y)} (F : HomotopyWith f₀ f₁ P) (G : Homotop
       · exact F.extend_prop _
       · exact G.extend_prop _ }
 #align continuous_map.homotopy_with.trans ContinuousMap.HomotopyWith.trans
+-/
 
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(Set.hasCoeToSort.{0} Real) unitInterval) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval))))) (Prod.fst.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X x))) (not_le.{0} Real Real.linearOrder ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval))))) (Prod.fst.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X x)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) h)) (And.right (LE.le.{0} Real (Preorder.toLE.{0} Real Real.preorder) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Subtype.val.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (Prod.fst.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X x))) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.preorder) (Subtype.val.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (Prod.fst.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X x)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (Subtype.property.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (Prod.fst.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X x)))))) (Prod.snd.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X x))))
+but is expected to have type
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {P : (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) -> Prop} {f₀ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₁ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {f₂ : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} (F : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P) (G : ContinuousMap.HomotopyWith.{u1, u2} X Y _inst_1 _inst_2 f₁ f₂ P) (x : Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X), Eq.{succ u2} Y (ContinuousMap.toFun.{u1, u2} (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2 (ContinuousMap.Homotopy.toContinuousMap.{u1, u2} X Y _inst_1 _inst_2 f₀ f₂ (ContinuousMap.HomotopyWith.toHomotopy.{u1, u2} X Y _inst_1 _inst_2 f₀ f₂ P (ContinuousMap.HomotopyWith.trans.{u1, u2} X Y _inst_1 _inst_2 P f₀ f₁ f₂ F G))) x) (dite.{succ u2} Y (LE.le.{0} Real Real.instLEReal (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (Real.decidableLE (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (fun (h : LE.le.{0} Real Real.instLEReal (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) => ContinuousMap.toFun.{u1, u2} (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2 (ContinuousMap.Homotopy.toContinuousMap.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ (ContinuousMap.HomotopyWith.toHomotopy.{u1, u2} X Y _inst_1 _inst_2 f₀ f₁ P F)) (Prod.mk.{0, u1} (Set.Elem.{0} Real unitInterval) X (Subtype.mk.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 (AddMonoidWithOne.toNatCast.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x))) (Iff.mpr (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 (AddMonoidWithOne.toNatCast.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x))) unitInterval) (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 (AddMonoidWithOne.toNatCast.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (unitInterval.mul_pos_mem_iff (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 (AddMonoidWithOne.toNatCast.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (zero_lt_two.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal)) Real.partialOrder (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring) (NeZero.one.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) Real.nontrivial) (OrderedAddCommGroup.to_covariantClass_left_le.{0} Real Real.orderedAddCommGroup))) (And.intro (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x))) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 (AddMonoidWithOne.toNatCast.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (And.left (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x))) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (Subtype.property.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x))) h))) (Prod.snd.{0, u1} (Set.Elem.{0} Real unitInterval) X x))) (fun (h : Not (LE.le.{0} Real Real.instLEReal (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) => ContinuousMap.toFun.{u1, u2} (Prod.{0, u1} (Set.Elem.{0} Real unitInterval) X) Y (instTopologicalSpaceProd.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) _inst_2 (ContinuousMap.Homotopy.toContinuousMap.{u1, u2} X Y _inst_1 _inst_2 f₁ f₂ (ContinuousMap.HomotopyWith.toHomotopy.{u1, u2} X Y _inst_1 _inst_2 f₁ f₂ P G)) (Prod.mk.{0, u1} (Set.Elem.{0} Real unitInterval) X (Subtype.mk.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (Iff.mpr (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) unitInterval) (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (Set.Icc.{0} Real Real.instPreorderReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) 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+Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy_with.trans_apply ContinuousMap.HomotopyWith.trans_applyₓ'. -/
 theorem trans_apply {f₀ f₁ f₂ : C(X, Y)} (F : HomotopyWith f₀ f₁ P) (G : HomotopyWith f₁ f₂ P)
     (x : I × X) :
     (F.trans G) x =
@@ -489,11 +675,14 @@ theorem trans_apply {f₀ f₁ f₂ : C(X, Y)} (F : HomotopyWith f₀ f₁ P) (G
   Homotopy.trans_apply _ _ _
 #align continuous_map.homotopy_with.trans_apply ContinuousMap.HomotopyWith.trans_apply
 
+#print ContinuousMap.HomotopyWith.symm_trans /-
 theorem symm_trans {f₀ f₁ f₂ : C(X, Y)} (F : HomotopyWith f₀ f₁ P) (G : HomotopyWith f₁ f₂ P) :
     (F.trans G).symm = G.symm.trans F.symm :=
   ext <| Homotopy.congr_fun <| Homotopy.symm_trans _ _
 #align continuous_map.homotopy_with.symm_trans ContinuousMap.HomotopyWith.symm_trans
+-/
 
+#print ContinuousMap.HomotopyWith.cast /-
 /-- Casting a `homotopy_with f₀ f₁ P` to a `homotopy_with g₀ g₁ P` where `f₀ = g₀` and `f₁ = g₁`.
 -/
 @[simps]
@@ -501,44 +690,55 @@ def cast {f₀ f₁ g₀ g₁ : C(X, Y)} (F : HomotopyWith f₀ f₁ P) (h₀ :
     HomotopyWith g₀ g₁ P :=
   { F.toHomotopy.cast h₀ h₁ with prop' := F.Prop }
 #align continuous_map.homotopy_with.cast ContinuousMap.HomotopyWith.cast
+-/
 
 end HomotopyWith
 
+#print ContinuousMap.HomotopicWith /-
 /-- Given continuous maps `f₀` and `f₁`, we say `f₀` and `f₁` are homotopic with respect to the
 predicate `P` if there exists a `homotopy_with f₀ f₁ P`.
 -/
 def HomotopicWith (f₀ f₁ : C(X, Y)) (P : C(X, Y) → Prop) : Prop :=
   Nonempty (HomotopyWith f₀ f₁ P)
 #align continuous_map.homotopic_with ContinuousMap.HomotopicWith
+-/
 
 namespace HomotopicWith
 
 variable {P : C(X, Y) → Prop}
 
+#print ContinuousMap.HomotopicWith.refl /-
 @[refl]
 theorem refl (f : C(X, Y)) (hf : P f) : HomotopicWith f f P :=
   ⟨HomotopyWith.refl f hf⟩
 #align continuous_map.homotopic_with.refl ContinuousMap.HomotopicWith.refl
+-/
 
+#print ContinuousMap.HomotopicWith.symm /-
 @[symm]
 theorem symm ⦃f g : C(X, Y)⦄ (h : HomotopicWith f g P) : HomotopicWith g f P :=
   ⟨h.some.symm⟩
 #align continuous_map.homotopic_with.symm ContinuousMap.HomotopicWith.symm
+-/
 
+#print ContinuousMap.HomotopicWith.trans /-
 @[trans]
 theorem trans ⦃f g h : C(X, Y)⦄ (h₀ : HomotopicWith f g P) (h₁ : HomotopicWith g h P) :
     HomotopicWith f h P :=
   ⟨h₀.some.trans h₁.some⟩
 #align continuous_map.homotopic_with.trans ContinuousMap.HomotopicWith.trans
+-/
 
 end HomotopicWith
 
+#print ContinuousMap.HomotopyRel /-
 /--
 A `homotopy_rel f₀ f₁ S` is a homotopy between `f₀` and `f₁` which is fixed on the points in `S`.
 -/
 abbrev HomotopyRel (f₀ f₁ : C(X, Y)) (S : Set X) :=
   HomotopyWith f₀ f₁ fun f => ∀ x ∈ S, f x = f₀ x ∧ f x = f₁ x
 #align continuous_map.homotopy_rel ContinuousMap.HomotopyRel
+-/
 
 namespace HomotopyRel
 
@@ -546,14 +746,32 @@ section
 
 variable {f₀ f₁ : C(X, Y)} {S : Set X}
 
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+Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy_rel.eq_fst ContinuousMap.HomotopyRel.eq_fstₓ'. -/
 theorem eq_fst (F : HomotopyRel f₀ f₁ S) (t : I) {x : X} (hx : x ∈ S) : F (t, x) = f₀ x :=
   (F.Prop t x hx).1
 #align continuous_map.homotopy_rel.eq_fst ContinuousMap.HomotopyRel.eq_fst
 
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+Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy_rel.eq_snd ContinuousMap.HomotopyRel.eq_sndₓ'. -/
 theorem eq_snd (F : HomotopyRel f₀ f₁ S) (t : I) {x : X} (hx : x ∈ S) : F (t, x) = f₁ x :=
   (F.Prop t x hx).2
 #align continuous_map.homotopy_rel.eq_snd ContinuousMap.HomotopyRel.eq_snd
 
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+Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy_rel.fst_eq_snd ContinuousMap.HomotopyRel.fst_eq_sndₓ'. -/
 theorem fst_eq_snd (F : HomotopyRel f₀ f₁ S) {x : X} (hx : x ∈ S) : f₀ x = f₁ x :=
   F.eq_fst 0 hx ▸ F.eq_snd 0 hx
 #align continuous_map.homotopy_rel.fst_eq_snd ContinuousMap.HomotopyRel.fst_eq_snd
@@ -562,6 +780,7 @@ end
 
 variable {f₀ f₁ f₂ : C(X, Y)} {S : Set X}
 
+#print ContinuousMap.HomotopyRel.refl /-
 /-- Given a map `f : C(X, Y)` and a set `S`, we can define a `homotopy_rel f f S` by setting
 `F (t, x) = f x` for all `t`. This is defined using `homotopy_with.refl`, but with the proof
 filled in.
@@ -570,7 +789,9 @@ filled in.
 def refl (f : C(X, Y)) (S : Set X) : HomotopyRel f f S :=
   HomotopyWith.refl f fun x hx => ⟨rfl, rfl⟩
 #align continuous_map.homotopy_rel.refl ContinuousMap.HomotopyRel.refl
+-/
 
+#print ContinuousMap.HomotopyRel.symm /-
 /--
 Given a `homotopy_rel f₀ f₁ S`, we can define a `homotopy_rel f₁ f₀ S` by reversing the homotopy.
 -/
@@ -578,12 +799,16 @@ Given a `homotopy_rel f₀ f₁ S`, we can define a `homotopy_rel f₁ f₀ S` b
 def symm (F : HomotopyRel f₀ f₁ S) : HomotopyRel f₁ f₀ S :=
   { HomotopyWith.symm F with prop' := fun t x hx => by simp [F.eq_snd _ hx, F.fst_eq_snd hx] }
 #align continuous_map.homotopy_rel.symm ContinuousMap.HomotopyRel.symm
+-/
 
+#print ContinuousMap.HomotopyRel.symm_symm /-
 @[simp]
 theorem symm_symm (F : HomotopyRel f₀ f₁ S) : F.symm.symm = F :=
   HomotopyWith.symm_symm F
 #align continuous_map.homotopy_rel.symm_symm ContinuousMap.HomotopyRel.symm_symm
+-/
 
+#print ContinuousMap.HomotopyRel.trans /-
 /-- Given `homotopy_rel f₀ f₁ S` and `homotopy_rel f₁ f₂ S`, we can define a `homotopy_rel f₀ f₂ S`
 by putting the first homotopy on `[0, 1/2]` and the second on `[1/2, 1]`.
 -/
@@ -597,7 +822,14 @@ def trans (F : HomotopyRel f₀ f₁ S) (G : HomotopyRel f₁ f₂ S) : Homotopy
       · simp [(homotopy_with.extend_prop F (2 * t) x hx).1, F.fst_eq_snd hx, G.fst_eq_snd hx]
       · simp [(homotopy_with.extend_prop G (2 * t - 1) x hx).1, F.fst_eq_snd hx, G.fst_eq_snd hx] }
 #align continuous_map.homotopy_rel.trans ContinuousMap.HomotopyRel.trans
+-/
 
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(instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (Iff.mpr (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) unitInterval) (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (Set.Icc.{0} Real Real.instPreorderReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (unitInterval.two_mul_sub_one_mem_iff (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x))) (And.intro (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x))) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (LT.lt.le.{0} Real Real.instPreorderReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (Iff.mp (Not (LE.le.{0} Real (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (LinearOrder.toPartialOrder.{0} Real Real.linearOrder))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (LT.lt.{0} Real (Preorder.toLT.{0} Real (PartialOrder.toPreorder.{0} Real (LinearOrder.toPartialOrder.{0} Real Real.linearOrder))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x))) (not_le.{0} Real Real.linearOrder (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) h)) (And.right (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x))) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (Subtype.property.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, u1} (Set.Elem.{0} Real unitInterval) X x)))))) (Prod.snd.{0, u1} (Set.Elem.{0} Real unitInterval) X x))))
+Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy_rel.trans_apply ContinuousMap.HomotopyRel.trans_applyₓ'. -/
 theorem trans_apply (F : HomotopyRel f₀ f₁ S) (G : HomotopyRel f₁ f₂ S) (x : I × X) :
     (F.trans G) x =
       if h : (x.1 : ℝ) ≤ 1 / 2 then
@@ -607,11 +839,14 @@ theorem trans_apply (F : HomotopyRel f₀ f₁ S) (G : HomotopyRel f₁ f₂ S)
   Homotopy.trans_apply _ _ _
 #align continuous_map.homotopy_rel.trans_apply ContinuousMap.HomotopyRel.trans_apply
 
+#print ContinuousMap.HomotopyRel.symm_trans /-
 theorem symm_trans (F : HomotopyRel f₀ f₁ S) (G : HomotopyRel f₁ f₂ S) :
     (F.trans G).symm = G.symm.trans F.symm :=
   HomotopyWith.ext <| Homotopy.congr_fun <| Homotopy.symm_trans _ _
 #align continuous_map.homotopy_rel.symm_trans ContinuousMap.HomotopyRel.symm_trans
+-/
 
+#print ContinuousMap.HomotopyRel.cast /-
 /-- Casting a `homotopy_rel f₀ f₁ S` to a `homotopy_rel g₀ g₁ S` where `f₀ = g₀` and `f₁ = g₁`.
 -/
 @[simps]
@@ -620,39 +855,50 @@ def cast {f₀ f₁ g₀ g₁ : C(X, Y)} (F : HomotopyRel f₀ f₁ S) (h₀ : f
   { Homotopy.cast F.toHomotopy h₀ h₁ with
     prop' := fun t x hx => by simpa [← h₀, ← h₁] using F.prop t x hx }
 #align continuous_map.homotopy_rel.cast ContinuousMap.HomotopyRel.cast
+-/
 
 end HomotopyRel
 
+#print ContinuousMap.HomotopicRel /-
 /-- Given continuous maps `f₀` and `f₁`, we say `f₀` and `f₁` are homotopic relative to a set `S` if
 there exists a `homotopy_rel f₀ f₁ S`.
 -/
 def HomotopicRel (f₀ f₁ : C(X, Y)) (S : Set X) : Prop :=
   Nonempty (HomotopyRel f₀ f₁ S)
 #align continuous_map.homotopic_rel ContinuousMap.HomotopicRel
+-/
 
 namespace HomotopicRel
 
 variable {S : Set X}
 
+#print ContinuousMap.HomotopicRel.refl /-
 @[refl]
 theorem refl (f : C(X, Y)) : HomotopicRel f f S :=
   ⟨HomotopyRel.refl f S⟩
 #align continuous_map.homotopic_rel.refl ContinuousMap.HomotopicRel.refl
+-/
 
+#print ContinuousMap.HomotopicRel.symm /-
 @[symm]
 theorem symm ⦃f g : C(X, Y)⦄ (h : HomotopicRel f g S) : HomotopicRel g f S :=
   h.map HomotopyRel.symm
 #align continuous_map.homotopic_rel.symm ContinuousMap.HomotopicRel.symm
+-/
 
+#print ContinuousMap.HomotopicRel.trans /-
 @[trans]
 theorem trans ⦃f g h : C(X, Y)⦄ (h₀ : HomotopicRel f g S) (h₁ : HomotopicRel g h S) :
     HomotopicRel f h S :=
   h₀.map2 HomotopyRel.trans h₁
 #align continuous_map.homotopic_rel.trans ContinuousMap.HomotopicRel.trans
+-/
 
+#print ContinuousMap.HomotopicRel.equivalence /-
 theorem equivalence : Equivalence fun f g : C(X, Y) => HomotopicRel f g S :=
   ⟨refl, symm, trans⟩
 #align continuous_map.homotopic_rel.equivalence ContinuousMap.HomotopicRel.equivalence
+-/
 
 end HomotopicRel

11c53f17

bump to nightly-2023-02-22-22

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

294ba122

Diff

@@ -259,7 +259,7 @@ theorem trans_apply {f₀ f₁ f₂ : C(X, Y)} (F : Homotopy f₀ f₁) (G : Hom
         G (⟨2 * x.1 - 1, unitInterval.two_mul_sub_one_mem_iff.2 ⟨(not_le.1 h).le, x.1.2.2⟩⟩, x.2) :=
   show ite _ _ _ = _ by
     split_ifs <;>
-      · rw [extend, ContinuousMap.coe_iccExtend, Set.IccExtend_of_mem]
+      · rw [extend, ContinuousMap.coe_IccExtend, Set.IccExtend_of_mem]
         rfl
 #align continuous_map.homotopy.trans_apply ContinuousMap.Homotopy.trans_apply

11c53f17

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

11c53f17

move(Topology/Order): Move anything that doesn't concern algebra (#11610)

Move files from Topology.Algebra.Order to Topology.Order when they do not contain any algebra. Also move Topology.LocalExtr to Topology.Order.LocalExtr.

According to git, the moves are:

Mathlib/Topology/{Algebra => }/Order/ExtendFrom.lean
Mathlib/Topology/{Algebra => }/Order/ExtrClosure.lean
Mathlib/Topology/{Algebra => }/Order/Filter.lean
Mathlib/Topology/{Algebra => }/Order/IntermediateValue.lean
Mathlib/Topology/{Algebra => }/Order/LeftRight.lean
Mathlib/Topology/{Algebra => }/Order/LeftRightLim.lean
Mathlib/Topology/{Algebra => }/Order/MonotoneContinuity.lean
Mathlib/Topology/{Algebra => }/Order/MonotoneConvergence.lean
Mathlib/Topology/{Algebra => }/Order/ProjIcc.lean
Mathlib/Topology/{Algebra => }/Order/T5.lean
Mathlib/Topology/{ => Order}/LocalExtr.lean

cd9902cc

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2021 Shing Tak Lam. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Shing Tak Lam
 -/
-import Mathlib.Topology.Algebra.Order.ProjIcc
+import Mathlib.Topology.Order.ProjIcc
 import Mathlib.Topology.ContinuousFunction.Ordered
 import Mathlib.Topology.CompactOpen
 import Mathlib.Topology.UnitInterval

11c53f17

chore(*): remove empty lines between variable statements (#11418)

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)

75c86f04

Diff

@@ -59,7 +59,6 @@ noncomputable section
 universe u v w x
 
 variable {F : Type*} {X : Type u} {Y : Type v} {Z : Type w} {Z' : Type x} {ι : Type*}
-
 variable [TopologicalSpace X] [TopologicalSpace Y] [TopologicalSpace Z] [TopologicalSpace Z']
 
 open unitInterval

11c53f17

chore: classify todo porting notes (#11216)

Classifies by adding issue number #11215 to porting notes claiming "TODO".

86f95a40

Diff

@@ -404,7 +404,7 @@ The type of homotopies between `f₀ f₁ : C(X, Y)`, where the intermediate map
 `P : C(X, Y) → Prop`
 -/
 structure HomotopyWith (f₀ f₁ : C(X, Y)) (P : C(X, Y) → Prop) extends Homotopy f₀ f₁ where
-  -- Porting note: todo: use `toHomotopy.curry t`
+  -- Porting note (#11215): TODO: use `toHomotopy.curry t`
   /-- the intermediate maps of the homotopy satisfy the property -/
   prop' : ∀ t, P ⟨fun x => toFun (t, x),
     Continuous.comp continuous_toFun (continuous_const.prod_mk continuous_id')⟩

11c53f17

chore: move Mathlib to v4.7.0-rc1 (#11162)

This is a very large PR, but it has been reviewed piecemeal already in PRs to the bump/v4.7.0 branch as we update to intermediate nightlies.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: damiano <adomani@gmail.com>

fa48894a

Diff

@@ -242,8 +242,8 @@ def trans {f₀ f₁ f₂ : C(X, Y)} (F : Homotopy f₀ f₁) (G : Homotopy f₁
         (G.continuous.comp (by continuity)).continuousOn _
     rintro x hx
     norm_num [hx]
-  map_zero_left x := by norm_num
-  map_one_left x := by norm_num
+  map_zero_left x := by set_option tactic.skipAssignedInstances false in norm_num
+  map_one_left x := by set_option tactic.skipAssignedInstances false in norm_num
 #align continuous_map.homotopy.trans ContinuousMap.Homotopy.trans
 
 theorem trans_apply {f₀ f₁ f₂ : C(X, Y)} (F : Homotopy f₀ f₁) (G : Homotopy f₁ f₂) (x : I × X) :

11c53f17

style: homogenise porting notes (#11145)

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".

8be0b69c

Diff

@@ -404,7 +404,7 @@ The type of homotopies between `f₀ f₁ : C(X, Y)`, where the intermediate map
 `P : C(X, Y) → Prop`
 -/
 structure HomotopyWith (f₀ f₁ : C(X, Y)) (P : C(X, Y) → Prop) extends Homotopy f₀ f₁ where
-  -- porting note: todo: use `toHomotopy.curry t`
+  -- Porting note: todo: use `toHomotopy.curry t`
   /-- the intermediate maps of the homotopy satisfy the property -/
   prop' : ∀ t, P ⟨fun x => toFun (t, x),
     Continuous.comp continuous_toFun (continuous_const.prod_mk continuous_id')⟩
@@ -457,7 +457,7 @@ theorem apply_one (F : HomotopyWith f₀ f₁ P) (x : X) : F (1, x) = f₁ x :=
   F.map_one_left x
 #align continuous_map.homotopy_with.apply_one ContinuousMap.HomotopyWith.apply_one
 
--- porting note: removed `simp`
+-- Porting note: removed `simp`
 theorem coe_toContinuousMap (F : HomotopyWith f₀ f₁ P) : ⇑F.toContinuousMap = F :=
   rfl
 #align continuous_map.homotopy_with.coe_to_continuous_map ContinuousMap.HomotopyWith.coe_toContinuousMap
@@ -559,7 +559,7 @@ namespace HomotopicWith
 
 variable {P : C(X, Y) → Prop}
 
--- porting note: removed @[refl]
+-- Porting note: removed @[refl]
 theorem refl (f : C(X, Y)) (hf : P f) : HomotopicWith f f P :=
   ⟨HomotopyWith.refl f hf⟩
 #align continuous_map.homotopic_with.refl ContinuousMap.HomotopicWith.refl
@@ -695,7 +695,7 @@ variable {S : Set X}
 protected theorem homotopic {f₀ f₁ : C(X, Y)} (h : HomotopicRel f₀ f₁ S) : Homotopic f₀ f₁ :=
   h.map fun F ↦ F.1
 
--- porting note: removed @[refl]
+-- Porting note: removed @[refl]
 theorem refl (f : C(X, Y)) : HomotopicRel f f S :=
   ⟨HomotopyRel.refl f S⟩
 #align continuous_map.homotopic_rel.refl ContinuousMap.HomotopicRel.refl

11c53f17

refactor(Data/FunLike): use unbundled inheritance from FunLike (#8386)

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>

c6a73d4f

Diff

@@ -86,7 +86,8 @@ section
 
 You should extend this class when you extend `ContinuousMap.Homotopy`. -/
 class HomotopyLike {X Y : outParam (Type*)} [TopologicalSpace X] [TopologicalSpace Y]
-    (F : Type*) (f₀ f₁ : outParam <| C(X, Y)) extends ContinuousMapClass F (I × X) Y where
+    (F : Type*) (f₀ f₁ : outParam <| C(X, Y)) [FunLike F (I × X) Y]
+    extends ContinuousMapClass F (I × X) Y : Prop where
   /-- value of the homotopy at 0 -/
   map_zero_left (f : F) : ∀ x, f (0, x) = f₀ x
   /-- value of the homotopy at 1 -/
@@ -101,22 +102,18 @@ section
 
 variable {f₀ f₁ : C(X, Y)}
 
-instance : HomotopyLike (Homotopy f₀ f₁) f₀ f₁ where
+instance instFunLike : FunLike (Homotopy f₀ f₁) (I × X) Y where
   coe f := f.toFun
   coe_injective' f g h := by
     obtain ⟨⟨_, _⟩, _⟩ := f
     obtain ⟨⟨_, _⟩, _⟩ := g
     congr
+
+instance : HomotopyLike (Homotopy f₀ f₁) f₀ f₁ where
   map_continuous f := f.continuous_toFun
   map_zero_left f := f.map_zero_left
   map_one_left f := f.map_one_left
 
-/- porting note: probably not needed anymore
-/-- Helper instance for when there's too many metavariables to apply `DFunLike.hasCoeToFun`
-directly. -/
-instance : CoeFun (Homotopy f₀ f₁) fun _ => I × X → Y :=
-  DFunLike.hasCoeToFun -/
-
 @[ext]
 theorem ext {F G : Homotopy f₀ f₁} (h : ∀ x, F x = G x) : F = G :=
   DFunLike.ext _ _ h
@@ -419,10 +416,12 @@ section
 
 variable {f₀ f₁ : C(X, Y)} {P : C(X, Y) → Prop}
 
-instance : HomotopyLike (HomotopyWith f₀ f₁ P) f₀ f₁ where
+instance instFunLike : FunLike (HomotopyWith f₀ f₁ P) (I × X) Y where
   coe F := ⇑F.toHomotopy
   coe_injective'
   | ⟨⟨⟨_, _⟩, _, _⟩, _⟩, ⟨⟨⟨_, _⟩, _, _⟩, _⟩, rfl => rfl
+
+instance : HomotopyLike (HomotopyWith f₀ f₁ P) f₀ f₁ where
   map_continuous F := F.continuous_toFun
   map_zero_left F := F.map_zero_left
   map_one_left F := F.map_one_left

11c53f17

chore(Topology): remove autoImplicit from most remaining files (#9865)

d1054e16

Diff

@@ -54,14 +54,11 @@ and for `ContinuousMap.homotopic` and `ContinuousMap.homotopic_rel`, we also def
 - [HOL-Analysis formalisation](https://isabelle.in.tum.de/library/HOL/HOL-Analysis/Homotopy.html)
 -/
 
-set_option autoImplicit true
-
-
 noncomputable section
 
 universe u v w x
 
-variable {F : Type*} {X : Type u} {Y : Type v} {Z : Type w} {Z' : Type x}
+variable {F : Type*} {X : Type u} {Y : Type v} {Z : Type w} {Z' : Type x} {ι : Type*}
 
 variable [TopologicalSpace X] [TopologicalSpace Y] [TopologicalSpace Z] [TopologicalSpace Z']

11c53f17

chore(*): rename FunLike to DFunLike (#9785)

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>

82656743

Diff

@@ -115,14 +115,14 @@ instance : HomotopyLike (Homotopy f₀ f₁) f₀ f₁ where
   map_one_left f := f.map_one_left
 
 /- porting note: probably not needed anymore
-/-- Helper instance for when there's too many metavariables to apply `FunLike.hasCoeToFun`
+/-- Helper instance for when there's too many metavariables to apply `DFunLike.hasCoeToFun`
 directly. -/
 instance : CoeFun (Homotopy f₀ f₁) fun _ => I × X → Y :=
-  FunLike.hasCoeToFun -/
+  DFunLike.hasCoeToFun -/
 
 @[ext]
 theorem ext {F G : Homotopy f₀ f₁} (h : ∀ x, F x = G x) : F = G :=
-  FunLike.ext _ _ h
+  DFunLike.ext _ _ h
 #align continuous_map.homotopy.ext ContinuousMap.Homotopy.ext
 
 /-- See Note [custom simps projection]. We need to specify this projection explicitly in this case,
@@ -431,11 +431,11 @@ instance : HomotopyLike (HomotopyWith f₀ f₁ P) f₀ f₁ where
   map_one_left F := F.map_one_left
 
 theorem coeFn_injective : @Function.Injective (HomotopyWith f₀ f₁ P) (I × X → Y) (⇑) :=
-  FunLike.coe_injective'
+  DFunLike.coe_injective'
 #align continuous_map.homotopy_with.coe_fn_injective ContinuousMap.HomotopyWith.coeFn_injective
 
 @[ext]
-theorem ext {F G : HomotopyWith f₀ f₁ P} (h : ∀ x, F x = G x) : F = G := FunLike.ext F G h
+theorem ext {F G : HomotopyWith f₀ f₁ P} (h : ∀ x, F x = G x) : F = G := DFunLike.ext F G h
 #align continuous_map.homotopy_with.ext ContinuousMap.HomotopyWith.ext
 
 /-- See Note [custom simps projection]. We need to specify this projection explicitly in this case,

11c53f17

feat(/Equiv/): Add symm_bijective lemmas next to symm_symms (#8444)

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: lines <34025592+linesthatinterlace@users.noreply.github.com>

e368f2a5

Diff

@@ -231,6 +231,10 @@ theorem symm_symm {f₀ f₁ : C(X, Y)} (F : Homotopy f₀ f₁) : F.symm.symm =
   simp
 #align continuous_map.homotopy.symm_symm ContinuousMap.Homotopy.symm_symm
 
+theorem symm_bijective {f₀ f₁ : C(X, Y)} :
+    Function.Bijective (Homotopy.symm : Homotopy f₀ f₁ → Homotopy f₁ f₀) :=
+  Function.bijective_iff_has_inverse.mpr ⟨_, symm_symm, symm_symm⟩
+
 /--
 Given `Homotopy f₀ f₁` and `Homotopy f₁ f₂`, we can define a `Homotopy f₀ f₂` by putting the first
 homotopy on `[0, 1/2]` and the second on `[1/2, 1]`.
@@ -503,6 +507,10 @@ theorem symm_symm {f₀ f₁ : C(X, Y)} (F : HomotopyWith f₀ f₁ P) : F.symm.
   ext <| Homotopy.congr_fun <| Homotopy.symm_symm _
 #align continuous_map.homotopy_with.symm_symm ContinuousMap.HomotopyWith.symm_symm
 
+theorem symm_bijective {f₀ f₁ : C(X, Y)} :
+    Function.Bijective (HomotopyWith.symm : HomotopyWith f₀ f₁ P → HomotopyWith f₁ f₀ P) :=
+  Function.bijective_iff_has_inverse.mpr ⟨_, symm_symm, symm_symm⟩
+
 /--
 Given `HomotopyWith f₀ f₁ P` and `HomotopyWith f₁ f₂ P`, we can define a `HomotopyWith f₀ f₂ P`
 by putting the first homotopy on `[0, 1/2]` and the second on `[1/2, 1]`.
@@ -629,6 +637,10 @@ theorem symm_symm (F : HomotopyRel f₀ f₁ S) : F.symm.symm = F :=
   HomotopyWith.symm_symm F
 #align continuous_map.homotopy_rel.symm_symm ContinuousMap.HomotopyRel.symm_symm
 
+theorem symm_bijective :
+    Function.Bijective (HomotopyRel.symm : HomotopyRel f₀ f₁ S → HomotopyRel f₁ f₀ S) :=
+  Function.bijective_iff_has_inverse.mpr ⟨_, symm_symm, symm_symm⟩
+
 /-- Given `HomotopyRel f₀ f₁ S` and `HomotopyRel f₁ f₂ S`, we can define a `HomotopyRel f₀ f₂ S`
 by putting the first homotopy on `[0, 1/2]` and the second on `[1/2, 1]`.
 -/

11c53f17

refactor: remove redundant condition in HomotopyRel (#7848)

For a homotopy F between f₀ and f₁ to be a homotopy relative to a set S, it suffices that F (t, x) = f₀ x for all x ∈ S and t : I, from which F (t, x) = f₁ x can be derived.

Also add HomotopyRel.compContinuousMap.

1beeb5e5

Diff

@@ -581,7 +581,7 @@ end HomotopicWith
 A `HomotopyRel f₀ f₁ S` is a homotopy between `f₀` and `f₁` which is fixed on the points in `S`.
 -/
 abbrev HomotopyRel (f₀ f₁ : C(X, Y)) (S : Set X) :=
-  HomotopyWith f₀ f₁ fun f => ∀ x ∈ S, f x = f₀ x ∧ f x = f₁ x
+  HomotopyWith f₀ f₁ fun f ↦ ∀ x ∈ S, f x = f₀ x
 #align continuous_map.homotopy_rel ContinuousMap.HomotopyRel
 
 namespace HomotopyRel
@@ -591,11 +591,11 @@ section
 variable {f₀ f₁ : C(X, Y)} {S : Set X}
 
 theorem eq_fst (F : HomotopyRel f₀ f₁ S) (t : I) {x : X} (hx : x ∈ S) : F (t, x) = f₀ x :=
-  (F.prop t x hx).1
+  F.prop t x hx
 #align continuous_map.homotopy_rel.eq_fst ContinuousMap.HomotopyRel.eq_fst
 
-theorem eq_snd (F : HomotopyRel f₀ f₁ S) (t : I) {x : X} (hx : x ∈ S) : F (t, x) = f₁ x :=
-  (F.prop t x hx).2
+theorem eq_snd (F : HomotopyRel f₀ f₁ S) (t : I) {x : X} (hx : x ∈ S) : F (t, x) = f₁ x := by
+  rw [F.eq_fst t hx, ← F.eq_fst 1 hx, F.apply_one]
 #align continuous_map.homotopy_rel.eq_snd ContinuousMap.HomotopyRel.eq_snd
 
 theorem fst_eq_snd (F : HomotopyRel f₀ f₁ S) {x : X} (hx : x ∈ S) : f₀ x = f₁ x :=
@@ -612,7 +612,7 @@ filled in.
 -/
 @[simps!]
 def refl (f : C(X, Y)) (S : Set X) : HomotopyRel f f S :=
-  HomotopyWith.refl f fun _ _ => ⟨rfl, rfl⟩
+  HomotopyWith.refl f fun _ _ ↦ rfl
 #align continuous_map.homotopy_rel.refl ContinuousMap.HomotopyRel.refl
 
 /--
@@ -621,7 +621,7 @@ Given a `HomotopyRel f₀ f₁ S`, we can define a `HomotopyRel f₁ f₀ S` by
 @[simps!]
 def symm (F : HomotopyRel f₀ f₁ S) : HomotopyRel f₁ f₀ S where
   toHomotopy := F.toHomotopy.symm
-  prop' := fun _ _ hx => ⟨F.eq_snd _ hx, F.eq_fst _ hx⟩
+  prop' := fun _ _ hx ↦ F.eq_snd _ hx
 #align continuous_map.homotopy_rel.symm ContinuousMap.HomotopyRel.symm
 
 @[simp]
@@ -632,14 +632,13 @@ theorem symm_symm (F : HomotopyRel f₀ f₁ S) : F.symm.symm = F :=
 /-- Given `HomotopyRel f₀ f₁ S` and `HomotopyRel f₁ f₂ S`, we can define a `HomotopyRel f₀ f₂ S`
 by putting the first homotopy on `[0, 1/2]` and the second on `[1/2, 1]`.
 -/
-def trans (F : HomotopyRel f₀ f₁ S) (G : HomotopyRel f₁ f₂ S) : HomotopyRel f₀ f₂ S :=
-  { Homotopy.trans F.toHomotopy G.toHomotopy with
-    prop' := fun t x hx => by
-      simp only [Homotopy.trans]
-      change (⟨fun _ => ite ((t : ℝ) ≤ _) _ _, _⟩ : C(X, Y)) _ = _ ∧ _ = _
-      split_ifs
-      · simp [(HomotopyWith.extendProp F (2 * t) x hx).1, F.fst_eq_snd hx, G.fst_eq_snd hx]
-      · simp [(HomotopyWith.extendProp G (2 * t - 1) x hx).1, F.fst_eq_snd hx, G.fst_eq_snd hx] }
+def trans (F : HomotopyRel f₀ f₁ S) (G : HomotopyRel f₁ f₂ S) : HomotopyRel f₀ f₂ S where
+  toHomotopy := F.toHomotopy.trans G.toHomotopy
+  prop' t x hx := by
+    simp only [Homotopy.trans]
+    split_ifs
+    · simp [HomotopyWith.extendProp F (2 * t) x hx, F.fst_eq_snd hx, G.fst_eq_snd hx]
+    · simp [HomotopyWith.extendProp G (2 * t - 1) x hx, F.fst_eq_snd hx, G.fst_eq_snd hx]
 #align continuous_map.homotopy_rel.trans ContinuousMap.HomotopyRel.trans
 
 theorem trans_apply (F : HomotopyRel f₀ f₁ S) (G : HomotopyRel f₁ f₂ S) (x : I × X) :
@@ -665,6 +664,12 @@ def cast {f₀ f₁ g₀ g₁ : C(X, Y)} (F : HomotopyRel f₀ f₁ S) (h₀ : f
   prop' t x hx := by simpa only [← h₀, ← h₁] using F.prop t x hx
 #align continuous_map.homotopy_rel.cast ContinuousMap.HomotopyRel.cast
 
+/-- Post-compose a homotopy relative to a set by a continuous function. -/
+@[simps!] def compContinuousMap {f₀ f₁ : C(X, Y)} (F : f₀.HomotopyRel f₁ S) (g : C(Y, Z)) :
+    (g.comp f₀).HomotopyRel (g.comp f₁) S where
+  toHomotopy := F.hcomp (ContinuousMap.Homotopy.refl g)
+  prop' t x hx := congr_arg g (F.prop t x hx)
+
 end HomotopyRel
 
 /-- Given continuous maps `f₀` and `f₁`, we say `f₀` and `f₁` are homotopic relative to a set `S` if

11c53f17

chore: remove invalid trans argument on EqOn.trans (#7285)

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

b85546bf

Diff

@@ -565,6 +565,10 @@ theorem symm ⦃f g : C(X, Y)⦄ (h : HomotopicWith f g P) : HomotopicWith g f P
   ⟨h.some.symm⟩
 #align continuous_map.homotopic_with.symm ContinuousMap.HomotopicWith.symm
 
+-- Note: this was formerly tagged with `@[trans]`, and although the `trans` attribute accepted it
+-- the `trans` tactic could not use it.
+-- An update to the trans tactic coming in mathlib4#7014 will reject this attribute.
+-- It could be restored by changing the argument order to `HomotopicWith P f g`.
 @[trans]
 theorem trans ⦃f g h : C(X, Y)⦄ (h₀ : HomotopicWith f g P) (h₁ : HomotopicWith g h P) :
     HomotopicWith f h P :=

11c53f17

feat: fix norm num with arguments (#6600)

norm_num was passing the wrong syntax node to elabSimpArgs when elaborating, which essentially had the effect of ignoring all arguments it was passed, i.e. norm_num [add_comm] would not try to commute addition in the simp step. The fix itself is very simple (though not obvious to debug!), probably using TSyntax more would help avoid such issues in future.

Due to this bug many norm_num [blah] became rw [blah]; norm_num or similar, sometimes with porting notes, sometimes not, we fix these porting notes and other regressions during the port also.

Interestingly cancel_denoms uses norm_num [<- mul_assoc] internally, so cancel_denoms also got stronger with this change.

49a849ef

Diff

@@ -243,8 +243,7 @@ def trans {f₀ f₁ f₂ : C(X, Y)} (F : Homotopy f₀ f₁) (G : Homotopy f₁
         (F.continuous.comp (by continuity)).continuousOn
         (G.continuous.comp (by continuity)).continuousOn _
     rintro x hx
-    rw [hx]
-    norm_num
+    norm_num [hx]
   map_zero_left x := by norm_num
   map_one_left x := by norm_num
 #align continuous_map.homotopy.trans ContinuousMap.Homotopy.trans
@@ -268,8 +267,7 @@ theorem symm_trans {f₀ f₁ f₂ : C(X, Y)} (F : Homotopy f₀ f₁) (G : Homo
   simp only [coe_symm_eq, symm_apply]
   split_ifs with h₁ h₂ h₂
   · have ht : (t : ℝ) = 1 / 2 := by linarith
-    simp only [ht]
-    norm_num
+    norm_num [ht]
   · congr 2
     apply Subtype.ext
     simp only [coe_symm_eq]

11c53f17

fix: disable autoImplicit globally (#6528)

Autoimplicits are highly controversial and also defeat the performance-improving work in #6474.

The intent of this PR is to make autoImplicit opt-in on a per-file basis, by disabling it in the lakefile and enabling it again with set_option autoImplicit true in the few files that rely on it.

That also keeps this PR small, as opposed to attempting to "fix" files to not need it any more.

I claim that many of the uses of autoImplicit in these files are accidental; situations such as:

Assuming variables are in scope, but pasting the lemma in the wrong section
Pasting in a lemma from a scratch file without checking to see if the variable names are consistent with the rest of the file
Making a copy-paste error between lemmas and forgetting to add an explicit arguments.

Having set_option autoImplicit false as the default prevents these types of mistake being made in the 90% of files where autoImplicits are not used at all, and causes them to be caught by CI during review.

I think there were various points during the port where we encouraged porters to delete the universes u v lines; I think having autoparams for universe variables only would cover a lot of the cases we actually use them, while avoiding any real shortcomings.

A Zulip poll (after combining overlapping votes accordingly) was in favor of this change with 5:5:18 as the no:dontcare:yes vote ratio.

While this PR was being reviewed, a handful of files gained some more likely-accidental autoImplicits. In these places, set_option autoImplicit true has been placed locally within a section, rather than at the top of the file.

0c24f831

Diff

@@ -54,6 +54,8 @@ and for `ContinuousMap.homotopic` and `ContinuousMap.homotopic_rel`, we also def
 - [HOL-Analysis formalisation](https://isabelle.in.tum.de/library/HOL/HOL-Analysis/Homotopy.html)
 -/
 
+set_option autoImplicit true
+
 
 noncomputable section

11c53f17

chore: banish Type _ and Sort _ (#6499)

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

This has nice performance benefits.

32de3f67

Diff

@@ -59,7 +59,7 @@ noncomputable section
 
 universe u v w x
 
-variable {F : Type _} {X : Type u} {Y : Type v} {Z : Type w} {Z' : Type x}
+variable {F : Type*} {X : Type u} {Y : Type v} {Z : Type w} {Z' : Type x}
 
 variable [TopologicalSpace X] [TopologicalSpace Y] [TopologicalSpace Z] [TopologicalSpace Z']
 
@@ -86,8 +86,8 @@ section
 `f₁`.
 
 You should extend this class when you extend `ContinuousMap.Homotopy`. -/
-class HomotopyLike {X Y : outParam (Type _)} [TopologicalSpace X] [TopologicalSpace Y]
-    (F : Type _) (f₀ f₁ : outParam <| C(X, Y)) extends ContinuousMapClass F (I × X) Y where
+class HomotopyLike {X Y : outParam (Type*)} [TopologicalSpace X] [TopologicalSpace Y]
+    (F : Type*) (f₀ f₁ : outParam <| C(X, Y)) extends ContinuousMapClass F (I × X) Y where
   /-- value of the homotopy at 0 -/
   map_zero_left (f : F) : ∀ x, f (0, x) = f₀ x
   /-- value of the homotopy at 1 -/
@@ -328,7 +328,7 @@ def prodMap {f₀ f₁ : C(X, Y)} {g₀ g₁ : C(Z, Z')} (F : Homotopy f₀ f₁
 
 /-- Given a family of homotopies `F i` between `f₀ i : C(X, Y i)` and `f₁ i : C(X, Y i)`, returns a
 homotopy between `ContinuousMap.pi f₀` and `ContinuousMap.pi f₁`. -/
-protected def pi {Y : ι → Type _} [∀ i, TopologicalSpace (Y i)] {f₀ f₁ : ∀ i, C(X, Y i)}
+protected def pi {Y : ι → Type*} [∀ i, TopologicalSpace (Y i)] {f₀ f₁ : ∀ i, C(X, Y i)}
     (F : ∀ i, Homotopy (f₀ i) (f₁ i)) :
     Homotopy (.pi f₀) (.pi f₁) where
   toContinuousMap := .pi fun i ↦ F i
@@ -337,7 +337,7 @@ protected def pi {Y : ι → Type _} [∀ i, TopologicalSpace (Y i)] {f₀ f₁
 
 /-- Given a family of homotopies `F i` between `f₀ i : C(X i, Y i)` and `f₁ i : C(X i, Y i)`,
 returns a homotopy between `ContinuousMap.piMap f₀` and `ContinuousMap.piMap f₁`. -/
-protected def piMap {X Y : ι → Type _} [∀ i, TopologicalSpace (X i)] [∀ i, TopologicalSpace (Y i)]
+protected def piMap {X Y : ι → Type*} [∀ i, TopologicalSpace (X i)] [∀ i, TopologicalSpace (Y i)]
     {f₀ f₁ : ∀ i, C(X i, Y i)} (F : ∀ i, Homotopy (f₀ i) (f₁ i)) :
     Homotopy (.piMap f₀) (.piMap f₁) :=
   .pi fun i ↦ .hcomp (.refl <| .eval i) (F i)
@@ -387,14 +387,14 @@ nonrec theorem prodMap {f₀ f₁ : C(X, Y)} {g₀ g₁ : C(Z, Z')} :
 
 /-- If each `f₀ i : C(X, Y i)` is homotopic to `f₁ i : C(X, Y i)`, then `ContinuousMap.pi f₀` is
 homotopic to `ContinuousMap.pi f₁`. -/
-protected theorem pi {Y : ι → Type _} [∀ i, TopologicalSpace (Y i)] {f₀ f₁ : ∀ i, C(X, Y i)}
+protected theorem pi {Y : ι → Type*} [∀ i, TopologicalSpace (Y i)] {f₀ f₁ : ∀ i, C(X, Y i)}
     (F : ∀ i, Homotopic (f₀ i) (f₁ i)) :
     Homotopic (.pi f₀) (.pi f₁) :=
   ⟨.pi fun i ↦ (F i).some⟩
 
 /-- If each `f₀ i : C(X, Y i)` is homotopic to `f₁ i : C(X, Y i)`, then `ContinuousMap.pi f₀` is
 homotopic to `ContinuousMap.pi f₁`. -/
-protected theorem piMap {X Y : ι → Type _} [∀ i, TopologicalSpace (X i)]
+protected theorem piMap {X Y : ι → Type*} [∀ i, TopologicalSpace (X i)]
     [∀ i, TopologicalSpace (Y i)] {f₀ f₁ : ∀ i, C(X i, Y i)} (F : ∀ i, Homotopic (f₀ i) (f₁ i)) :
     Homotopic (.piMap f₀) (.piMap f₁) :=
   .pi fun i ↦ .hcomp (.refl <| .eval i) (F i)

11c53f17

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

depends on: #5966

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

89aa3a3b

Diff

@@ -2,17 +2,14 @@
 Copyright (c) 2021 Shing Tak Lam. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Shing Tak Lam
-
-! This file was ported from Lean 3 source module topology.homotopy.basic
-! leanprover-community/mathlib commit 11c53f174270aa43140c0b26dabce5fc4a253e80
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Topology.Algebra.Order.ProjIcc
 import Mathlib.Topology.ContinuousFunction.Ordered
 import Mathlib.Topology.CompactOpen
 import Mathlib.Topology.UnitInterval
 
+#align_import topology.homotopy.basic from "leanprover-community/mathlib"@"11c53f174270aa43140c0b26dabce5fc4a253e80"
+
 /-!
 # Homotopy between functions

11c53f17

chore: fix many typos (#4535)

Run codespell Mathlib and keep some suggestions.

92f5c622

Diff

@@ -154,7 +154,7 @@ theorem coe_toContinuousMap (F : Homotopy f₀ f₁) : ⇑F.toContinuousMap = F
   rfl
 #align continuous_map.homotopy.coe_to_continuous_map ContinuousMap.Homotopy.coe_toContinuousMap
 
-/-- Currying a homotopy to a continuous function fron `I` to `C(X, Y)`.
+/-- Currying a homotopy to a continuous function from `I` to `C(X, Y)`.
 -/
 def curry (F : Homotopy f₀ f₁) : C(I, C(X, Y)) :=
   F.toContinuousMap.curry

11c53f17

feat: port Topology.Homotopy.HomotopyGroup (#4485)

ff4f0707

Diff

@@ -132,7 +132,7 @@ def Simps.apply (F : Homotopy f₀ f₁) : I × X → Y :=
   F
 #align continuous_map.homotopy.simps.apply ContinuousMap.Homotopy.Simps.apply
 
-initialize_simps_projections Homotopy (toContinuousMap_toFun → apply, -toContinuousMap)
+initialize_simps_projections Homotopy (toFun → apply, -toContinuousMap)
 
 /-- Deprecated. Use `map_continuous` instead. -/
 protected theorem continuous (F : Homotopy f₀ f₁) : Continuous F :=
@@ -293,6 +293,15 @@ def cast {f₀ f₁ g₀ g₁ : C(X, Y)} (F : Homotopy f₀ f₁) (h₀ : f₀ =
   map_one_left := by simp [← h₁]
 #align continuous_map.homotopy.cast ContinuousMap.Homotopy.cast
 
+/-- Composition of a `Homotopy g₀ g₁` and `f : C(X, Y)` as a homotopy between `g₀.comp f` and
+`g₁.comp f`. -/
+@[simps!]
+def compContinuousMap {g₀ g₁ : C(Y, Z)} (G : Homotopy g₀ g₁) (f : C(X, Y)) :
+    Homotopy (g₀.comp f) (g₁.comp f) where
+  toContinuousMap := G.comp (.prodMap (.id _) f)
+  map_zero_left _ := G.map_zero_left _
+  map_one_left _ := G.map_one_left _
+
 /-- If we have a `Homotopy f₀ f₁` and a `Homotopy g₀ g₁`, then we can compose them and get a
 `Homotopy (g₀.comp f₀) (g₁.comp f₁)`.
 -/
@@ -668,6 +677,10 @@ namespace HomotopicRel
 
 variable {S : Set X}
 
+/-- If two maps are homotopic relative to a set, then they are homotopic. -/
+protected theorem homotopic {f₀ f₁ : C(X, Y)} (h : HomotopicRel f₀ f₁ S) : Homotopic f₀ f₁ :=
+  h.map fun F ↦ F.1
+
 -- porting note: removed @[refl]
 theorem refl (f : C(X, Y)) : HomotopicRel f f S :=
   ⟨HomotopyRel.refl f S⟩
@@ -690,4 +703,7 @@ theorem equivalence : Equivalence fun f g : C(X, Y) => HomotopicRel f g S :=
 
 end HomotopicRel
 
+@[simp] theorem homotopicRel_empty {f₀ f₁ : C(X, Y)} : HomotopicRel f₀ f₁ ∅ ↔ Homotopic f₀ f₁ :=
+  ⟨fun h ↦ h.homotopic, fun ⟨F⟩ ↦ ⟨⟨F, fun _ _ ↦ False.elim⟩⟩⟩
+
 end ContinuousMap

11c53f17

feat: add Set.IccExtend_eq_self (#4454)

Partial forward-port of leanprover-community/mathlib#19097 Also rename Set.Icc_extend_coe to Set.IccExtend_val.

0f5133e2

Diff

@@ -185,7 +185,7 @@ theorem extend_apply_of_one_le (F : Homotopy f₀ f₁) {t : ℝ} (ht : 1 ≤ t)
 
 @[simp]
 theorem extend_apply_coe (F : Homotopy f₀ f₁) (t : I) (x : X) : F.extend t x = F (t, x) :=
-  ContinuousMap.congr_fun (Set.Icc_extend_coe (zero_le_one' ℝ) F.curry t) x
+  ContinuousMap.congr_fun (Set.IccExtend_val (zero_le_one' ℝ) F.curry t) x
 #align continuous_map.homotopy.extend_apply_coe ContinuousMap.Homotopy.extend_apply_coe
 
 @[simp]

11c53f17

chore: tidy various files (#3848)

66cb7cc4

Diff

@@ -29,7 +29,7 @@ on `S`.
 * `ContinuousMap.Homotopy f₀ f₁` is the type of homotopies between `f₀` and `f₁`.
 * `ContinuousMap.HomotopyWith f₀ f₁ P` is the type of homotopies between `f₀` and `f₁`, where
   the intermediate maps satisfy the predicate `P`.
-* `ContinuousMap.HomotopyEel f₀ f₁ S` is the type of homotopies between `f₀` and `f₁` which
+* `ContinuousMap.HomotopyRel f₀ f₁ S` is the type of homotopies between `f₀` and `f₁` which
   are fixed on `S`.
 
 For each of the above, we have
@@ -220,8 +220,7 @@ instance : Inhabited (Homotopy (ContinuousMap.id X) (ContinuousMap.id X)) :=
 /-- Given a `Homotopy f₀ f₁`, we can define a `Homotopy f₁ f₀` by reversing the homotopy.
 -/
 @[simps]
-def symm {f₀ f₁ : C(X, Y)} (F : Homotopy f₀ f₁) : Homotopy f₁ f₀
-    where
+def symm {f₀ f₁ : C(X, Y)} (F : Homotopy f₀ f₁) : Homotopy f₁ f₀ where
   toFun x := F (σ x.1, x.2)
   map_zero_left := by norm_num
   map_one_left := by norm_num
@@ -269,18 +268,18 @@ theorem symm_trans {f₀ f₁ f₂ : C(X, Y)} (F : Homotopy f₀ f₁) (G : Homo
   rw [trans_apply, symm_apply, trans_apply]
   simp only [coe_symm_eq, symm_apply]
   split_ifs with h₁ h₂ h₂
-  . have ht : (t : ℝ) = 1 / 2 := by linarith
+  · have ht : (t : ℝ) = 1 / 2 := by linarith
     simp only [ht]
     norm_num
-  . congr 2
+  · congr 2
     apply Subtype.ext
     simp only [coe_symm_eq]
     linarith
-  . congr 2
+  · congr 2
     apply Subtype.ext
     simp only [coe_symm_eq]
     linarith
-  . exfalso
+  · exfalso
     linarith
 #align continuous_map.homotopy.symm_trans ContinuousMap.Homotopy.symm_trans
 
@@ -597,7 +596,7 @@ end
 
 variable {f₀ f₁ f₂ : C(X, Y)} {S : Set X}
 
-/-- Given a map `f : C(X, Y)` and a set `S`, we can define a `HomotopyEel f f S` by setting
+/-- Given a map `f : C(X, Y)` and a set `S`, we can define a `HomotopyRel f f S` by setting
 `F (t, x) = f x` for all `t`. This is defined using `HomotopyWith.refl`, but with the proof
 filled in.
 -/

11c53f17

chore: bye-bye, solo bys! (#3825)

This PR puts, with one exception, every single remaining by that lies all by itself on its own line to the previous line, thus matching the current behaviour of start-port.sh. The exception is when the by begins the second or later argument to a tuple or anonymous constructor; see https://github.com/leanprover-community/mathlib4/pull/3825#discussion_r1186702599.

Essentially this is s/\n *by$/ by/g, but with manual editing to satisfy the linter's max-100-char-line requirement. The Python style linter is also modified to catch these "isolated bys".

14167e48

Diff

@@ -239,8 +239,7 @@ homotopy on `[0, 1/2]` and the second on `[1/2, 1]`.
 -/
 def trans {f₀ f₁ f₂ : C(X, Y)} (F : Homotopy f₀ f₁) (G : Homotopy f₁ f₂) : Homotopy f₀ f₂ where
   toFun x := if (x.1 : ℝ) ≤ 1 / 2 then F.extend (2 * x.1) x.2 else G.extend (2 * x.1 - 1) x.2
-  continuous_toFun :=
-    by
+  continuous_toFun := by
     refine'
       continuous_if_le (continuous_induced_dom.comp continuous_fst) continuous_const
         (F.continuous.comp (by continuity)).continuousOn

11c53f17

feat: enable cancel_denoms preprocessor in linarith (#3801)

Enable the cancelDenoms preprocessor in linarith. Closes #2714.

depends on: #3797

Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: Patrick Massot <patrickmassot@free.fr> Co-authored-by: Floris van Doorn <fpvdoorn@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

38dbcd82

Diff

@@ -270,9 +270,7 @@ theorem symm_trans {f₀ f₁ f₂ : C(X, Y)} (F : Homotopy f₀ f₁) (G : Homo
   rw [trans_apply, symm_apply, trans_apply]
   simp only [coe_symm_eq, symm_apply]
   split_ifs with h₁ h₂ h₂
-  . have ht : (t : ℝ) = 1 / 2 :=
-      -- porting note: this was proved by linarith in mathlib
-      le_antisymm h₂ (by convert sub_le_comm.mp h₁ using 1; norm_num)
+  . have ht : (t : ℝ) = 1 / 2 := by linarith
     simp only [ht]
     norm_num
   . congr 2
@@ -284,11 +282,7 @@ theorem symm_trans {f₀ f₁ f₂ : C(X, Y)} (F : Homotopy f₀ f₁) (G : Homo
     simp only [coe_symm_eq]
     linarith
   . exfalso
-    -- porting note: this was proved by linarith in mathlib
-    apply h₂
-    rw [sub_le_comm, not_le] at h₁
-    convert le_of_lt h₁ using 1
-    norm_num
+    linarith
 #align continuous_map.homotopy.symm_trans ContinuousMap.Homotopy.symm_trans
 
 /-- Casting a `Homotopy f₀ f₁` to a `Homotopy g₀ g₁` where `f₀ = g₀` and `f₁ = g₁`.

11c53f17

feat: use HomotopyLike for HomotopyWith (#3197)

Also fix some simp/simps.

35acfaa7

Diff

@@ -420,29 +420,25 @@ section
 
 variable {f₀ f₁ : C(X, Y)} {P : C(X, Y) → Prop}
 
-instance : CoeFun (HomotopyWith f₀ f₁ P) fun _ => I × X → Y :=
-  ⟨fun F => F.toFun⟩
-
-/- porting note: this lemma seems unnecessary
-@[simp]
-theorem coe_toFun (F : HomotopyWith f₀ f₁ P) : ⇑F = F.toFun := by rfl-/
-
-theorem coeFn_injective : @Function.Injective (HomotopyWith f₀ f₁ P) (I × X → Y) (⇑) := by
-  rintro ⟨⟨⟨F, _⟩, _⟩, _⟩ ⟨⟨⟨G, _⟩, _⟩, _⟩ h
-  congr 3
+instance : HomotopyLike (HomotopyWith f₀ f₁ P) f₀ f₁ where
+  coe F := ⇑F.toHomotopy
+  coe_injective'
+  | ⟨⟨⟨_, _⟩, _, _⟩, _⟩, ⟨⟨⟨_, _⟩, _, _⟩, _⟩, rfl => rfl
+  map_continuous F := F.continuous_toFun
+  map_zero_left F := F.map_zero_left
+  map_one_left F := F.map_one_left
+
+theorem coeFn_injective : @Function.Injective (HomotopyWith f₀ f₁ P) (I × X → Y) (⇑) :=
+  FunLike.coe_injective'
 #align continuous_map.homotopy_with.coe_fn_injective ContinuousMap.HomotopyWith.coeFn_injective
 
 @[ext]
-theorem ext {F G : HomotopyWith f₀ f₁ P} (h : ∀ x, F x = G x) : F = G := by
-  apply coeFn_injective
-  funext
-  apply h
+theorem ext {F G : HomotopyWith f₀ f₁ P} (h : ∀ x, F x = G x) : F = G := FunLike.ext F G h
 #align continuous_map.homotopy_with.ext ContinuousMap.HomotopyWith.ext
 
 /-- See Note [custom simps projection]. We need to specify this projection explicitly in this case,
 because it is a composition of multiple projections. -/
-def Simps.apply (F : HomotopyWith f₀ f₁ P) : I × X → Y :=
-  F
+def Simps.apply (F : HomotopyWith f₀ f₁ P) : I × X → Y := F
 #align continuous_map.homotopy_with.simps.apply ContinuousMap.HomotopyWith.Simps.apply
 
 initialize_simps_projections HomotopyWith (toHomotopy_toContinuousMap_toFun → apply,
@@ -463,12 +459,12 @@ theorem apply_one (F : HomotopyWith f₀ f₁ P) (x : X) : F (1, x) = f₁ x :=
   F.map_one_left x
 #align continuous_map.homotopy_with.apply_one ContinuousMap.HomotopyWith.apply_one
 
-@[simp]
+-- porting note: removed `simp`
 theorem coe_toContinuousMap (F : HomotopyWith f₀ f₁ P) : ⇑F.toContinuousMap = F :=
   rfl
 #align continuous_map.homotopy_with.coe_to_continuous_map ContinuousMap.HomotopyWith.coe_toContinuousMap
 
--- porting note: removed @[simp] as it makes the linter timeout
+@[simp]
 theorem coe_toHomotopy (F : HomotopyWith f₀ f₁ P) : ⇑F.toHomotopy = F :=
   rfl
 #align continuous_map.homotopy_with.coe_to_homotopy ContinuousMap.HomotopyWith.coe_toHomotopy
@@ -476,16 +472,7 @@ theorem coe_toHomotopy (F : HomotopyWith f₀ f₁ P) : ⇑F.toHomotopy = F :=
 theorem prop (F : HomotopyWith f₀ f₁ P) (t : I) : P (F.toHomotopy.curry t) := F.prop' t
 #align continuous_map.homotopy_with.prop ContinuousMap.HomotopyWith.prop
 
-theorem extendProp (F : HomotopyWith f₀ f₁ P) (t : ℝ) : P (F.toHomotopy.extend t) := by
-  by_cases ht₀ : 0 ≤ t
-  · by_cases ht₁ : t ≤ 1
-    · apply F.prop
-    · convert F.prop 1
-      ext x
-      simp [F.toHomotopy.extend_apply_of_one_le (le_of_not_le ht₁)]
-  · convert F.prop 0
-    ext x
-    simp [F.toHomotopy.extend_apply_of_le_zero (le_of_not_le ht₀)]
+theorem extendProp (F : HomotopyWith f₀ f₁ P) (t : ℝ) : P (F.toHomotopy.extend t) := F.prop _
 #align continuous_map.homotopy_with.extend_prop ContinuousMap.HomotopyWith.extendProp
 
 end
@@ -496,9 +483,9 @@ variable {P : C(X, Y) → Prop}
 `F (t, x) = f x`
 -/
 @[simps!]
-def refl (f : C(X, Y)) (hf : P f) : HomotopyWith f f P :=
-  { Homotopy.refl f with
-    prop' := fun _ => hf }
+def refl (f : C(X, Y)) (hf : P f) : HomotopyWith f f P where
+  toHomotopy := Homotopy.refl f
+  prop' := fun _ => hf
 #align continuous_map.homotopy_with.refl ContinuousMap.HomotopyWith.refl
 
 instance : Inhabited (HomotopyWith (ContinuousMap.id X) (ContinuousMap.id X) fun _ => True) :=
@@ -507,10 +494,10 @@ instance : Inhabited (HomotopyWith (ContinuousMap.id X) (ContinuousMap.id X) fun
 /--
 Given a `HomotopyWith f₀ f₁ P`, we can define a `HomotopyWith f₁ f₀ P` by reversing the homotopy.
 -/
---@[simps]
-def symm {f₀ f₁ : C(X, Y)} (F : HomotopyWith f₀ f₁ P) : HomotopyWith f₁ f₀ P :=
-  { F.toHomotopy.symm with
-      prop' := fun t => F.prop (σ t) }
+@[simps!]
+def symm {f₀ f₁ : C(X, Y)} (F : HomotopyWith f₀ f₁ P) : HomotopyWith f₁ f₀ P where
+  toHomotopy := F.toHomotopy.symm
+  prop' := fun t => F.prop (σ t)
 #align continuous_map.homotopy_with.symm ContinuousMap.HomotopyWith.symm
 
 @[simp]
@@ -550,10 +537,11 @@ theorem symm_trans {f₀ f₁ f₂ : C(X, Y)} (F : HomotopyWith f₀ f₁ P) (G
 
 /-- Casting a `HomotopyWith f₀ f₁ P` to a `HomotopyWith g₀ g₁ P` where `f₀ = g₀` and `f₁ = g₁`.
 -/
-@[simp]
+@[simps!]
 def cast {f₀ f₁ g₀ g₁ : C(X, Y)} (F : HomotopyWith f₀ f₁ P) (h₀ : f₀ = g₀) (h₁ : f₁ = g₁) :
-    HomotopyWith g₀ g₁ P :=
-  { F.toHomotopy.cast h₀ h₁ with prop' := F.prop }
+    HomotopyWith g₀ g₁ P where
+  toHomotopy := F.toHomotopy.cast h₀ h₁
+  prop' := F.prop
 #align continuous_map.homotopy_with.cast ContinuousMap.HomotopyWith.cast
 
 end HomotopyWith
@@ -628,13 +616,13 @@ def refl (f : C(X, Y)) (S : Set X) : HomotopyRel f f S :=
 /--
 Given a `HomotopyRel f₀ f₁ S`, we can define a `HomotopyRel f₁ f₀ S` by reversing the homotopy.
 -/
-@[simp]
-def symm (F : HomotopyRel f₀ f₁ S) : HomotopyRel f₁ f₀ S :=
-  { HomotopyWith.symm F with
-      prop' := fun _ _ hx => ⟨F.eq_snd _ hx, F.eq_fst _ hx⟩ }
+@[simps!]
+def symm (F : HomotopyRel f₀ f₁ S) : HomotopyRel f₁ f₀ S where
+  toHomotopy := F.toHomotopy.symm
+  prop' := fun _ _ hx => ⟨F.eq_snd _ hx, F.eq_fst _ hx⟩
 #align continuous_map.homotopy_rel.symm ContinuousMap.HomotopyRel.symm
 
--- porting note: removed @[simp] as the linter complains
+@[simp]
 theorem symm_symm (F : HomotopyRel f₀ f₁ S) : F.symm.symm = F :=
   HomotopyWith.symm_symm F
 #align continuous_map.homotopy_rel.symm_symm ContinuousMap.HomotopyRel.symm_symm
@@ -644,8 +632,7 @@ by putting the first homotopy on `[0, 1/2]` and the second on `[1/2, 1]`.
 -/
 def trans (F : HomotopyRel f₀ f₁ S) (G : HomotopyRel f₁ f₂ S) : HomotopyRel f₀ f₂ S :=
   { Homotopy.trans F.toHomotopy G.toHomotopy with
-    prop' := fun t => by
-      intro x hx
+    prop' := fun t x hx => by
       simp only [Homotopy.trans]
       change (⟨fun _ => ite ((t : ℝ) ≤ _) _ _, _⟩ : C(X, Y)) _ = _ ∧ _ = _
       split_ifs
@@ -669,13 +656,11 @@ theorem symm_trans (F : HomotopyRel f₀ f₁ S) (G : HomotopyRel f₁ f₂ S) :
 
 /-- Casting a `HomotopyRel f₀ f₁ S` to a `HomotopyRel g₀ g₁ S` where `f₀ = g₀` and `f₁ = g₁`.
 -/
-@[simp]
+@[simps!]
 def cast {f₀ f₁ g₀ g₁ : C(X, Y)} (F : HomotopyRel f₀ f₁ S) (h₀ : f₀ = g₀) (h₁ : f₁ = g₁) :
-    HomotopyRel g₀ g₁ S :=
-  { Homotopy.cast F.toHomotopy h₀ h₁ with
-    prop' := fun t x hx => by
-      simp only [← h₀, ← h₁]
-      exact F.prop t x hx }
+    HomotopyRel g₀ g₁ S where
+  toHomotopy := Homotopy.cast F.toHomotopy h₀ h₁
+  prop' t x hx := by simpa only [← h₀, ← h₁] using F.prop t x hx
 #align continuous_map.homotopy_rel.cast ContinuousMap.HomotopyRel.cast
 
 end HomotopyRel

11c53f17

feat: add constructions about continuous map and homotopies (#2984)

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.

a51c8652

Diff

@@ -60,11 +60,11 @@ and for `ContinuousMap.homotopic` and `ContinuousMap.homotopic_rel`, we also def
 
 noncomputable section
 
-universe u v w
+universe u v w x
 
-variable {F : Type _} {X : Type u} {Y : Type v} {Z : Type w}
+variable {F : Type _} {X : Type u} {Y : Type v} {Z : Type w} {Z' : Type x}
 
-variable [TopologicalSpace X] [TopologicalSpace Y] [TopologicalSpace Z]
+variable [TopologicalSpace X] [TopologicalSpace Y] [TopologicalSpace Z] [TopologicalSpace Z']
 
 open unitInterval
 
@@ -105,8 +105,7 @@ section
 
 variable {f₀ f₁ : C(X, Y)}
 
-instance : HomotopyLike (Homotopy f₀ f₁) f₀ f₁
-    where
+instance : HomotopyLike (Homotopy f₀ f₁) f₀ f₁ where
   coe f := f.toFun
   coe_injective' f g h := by
     obtain ⟨⟨_, _⟩, _⟩ := f
@@ -238,8 +237,7 @@ theorem symm_symm {f₀ f₁ : C(X, Y)} (F : Homotopy f₀ f₁) : F.symm.symm =
 Given `Homotopy f₀ f₁` and `Homotopy f₁ f₂`, we can define a `Homotopy f₀ f₂` by putting the first
 homotopy on `[0, 1/2]` and the second on `[1/2, 1]`.
 -/
-def trans {f₀ f₁ f₂ : C(X, Y)} (F : Homotopy f₀ f₁) (G : Homotopy f₁ f₂) : Homotopy f₀ f₂
-    where
+def trans {f₀ f₁ f₂ : C(X, Y)} (F : Homotopy f₀ f₁) (G : Homotopy f₁ f₂) : Homotopy f₀ f₂ where
   toFun x := if (x.1 : ℝ) ≤ 1 / 2 then F.extend (2 * x.1) x.2 else G.extend (2 * x.1 - 1) x.2
   continuous_toFun :=
     by
@@ -296,8 +294,8 @@ theorem symm_trans {f₀ f₁ f₂ : C(X, Y)} (F : Homotopy f₀ f₁) (G : Homo
 /-- Casting a `Homotopy f₀ f₁` to a `Homotopy g₀ g₁` where `f₀ = g₀` and `f₁ = g₁`.
 -/
 @[simps]
-def cast {f₀ f₁ g₀ g₁ : C(X, Y)} (F : Homotopy f₀ f₁) (h₀ : f₀ = g₀) (h₁ : f₁ = g₁) : Homotopy g₀ g₁
-    where
+def cast {f₀ f₁ g₀ g₁ : C(X, Y)} (F : Homotopy f₀ f₁) (h₀ : f₀ = g₀) (h₁ : f₁ = g₁) :
+    Homotopy g₀ g₁ where
   toFun := F
   map_zero_left := by simp [← h₀]
   map_one_left := by simp [← h₁]
@@ -308,13 +306,44 @@ def cast {f₀ f₁ g₀ g₁ : C(X, Y)} (F : Homotopy f₀ f₁) (h₀ : f₀ =
 -/
 @[simps]
 def hcomp {f₀ f₁ : C(X, Y)} {g₀ g₁ : C(Y, Z)} (F : Homotopy f₀ f₁) (G : Homotopy g₀ g₁) :
-    Homotopy (g₀.comp f₀) (g₁.comp f₁)
-    where
+    Homotopy (g₀.comp f₀) (g₁.comp f₁) where
   toFun x := G (x.1, F x)
   map_zero_left := by simp
   map_one_left := by simp
 #align continuous_map.homotopy.hcomp ContinuousMap.Homotopy.hcomp
 
+/-- Let `F` be a homotopy between `f₀ : C(X, Y)` and `f₁ : C(X, Y)`. Let `G` be a homotopy between
+`g₀ : C(X, Z)` and `g₁ : C(X, Z)`. Then `F.prodMk G` is the homotopy between `f₀.prodMk g₀` and
+`f₁.prodMk g₁` that sends `p` to `(F p, G p)`. -/
+nonrec def prodMk {f₀ f₁ : C(X, Y)} {g₀ g₁ : C(X, Z)} (F : Homotopy f₀ f₁) (G : Homotopy g₀ g₁) :
+    Homotopy (f₀.prodMk g₀) (f₁.prodMk g₁) where
+  toContinuousMap := F.prodMk G
+  map_zero_left _ := Prod.ext (F.map_zero_left _) (G.map_zero_left _)
+  map_one_left _ := Prod.ext (F.map_one_left _) (G.map_one_left _)
+
+/-- Let `F` be a homotopy between `f₀ : C(X, Y)` and `f₁ : C(X, Y)`. Let `G` be a homotopy between
+`g₀ : C(Z, Z')` and `g₁ : C(Z, Z')`. Then `F.prodMap G` is the homotopy between `f₀.prodMap g₀` and
+`f₁.prodMap g₁` that sends `(t, x, z)` to `(F (t, x), G (t, z))`. -/
+def prodMap {f₀ f₁ : C(X, Y)} {g₀ g₁ : C(Z, Z')} (F : Homotopy f₀ f₁) (G : Homotopy g₀ g₁) :
+    Homotopy (f₀.prodMap g₀) (f₁.prodMap g₁) :=
+  .prodMk (.hcomp (.refl .fst) F) (.hcomp (.refl .snd) G)
+
+/-- Given a family of homotopies `F i` between `f₀ i : C(X, Y i)` and `f₁ i : C(X, Y i)`, returns a
+homotopy between `ContinuousMap.pi f₀` and `ContinuousMap.pi f₁`. -/
+protected def pi {Y : ι → Type _} [∀ i, TopologicalSpace (Y i)] {f₀ f₁ : ∀ i, C(X, Y i)}
+    (F : ∀ i, Homotopy (f₀ i) (f₁ i)) :
+    Homotopy (.pi f₀) (.pi f₁) where
+  toContinuousMap := .pi fun i ↦ F i
+  map_zero_left x := funext fun i ↦ (F i).map_zero_left x
+  map_one_left x := funext fun i ↦ (F i).map_one_left x
+
+/-- Given a family of homotopies `F i` between `f₀ i : C(X i, Y i)` and `f₁ i : C(X i, Y i)`,
+returns a homotopy between `ContinuousMap.piMap f₀` and `ContinuousMap.piMap f₁`. -/
+protected def piMap {X Y : ι → Type _} [∀ i, TopologicalSpace (X i)] [∀ i, TopologicalSpace (Y i)]
+    {f₀ f₁ : ∀ i, C(X i, Y i)} (F : ∀ i, Homotopy (f₀ i) (f₁ i)) :
+    Homotopy (.piMap f₀) (.piMap f₁) :=
+  .pi fun i ↦ .hcomp (.refl <| .eval i) (F i)
+
 end Homotopy
 
 /-- Given continuous maps `f₀` and `f₁`, we say `f₀` and `f₁` are homotopic if there exists a
@@ -350,6 +379,28 @@ theorem equivalence : Equivalence (@Homotopic X Y _ _) :=
   ⟨refl, by apply symm, by apply trans⟩
 #align continuous_map.homotopic.equivalence ContinuousMap.Homotopic.equivalence
 
+nonrec theorem prodMk {f₀ f₁ : C(X, Y)} {g₀ g₁ : C(X, Z)} :
+    Homotopic f₀ f₁ → Homotopic g₀ g₁ → Homotopic (f₀.prodMk g₀) (f₁.prodMk g₁)
+  | ⟨F⟩, ⟨G⟩ => ⟨F.prodMk G⟩
+
+nonrec theorem prodMap {f₀ f₁ : C(X, Y)} {g₀ g₁ : C(Z, Z')} :
+    Homotopic f₀ f₁ → Homotopic g₀ g₁ → Homotopic (f₀.prodMap g₀) (f₁.prodMap g₁)
+  | ⟨F⟩, ⟨G⟩ => ⟨F.prodMap G⟩
+
+/-- If each `f₀ i : C(X, Y i)` is homotopic to `f₁ i : C(X, Y i)`, then `ContinuousMap.pi f₀` is
+homotopic to `ContinuousMap.pi f₁`. -/
+protected theorem pi {Y : ι → Type _} [∀ i, TopologicalSpace (Y i)] {f₀ f₁ : ∀ i, C(X, Y i)}
+    (F : ∀ i, Homotopic (f₀ i) (f₁ i)) :
+    Homotopic (.pi f₀) (.pi f₁) :=
+  ⟨.pi fun i ↦ (F i).some⟩
+
+/-- If each `f₀ i : C(X, Y i)` is homotopic to `f₁ i : C(X, Y i)`, then `ContinuousMap.pi f₀` is
+homotopic to `ContinuousMap.pi f₁`. -/
+protected theorem piMap {X Y : ι → Type _} [∀ i, TopologicalSpace (X i)]
+    [∀ i, TopologicalSpace (Y i)] {f₀ f₁ : ∀ i, C(X i, Y i)} (F : ∀ i, Homotopic (f₀ i) (f₁ i)) :
+    Homotopic (.piMap f₀) (.piMap f₁) :=
+  .pi fun i ↦ .hcomp (.refl <| .eval i) (F i)
+
 end Homotopic
 
 /--

11c53f17

fix: correctly mark outparams in HomotopyLike (#3089)

03015c84

Diff

@@ -89,8 +89,8 @@ section
 `f₁`.
 
 You should extend this class when you extend `ContinuousMap.Homotopy`. -/
-class HomotopyLike (F : Type _) (f₀ f₁ : outParam <| C(X, Y)) extends
-  ContinuousMapClass F (I × X) Y where
+class HomotopyLike {X Y : outParam (Type _)} [TopologicalSpace X] [TopologicalSpace Y]
+    (F : Type _) (f₀ f₁ : outParam <| C(X, Y)) extends ContinuousMapClass F (I × X) Y where
   /-- value of the homotopy at 0 -/
   map_zero_left (f : F) : ∀ x, f (0, x) = f₀ x
   /-- value of the homotopy at 1 -/
@@ -99,9 +99,6 @@ class HomotopyLike (F : Type _) (f₀ f₁ : outParam <| C(X, Y)) extends
 
 end
 
--- `f₀` and `f₁` are `outParam` so this is not dangerous
-attribute [nolint dangerousInstance] HomotopyLike.toContinuousMapClass
-
 namespace Homotopy
 
 section

11c53f17

fix a typo in Topology.Homotopy.Basic (#2921)

The prop' field used continuous_to_fun instead of continuous_toFun. Lean 4 silently introduced an implicit argument continuous_to_fun, so one had to specify it in the .prop theorem below.

Also golf a proof using new Lean 4 rfl for structures.

19ace550

Diff

@@ -360,12 +360,10 @@ The type of homotopies between `f₀ f₁ : C(X, Y)`, where the intermediate map
 `P : C(X, Y) → Prop`
 -/
 structure HomotopyWith (f₀ f₁ : C(X, Y)) (P : C(X, Y) → Prop) extends Homotopy f₀ f₁ where
-  /-- the intermediate maps of the homotopy satisfy the proprerty -/
-  prop' :
-    ∀ t,
-      P
-        ⟨fun x => toFun (t, x),
-          Continuous.comp continuous_to_fun (continuous_const.prod_mk continuous_id')⟩
+  -- porting note: todo: use `toHomotopy.curry t`
+  /-- the intermediate maps of the homotopy satisfy the property -/
+  prop' : ∀ t, P ⟨fun x => toFun (t, x),
+    Continuous.comp continuous_toFun (continuous_const.prod_mk continuous_id')⟩
 #align continuous_map.homotopy_with ContinuousMap.HomotopyWith
 
 namespace HomotopyWith
@@ -427,8 +425,7 @@ theorem coe_toHomotopy (F : HomotopyWith f₀ f₁ P) : ⇑F.toHomotopy = F :=
   rfl
 #align continuous_map.homotopy_with.coe_to_homotopy ContinuousMap.HomotopyWith.coe_toHomotopy
 
-theorem prop (F : HomotopyWith f₀ f₁ P) (t : I) : P (F.toHomotopy.curry t) :=
-  @HomotopyWith.prop' _ _ _ _ _ _ _ F (ContinuousMap.continuous_toFun _) _
+theorem prop (F : HomotopyWith f₀ f₁ P) (t : I) : P (F.toHomotopy.curry t) := F.prop' t
 #align continuous_map.homotopy_with.prop ContinuousMap.HomotopyWith.prop
 
 theorem extendProp (F : HomotopyWith f₀ f₁ P) (t : ℝ) : P (F.toHomotopy.extend t) := by

11c53f17

feat: improvements to congr! and convert (#2606)

There is now configuration for congr!, convert, and convert_to to control parts of the congruence algorithm, in particular transparency settings when applying congruence lemmas.
congr! now applies congruence lemmas with reducible transparency by default. This prevents it from unfolding definitions when applying congruence lemmas. It also now tries both the LHS-biased and RHS-biased simp congruence lemmas, with a configuration option to set which it should try first.
There is now a new HEq congruence lemma generator that gives each hypothesis access to the proofs of previous hypotheses. This means that if you have an equality ⊢ ⟨a, x⟩ = ⟨b, y⟩ of sigma types, congr! turns this into goals ⊢ a = b and ⊢ a = b → HEq x y (note that congr! will also auto-introduce a = b for you in the second goal). This congruence lemma generator applies to more cases than the simp congruence lemma generator does.
congr! (and hence convert) are more careful about applying lemmas that don't force definitions to unfold. There were a number of cases in mathlib where the implementation of congr was being abused to unfold definitions.
With set_option trace.congr! true you can see what congr! sees when it is deciding on congruence lemmas.
There is also a bug fix in convert_to to do using 1 when there is no using clause, to match its documentation.

Note that congr! is more capable than congr at finding a way to equate left-hand sides and right-hand sides, so you will frequently need to limit its depth with a using clause. However, there is also a new heuristic to prevent considering unlikely-to-be-provable type equalities (controlled by the typeEqs option), which can help limit the depth automatically.

There is also a predefined configuration that you can invoke with, for example, convert (config := .unfoldSameFun) h, that causes it to behave more like congr, including using default transparency when unfolding.

61ca0ea8

Diff

@@ -277,7 +277,7 @@ theorem symm_trans {f₀ f₁ f₂ : C(X, Y)} (F : Homotopy f₀ f₁) (G : Homo
   split_ifs with h₁ h₂ h₂
   . have ht : (t : ℝ) = 1 / 2 :=
       -- porting note: this was proved by linarith in mathlib
-      le_antisymm h₂ (by convert sub_le_comm.mp h₁; norm_num)
+      le_antisymm h₂ (by convert sub_le_comm.mp h₁ using 1; norm_num)
     simp only [ht]
     norm_num
   . congr 2
@@ -292,7 +292,7 @@ theorem symm_trans {f₀ f₁ f₂ : C(X, Y)} (F : Homotopy f₀ f₁) (G : Homo
     -- porting note: this was proved by linarith in mathlib
     apply h₂
     rw [sub_le_comm, not_le] at h₁
-    convert le_of_lt h₁
+    convert le_of_lt h₁ using 1
     norm_num
 #align continuous_map.homotopy.symm_trans ContinuousMap.Homotopy.symm_trans
 
@@ -435,11 +435,10 @@ theorem extendProp (F : HomotopyWith f₀ f₁ P) (t : ℝ) : P (F.toHomotopy.ex
   by_cases ht₀ : 0 ≤ t
   · by_cases ht₁ : t ≤ 1
     · apply F.prop
-    · -- porting note: `convert F.prop 1` does not create the expected goal
-      refine' Eq.subst _ (F.prop 1)
+    · convert F.prop 1
       ext x
       simp [F.toHomotopy.extend_apply_of_one_le (le_of_not_le ht₁)]
-  · refine' Eq.subst _ (F.prop 0)
+  · convert F.prop 0
     ext x
     simp [F.toHomotopy.extend_apply_of_le_zero (le_of_not_le ht₀)]
 #align continuous_map.homotopy_with.extend_prop ContinuousMap.HomotopyWith.extendProp
@@ -454,10 +453,7 @@ variable {P : C(X, Y) → Prop}
 @[simps!]
 def refl (f : C(X, Y)) (hf : P f) : HomotopyWith f f P :=
   { Homotopy.refl f with
-    prop' := fun t => by
-      refine' Eq.subst _ hf
-      cases f
-      rfl }
+    prop' := fun _ => hf }
 #align continuous_map.homotopy_with.refl ContinuousMap.HomotopyWith.refl
 
 instance : Inhabited (HomotopyWith (ContinuousMap.id X) (ContinuousMap.id X) fun _ => True) :=

11c53f17

feat: port Topology.Homotopy.Basic (#2825)

e1f0c176

`topology.homotopy.basic` ⟷ `Mathlib.Topology.Homotopy.Basic`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Important changes

Remaining issues

Slower (failing) search

`simp` not firing sometimes

Missing instances due to unification failing

Workaround for issues

Dependencies 10 + 515

topology.homotopy.basic ⟷ Mathlib.Topology.Homotopy.Basic

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Important changes

Remaining issues

Slower (failing) search

simp not firing sometimes

Missing instances due to unification failing

Workaround for issues

Dependencies 10 + 515

`topology.homotopy.basic` ⟷ `Mathlib.Topology.Homotopy.Basic`

`simp` not firing sometimes