topology.homotopy.path | 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

bb9d1c50

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

dbdf71ce

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Shing Tak Lam
 -/
 import Topology.Homotopy.Basic
-import Topology.PathConnected
+import Topology.Connected.PathConnected
 import Analysis.Convex.Basic
 
 #align_import topology.homotopy.path from "leanprover-community/mathlib"@"dbdf71cee7bb20367cb7e37279c08b0c218cf967"

dbdf71ce

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -218,7 +218,7 @@ def hcomp (F : Homotopy p₀ q₀) (G : Homotopy p₁ q₁) : Homotopy (p₀.tra
     cases ht
     · rw [ht]
       simp
-    · rw [Set.mem_singleton_iff] at ht 
+    · rw [Set.mem_singleton_iff] at ht
       rw [ht]
       norm_num
 #align path.homotopy.hcomp Path.Homotopy.hcomp
@@ -262,7 +262,7 @@ def reparam (p : Path x₀ x₁) (f : I → I) (hf : Continuous f) (hf₀ : f 0
   prop' t x hx := by
     cases hx
     · rw [hx]; norm_num [hf₀]
-    · rw [Set.mem_singleton_iff] at hx 
+    · rw [Set.mem_singleton_iff] at hx
       rw [hx]
       norm_num [hf₁]
 #align path.homotopy.reparam Path.Homotopy.reparam
@@ -281,7 +281,7 @@ def symm₂ {p q : Path x₀ x₁} (F : p.Homotopy q) : p.symm.Homotopy q.symm
   prop' t x hx := by
     cases hx
     · rw [hx]; simp
-    · rw [Set.mem_singleton_iff] at hx 
+    · rw [Set.mem_singleton_iff] at hx
       rw [hx]
       simp
 #align path.homotopy.symm₂ Path.Homotopy.symm₂
@@ -302,7 +302,7 @@ def map {p q : Path x₀ x₁} (F : p.Homotopy q) (f : C(X, Y)) :
   prop' t x hx := by
     cases hx
     · simp [hx]
-    · rw [Set.mem_singleton_iff] at hx 
+    · rw [Set.mem_singleton_iff] at hx
       simp [hx]
 #align path.homotopy.map Path.Homotopy.map
 -/

dbdf71ce

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,9 +3,9 @@ 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.Homotopy.Basic
-import Mathbin.Topology.PathConnected
-import Mathbin.Analysis.Convex.Basic
+import Topology.Homotopy.Basic
+import Topology.PathConnected
+import Analysis.Convex.Basic
 
 #align_import topology.homotopy.path from "leanprover-community/mathlib"@"dbdf71cee7bb20367cb7e37279c08b0c218cf967"

dbdf71ce

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,16 +2,13 @@
 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.path
-! leanprover-community/mathlib commit dbdf71cee7bb20367cb7e37279c08b0c218cf967
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Topology.Homotopy.Basic
 import Mathbin.Topology.PathConnected
 import Mathbin.Analysis.Convex.Basic
 
+#align_import topology.homotopy.path from "leanprover-community/mathlib"@"dbdf71cee7bb20367cb7e37279c08b0c218cf967"
+
 /-!
 # Homotopy between paths

dbdf71ce

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -67,10 +67,13 @@ variable {p₀ p₁ : Path x₀ x₁}
 instance : CoeFun (Homotopy p₀ p₁) fun _ => I × I → X :=
   ⟨fun F => F.toFun⟩
 
+#print Path.Homotopy.coeFn_injective /-
 theorem coeFn_injective : @Function.Injective (Homotopy p₀ p₁) (I × I → X) coeFn :=
   ContinuousMap.HomotopyWith.coeFn_injective
 #align path.homotopy.coe_fn_injective Path.Homotopy.coeFn_injective
+-/
 
+#print Path.Homotopy.source /-
 @[simp]
 theorem source (F : Homotopy p₀ p₁) (t : I) : F (t, 0) = x₀ :=
   by
@@ -78,7 +81,9 @@ theorem source (F : Homotopy p₀ p₁) (t : I) : F (t, 0) = x₀ :=
   apply ContinuousMap.HomotopyRel.eq_fst
   simp
 #align path.homotopy.source Path.Homotopy.source
+-/
 
+#print Path.Homotopy.target /-
 @[simp]
 theorem target (F : Homotopy p₀ p₁) (t : I) : F (t, 1) = x₁ :=
   by
@@ -86,6 +91,7 @@ theorem target (F : Homotopy p₀ p₁) (t : I) : F (t, 1) = x₁ :=
   apply ContinuousMap.HomotopyRel.eq_snd
   simp
 #align path.homotopy.target Path.Homotopy.target
+-/
 
 #print Path.Homotopy.eval /-
 /-- Evaluating a path homotopy at an intermediate point, giving us a `path`.
@@ -157,6 +163,7 @@ def trans (F : Homotopy p₀ p₁) (G : Homotopy p₁ p₂) : Homotopy p₀ p₂
 #align path.homotopy.trans Path.Homotopy.trans
 -/
 
+#print Path.Homotopy.trans_apply /-
 theorem trans_apply (F : Homotopy p₀ p₁) (G : Homotopy p₁ p₂) (x : I × I) :
     (F.trans G) x =
       if h : (x.1 : ℝ) ≤ 1 / 2 then
@@ -165,6 +172,7 @@ theorem trans_apply (F : Homotopy p₀ p₁) (G : Homotopy p₁ p₂) (x : I ×
         G (⟨2 * x.1 - 1, unitInterval.two_mul_sub_one_mem_iff.2 ⟨(not_le.1 h).le, x.1.2.2⟩⟩, x.2) :=
   ContinuousMap.HomotopyRel.trans_apply _ _ _
 #align path.homotopy.trans_apply Path.Homotopy.trans_apply
+-/
 
 #print Path.Homotopy.symm_trans /-
 theorem symm_trans (F : Homotopy p₀ p₁) (G : Homotopy p₁ p₂) :
@@ -219,6 +227,7 @@ def hcomp (F : Homotopy p₀ q₀) (G : Homotopy p₁ q₁) : Homotopy (p₀.tra
 #align path.homotopy.hcomp Path.Homotopy.hcomp
 -/
 
+#print Path.Homotopy.hcomp_apply /-
 theorem hcomp_apply (F : Homotopy p₀ q₀) (G : Homotopy p₁ q₁) (x : I × I) :
     F.hcomp G x =
       if h : (x.2 : ℝ) ≤ 1 / 2 then
@@ -228,11 +237,14 @@ theorem hcomp_apply (F : Homotopy p₀ q₀) (G : Homotopy p₁ q₁) (x : I ×
           ⟨2 * x.2 - 1, unitInterval.two_mul_sub_one_mem_iff.2 ⟨(not_le.1 h).le, x.2.2.2⟩⟩ :=
   show ite _ _ _ = _ by split_ifs <;> exact Path.extend_extends _ _
 #align path.homotopy.hcomp_apply Path.Homotopy.hcomp_apply
+-/
 
+#print Path.Homotopy.hcomp_half /-
 theorem hcomp_half (F : Homotopy p₀ q₀) (G : Homotopy p₁ q₁) (t : I) :
     F.hcomp G (t, ⟨1 / 2, by norm_num, by norm_num⟩) = x₁ :=
   show ite _ _ _ = _ by norm_num
 #align path.homotopy.hcomp_half Path.Homotopy.hcomp_half
+-/
 
 end
 
@@ -278,6 +290,7 @@ def symm₂ {p q : Path x₀ x₁} (F : p.Homotopy q) : p.symm.Homotopy q.symm
 #align path.homotopy.symm₂ Path.Homotopy.symm₂
 -/
 
+#print Path.Homotopy.map /-
 /--
 Given `F : homotopy p q`, and `f : C(X, Y)`, we can define a homotopy from `p.map f.continuous` to
 `q.map f.continuous`.
@@ -295,6 +308,7 @@ def map {p q : Path x₀ x₁} (F : p.Homotopy q) (f : C(X, Y)) :
     · rw [Set.mem_singleton_iff] at hx 
       simp [hx]
 #align path.homotopy.map Path.Homotopy.map
+-/
 
 end Homotopy
 
@@ -336,10 +350,12 @@ theorem equivalence : Equivalence (@Homotopic X _ x₀ x₁) :=
 #align path.homotopic.equivalence Path.Homotopic.equivalence
 -/
 
+#print Path.Homotopic.map /-
 theorem map {p q : Path x₀ x₁} (h : p.Homotopic q) (f : C(X, Y)) :
     Homotopic (p.map f.Continuous) (q.map f.Continuous) :=
   h.map fun F => F.map f
 #align path.homotopic.map Path.Homotopic.map
+-/
 
 #print Path.Homotopic.hcomp /-
 theorem hcomp {p₀ p₁ : Path x₀ x₁} {q₀ q₁ : Path x₁ x₂} (hp : p₀.Homotopic p₁)
@@ -386,16 +402,20 @@ theorem comp_lift (P₀ : Path x₀ x₁) (P₁ : Path x₁ x₂) : ⟦P₀.tran
 #align path.homotopic.comp_lift Path.Homotopic.comp_lift
 -/
 
+#print Path.Homotopic.Quotient.mapFn /-
 /-- The image of a path homotopy class `P₀` under a map `f`.
     This is `path.map` descended to the quotient -/
 def Quotient.mapFn (P₀ : Path.Homotopic.Quotient x₀ x₁) (f : C(X, Y)) :
     Path.Homotopic.Quotient (f x₀) (f x₁) :=
   Quotient.map (fun q : Path x₀ x₁ => q.map f.Continuous) (fun p₀ p₁ h => Path.Homotopic.map h f) P₀
 #align path.homotopic.quotient.map_fn Path.Homotopic.Quotient.mapFn
+-/
 
+#print Path.Homotopic.map_lift /-
 theorem map_lift (P₀ : Path x₀ x₁) (f : C(X, Y)) : ⟦P₀.map f.Continuous⟧ = Quotient.mapFn ⟦P₀⟧ f :=
   rfl
 #align path.homotopic.map_lift Path.Homotopic.map_lift
+-/
 
 #print Path.Homotopic.hpath_hext /-
 theorem hpath_hext {p₁ : Path x₀ x₁} {p₂ : Path x₂ x₃} (hp : ∀ t, p₁ t = p₂ t) : HEq ⟦p₁⟧ ⟦p₂⟧ :=
@@ -412,6 +432,7 @@ end Path
 
 namespace ContinuousMap.Homotopy
 
+#print ContinuousMap.Homotopy.evalAt /-
 /-- Given a homotopy H: f ∼ g, get the path traced by the point `x` as it moves from
 `f x` to `g x`
 -/
@@ -422,6 +443,7 @@ def evalAt {X : Type _} {Y : Type _} [TopologicalSpace X] [TopologicalSpace Y] {
   source' := H.apply_zero x
   target' := H.apply_one x
 #align continuous_map.homotopy.eval_at ContinuousMap.Homotopy.evalAt
+-/
 
 end ContinuousMap.Homotopy

dbdf71ce

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -213,7 +213,7 @@ def hcomp (F : Homotopy p₀ q₀) (G : Homotopy p₁ q₁) : Homotopy (p₀.tra
     cases ht
     · rw [ht]
       simp
-    · rw [Set.mem_singleton_iff] at ht
+    · rw [Set.mem_singleton_iff] at ht 
       rw [ht]
       norm_num
 #align path.homotopy.hcomp Path.Homotopy.hcomp
@@ -253,7 +253,7 @@ def reparam (p : Path x₀ x₁) (f : I → I) (hf : Continuous f) (hf₀ : f 0
   prop' t x hx := by
     cases hx
     · rw [hx]; norm_num [hf₀]
-    · rw [Set.mem_singleton_iff] at hx
+    · rw [Set.mem_singleton_iff] at hx 
       rw [hx]
       norm_num [hf₁]
 #align path.homotopy.reparam Path.Homotopy.reparam
@@ -272,7 +272,7 @@ def symm₂ {p q : Path x₀ x₁} (F : p.Homotopy q) : p.symm.Homotopy q.symm
   prop' t x hx := by
     cases hx
     · rw [hx]; simp
-    · rw [Set.mem_singleton_iff] at hx
+    · rw [Set.mem_singleton_iff] at hx 
       rw [hx]
       simp
 #align path.homotopy.symm₂ Path.Homotopy.symm₂
@@ -292,7 +292,7 @@ def map {p q : Path x₀ x₁} (F : p.Homotopy q) (f : C(X, Y)) :
   prop' t x hx := by
     cases hx
     · simp [hx]
-    · rw [Set.mem_singleton_iff] at hx
+    · rw [Set.mem_singleton_iff] at hx 
       simp [hx]
 #align path.homotopy.map Path.Homotopy.map
 
@@ -402,7 +402,7 @@ theorem hpath_hext {p₁ : Path x₀ x₁} {p₂ : Path x₂ x₃} (hp : ∀ t,
   by
   obtain rfl : x₀ = x₂ := by convert hp 0 <;> simp
   obtain rfl : x₁ = x₃ := by convert hp 1 <;> simp
-  rw [heq_iff_eq]; congr ; ext t; exact hp t
+  rw [heq_iff_eq]; congr; ext t; exact hp t
 #align path.homotopic.hpath_hext Path.Homotopic.hpath_hext
 -/

dbdf71ce

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -46,7 +46,7 @@ variable {x₀ x₁ x₂ x₃ : X}
 
 noncomputable section
 
-open unitInterval
+open scoped unitInterval
 
 namespace Path

dbdf71ce

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -67,16 +67,10 @@ variable {p₀ p₁ : Path x₀ x₁}
 instance : CoeFun (Homotopy p₀ p₁) fun _ => I × I → X :=
   ⟨fun F => F.toFun⟩
 
-/- warning: path.homotopy.coe_fn_injective -> Path.Homotopy.coeFn_injective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align path.homotopy.coe_fn_injective Path.Homotopy.coeFn_injectiveₓ'. -/
 theorem coeFn_injective : @Function.Injective (Homotopy p₀ p₁) (I × I → X) coeFn :=
   ContinuousMap.HomotopyWith.coeFn_injective
 #align path.homotopy.coe_fn_injective Path.Homotopy.coeFn_injective
 
-/- warning: path.homotopy.source -> Path.Homotopy.source is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align path.homotopy.source Path.Homotopy.sourceₓ'. -/
 @[simp]
 theorem source (F : Homotopy p₀ p₁) (t : I) : F (t, 0) = x₀ :=
   by
@@ -85,9 +79,6 @@ theorem source (F : Homotopy p₀ p₁) (t : I) : F (t, 0) = x₀ :=
   simp
 #align path.homotopy.source Path.Homotopy.source
 
-/- warning: path.homotopy.target -> Path.Homotopy.target is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align path.homotopy.target Path.Homotopy.targetₓ'. -/
 @[simp]
 theorem target (F : Homotopy p₀ p₁) (t : I) : F (t, 1) = x₁ :=
   by
@@ -166,9 +157,6 @@ def trans (F : Homotopy p₀ p₁) (G : Homotopy p₁ p₂) : Homotopy p₀ p₂
 #align path.homotopy.trans Path.Homotopy.trans
 -/
 
-/- warning: path.homotopy.trans_apply -> Path.Homotopy.trans_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align path.homotopy.trans_apply Path.Homotopy.trans_applyₓ'. -/
 theorem trans_apply (F : Homotopy p₀ p₁) (G : Homotopy p₁ p₂) (x : I × I) :
     (F.trans G) x =
       if h : (x.1 : ℝ) ≤ 1 / 2 then
@@ -231,9 +219,6 @@ def hcomp (F : Homotopy p₀ q₀) (G : Homotopy p₁ q₁) : Homotopy (p₀.tra
 #align path.homotopy.hcomp Path.Homotopy.hcomp
 -/
 
-/- warning: path.homotopy.hcomp_apply -> Path.Homotopy.hcomp_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align path.homotopy.hcomp_apply Path.Homotopy.hcomp_applyₓ'. -/
 theorem hcomp_apply (F : Homotopy p₀ q₀) (G : Homotopy p₁ q₁) (x : I × I) :
     F.hcomp G x =
       if h : (x.2 : ℝ) ≤ 1 / 2 then
@@ -244,9 +229,6 @@ theorem hcomp_apply (F : Homotopy p₀ q₀) (G : Homotopy p₁ q₁) (x : I ×
   show ite _ _ _ = _ by split_ifs <;> exact Path.extend_extends _ _
 #align path.homotopy.hcomp_apply Path.Homotopy.hcomp_apply
 
-/- warning: path.homotopy.hcomp_half -> Path.Homotopy.hcomp_half is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align path.homotopy.hcomp_half Path.Homotopy.hcomp_halfₓ'. -/
 theorem hcomp_half (F : Homotopy p₀ q₀) (G : Homotopy p₁ q₁) (t : I) :
     F.hcomp G (t, ⟨1 / 2, by norm_num, by norm_num⟩) = x₁ :=
   show ite _ _ _ = _ by norm_num
@@ -296,12 +278,6 @@ def symm₂ {p q : Path x₀ x₁} (F : p.Homotopy q) : p.symm.Homotopy q.symm
 #align path.homotopy.symm₂ Path.Homotopy.symm₂
 -/
 
-/- warning: path.homotopy.map -> Path.Homotopy.map is a dubious translation:
-lean 3 declaration is
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 /--
 Given `F : homotopy p q`, and `f : C(X, Y)`, we can define a homotopy from `p.map f.continuous` to
 `q.map f.continuous`.
@@ -360,12 +336,6 @@ theorem equivalence : Equivalence (@Homotopic X _ x₀ x₁) :=
 #align path.homotopic.equivalence Path.Homotopic.equivalence
 -/
 
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 theorem map {p q : Path x₀ x₁} (h : p.Homotopic q) (f : C(X, Y)) :
     Homotopic (p.map f.Continuous) (q.map f.Continuous) :=
   h.map fun F => F.map f
@@ -416,12 +386,6 @@ theorem comp_lift (P₀ : Path x₀ x₁) (P₁ : Path x₁ x₂) : ⟦P₀.tran
 #align path.homotopic.comp_lift Path.Homotopic.comp_lift
 -/
 
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 /-- The image of a path homotopy class `P₀` under a map `f`.
     This is `path.map` descended to the quotient -/
 def Quotient.mapFn (P₀ : Path.Homotopic.Quotient x₀ x₁) (f : C(X, Y)) :
@@ -429,12 +393,6 @@ def Quotient.mapFn (P₀ : Path.Homotopic.Quotient x₀ x₁) (f : C(X, Y)) :
   Quotient.map (fun q : Path x₀ x₁ => q.map f.Continuous) (fun p₀ p₁ h => Path.Homotopic.map h f) P₀
 #align path.homotopic.quotient.map_fn Path.Homotopic.Quotient.mapFn
 
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-Case conversion may be inaccurate. Consider using '#align path.homotopic.map_lift Path.Homotopic.map_liftₓ'. -/
 theorem map_lift (P₀ : Path x₀ x₁) (f : C(X, Y)) : ⟦P₀.map f.Continuous⟧ = Quotient.mapFn ⟦P₀⟧ f :=
   rfl
 #align path.homotopic.map_lift Path.Homotopic.map_lift
@@ -454,12 +412,6 @@ end Path
 
 namespace ContinuousMap.Homotopy
 
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 /-- Given a homotopy H: f ∼ g, get the path traced by the point `x` as it moves from
 `f x` to `g x`
 -/

dbdf71ce

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -270,8 +270,7 @@ def reparam (p : Path x₀ x₁) (f : I → I) (hf : Continuous f) (hf₀ : f 0
   map_one_left' x := by norm_num
   prop' t x hx := by
     cases hx
-    · rw [hx]
-      norm_num [hf₀]
+    · rw [hx]; norm_num [hf₀]
     · rw [Set.mem_singleton_iff] at hx
       rw [hx]
       norm_num [hf₁]
@@ -290,8 +289,7 @@ def symm₂ {p q : Path x₀ x₁} (F : p.Homotopy q) : p.symm.Homotopy q.symm
   map_one_left' := by simp [Path.symm]
   prop' t x hx := by
     cases hx
-    · rw [hx]
-      simp
+    · rw [hx]; simp
     · rw [Set.mem_singleton_iff] at hx
       rw [hx]
       simp

dbdf71ce

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -68,20 +68,14 @@ instance : CoeFun (Homotopy p₀ p₁) fun _ => I × I → X :=
   ⟨fun F => F.toFun⟩
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align path.homotopy.coe_fn_injective Path.Homotopy.coeFn_injectiveₓ'. -/
 theorem coeFn_injective : @Function.Injective (Homotopy p₀ p₁) (I × I → X) coeFn :=
   ContinuousMap.HomotopyWith.coeFn_injective
 #align path.homotopy.coe_fn_injective Path.Homotopy.coeFn_injective
 
 /- warning: path.homotopy.source -> Path.Homotopy.source is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align path.homotopy.source Path.Homotopy.sourceₓ'. -/
 @[simp]
 theorem source (F : Homotopy p₀ p₁) (t : I) : F (t, 0) = x₀ :=
@@ -92,10 +86,7 @@ theorem source (F : Homotopy p₀ p₁) (t : I) : F (t, 0) = x₀ :=
 #align path.homotopy.source Path.Homotopy.source
 
 /- warning: path.homotopy.target -> Path.Homotopy.target is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align path.homotopy.target Path.Homotopy.targetₓ'. -/
 @[simp]
 theorem target (F : Homotopy p₀ p₁) (t : I) : F (t, 1) = x₁ :=
@@ -176,10 +167,7 @@ def trans (F : Homotopy p₀ p₁) (G : Homotopy p₁ p₂) : Homotopy p₀ p₂
 -/
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align path.homotopy.trans_apply Path.Homotopy.trans_applyₓ'. -/
 theorem trans_apply (F : Homotopy p₀ p₁) (G : Homotopy p₁ p₂) (x : I × I) :
     (F.trans G) x =
@@ -244,10 +232,7 @@ def hcomp (F : Homotopy p₀ q₀) (G : Homotopy p₁ q₁) : Homotopy (p₀.tra
 -/
 
 /- warning: path.homotopy.hcomp_apply -> Path.Homotopy.hcomp_apply is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align path.homotopy.hcomp_apply Path.Homotopy.hcomp_applyₓ'. -/
 theorem hcomp_apply (F : Homotopy p₀ q₀) (G : Homotopy p₁ q₁) (x : I × I) :
     F.hcomp G x =
@@ -260,10 +245,7 @@ theorem hcomp_apply (F : Homotopy p₀ q₀) (G : Homotopy p₁ q₁) (x : I ×
 #align path.homotopy.hcomp_apply Path.Homotopy.hcomp_apply
 
 /- warning: path.homotopy.hcomp_half -> Path.Homotopy.hcomp_half is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align path.homotopy.hcomp_half Path.Homotopy.hcomp_halfₓ'. -/
 theorem hcomp_half (F : Homotopy p₀ q₀) (G : Homotopy p₁ q₁) (t : I) :
     F.hcomp G (t, ⟨1 / 2, by norm_num, by norm_num⟩) = x₁ :=

dbdf71ce

bump to nightly-2023-05-16-16

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

9cb92e8c

Diff

@@ -177,7 +177,7 @@ def trans (F : Homotopy p₀ p₁) (G : Homotopy p₁ p₂) : Homotopy p₀ p₂
 
 /- warning: path.homotopy.trans_apply -> Path.Homotopy.trans_apply is a dubious translation:
 lean 3 declaration is
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+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x₀ : X} {x₁ : X} {p₀ : Path.{u1} X _inst_1 x₀ x₁} {p₁ : Path.{u1} X _inst_1 x₀ x₁} {p₂ : Path.{u1} X _inst_1 x₀ x₁} (F : Path.Homotopy.{u1} X _inst_1 x₀ x₁ p₀ p₁) (G : Path.Homotopy.{u1} X _inst_1 x₀ x₁ p₁ p₂) (x : Prod.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)), Eq.{succ u1} X (coeFn.{succ u1, succ u1} (Path.Homotopy.{u1} X _inst_1 x₀ x₁ p₀ p₂) (fun (_x : Path.Homotopy.{u1} X _inst_1 x₀ x₁ p₀ p₂) => (Prod.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)) -> X) (Path.Homotopy.hasCoeToFun.{u1} X _inst_1 x₀ x₁ p₀ p₂) (Path.Homotopy.trans.{u1} X _inst_1 x₀ x₁ p₀ p₁ p₂ F G) x) (dite.{succ u1} X (LE.le.{0} Real Real.hasLe ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) 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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, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) x))) (LE.le.{0} Real (Preorder.toHasLe.{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, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) 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, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) x)) (Iff.mp (Not (LE.le.{0} Real (Preorder.toHasLe.{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, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) 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.toHasLt.{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, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) 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, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) 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.toHasLe.{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, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) x))) (LE.le.{0} Real (Preorder.toHasLe.{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, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) 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, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) x)))))) (Prod.snd.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) x))))
 but is expected to have type
   forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x₀ : X} {x₁ : X} {p₀ : Path.{u1} X _inst_1 x₀ x₁} {p₁ : Path.{u1} X _inst_1 x₀ x₁} {p₂ : Path.{u1} X _inst_1 x₀ x₁} (F : Path.Homotopy.{u1} X _inst_1 x₀ x₁ p₀ p₁) (G : Path.Homotopy.{u1} X _inst_1 x₀ x₁ p₁ p₂) (x : Prod.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval)), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval)) => X) x) (FunLike.coe.{succ u1, 1, succ u1} (Path.Homotopy.{u1} X _inst_1 x₀ x₁ p₀ p₂) (Prod.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval)) (fun (_x : Prod.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval)) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval)) => X) _x) (ContinuousMapClass.toFunLike.{u1, 0, u1} (Path.Homotopy.{u1} X _inst_1 x₀ x₁ p₀ p₂) (Prod.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval)) X (instTopologicalSpaceProd.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) (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))) (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 (ContinuousMap.HomotopyLike.toContinuousMapClass.{0, u1, 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 (Path.Homotopy.{u1} X _inst_1 x₀ x₁ p₀ p₂) (Path.toContinuousMap.{u1} X _inst_1 x₀ x₁ p₀) (Path.toContinuousMap.{u1} X _inst_1 x₀ x₁ p₂) (ContinuousMap.HomotopyWith.instHomotopyLikeHomotopyWith.{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 (Path.toContinuousMap.{u1} X _inst_1 x₀ x₁ p₀) (Path.toContinuousMap.{u1} X _inst_1 x₀ x₁ p₂) (fun (f : ContinuousMap.{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) => forall (x : Set.Elem.{0} Real unitInterval), (Membership.mem.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.{0} (Set.Elem.{0} Real unitInterval)) (Set.instMembershipSet.{0} (Set.Elem.{0} Real unitInterval)) x (Insert.insert.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.{0} (Set.Elem.{0} Real unitInterval)) (Set.instInsertSet.{0} (Set.Elem.{0} Real unitInterval)) (OfNat.ofNat.{0} (Set.Elem.{0} Real unitInterval) 0 (Zero.toOfNat0.{0} (Set.Elem.{0} Real unitInterval) unitInterval.hasZero)) (Singleton.singleton.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.{0} (Set.Elem.{0} Real unitInterval)) (Set.instSingletonSet.{0} (Set.Elem.{0} Real unitInterval)) (OfNat.ofNat.{0} (Set.Elem.{0} Real unitInterval) 1 (One.toOfNat1.{0} (Set.Elem.{0} Real unitInterval) unitInterval.hasOne))))) -> (And (Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) x) (FunLike.coe.{succ u1, 1, succ u1} (ContinuousMap.{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) (Set.Elem.{0} Real unitInterval) (fun (a : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) a) (ContinuousMapClass.toFunLike.{u1, 0, u1} (ContinuousMap.{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) (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 (ContinuousMap.instContinuousMapClassContinuousMap.{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)) f x) (FunLike.coe.{succ u1, 1, succ u1} (ContinuousMap.{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) (Set.Elem.{0} Real unitInterval) (fun (a : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) a) (ContinuousMapClass.toFunLike.{u1, 0, u1} (ContinuousMap.{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) (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 (ContinuousMap.instContinuousMapClassContinuousMap.{0, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) 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unitInterval) 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, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) 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, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) x)))))) (Prod.snd.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) x))))
 Case conversion may be inaccurate. Consider using '#align path.homotopy.trans_apply Path.Homotopy.trans_applyₓ'. -/
@@ -245,7 +245,7 @@ def hcomp (F : Homotopy p₀ q₀) (G : Homotopy p₁ q₁) : Homotopy (p₀.tra
 
 /- warning: path.homotopy.hcomp_apply -> Path.Homotopy.hcomp_apply is a dubious translation:
 lean 3 declaration is
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_inst_1 x₁ x₂ p₁ q₁ G (Prod.fst.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) x)) (Subtype.mk.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (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) 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(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.snd.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) 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 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(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} 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(coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) 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.snd.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) 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} 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+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x₀ : X} {x₁ : X} {x₂ : X} {p₀ : Path.{u1} X _inst_1 x₀ x₁} {q₀ : Path.{u1} X _inst_1 x₀ x₁} {p₁ : Path.{u1} X _inst_1 x₁ x₂} {q₁ : Path.{u1} X _inst_1 x₁ x₂} (F : Path.Homotopy.{u1} X _inst_1 x₀ x₁ p₀ q₀) (G : Path.Homotopy.{u1} X _inst_1 x₁ x₂ p₁ q₁) (x : Prod.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)), Eq.{succ u1} X (coeFn.{succ u1, succ u1} (Path.Homotopy.{u1} X _inst_1 x₀ x₂ (Path.trans.{u1} X _inst_1 x₀ x₁ x₂ p₀ p₁) (Path.trans.{u1} X _inst_1 x₀ x₁ x₂ q₀ q₁)) (fun (_x : Path.Homotopy.{u1} X _inst_1 x₀ x₂ (Path.trans.{u1} X _inst_1 x₀ x₁ x₂ p₀ p₁) (Path.trans.{u1} X _inst_1 x₀ x₁ x₂ q₀ q₁)) => (Prod.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)) -> X) (Path.Homotopy.hasCoeToFun.{u1} X _inst_1 x₀ x₂ (Path.trans.{u1} X _inst_1 x₀ x₁ x₂ p₀ p₁) (Path.trans.{u1} X _inst_1 x₀ x₁ x₂ q₀ q₁)) (Path.Homotopy.hcomp.{u1} X _inst_1 x₀ x₁ x₂ p₀ q₀ p₁ q₁ F G) x) (dite.{succ u1} X (LE.le.{0} Real Real.hasLe ((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.snd.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) x)) (HDiv.hDiv.{0, 0, 0} Real Real 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(Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (Prod.snd.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) 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.snd.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) x))))))))
 but is expected to have type
   forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x₀ : X} {x₁ : X} {x₂ : X} {p₀ : Path.{u1} X _inst_1 x₀ x₁} {q₀ : Path.{u1} X _inst_1 x₀ x₁} {p₁ : Path.{u1} X _inst_1 x₁ x₂} {q₁ : Path.{u1} X _inst_1 x₁ x₂} (F : Path.Homotopy.{u1} X _inst_1 x₀ x₁ p₀ q₀) (G : Path.Homotopy.{u1} X _inst_1 x₁ x₂ p₁ q₁) (x : Prod.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval)), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval)) => X) x) (FunLike.coe.{succ u1, 1, succ u1} (Path.Homotopy.{u1} X _inst_1 x₀ x₂ (Path.trans.{u1} X _inst_1 x₀ x₁ x₂ p₀ p₁) (Path.trans.{u1} X _inst_1 x₀ x₁ x₂ q₀ q₁)) (Prod.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval)) (fun (_x : Prod.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval)) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, 0} (Set.Elem.{0} Real 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=> Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.snd.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) 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.snd.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) 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.snd.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) 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.snd.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) 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.snd.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) 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.snd.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) 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.snd.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) 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.snd.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) 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.snd.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) 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.snd.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) 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.snd.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) x))))))))
 Case conversion may be inaccurate. Consider using '#align path.homotopy.hcomp_apply Path.Homotopy.hcomp_applyₓ'. -/
@@ -261,7 +261,7 @@ theorem hcomp_apply (F : Homotopy p₀ q₀) (G : Homotopy p₁ q₁) (x : I ×
 
 /- warning: path.homotopy.hcomp_half -> Path.Homotopy.hcomp_half is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x₀ : X} {x₁ : X} {x₂ : X} {p₀ : Path.{u1} X _inst_1 x₀ x₁} {q₀ : Path.{u1} X _inst_1 x₀ x₁} {p₁ : Path.{u1} X _inst_1 x₁ x₂} {q₁ : Path.{u1} X _inst_1 x₁ x₂} (F : Path.Homotopy.{u1} X _inst_1 x₀ x₁ p₀ q₀) (G : Path.Homotopy.{u1} X _inst_1 x₁ x₂ p₁ q₁) (t : coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval), Eq.{succ u1} X (coeFn.{succ u1, succ u1} (Path.Homotopy.{u1} X _inst_1 x₀ x₂ (Path.trans.{u1} X _inst_1 x₀ x₁ x₂ p₀ p₁) (Path.trans.{u1} X _inst_1 x₀ x₁ x₂ q₀ q₁)) (fun (_x : Path.Homotopy.{u1} X _inst_1 x₀ x₂ (Path.trans.{u1} X _inst_1 x₀ x₁ x₂ p₀ p₁) (Path.trans.{u1} X _inst_1 x₀ x₁ x₂ q₀ q₁)) => (Prod.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)) -> X) (Path.Homotopy.hasCoeToFun.{u1} X _inst_1 x₀ x₂ (Path.trans.{u1} X _inst_1 x₀ x₁ x₂ p₀ p₁) (Path.trans.{u1} X _inst_1 x₀ x₁ x₂ q₀ q₁)) (Path.Homotopy.hcomp.{u1} X _inst_1 x₀ x₁ x₂ p₀ q₀ p₁ q₁ F G) (Prod.mk.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) t (Subtype.mk.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (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))))) (And.intro (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))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) 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(Preorder.toLE.{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)))) True) (eq_true (LE.le.{0} Real (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedCancelAddCommMonoid.toPartialOrder.{0} Real (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Real (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Real Real.linearOrderedSemiring))))) (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} 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(NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) (one_mul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (one_mul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) (NormNum.le_one_bit0.{0} Real Real.linearOrderedSemiring (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (le_refl.{0} Real Real.preorder (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))))) trivial))))) x₁
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x₀ : X} {x₁ : X} {x₂ : X} {p₀ : Path.{u1} X _inst_1 x₀ x₁} {q₀ : Path.{u1} X _inst_1 x₀ x₁} {p₁ : Path.{u1} X _inst_1 x₁ x₂} {q₁ : Path.{u1} X _inst_1 x₁ x₂} (F : Path.Homotopy.{u1} X _inst_1 x₀ x₁ p₀ q₀) (G : Path.Homotopy.{u1} X _inst_1 x₁ x₂ p₁ q₁) (t : coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval), Eq.{succ u1} X (coeFn.{succ u1, succ u1} (Path.Homotopy.{u1} X _inst_1 x₀ x₂ (Path.trans.{u1} X _inst_1 x₀ x₁ x₂ p₀ p₁) (Path.trans.{u1} X _inst_1 x₀ x₁ x₂ q₀ q₁)) (fun (_x : Path.Homotopy.{u1} X _inst_1 x₀ x₂ (Path.trans.{u1} X _inst_1 x₀ x₁ x₂ p₀ p₁) (Path.trans.{u1} X _inst_1 x₀ x₁ x₂ q₀ q₁)) => (Prod.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)) -> X) (Path.Homotopy.hasCoeToFun.{u1} X _inst_1 x₀ x₂ (Path.trans.{u1} X _inst_1 x₀ x₁ x₂ p₀ p₁) (Path.trans.{u1} X _inst_1 x₀ x₁ x₂ q₀ q₁)) (Path.Homotopy.hcomp.{u1} X _inst_1 x₀ x₁ x₂ p₀ q₀ p₁ q₁ F G) (Prod.mk.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) t (Subtype.mk.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (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))))) (And.intro (LE.le.{0} Real (Preorder.toHasLe.{0} Real Real.preorder) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (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)))))) (LE.le.{0} Real (Preorder.toHasLe.{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)))) (Eq.mpr.{0} (LE.le.{0} Real (Preorder.toHasLe.{0} Real Real.preorder) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (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)))))) True (id_tag Unit.unit (Eq.{1} Prop (LE.le.{0} Real (Preorder.toHasLe.{0} Real Real.preorder) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (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)))))) True) (eq_true (LE.le.{0} Real (Preorder.toHasLe.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedCancelAddCommMonoid.toPartialOrder.{0} Real Real.orderedCancelAddCommMonoid))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real (AddZeroClass.toHasZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddRightCancelMonoid.toAddMonoid.{0} Real (AddCancelMonoid.toAddRightCancelMonoid.{0} Real (AddCancelCommMonoid.toAddCancelMonoid.{0} Real (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Real Real.orderedCancelAddCommMonoid))))))))) (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)))))) (NormNum.nonneg_pos.{0} Real Real.orderedCancelAddCommMonoid (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))))) (div_pos.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.linearOrderedField) (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)))) (NormNum.zero_lt_one.{0} Real Real.linearOrderedSemiring) (bit0_pos.{0} Real Real.orderedAddCommMonoid (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (NormNum.zero_lt_one.{0} Real Real.linearOrderedSemiring)))))) trivial) (Eq.mpr.{0} (LE.le.{0} Real (Preorder.toHasLe.{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)))) True (id_tag Unit.unit (Eq.{1} Prop (LE.le.{0} Real (Preorder.toHasLe.{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)))) True) (eq_true (LE.le.{0} Real (Preorder.toHasLe.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedCancelAddCommMonoid.toPartialOrder.{0} Real (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Real (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Real Real.linearOrderedSemiring))))) (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)))) (NormNum.clear_denom_le.{0} Real Real.linearOrderedSemiring (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))) (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 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) (bit0_pos.{0} Real Real.orderedAddCommMonoid (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (NormNum.zero_lt_one.{0} Real Real.linearOrderedSemiring)) (NormNum.clear_denom_div.{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))) (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)))) (NormNum.ne_zero_of_pos.{0} Real Real.orderedAddCommGroup (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) (bit0_pos.{0} Real Real.orderedAddCommMonoid (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (NormNum.zero_lt_one.{0} Real Real.linearOrderedSemiring))) (mul_one.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) (one_mul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (one_mul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) (NormNum.le_one_bit0.{0} Real Real.linearOrderedSemiring (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (le_refl.{0} Real Real.preorder (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))))) trivial))))) x₁
 but is expected to have type
   forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x₀ : X} {x₁ : X} {x₂ : X} {p₀ : Path.{u1} X _inst_1 x₀ x₁} {q₀ : Path.{u1} X _inst_1 x₀ x₁} {p₁ : Path.{u1} X _inst_1 x₁ x₂} {q₁ : Path.{u1} X _inst_1 x₁ x₂} (F : Path.Homotopy.{u1} X _inst_1 x₀ x₁ p₀ q₀) (G : Path.Homotopy.{u1} X _inst_1 x₁ x₂ p₁ q₁) (t : Set.Elem.{0} Real unitInterval), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval)) => X) (Prod.mk.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) t (Subtype.mk.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (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)))))) (And.intro (LE.le.{0} Real (Preorder.toLE.{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 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (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)))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (of_eq_true (LE.le.{0} Real (Preorder.toLE.{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 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (eq_true (LE.le.{0} Real (Preorder.toLE.{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 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (Mathlib.Meta.NormNum.isRat_le_true.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal)) (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 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (Int.ofNat 0) (Int.ofNat 1) 1 2 (Mathlib.Meta.NormNum.IsNat.to_isRat.{0} Real (DivisionRing.toRing.{0} Real (Field.toDivisionRing.{0} Real (LinearOrderedField.toField.{0} Real Real.instLinearOrderedFieldReal))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) 0 (Mathlib.Meta.NormNum.isNat_ofNat.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) 0 (Nat.cast_zero.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))))) (Mathlib.Meta.NormNum.isRat_div.{0} Real Real.instDivisionRingReal (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))))) (Int.ofNat 1) 2 (Mathlib.Meta.NormNum.isRat_mul.{0} Real (DivisionRing.toRing.{0} Real Real.instDivisionRingReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Inv.inv.{0} Real (DivisionRing.toInv.{0} Real Real.instDivisionRingReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (Int.ofNat 1) (Int.ofNat 1) (Int.ofNat 1) 1 2 2 1 (Mathlib.Meta.NormNum.IsNat.to_isRat.{0} 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(AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat 0))))))) (Eq.refl.{1} Int (Int.mul (Int.ofNat 1) (Int.ofNat 1))) (Eq.refl.{1} Nat 2))) (Mathlib.Meta.NormNum.IsNat.to_isRat.{0} Real (DivisionRing.toRing.{0} Real (Field.toDivisionRing.{0} Real (LinearOrderedField.toField.{0} Real Real.instLinearOrderedFieldReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) 1 (Mathlib.Meta.NormNum.isNat_ofNat.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) 1 (Nat.cast_one.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))))) (Eq.refl.{1} Bool Bool.true)))))))) x₁
 Case conversion may be inaccurate. Consider using '#align path.homotopy.hcomp_half Path.Homotopy.hcomp_halfₓ'. -/

dbdf71ce

bump to nightly-2023-05-16-03

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

4c01fe25

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.path
-! leanprover-community/mathlib commit bb9d1c5085e0b7ea619806a68c5021927cecb2a6
+! leanprover-community/mathlib commit dbdf71cee7bb20367cb7e37279c08b0c218cf967
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Analysis.Convex.Basic
 /-!
 # Homotopy between paths
 
+> 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 `path`s. In addition, we define a relation
 `homotopic` on `path`s, and prove that it is an equivalence relation.

bb9d1c50

bump to nightly-2023-05-13-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/403190b5419b3f03f1a2893ad9352ca7f7d8bff6

a0be3cad

Diff

@@ -47,11 +47,13 @@ open unitInterval
 
 namespace Path
 
+#print Path.Homotopy /-
 /-- The type of homotopies between two paths.
 -/
 abbrev Homotopy (p₀ p₁ : Path x₀ x₁) :=
   ContinuousMap.HomotopyRel p₀.toContinuousMap p₁.toContinuousMap {0, 1}
 #align path.homotopy Path.Homotopy
+-/
 
 namespace Homotopy
 
@@ -62,10 +64,22 @@ variable {p₀ p₁ : Path x₀ x₁}
 instance : CoeFun (Homotopy p₀ p₁) fun _ => I × I → X :=
   ⟨fun F => F.toFun⟩
 
+/- warning: path.homotopy.coe_fn_injective -> Path.Homotopy.coeFn_injective is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(ContinuousMap.instContinuousMapClassContinuousMap.{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)) f x) (FunLike.coe.{succ u1, 1, succ u1} (ContinuousMap.{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) (Set.Elem.{0} Real unitInterval) (fun (a : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) a) (ContinuousMapClass.toFunLike.{u1, 0, u1} (ContinuousMap.{0, u1} (Set.Elem.{0} Real 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(Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) x) (FunLike.coe.{succ u1, 1, succ u1} (ContinuousMap.{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) (Set.Elem.{0} Real unitInterval) (fun (a : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) a) (ContinuousMapClass.toFunLike.{u1, 0, u1} (ContinuousMap.{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) (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 (ContinuousMap.instContinuousMapClassContinuousMap.{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)) f x) (FunLike.coe.{succ u1, 1, succ u1} (ContinuousMap.{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) (Set.Elem.{0} Real unitInterval) (fun (a : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) a) (ContinuousMapClass.toFunLike.{u1, 0, u1} (ContinuousMap.{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) (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 (ContinuousMap.instContinuousMapClassContinuousMap.{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)) (Path.toContinuousMap.{u1} X _inst_1 x₀ x₁ p₁) x))))))))
+Case conversion may be inaccurate. Consider using '#align path.homotopy.coe_fn_injective Path.Homotopy.coeFn_injectiveₓ'. -/
 theorem coeFn_injective : @Function.Injective (Homotopy p₀ p₁) (I × I → X) coeFn :=
   ContinuousMap.HomotopyWith.coeFn_injective
 #align path.homotopy.coe_fn_injective Path.Homotopy.coeFn_injective
 
+/- warning: path.homotopy.source -> Path.Homotopy.source is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x₀ : X} {x₁ : X} {p₀ : Path.{u1} X _inst_1 x₀ x₁} {p₁ : Path.{u1} X _inst_1 x₀ x₁} (F : Path.Homotopy.{u1} X _inst_1 x₀ x₁ p₀ p₁) (t : coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval), Eq.{succ u1} X (coeFn.{succ u1, succ u1} (Path.Homotopy.{u1} X _inst_1 x₀ x₁ p₀ p₁) (fun (_x : Path.Homotopy.{u1} X _inst_1 x₀ x₁ p₀ p₁) => (Prod.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)) -> X) (Path.Homotopy.hasCoeToFun.{u1} X _inst_1 x₀ x₁ p₀ p₁) F (Prod.mk.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) t (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))))) x₀
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x₀ : X} {x₁ : X} {p₀ : Path.{u1} X _inst_1 x₀ x₁} {p₁ : Path.{u1} X _inst_1 x₀ x₁} (F : Path.Homotopy.{u1} X _inst_1 x₀ x₁ p₀ p₁) (t : Set.Elem.{0} Real unitInterval), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval)) => X) (Prod.mk.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) t (OfNat.ofNat.{0} (Set.Elem.{0} Real unitInterval) 0 (Zero.toOfNat0.{0} (Set.Elem.{0} Real unitInterval) unitInterval.hasZero)))) (FunLike.coe.{succ u1, 1, succ u1} (Path.Homotopy.{u1} X _inst_1 x₀ x₁ p₀ p₁) (Prod.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval)) (fun (_x : Prod.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval)) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval)) => X) _x) (ContinuousMapClass.toFunLike.{u1, 0, u1} (Path.Homotopy.{u1} X _inst_1 x₀ x₁ p₀ p₁) (Prod.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval)) X (instTopologicalSpaceProd.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) (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))) (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 (ContinuousMap.HomotopyLike.toContinuousMapClass.{0, u1, 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 (Path.Homotopy.{u1} X _inst_1 x₀ x₁ p₀ p₁) (Path.toContinuousMap.{u1} X _inst_1 x₀ x₁ p₀) (Path.toContinuousMap.{u1} X _inst_1 x₀ x₁ p₁) (ContinuousMap.HomotopyWith.instHomotopyLikeHomotopyWith.{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 (Path.toContinuousMap.{u1} X _inst_1 x₀ x₁ p₀) (Path.toContinuousMap.{u1} X _inst_1 x₀ x₁ p₁) (fun (f : ContinuousMap.{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) => forall (x : Set.Elem.{0} Real unitInterval), (Membership.mem.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.{0} (Set.Elem.{0} Real unitInterval)) (Set.instMembershipSet.{0} (Set.Elem.{0} Real unitInterval)) x (Insert.insert.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.{0} (Set.Elem.{0} Real unitInterval)) (Set.instInsertSet.{0} (Set.Elem.{0} Real unitInterval)) (OfNat.ofNat.{0} (Set.Elem.{0} Real unitInterval) 0 (Zero.toOfNat0.{0} (Set.Elem.{0} Real unitInterval) unitInterval.hasZero)) (Singleton.singleton.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.{0} (Set.Elem.{0} Real unitInterval)) (Set.instSingletonSet.{0} (Set.Elem.{0} Real unitInterval)) (OfNat.ofNat.{0} (Set.Elem.{0} Real unitInterval) 1 (One.toOfNat1.{0} (Set.Elem.{0} Real unitInterval) unitInterval.hasOne))))) -> (And (Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) x) (FunLike.coe.{succ u1, 1, succ u1} (ContinuousMap.{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) (Set.Elem.{0} Real unitInterval) (fun (a : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) a) (ContinuousMapClass.toFunLike.{u1, 0, u1} (ContinuousMap.{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) (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 (ContinuousMap.instContinuousMapClassContinuousMap.{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)) f x) (FunLike.coe.{succ u1, 1, succ u1} (ContinuousMap.{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) (Set.Elem.{0} Real unitInterval) (fun (a : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) a) (ContinuousMapClass.toFunLike.{u1, 0, u1} (ContinuousMap.{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) (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 (ContinuousMap.instContinuousMapClassContinuousMap.{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)) (Path.toContinuousMap.{u1} X _inst_1 x₀ x₁ p₀) x)) (Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) x) (FunLike.coe.{succ u1, 1, succ u1} (ContinuousMap.{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) (Set.Elem.{0} Real unitInterval) (fun (a : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) a) (ContinuousMapClass.toFunLike.{u1, 0, u1} (ContinuousMap.{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) (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 (ContinuousMap.instContinuousMapClassContinuousMap.{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)) f x) (FunLike.coe.{succ u1, 1, succ u1} (ContinuousMap.{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) (Set.Elem.{0} Real unitInterval) (fun (a : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) a) (ContinuousMapClass.toFunLike.{u1, 0, u1} (ContinuousMap.{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) (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 (ContinuousMap.instContinuousMapClassContinuousMap.{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)) (Path.toContinuousMap.{u1} X _inst_1 x₀ x₁ p₁) x))))))) F (Prod.mk.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) t (OfNat.ofNat.{0} (Set.Elem.{0} Real unitInterval) 0 (Zero.toOfNat0.{0} (Set.Elem.{0} Real unitInterval) unitInterval.hasZero)))) x₀
+Case conversion may be inaccurate. Consider using '#align path.homotopy.source Path.Homotopy.sourceₓ'. -/
 @[simp]
 theorem source (F : Homotopy p₀ p₁) (t : I) : F (t, 0) = x₀ :=
   by
@@ -74,6 +88,12 @@ theorem source (F : Homotopy p₀ p₁) (t : I) : F (t, 0) = x₀ :=
   simp
 #align path.homotopy.source Path.Homotopy.source
 
+/- warning: path.homotopy.target -> Path.Homotopy.target is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x₀ : X} {x₁ : X} {p₀ : Path.{u1} X _inst_1 x₀ x₁} {p₁ : Path.{u1} X _inst_1 x₀ x₁} (F : Path.Homotopy.{u1} X _inst_1 x₀ x₁ p₀ p₁) (t : coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval), Eq.{succ u1} X (coeFn.{succ u1, succ u1} (Path.Homotopy.{u1} X _inst_1 x₀ x₁ p₀ p₁) (fun (_x : Path.Homotopy.{u1} X _inst_1 x₀ x₁ p₀ p₁) => (Prod.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)) -> X) (Path.Homotopy.hasCoeToFun.{u1} X _inst_1 x₀ x₁ p₀ p₁) F (Prod.mk.{0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) t (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))))) x₁
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x₀ : X} {x₁ : X} {p₀ : Path.{u1} X _inst_1 x₀ x₁} {p₁ : Path.{u1} X _inst_1 x₀ x₁} (F : Path.Homotopy.{u1} X _inst_1 x₀ x₁ p₀ p₁) (t : Set.Elem.{0} Real unitInterval), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval)) => X) (Prod.mk.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) t (OfNat.ofNat.{0} (Set.Elem.{0} Real unitInterval) 1 (One.toOfNat1.{0} (Set.Elem.{0} Real unitInterval) unitInterval.hasOne)))) (FunLike.coe.{succ u1, 1, succ u1} (Path.Homotopy.{u1} X _inst_1 x₀ x₁ p₀ p₁) (Prod.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval)) (fun (_x : Prod.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval)) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval)) => X) _x) (ContinuousMapClass.toFunLike.{u1, 0, u1} (Path.Homotopy.{u1} X _inst_1 x₀ x₁ p₀ p₁) (Prod.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval)) X (instTopologicalSpaceProd.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) (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))) (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 (ContinuousMap.HomotopyLike.toContinuousMapClass.{0, u1, u1} (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) 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(UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) => forall (x : Set.Elem.{0} Real unitInterval), (Membership.mem.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.{0} (Set.Elem.{0} Real unitInterval)) (Set.instMembershipSet.{0} (Set.Elem.{0} Real unitInterval)) x (Insert.insert.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.{0} (Set.Elem.{0} Real unitInterval)) (Set.instInsertSet.{0} (Set.Elem.{0} Real unitInterval)) (OfNat.ofNat.{0} (Set.Elem.{0} Real unitInterval) 0 (Zero.toOfNat0.{0} (Set.Elem.{0} Real unitInterval) unitInterval.hasZero)) (Singleton.singleton.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.{0} (Set.Elem.{0} Real unitInterval)) (Set.instSingletonSet.{0} (Set.Elem.{0} Real unitInterval)) (OfNat.ofNat.{0} (Set.Elem.{0} Real unitInterval) 1 (One.toOfNat1.{0} (Set.Elem.{0} Real unitInterval) unitInterval.hasOne))))) -> (And (Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : 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+Case conversion may be inaccurate. Consider using '#align path.homotopy.target Path.Homotopy.targetₓ'. -/
 @[simp]
 theorem target (F : Homotopy p₀ p₁) (t : I) : F (t, 1) = x₁ :=
   by
@@ -82,6 +102,7 @@ theorem target (F : Homotopy p₀ p₁) (t : I) : F (t, 1) = x₁ :=
   simp
 #align path.homotopy.target Path.Homotopy.target
 
+#print Path.Homotopy.eval /-
 /-- Evaluating a path homotopy at an intermediate point, giving us a `path`.
 -/
 def eval (F : Homotopy p₀ p₁) (t : I) : Path x₀ x₁
@@ -90,20 +111,25 @@ def eval (F : Homotopy p₀ p₁) (t : I) : Path x₀ x₁
   source' := by simp
   target' := by simp
 #align path.homotopy.eval Path.Homotopy.eval
+-/
 
+#print Path.Homotopy.eval_zero /-
 @[simp]
 theorem eval_zero (F : Homotopy p₀ p₁) : F.eval 0 = p₀ :=
   by
   ext t
   simp [eval]
 #align path.homotopy.eval_zero Path.Homotopy.eval_zero
+-/
 
+#print Path.Homotopy.eval_one /-
 @[simp]
 theorem eval_one (F : Homotopy p₀ p₁) : F.eval 1 = p₁ :=
   by
   ext t
   simp [eval]
 #align path.homotopy.eval_one Path.Homotopy.eval_one
+-/
 
 end
 
@@ -111,25 +137,32 @@ section
 
 variable {p₀ p₁ p₂ : Path x₀ x₁}
 
+#print Path.Homotopy.refl /-
 /-- Given a path `p`, we can define a `homotopy p p` by `F (t, x) = p x`
 -/
 @[simps]
 def refl (p : Path x₀ x₁) : Homotopy p p :=
   ContinuousMap.HomotopyRel.refl p.toContinuousMap {0, 1}
 #align path.homotopy.refl Path.Homotopy.refl
+-/
 
+#print Path.Homotopy.symm /-
 /-- Given a `homotopy p₀ p₁`, we can define a `homotopy p₁ p₀` by reversing the homotopy.
 -/
 @[simps]
 def symm (F : Homotopy p₀ p₁) : Homotopy p₁ p₀ :=
   ContinuousMap.HomotopyRel.symm F
 #align path.homotopy.symm Path.Homotopy.symm
+-/
 
+#print Path.Homotopy.symm_symm /-
 @[simp]
 theorem symm_symm (F : Homotopy p₀ p₁) : F.symm.symm = F :=
   ContinuousMap.HomotopyRel.symm_symm F
 #align path.homotopy.symm_symm Path.Homotopy.symm_symm
+-/
 
+#print Path.Homotopy.trans /-
 /--
 Given `homotopy p₀ p₁` and `homotopy p₁ p₂`, we can define a `homotopy p₀ p₂` by putting the first
 homotopy on `[0, 1/2]` and the second on `[1/2, 1]`.
@@ -137,7 +170,14 @@ homotopy on `[0, 1/2]` and the second on `[1/2, 1]`.
 def trans (F : Homotopy p₀ p₁) (G : Homotopy p₁ p₂) : Homotopy p₀ p₂ :=
   ContinuousMap.HomotopyRel.trans F G
 #align path.homotopy.trans Path.Homotopy.trans
+-/
 
+/- warning: path.homotopy.trans_apply -> Path.Homotopy.trans_apply is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) => forall (x : Set.Elem.{0} Real unitInterval), (Membership.mem.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.{0} (Set.Elem.{0} Real unitInterval)) (Set.instMembershipSet.{0} (Set.Elem.{0} Real unitInterval)) x (Insert.insert.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.{0} (Set.Elem.{0} Real unitInterval)) (Set.instInsertSet.{0} (Set.Elem.{0} Real unitInterval)) (OfNat.ofNat.{0} (Set.Elem.{0} Real unitInterval) 0 (Zero.toOfNat0.{0} (Set.Elem.{0} Real unitInterval) unitInterval.hasZero)) (Singleton.singleton.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.{0} (Set.Elem.{0} Real unitInterval)) (Set.instSingletonSet.{0} (Set.Elem.{0} Real unitInterval)) (OfNat.ofNat.{0} (Set.Elem.{0} Real unitInterval) 1 (One.toOfNat1.{0} (Set.Elem.{0} Real unitInterval) unitInterval.hasOne))))) -> (And (Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) x) 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=> 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 (ContinuousMap.instContinuousMapClassContinuousMap.{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)) f x) (FunLike.coe.{succ u1, 1, succ u1} (ContinuousMap.{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) (Set.Elem.{0} Real unitInterval) (fun (a : Set.Elem.{0} 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(Set.instMembershipSet.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1)) (Path.toContinuousMap.{u1} X _inst_1 x₀ x₁ p₀) x)) (Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) x) (FunLike.coe.{succ u1, 1, succ u1} (ContinuousMap.{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) (Set.Elem.{0} Real unitInterval) (fun (a : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) a) (ContinuousMapClass.toFunLike.{u1, 0, u1} (ContinuousMap.{0, u1} (Set.Elem.{0} Real unitInterval) X 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(Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (Prod.fst.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) 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.{succ u1, 1, succ u1} (Path.Homotopy.{u1} X _inst_1 x₀ x₁ p₁ p₂) (Prod.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval)) (fun (_x : Prod.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval)) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval)) => X) _x) (ContinuousMapClass.toFunLike.{u1, 0, u1} (Path.Homotopy.{u1} X _inst_1 x₀ x₁ p₁ p₂) (Prod.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval)) X (instTopologicalSpaceProd.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) (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))) (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 (ContinuousMap.HomotopyLike.toContinuousMapClass.{0, u1, 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 (Path.Homotopy.{u1} X _inst_1 x₀ x₁ p₁ p₂) (Path.toContinuousMap.{u1} X _inst_1 x₀ x₁ p₁) (Path.toContinuousMap.{u1} X _inst_1 x₀ x₁ p₂) (ContinuousMap.HomotopyWith.instHomotopyLikeHomotopyWith.{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 (Path.toContinuousMap.{u1} X _inst_1 x₀ x₁ p₁) (Path.toContinuousMap.{u1} X _inst_1 x₀ x₁ p₂) (fun (f : ContinuousMap.{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) => forall (x : Set.Elem.{0} Real unitInterval), (Membership.mem.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.{0} (Set.Elem.{0} Real unitInterval)) (Set.instMembershipSet.{0} (Set.Elem.{0} Real unitInterval)) x (Insert.insert.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.{0} (Set.Elem.{0} Real unitInterval)) (Set.instInsertSet.{0} (Set.Elem.{0} Real unitInterval)) (OfNat.ofNat.{0} (Set.Elem.{0} Real unitInterval) 0 (Zero.toOfNat0.{0} (Set.Elem.{0} Real unitInterval) unitInterval.hasZero)) (Singleton.singleton.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.{0} (Set.Elem.{0} Real unitInterval)) (Set.instSingletonSet.{0} (Set.Elem.{0} Real unitInterval)) (OfNat.ofNat.{0} (Set.Elem.{0} Real unitInterval) 1 (One.toOfNat1.{0} (Set.Elem.{0} Real unitInterval) unitInterval.hasOne))))) -> (And (Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) x) (FunLike.coe.{succ u1, 1, succ u1} (ContinuousMap.{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) (Set.Elem.{0} Real unitInterval) (fun (a : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) a) (ContinuousMapClass.toFunLike.{u1, 0, u1} (ContinuousMap.{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) (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} 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(x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) a) (ContinuousMapClass.toFunLike.{u1, 0, u1} (ContinuousMap.{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) (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 (ContinuousMap.instContinuousMapClassContinuousMap.{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)) (Path.toContinuousMap.{u1} X _inst_1 x₀ x₁ p₁) x)) (Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) x) (FunLike.coe.{succ u1, 1, succ u1} (ContinuousMap.{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) (Set.Elem.{0} Real unitInterval) (fun (a : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) a) (ContinuousMapClass.toFunLike.{u1, 0, u1} (ContinuousMap.{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) (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 (ContinuousMap.instContinuousMapClassContinuousMap.{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)) f x) (FunLike.coe.{succ u1, 1, succ u1} (ContinuousMap.{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) (Set.Elem.{0} Real unitInterval) (fun (a : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) a) (ContinuousMapClass.toFunLike.{u1, 0, u1} (ContinuousMap.{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) (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 (ContinuousMap.instContinuousMapClassContinuousMap.{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)) (Path.toContinuousMap.{u1} X _inst_1 x₀ x₁ p₂) x))))))) G (Prod.mk.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) (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, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) 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, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) 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, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) 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, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) 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, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) 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, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) 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, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) 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, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) 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, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) 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, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) 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, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) 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, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) 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, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) x)))))) (Prod.snd.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) x))))
+Case conversion may be inaccurate. Consider using '#align path.homotopy.trans_apply Path.Homotopy.trans_applyₓ'. -/
 theorem trans_apply (F : Homotopy p₀ p₁) (G : Homotopy p₁ p₂) (x : I × I) :
     (F.trans G) x =
       if h : (x.1 : ℝ) ≤ 1 / 2 then
@@ -147,11 +187,14 @@ theorem trans_apply (F : Homotopy p₀ p₁) (G : Homotopy p₁ p₂) (x : I ×
   ContinuousMap.HomotopyRel.trans_apply _ _ _
 #align path.homotopy.trans_apply Path.Homotopy.trans_apply
 
+#print Path.Homotopy.symm_trans /-
 theorem symm_trans (F : Homotopy p₀ p₁) (G : Homotopy p₁ p₂) :
     (F.trans G).symm = G.symm.trans F.symm :=
   ContinuousMap.HomotopyRel.symm_trans _ _
 #align path.homotopy.symm_trans Path.Homotopy.symm_trans
+-/
 
+#print Path.Homotopy.cast /-
 /-- Casting a `homotopy p₀ p₁` to a `homotopy q₀ q₁` where `p₀ = q₀` and `p₁ = q₁`.
 -/
 @[simps]
@@ -159,6 +202,7 @@ def cast {p₀ p₁ q₀ q₁ : Path x₀ x₁} (F : Homotopy p₀ p₁) (h₀ :
     Homotopy q₀ q₁ :=
   ContinuousMap.HomotopyRel.cast F (congr_arg _ h₀) (congr_arg _ h₁)
 #align path.homotopy.cast Path.Homotopy.cast
+-/
 
 end
 
@@ -166,6 +210,7 @@ section
 
 variable {p₀ q₀ : Path x₀ x₁} {p₁ q₁ : Path x₁ x₂}
 
+#print Path.Homotopy.hcomp /-
 /-- Suppose `p₀` and `q₀` are paths from `x₀` to `x₁`, `p₁` and `q₁` are paths from `x₁` to `x₂`.
 Furthermore, suppose `F : homotopy p₀ q₀` and `G : homotopy p₁ q₁`. Then we can define a homotopy
 from `p₀.trans p₁` to `q₀.trans q₁`.
@@ -193,7 +238,14 @@ def hcomp (F : Homotopy p₀ q₀) (G : Homotopy p₁ q₁) : Homotopy (p₀.tra
       rw [ht]
       norm_num
 #align path.homotopy.hcomp Path.Homotopy.hcomp
+-/
 
+/- warning: path.homotopy.hcomp_apply -> Path.Homotopy.hcomp_apply 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 path.homotopy.hcomp_apply Path.Homotopy.hcomp_applyₓ'. -/
 theorem hcomp_apply (F : Homotopy p₀ q₀) (G : Homotopy p₁ q₁) (x : I × I) :
     F.hcomp G x =
       if h : (x.2 : ℝ) ≤ 1 / 2 then
@@ -204,6 +256,12 @@ theorem hcomp_apply (F : Homotopy p₀ q₀) (G : Homotopy p₁ q₁) (x : I ×
   show ite _ _ _ = _ by split_ifs <;> exact Path.extend_extends _ _
 #align path.homotopy.hcomp_apply Path.Homotopy.hcomp_apply
 
+/- warning: path.homotopy.hcomp_half -> Path.Homotopy.hcomp_half is a dubious translation:
+lean 3 declaration is
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(NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) (one_mul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (one_mul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) (NormNum.le_one_bit0.{0} Real Real.linearOrderedSemiring (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (le_refl.{0} Real Real.preorder (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))))) trivial))))) x₁
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x₀ : X} {x₁ : X} {x₂ : X} {p₀ : Path.{u1} X _inst_1 x₀ x₁} {q₀ : Path.{u1} X _inst_1 x₀ x₁} {p₁ : Path.{u1} X _inst_1 x₁ x₂} {q₁ : Path.{u1} X _inst_1 x₁ x₂} (F : Path.Homotopy.{u1} X _inst_1 x₀ x₁ p₀ q₀) (G : Path.Homotopy.{u1} X _inst_1 x₁ x₂ p₁ q₁) (t : Set.Elem.{0} Real unitInterval), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval)) => X) (Prod.mk.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) t (Subtype.mk.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (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)))))) (And.intro (LE.le.{0} Real (Preorder.toLE.{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 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (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)))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (of_eq_true (LE.le.{0} Real (Preorder.toLE.{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 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (eq_true (LE.le.{0} Real (Preorder.toLE.{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 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (Mathlib.Meta.NormNum.isRat_le_true.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal)) (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 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (Int.ofNat 0) (Int.ofNat 1) 1 2 (Mathlib.Meta.NormNum.IsNat.to_isRat.{0} Real (DivisionRing.toRing.{0} Real (Field.toDivisionRing.{0} Real (LinearOrderedField.toField.{0} Real Real.instLinearOrderedFieldReal))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) 0 (Mathlib.Meta.NormNum.isNat_ofNat.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} 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Real (DivisionRing.toRing.{0} Real Real.instDivisionRingReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) 1 (Mathlib.Meta.NormNum.isNat_ofNat.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) 1 (Nat.cast_one.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))))) (Mathlib.Meta.NormNum.isRat_inv_pos.{0} Real Real.instDivisionRingReal (StrictOrderedSemiring.to_charZero.{0} Real Real.strictOrderedSemiring) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) 1 1 (Mathlib.Meta.NormNum.IsNat.to_isRat.{0} Real (DivisionRing.toRing.{0} Real Real.instDivisionRingReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) 2 (Mathlib.Meta.NormNum.isNat_ofNat.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) 2 (Eq.refl.{1} Real (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 (AddMonoidWithOne.toNatCast.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat 0))))))) (Eq.refl.{1} Int (Int.mul (Int.ofNat 1) (Int.ofNat 1))) (Eq.refl.{1} Nat 2))) (Eq.refl.{1} Bool Bool.true)))) (of_eq_true (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)))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (eq_true (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)))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (Mathlib.Meta.NormNum.isRat_le_true.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.instLinearOrderedFieldReal)) (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} 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(Mathlib.Meta.NormNum.isNat_ofNat.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) 1 (Nat.cast_one.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))))) (Eq.refl.{1} Bool Bool.true)))))))) (FunLike.coe.{succ u1, 1, succ u1} (Path.Homotopy.{u1} X _inst_1 x₀ x₂ (Path.trans.{u1} X _inst_1 x₀ x₁ x₂ p₀ p₁) (Path.trans.{u1} X _inst_1 x₀ x₁ x₂ q₀ q₁)) (Prod.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval)) (fun (_x : Prod.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval)) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval)) => X) _x) (ContinuousMapClass.toFunLike.{u1, 0, u1} (Path.Homotopy.{u1} X _inst_1 x₀ x₂ (Path.trans.{u1} X _inst_1 x₀ x₁ x₂ p₀ p₁) (Path.trans.{u1} X _inst_1 x₀ x₁ x₂ q₀ q₁)) (Prod.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval)) X (instTopologicalSpaceProd.{0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) (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))) (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 (ContinuousMap.HomotopyLike.toContinuousMapClass.{0, u1, 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 (Path.Homotopy.{u1} X _inst_1 x₀ x₂ (Path.trans.{u1} X _inst_1 x₀ x₁ x₂ p₀ p₁) (Path.trans.{u1} X _inst_1 x₀ x₁ x₂ q₀ q₁)) (Path.toContinuousMap.{u1} X _inst_1 x₀ x₂ (Path.trans.{u1} X _inst_1 x₀ x₁ x₂ p₀ p₁)) (Path.toContinuousMap.{u1} X _inst_1 x₀ x₂ (Path.trans.{u1} X _inst_1 x₀ x₁ x₂ q₀ q₁)) (ContinuousMap.HomotopyWith.instHomotopyLikeHomotopyWith.{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 (Path.toContinuousMap.{u1} X _inst_1 x₀ x₂ (Path.trans.{u1} X _inst_1 x₀ x₁ x₂ p₀ p₁)) (Path.toContinuousMap.{u1} X _inst_1 x₀ x₂ (Path.trans.{u1} X _inst_1 x₀ x₁ x₂ q₀ q₁)) (fun (f : ContinuousMap.{0, u1} 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+Case conversion may be inaccurate. Consider using '#align path.homotopy.hcomp_half Path.Homotopy.hcomp_halfₓ'. -/
 theorem hcomp_half (F : Homotopy p₀ q₀) (G : Homotopy p₁ q₁) (t : I) :
     F.hcomp G (t, ⟨1 / 2, by norm_num, by norm_num⟩) = x₁ :=
   show ite _ _ _ = _ by norm_num
@@ -211,6 +269,7 @@ theorem hcomp_half (F : Homotopy p₀ q₀) (G : Homotopy p₁ q₁) (t : I) :
 
 end
 
+#print Path.Homotopy.reparam /-
 /--
 Suppose `p` is a path, then we have a homotopy from `p` to `p.reparam f` by the convexity of `I`.
 -/
@@ -232,7 +291,9 @@ def reparam (p : Path x₀ x₁) (f : I → I) (hf : Continuous f) (hf₀ : f 0
       rw [hx]
       norm_num [hf₁]
 #align path.homotopy.reparam Path.Homotopy.reparam
+-/
 
+#print Path.Homotopy.symm₂ /-
 /-- Suppose `F : homotopy p q`. Then we have a `homotopy p.symm q.symm` by reversing the second
 argument.
 -/
@@ -250,7 +311,14 @@ def symm₂ {p q : Path x₀ x₁} (F : p.Homotopy q) : p.symm.Homotopy q.symm
       rw [hx]
       simp
 #align path.homotopy.symm₂ Path.Homotopy.symm₂
+-/
 
+/- warning: path.homotopy.map -> Path.Homotopy.map is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align path.homotopy.map Path.Homotopy.mapₓ'. -/
 /--
 Given `F : homotopy p q`, and `f : C(X, Y)`, we can define a homotopy from `p.map f.continuous` to
 `q.map f.continuous`.
@@ -271,44 +339,63 @@ def map {p q : Path x₀ x₁} (F : p.Homotopy q) (f : C(X, Y)) :
 
 end Homotopy
 
+#print Path.Homotopic /-
 /-- Two paths `p₀` and `p₁` are `path.homotopic` if there exists a `homotopy` between them.
 -/
 def Homotopic (p₀ p₁ : Path x₀ x₁) : Prop :=
   Nonempty (p₀.Homotopy p₁)
 #align path.homotopic Path.Homotopic
+-/
 
 namespace homotopic
 
+#print Path.Homotopic.refl /-
 @[refl]
 theorem refl (p : Path x₀ x₁) : p.Homotopic p :=
   ⟨Homotopy.refl p⟩
 #align path.homotopic.refl Path.Homotopic.refl
+-/
 
+#print Path.Homotopic.symm /-
 @[symm]
 theorem symm ⦃p₀ p₁ : Path x₀ x₁⦄ (h : p₀.Homotopic p₁) : p₁.Homotopic p₀ :=
   h.map Homotopy.symm
 #align path.homotopic.symm Path.Homotopic.symm
+-/
 
+#print Path.Homotopic.trans /-
 @[trans]
 theorem trans ⦃p₀ p₁ p₂ : Path x₀ x₁⦄ (h₀ : p₀.Homotopic p₁) (h₁ : p₁.Homotopic p₂) :
     p₀.Homotopic p₂ :=
   h₀.map2 Homotopy.trans h₁
 #align path.homotopic.trans Path.Homotopic.trans
+-/
 
+#print Path.Homotopic.equivalence /-
 theorem equivalence : Equivalence (@Homotopic X _ x₀ x₁) :=
   ⟨refl, symm, trans⟩
 #align path.homotopic.equivalence Path.Homotopic.equivalence
+-/
 
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+Case conversion may be inaccurate. Consider using '#align path.homotopic.map Path.Homotopic.mapₓ'. -/
 theorem map {p q : Path x₀ x₁} (h : p.Homotopic q) (f : C(X, Y)) :
     Homotopic (p.map f.Continuous) (q.map f.Continuous) :=
   h.map fun F => F.map f
 #align path.homotopic.map Path.Homotopic.map
 
+#print Path.Homotopic.hcomp /-
 theorem hcomp {p₀ p₁ : Path x₀ x₁} {q₀ q₁ : Path x₁ x₂} (hp : p₀.Homotopic p₁)
     (hq : q₀.Homotopic q₁) : (p₀.trans q₀).Homotopic (p₁.trans q₁) :=
   hp.map2 Homotopy.hcomp hq
 #align path.homotopic.hcomp Path.Homotopic.hcomp
+-/
 
+#print Path.Homotopic.setoid /-
 /--
 The setoid on `path`s defined by the equivalence relation `path.homotopic`. That is, two paths are
 equivalent if there is a `homotopy` between them.
@@ -316,29 +403,42 @@ equivalent if there is a `homotopy` between them.
 protected def setoid (x₀ x₁ : X) : Setoid (Path x₀ x₁) :=
   ⟨Homotopic, equivalence⟩
 #align path.homotopic.setoid Path.Homotopic.setoid
+-/
 
+#print Path.Homotopic.Quotient /-
 /-- The quotient on `path x₀ x₁` by the equivalence relation `path.homotopic`.
 -/
 protected def Quotient (x₀ x₁ : X) :=
   Quotient (Homotopic.setoid x₀ x₁)
 #align path.homotopic.quotient Path.Homotopic.Quotient
+-/
 
 attribute [local instance] homotopic.setoid
 
 instance : Inhabited (Homotopic.Quotient () ()) :=
   ⟨Quotient.mk' <| Path.refl ()⟩
 
+#print Path.Homotopic.Quotient.comp /-
 /-- The composition of path homotopy classes. This is `path.trans` descended to the quotient. -/
 def Quotient.comp (P₀ : Path.Homotopic.Quotient x₀ x₁) (P₁ : Path.Homotopic.Quotient x₁ x₂) :
     Path.Homotopic.Quotient x₀ x₂ :=
   Quotient.map₂ Path.trans (fun (p₀ : Path x₀ x₁) p₁ hp (q₀ : Path x₁ x₂) q₁ hq => hcomp hp hq) P₀
     P₁
 #align path.homotopic.quotient.comp Path.Homotopic.Quotient.comp
+-/
 
+#print Path.Homotopic.comp_lift /-
 theorem comp_lift (P₀ : Path x₀ x₁) (P₁ : Path x₁ x₂) : ⟦P₀.trans P₁⟧ = Quotient.comp ⟦P₀⟧ ⟦P₁⟧ :=
   rfl
 #align path.homotopic.comp_lift Path.Homotopic.comp_lift
+-/
 
+/- warning: path.homotopic.quotient.map_fn -> Path.Homotopic.Quotient.mapFn is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align path.homotopic.quotient.map_fn Path.Homotopic.Quotient.mapFnₓ'. -/
 /-- The image of a path homotopy class `P₀` under a map `f`.
     This is `path.map` descended to the quotient -/
 def Quotient.mapFn (P₀ : Path.Homotopic.Quotient x₀ x₁) (f : C(X, Y)) :
@@ -346,16 +446,24 @@ def Quotient.mapFn (P₀ : Path.Homotopic.Quotient x₀ x₁) (f : C(X, Y)) :
   Quotient.map (fun q : Path x₀ x₁ => q.map f.Continuous) (fun p₀ p₁ h => Path.Homotopic.map h f) P₀
 #align path.homotopic.quotient.map_fn Path.Homotopic.Quotient.mapFn
 
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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] {x₀ : X} {x₁ : X} (P₀ : Path.{u1} X _inst_1 x₀ x₁) (f : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2), Eq.{succ u2} (Quotient.{succ u2} (Path.{u2} Y _inst_2 (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)) f x₀) (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)) f x₁)) (Path.Homotopic.setoid.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : X) => Y) x₀) _inst_2 (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)) f x₀) (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)) f x₁))) (Quotient.mk.{succ u2} (Path.{u2} Y _inst_2 (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)) f x₀) (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)) f x₁)) (Path.Homotopic.setoid.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : X) => Y) x₀) _inst_2 (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)) f x₀) (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)) f x₁)) (Path.map.{u1, u2} X _inst_1 x₀ x₁ P₀ Y _inst_2 (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)) f) (ContinuousMap.continuous.{u2, u1} X Y _inst_1 _inst_2 f))) (Path.Homotopic.Quotient.mapFn.{u1, u2} X Y _inst_1 _inst_2 x₀ x₁ (Quotient.mk.{succ u1} (Path.{u1} X _inst_1 x₀ x₁) (Path.Homotopic.setoid.{u1} X _inst_1 x₀ x₁) P₀) f)
+Case conversion may be inaccurate. Consider using '#align path.homotopic.map_lift Path.Homotopic.map_liftₓ'. -/
 theorem map_lift (P₀ : Path x₀ x₁) (f : C(X, Y)) : ⟦P₀.map f.Continuous⟧ = Quotient.mapFn ⟦P₀⟧ f :=
   rfl
 #align path.homotopic.map_lift Path.Homotopic.map_lift
 
+#print Path.Homotopic.hpath_hext /-
 theorem hpath_hext {p₁ : Path x₀ x₁} {p₂ : Path x₂ x₃} (hp : ∀ t, p₁ t = p₂ t) : HEq ⟦p₁⟧ ⟦p₂⟧ :=
   by
   obtain rfl : x₀ = x₂ := by convert hp 0 <;> simp
   obtain rfl : x₁ = x₃ := by convert hp 1 <;> simp
   rw [heq_iff_eq]; congr ; ext t; exact hp t
 #align path.homotopic.hpath_hext Path.Homotopic.hpath_hext
+-/
 
 end homotopic
 
@@ -363,6 +471,12 @@ end Path
 
 namespace ContinuousMap.Homotopy
 
+/- warning: continuous_map.homotopy.eval_at -> ContinuousMap.Homotopy.evalAt is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_3 : TopologicalSpace.{u1} X] [_inst_4 : TopologicalSpace.{u2} Y] {f : ContinuousMap.{u1, u2} X Y _inst_3 _inst_4} {g : ContinuousMap.{u1, u2} X Y _inst_3 _inst_4}, (ContinuousMap.Homotopy.{u1, u2} X Y _inst_3 _inst_4 f g) -> (forall (x : X), Path.{u2} Y _inst_4 (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} X Y _inst_3 _inst_4) (fun (_x : ContinuousMap.{u1, u2} X Y _inst_3 _inst_4) => X -> Y) (ContinuousMap.hasCoeToFun.{u1, u2} X Y _inst_3 _inst_4) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} X Y _inst_3 _inst_4) (fun (_x : ContinuousMap.{u1, u2} X Y _inst_3 _inst_4) => X -> Y) (ContinuousMap.hasCoeToFun.{u1, u2} X Y _inst_3 _inst_4) g x))
+but is expected to have type
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_3 : TopologicalSpace.{u1} X] [_inst_4 : TopologicalSpace.{u2} Y] {f : ContinuousMap.{u1, u2} X Y _inst_3 _inst_4} {g : ContinuousMap.{u1, u2} X Y _inst_3 _inst_4}, (ContinuousMap.Homotopy.{u1, u2} X Y _inst_3 _inst_4 f g) -> (forall (x : X), Path.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : X) => Y) x) _inst_4 (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.{u1, u2} X Y _inst_3 _inst_4) 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_3 _inst_4) X Y _inst_3 _inst_4 (ContinuousMap.instContinuousMapClassContinuousMap.{u1, u2} X Y _inst_3 _inst_4)) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousMap.{u1, u2} X Y _inst_3 _inst_4) 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_3 _inst_4) X Y _inst_3 _inst_4 (ContinuousMap.instContinuousMapClassContinuousMap.{u1, u2} X Y _inst_3 _inst_4)) g x))
+Case conversion may be inaccurate. Consider using '#align continuous_map.homotopy.eval_at ContinuousMap.Homotopy.evalAtₓ'. -/
 /-- Given a homotopy H: f ∼ g, get the path traced by the point `x` as it moves from
 `f x` to `g x`
 -/

bb9d1c50

bump to nightly-2023-04-24-08

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

1d7f47bc

Diff

@@ -277,7 +277,7 @@ def Homotopic (p₀ p₁ : Path x₀ x₁) : Prop :=
   Nonempty (p₀.Homotopy p₁)
 #align path.homotopic Path.Homotopic
 
-namespace Homotopic
+namespace homotopic
 
 @[refl]
 theorem refl (p : Path x₀ x₁) : p.Homotopic p :=
@@ -357,7 +357,7 @@ theorem hpath_hext {p₁ : Path x₀ x₁} {p₂ : Path x₂ x₃} (hp : ∀ t,
   rw [heq_iff_eq]; congr ; ext t; exact hp t
 #align path.homotopic.hpath_hext Path.Homotopic.hpath_hext
 
-end Homotopic
+end homotopic
 
 end Path

bb9d1c50

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

bb9d1c50

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

@@ -35,7 +35,6 @@ In this file, we define a `Homotopy` between two `Path`s. In addition, we define
 universe u v
 
 variable {X : Type u} {Y : Type v} [TopologicalSpace X] [TopologicalSpace Y]
-
 variable {x₀ x₁ x₂ x₃ : X}
 
 noncomputable section

bb9d1c50

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

@@ -169,9 +169,9 @@ def hcomp (F : Homotopy p₀ q₀) (G : Homotopy p₁ q₁) : Homotopy (p₀.tra
   map_one_left x := by simp [Path.trans]
   prop' x t ht := by
     cases' ht with ht ht
-    · norm_num [ht]
+    · set_option tactic.skipAssignedInstances false in norm_num [ht]
     · rw [Set.mem_singleton_iff] at ht
-      norm_num [ht]
+      set_option tactic.skipAssignedInstances false in norm_num [ht]
 #align path.homotopy.hcomp Path.Homotopy.hcomp
 
 theorem hcomp_apply (F : Homotopy p₀ q₀) (G : Homotopy p₁ q₁) (x : I × I) :

bb9d1c50

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

@@ -57,7 +57,7 @@ section
 variable {p₀ p₁ : Path x₀ x₁}
 
 theorem coeFn_injective : @Function.Injective (Homotopy p₀ p₁) (I × I → X) (⇑) :=
-  FunLike.coe_injective
+  DFunLike.coe_injective
 #align path.homotopy.coe_fn_injective Path.Homotopy.coeFn_injective
 
 @[simp]

bb9d1c50

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

@@ -117,6 +117,9 @@ theorem symm_symm (F : Homotopy p₀ p₁) : F.symm.symm = F :=
   ContinuousMap.HomotopyRel.symm_symm F
 #align path.homotopy.symm_symm Path.Homotopy.symm_symm
 
+theorem symm_bijective : Function.Bijective (Homotopy.symm : Homotopy p₀ p₁ → Homotopy p₁ p₀) :=
+  Function.bijective_iff_has_inverse.mpr ⟨_, symm_symm, symm_symm⟩
+
 /--
 Given `Homotopy p₀ p₁` and `Homotopy p₁ p₂`, we can define a `Homotopy p₀ p₂` by putting the first
 homotopy on `[0, 1/2]` and the second on `[1/2, 1]`.

bb9d1c50

feat: split Topology/Connected.lean (#7646)

In the last step, I have removed redundant imports: those which are implied by the other imports. I can revert those changes if desired/if this seems too brittle.

51c79693

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Shing Tak Lam
 -/
 import Mathlib.Topology.Homotopy.Basic
-import Mathlib.Topology.PathConnected
+import Mathlib.Topology.Connected.PathConnected
 import Mathlib.Analysis.Convex.Basic
 
 #align_import topology.homotopy.path from "leanprover-community/mathlib"@"bb9d1c5085e0b7ea619806a68c5021927cecb2a6"

bb9d1c50

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

@@ -161,16 +161,14 @@ def hcomp (F : Homotopy p₀ q₀) (G : Homotopy p₁ q₁) : Homotopy (p₀.tra
     if (x.2 : ℝ) ≤ 1 / 2 then (F.eval x.1).extend (2 * x.2) else (G.eval x.1).extend (2 * x.2 - 1)
   continuous_toFun := continuous_if_le (continuous_induced_dom.comp continuous_snd) continuous_const
     (F.toHomotopy.continuous.comp (by continuity)).continuousOn
-    (G.toHomotopy.continuous.comp (by continuity)).continuousOn fun x hx => by rw [hx]; norm_num
+    (G.toHomotopy.continuous.comp (by continuity)).continuousOn fun x hx => by norm_num [hx]
   map_zero_left x := by simp [Path.trans]
   map_one_left x := by simp [Path.trans]
   prop' x t ht := by
     cases' ht with ht ht
-    · rw [ht]
-      norm_num
+    · norm_num [ht]
     · rw [Set.mem_singleton_iff] at ht
-      rw [ht]
-      norm_num
+      norm_num [ht]
 #align path.homotopy.hcomp Path.Homotopy.hcomp
 
 theorem hcomp_apply (F : Homotopy p₀ q₀) (G : Homotopy p₁ q₁) (x : I × I) :
@@ -203,10 +201,10 @@ def reparam (p : Path x₀ x₁) (f : I → I) (hf : Continuous f) (hf₀ : f 0
   prop' t x hx := by
     cases' hx with hx hx
     · rw [hx]
-      simp [hf₀] -- Porting note: Originally `norm_num [hf₀]`
+      simp [hf₀]
     · rw [Set.mem_singleton_iff] at hx
       rw [hx]
-      simp [hf₁] -- Porting note: Originally `norm_num [hf₀]`
+      simp [hf₁]
   continuous_toFun := by
     -- Porting note: was `continuity` in auto-param
     refine continuous_const.path_eval ?_

bb9d1c50

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

@@ -367,7 +367,7 @@ namespace ContinuousMap.Homotopy
 /-- Given a homotopy `H : f ∼ g`, get the path traced by the point `x` as it moves from
 `f x` to `g x`.
 -/
-def evalAt {X : Type _} {Y : Type _} [TopologicalSpace X] [TopologicalSpace Y] {f g : C(X, Y)}
+def evalAt {X : Type*} {Y : Type*} [TopologicalSpace X] [TopologicalSpace Y] {f g : C(X, Y)}
     (H : ContinuousMap.Homotopy f g) (x : X) : Path (f x) (g x) where
   toFun t := H (t, x)
   source' := H.apply_zero x

bb9d1c50

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

@@ -2,16 +2,13 @@
 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.path
-! leanprover-community/mathlib commit bb9d1c5085e0b7ea619806a68c5021927cecb2a6
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Topology.Homotopy.Basic
 import Mathlib.Topology.PathConnected
 import Mathlib.Analysis.Convex.Basic
 
+#align_import topology.homotopy.path from "leanprover-community/mathlib"@"bb9d1c5085e0b7ea619806a68c5021927cecb2a6"
+
 /-!
 # Homotopy between paths

bb9d1c50

chore: remove occurrences of semicolon after space (#5713)

This is the second half of the changes originally in #5699, removing all occurrences of ; after a space and implementing a linter rule to enforce it.

In most cases this 2-character substring has a space after it, so the following command was run first:

find . -type f -name "*.lean" -exec sed -i -E 's/ ; /; /g' {} \;

The remaining cases were few enough in number that they were done manually.

c795bd35

Diff

@@ -340,7 +340,7 @@ theorem hpath_hext {p₁ : Path x₀ x₁} {p₂ : Path x₂ x₃} (hp : ∀ t,
     @HEq (Path.Homotopic.Quotient _ _) ⟦p₁⟧ (Path.Homotopic.Quotient _ _) ⟦p₂⟧ := by
   obtain rfl : x₀ = x₂ := by convert hp 0 <;> simp
   obtain rfl : x₁ = x₃ := by convert hp 1 <;> simp
-  rw [heq_iff_eq]; congr ; ext t; exact hp t
+  rw [heq_iff_eq]; congr; ext t; exact hp t
 #align path.homotopic.hpath_hext Path.Homotopic.hpath_hext
 
 end Homotopic

bb9d1c50

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

ff4f0707

Diff

@@ -345,8 +345,26 @@ theorem hpath_hext {p₁ : Path x₀ x₁} {p₂ : Path x₂ x₃} (hp : ∀ t,
 
 end Homotopic
 
+/-- A path `Path x₀ x₁` generates a homotopy between constant functions `fun _ ↦ x₀` and
+`fun _ ↦ x₁`. -/
+@[simps!]
+def toHomotopyConst (p : Path x₀ x₁) :
+    (ContinuousMap.const Y x₀).Homotopy (ContinuousMap.const Y x₁) where
+  toContinuousMap := p.toContinuousMap.comp ContinuousMap.fst
+  map_zero_left _ := p.source
+  map_one_left _ := p.target
+
 end Path
 
+/-- Two constant continuous maps with nonempty domain are homotopic if and only if their values are
+joined by a path in the codomain. -/
+@[simp]
+theorem ContinuousMap.homotopic_const_iff [Nonempty Y] :
+    (ContinuousMap.const Y x₀).Homotopic (ContinuousMap.const Y x₁) ↔ Joined x₀ x₁ := by
+  inhabit Y
+  refine ⟨fun ⟨H⟩ ↦ ⟨⟨(H.toContinuousMap.comp .prodSwap).curry default, ?_, ?_⟩⟩,
+    fun ⟨p⟩ ↦ ⟨p.toHomotopyConst⟩⟩ <;> simp
+
 namespace ContinuousMap.Homotopy
 
 /-- Given a homotopy `H : f ∼ g`, get the path traced by the point `x` as it moves from

bb9d1c50

feat: port Topology.Homotopy.Path (#3186)

Co-authored-by: Yury G. Kudryashov <urkud@urkud.name> Co-authored-by: int-y1 <jason_yuen2007@hotmail.com>

956490f6

`topology.homotopy.path` ⟷ `Mathlib.Topology.Homotopy.Path`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 560

topology.homotopy.path ⟷ Mathlib.Topology.Homotopy.Path

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 560

`topology.homotopy.path` ⟷ `Mathlib.Topology.Homotopy.Path`