topology.path_connected ⟷ Mathlib.Topology.Connected.PathConnected

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

@@ -3,7 +3,7 @@ Copyright (c) 2020 Patrick Massot. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Patrick Massot
 -/
-import Topology.Algebra.Order.ProjIcc
+import Topology.Order.ProjIcc
 import Topology.CompactOpen
 import Topology.ContinuousFunction.Basic
 import Topology.UnitInterval
@@ -1164,7 +1164,7 @@ theorem isPathConnected_iff_eq : IsPathConnected F ↔ ∃ x ∈ F, pathComponen
 #align is_path_connected_iff_eq isPathConnected_iff_eq
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » F) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x y «expr ∈ » F) -/
 #print IsPathConnected.joinedIn /-
 theorem IsPathConnected.joinedIn (h : IsPathConnected F) :
     ∀ (x) (_ : x ∈ F) (y) (_ : y ∈ F), JoinedIn F x y := fun x x_in x y_in =>
@@ -1173,7 +1173,7 @@ theorem IsPathConnected.joinedIn (h : IsPathConnected F) :
 #align is_path_connected.joined_in IsPathConnected.joinedIn
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » F) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x y «expr ∈ » F) -/
 #print isPathConnected_iff /-
 theorem isPathConnected_iff :
     IsPathConnected F ↔ F.Nonempty ∧ ∀ (x) (_ : x ∈ F) (y) (_ : y ∈ F), JoinedIn F x y :=

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

@@ -391,7 +391,7 @@ theorem trans_symm (γ : Path x y) (γ' : Path y z) : (γ.trans γ').symm = γ'.
   by
   ext t
   simp only [trans_apply, ← one_div, symm_apply, not_le, comp_app]
-  split_ifs with h h₁ h₂ h₃ h₄ <;> rw [coe_symm_eq] at h 
+  split_ifs with h h₁ h₂ h₃ h₄ <;> rw [coe_symm_eq] at h
   · have ht : (t : ℝ) = 1 / 2 := by linarith [unitInterval.nonneg t, unitInterval.le_one t]
     norm_num [ht]
   · refine' congr_arg _ (Subtype.ext _)
@@ -425,14 +425,14 @@ theorem trans_range {X : Type _} [TopologicalSpace X] {a b c : X} (γ₁ : Path
     · left
       use 2 * t, ⟨by linarith, by linarith⟩
       rw [← γ₁.extend_extends]
-      unfold_coes at hxt 
-      simp only [h, comp_app, if_true] at hxt 
+      unfold_coes at hxt
+      simp only [h, comp_app, if_true] at hxt
       exact hxt
     · right
       use 2 * t - 1, ⟨by linarith, by linarith⟩
       rw [← γ₂.extend_extends]
-      unfold_coes at hxt 
-      simp only [h, comp_app, if_false] at hxt 
+      unfold_coes at hxt
+      simp only [h, comp_app, if_false] at hxt
       exact hxt
   · rintro x (⟨⟨t, ht0, ht1⟩, hxt⟩ | ⟨⟨t, ht0, ht1⟩, hxt⟩)
     · use⟨t / 2, ⟨by linarith, by linarith⟩⟩
@@ -446,10 +446,10 @@ theorem trans_range {X : Type _} [TopologicalSpace X] {a b c : X} (γ₁ : Path
         unfold_coes
         simp only [h, comp_app, if_true, le_refl, mul_one_div_cancel (two_ne_zero' ℝ)]
         rw [γ₁.extend_one]
-        rwa [← γ₂.extend_extends, h, γ₂.extend_zero] at hxt 
+        rwa [← γ₂.extend_extends, h, γ₂.extend_zero] at hxt
       · use⟨(t + 1) / 2, ⟨by linarith, by linarith⟩⟩
         unfold_coes
-        change t ≠ 0 at h 
+        change t ≠ 0 at h
         have ht0 := lt_of_le_of_ne ht0 h.symm
         have : ¬(t + 1) / 2 ≤ 1 / 2 := by rw [not_le]; linarith
         simp only [comp_app, if_false, this]
@@ -867,11 +867,11 @@ theorem range_reparam (γ : Path x y) {f : I → I} (hfcont : Continuous f) (hf
     intro t
     have h₁ : Continuous (Icc_extend (zero_le_one' ℝ) f) := by continuity
     have := intermediate_value_Icc (zero_le_one' ℝ) h₁.continuous_on
-    · rw [Icc_extend_left, Icc_extend_right] at this 
-      change Icc (f 0) (f 1) ⊆ _ at this 
-      rw [hf₀, hf₁] at this 
+    · rw [Icc_extend_left, Icc_extend_right] at this
+      change Icc (f 0) (f 1) ⊆ _ at this
+      rw [hf₀, hf₁] at this
       rcases this t.2 with ⟨w, hw₁, hw₂⟩
-      rw [Icc_extend_of_mem _ _ hw₁] at hw₂ 
+      rw [Icc_extend_of_mem _ _ hw₁] at hw₂
       use⟨w, hw₁⟩, hw₂
   rw [range_comp, this, image_univ]
 #align path.range_reparam Path.range_reparam
@@ -1160,7 +1160,7 @@ theorem isPathConnected_iff_eq : IsPathConnected F ↔ ∃ x ∈ F, pathComponen
   · ext y
     exact ⟨fun hy => hy.Mem.2, h⟩
   · intro y y_in
-    rwa [← h] at y_in 
+    rwa [← h] at y_in
 #align is_path_connected_iff_eq isPathConnected_iff_eq
 -/
 
@@ -1264,7 +1264,7 @@ theorem IsPathConnected.exists_path_through_family {X : Type _} [TopologicalSpac
         · rw [range_eq]
           left
           exact hγ₀.1 i hi'
-        · rw [not_le, ← Nat.succ_le_iff] at hi' 
+        · rw [not_le, ← Nat.succ_le_iff] at hi'
           have : i = n.succ := by linarith
           rw [this]
           use 1
@@ -1293,8 +1293,8 @@ theorem IsPathConnected.exists_path_through_family' {X : Type _} [TopologicalSpa
   by
   rcases h.exists_path_through_family p hp with ⟨γ, hγ⟩
   rcases hγ with ⟨h₁, h₂⟩
-  simp only [range, mem_set_of_eq] at h₂ 
-  rw [range_subset_iff] at h₁ 
+  simp only [range, mem_set_of_eq] at h₂
+  rw [range_subset_iff] at h₁
   choose! t ht using h₂
   exact ⟨γ, t, h₁, ht⟩
 #align is_path_connected.exists_path_through_family' IsPathConnected.exists_path_through_family'
@@ -1351,7 +1351,7 @@ theorem isPathConnected_iff_pathConnectedSpace : IsPathConnected F ↔ PathConne
     refine' ⟨⟨⟨x, x_in⟩⟩, _⟩
     rintro ⟨y, y_in⟩ ⟨z, z_in⟩
     have H := h y y_in z z_in
-    rwa [joinedIn_iff_joined y_in z_in] at H 
+    rwa [joinedIn_iff_joined y_in z_in] at H
   · rintro ⟨⟨x, x_in⟩, H⟩
     refine' ⟨⟨x, x_in⟩, fun y y_in z z_in => _⟩
     rw [joinedIn_iff_joined y_in z_in]
@@ -1397,7 +1397,7 @@ instance (priority := 100) PathConnectedSpace.connectedSpace [PathConnectedSpace
 theorem IsPathConnected.isConnected (hF : IsPathConnected F) : IsConnected F :=
   by
   rw [isConnected_iff_connectedSpace]
-  rw [isPathConnected_iff_pathConnectedSpace] at hF 
+  rw [isPathConnected_iff_pathConnectedSpace] at hF
   exact @PathConnectedSpace.connectedSpace _ _ hF
 #align is_path_connected.is_connected IsPathConnected.isConnected
 -/

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

@@ -221,7 +221,7 @@ instance : TopologicalSpace (Path x y) :=
 
 #print Path.continuous_eval /-
 theorem continuous_eval : Continuous fun p : Path x y × I => p.1 p.2 :=
-  continuous_eval'.comp <| continuous_induced_dom.Prod_map continuous_id
+  continuous_eval.comp <| continuous_induced_dom.Prod_map continuous_id
 #align path.continuous_eval Path.continuous_eval
 -/
 

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

@@ -3,10 +3,10 @@ Copyright (c) 2020 Patrick Massot. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Patrick Massot
 -/
-import Mathbin.Topology.Algebra.Order.ProjIcc
-import Mathbin.Topology.CompactOpen
-import Mathbin.Topology.ContinuousFunction.Basic
-import Mathbin.Topology.UnitInterval
+import Topology.Algebra.Order.ProjIcc
+import Topology.CompactOpen
+import Topology.ContinuousFunction.Basic
+import Topology.UnitInterval
 
 #align_import topology.path_connected from "leanprover-community/mathlib"@"97eab48559068f3d6313da387714ef25768fb730"
 
@@ -1164,7 +1164,7 @@ theorem isPathConnected_iff_eq : IsPathConnected F ↔ ∃ x ∈ F, pathComponen
 #align is_path_connected_iff_eq isPathConnected_iff_eq
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » F) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » F) -/
 #print IsPathConnected.joinedIn /-
 theorem IsPathConnected.joinedIn (h : IsPathConnected F) :
     ∀ (x) (_ : x ∈ F) (y) (_ : y ∈ F), JoinedIn F x y := fun x x_in x y_in =>
@@ -1173,7 +1173,7 @@ theorem IsPathConnected.joinedIn (h : IsPathConnected F) :
 #align is_path_connected.joined_in IsPathConnected.joinedIn
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » F) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » F) -/
 #print isPathConnected_iff /-
 theorem isPathConnected_iff :
     IsPathConnected F ↔ F.Nonempty ∧ ∀ (x) (_ : x ∈ F) (y) (_ : y ∈ F), JoinedIn F x y :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/63721b2c3eba6c325ecf8ae8cca27155a4f6306f

@@ -435,19 +435,19 @@ theorem trans_range {X : Type _} [TopologicalSpace X] {a b c : X} (γ₁ : Path
       simp only [h, comp_app, if_false] at hxt 
       exact hxt
   · rintro x (⟨⟨t, ht0, ht1⟩, hxt⟩ | ⟨⟨t, ht0, ht1⟩, hxt⟩)
-    · use ⟨t / 2, ⟨by linarith, by linarith⟩⟩
+    · use⟨t / 2, ⟨by linarith, by linarith⟩⟩
       unfold_coes
       have : t / 2 ≤ 1 / 2 := by linarith
       simp only [this, comp_app, if_true]
       ring_nf
       rwa [γ₁.extend_extends]
     · by_cases h : t = 0
-      · use ⟨1 / 2, ⟨by linarith, by linarith⟩⟩
+      · use⟨1 / 2, ⟨by linarith, by linarith⟩⟩
         unfold_coes
         simp only [h, comp_app, if_true, le_refl, mul_one_div_cancel (two_ne_zero' ℝ)]
         rw [γ₁.extend_one]
         rwa [← γ₂.extend_extends, h, γ₂.extend_zero] at hxt 
-      · use ⟨(t + 1) / 2, ⟨by linarith, by linarith⟩⟩
+      · use⟨(t + 1) / 2, ⟨by linarith, by linarith⟩⟩
         unfold_coes
         change t ≠ 0 at h 
         have ht0 := lt_of_le_of_ne ht0 h.symm
@@ -872,7 +872,7 @@ theorem range_reparam (γ : Path x y) {f : I → I} (hfcont : Continuous f) (hf
       rw [hf₀, hf₁] at this 
       rcases this t.2 with ⟨w, hw₁, hw₂⟩
       rw [Icc_extend_of_mem _ _ hw₁] at hw₂ 
-      use ⟨w, hw₁⟩, hw₂
+      use⟨w, hw₁⟩, hw₂
   rw [range_comp, this, image_univ]
 #align path.range_reparam Path.range_reparam
 -/
@@ -1228,7 +1228,7 @@ theorem IsPathConnected.preimage_coe {U W : Set X} (hW : IsPathConnected W) (hWU
     IsPathConnected ((coe : U → X) ⁻¹' W) :=
   by
   rcases hW with ⟨x, x_in, hx⟩
-  use ⟨x, hWU x_in⟩, by simp [x_in]
+  use⟨x, hWU x_in⟩, by simp [x_in]
   rintro ⟨y, hyU⟩ hyW
   exact ⟨(hx hyW).joined_subtype.somePath.map (continuous_inclusion hWU), by simp⟩
 #align is_path_connected.preimage_coe IsPathConnected.preimage_coe

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

@@ -2,17 +2,14 @@
 Copyright (c) 2020 Patrick Massot. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Patrick Massot
-
-! This file was ported from Lean 3 source module topology.path_connected
-! leanprover-community/mathlib commit 97eab48559068f3d6313da387714ef25768fb730
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Topology.Algebra.Order.ProjIcc
 import Mathbin.Topology.CompactOpen
 import Mathbin.Topology.ContinuousFunction.Basic
 import Mathbin.Topology.UnitInterval
 
+#align_import topology.path_connected from "leanprover-community/mathlib"@"97eab48559068f3d6313da387714ef25768fb730"
+
 /-!
 # Path connectedness
 
@@ -1167,7 +1164,7 @@ theorem isPathConnected_iff_eq : IsPathConnected F ↔ ∃ x ∈ F, pathComponen
 #align is_path_connected_iff_eq isPathConnected_iff_eq
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » F) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » F) -/
 #print IsPathConnected.joinedIn /-
 theorem IsPathConnected.joinedIn (h : IsPathConnected F) :
     ∀ (x) (_ : x ∈ F) (y) (_ : y ∈ F), JoinedIn F x y := fun x x_in x y_in =>
@@ -1176,7 +1173,7 @@ theorem IsPathConnected.joinedIn (h : IsPathConnected F) :
 #align is_path_connected.joined_in IsPathConnected.joinedIn
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » F) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » F) -/
 #print isPathConnected_iff /-
 theorem isPathConnected_iff :
     IsPathConnected F ↔ F.Nonempty ∧ ∀ (x) (_ : x ∈ F) (y) (_ : y ∈ F), JoinedIn F x y :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

@@ -676,7 +676,7 @@ theorem pi_coe (γ : ∀ i, Path (as i) (bs i)) : coeFn (Path.pi γ) = fun t i =
 theorem trans_pi_eq_pi_trans (γ₀ : ∀ i, Path (as i) (bs i)) (γ₁ : ∀ i, Path (bs i) (cs i)) :
     (Path.pi γ₀).trans (Path.pi γ₁) = Path.pi fun i => (γ₀ i).trans (γ₁ i) :=
   by
-  ext (t i)
+  ext t i
   unfold Path.trans
   simp only [Path.coe_mk_mk, Function.comp_apply, pi_coe_fn]
   split_ifs <;> rfl

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

@@ -140,10 +140,12 @@ def simps.apply : I → X :=
 
 initialize_simps_projections Path (to_continuous_map_to_fun → simps.apply, -toContinuousMap)
 
+#print Path.coe_toContinuousMap /-
 @[simp]
 theorem coe_toContinuousMap : ⇑γ.toContinuousMap = γ :=
   rfl
 #align path.coe_to_continuous_map Path.coe_toContinuousMap
+-/
 
 #print Path.hasUncurryPath /-
 /-- Any function `φ : Π (a : α), path (x a) (y a)` can be seen as a function `α × I → X`. -/
@@ -220,9 +222,11 @@ compact-open topology on the space `C(I,X)` of continuous maps from `I` to `X`.
 instance : TopologicalSpace (Path x y) :=
   TopologicalSpace.induced (coe : _ → C(I, X)) ContinuousMap.compactOpen
 
+#print Path.continuous_eval /-
 theorem continuous_eval : Continuous fun p : Path x y × I => p.1 p.2 :=
   continuous_eval'.comp <| continuous_induced_dom.Prod_map continuous_id
 #align path.continuous_eval Path.continuous_eval
+-/
 
 #print Continuous.path_eval /-
 @[continuity]
@@ -232,12 +236,14 @@ theorem Continuous.path_eval {Y} [TopologicalSpace Y] {f : Y → Path x y} {g :
 #align continuous.path_eval Continuous.path_eval
 -/
 
+#print Path.continuous_uncurry_iff /-
 theorem continuous_uncurry_iff {Y} [TopologicalSpace Y] {g : Y → Path x y} :
     Continuous ↿g ↔ Continuous g :=
   Iff.symm <|
     continuous_induced_rng.trans
       ⟨fun h => continuous_uncurry_of_continuous ⟨_, h⟩, continuous_of_continuous_uncurry ↑g⟩
 #align path.continuous_uncurry_iff Path.continuous_uncurry_iff
+-/
 
 #print Path.extend /-
 /-- A continuous map extending a path to `ℝ`, constant before `0` and after `1`. -/
@@ -246,11 +252,13 @@ def extend : ℝ → X :=
 #align path.extend Path.extend
 -/
 
+#print Continuous.path_extend /-
 /-- See Note [continuity lemma statement]. -/
 theorem Continuous.path_extend {γ : Y → Path x y} {f : Y → ℝ} (hγ : Continuous ↿γ)
     (hf : Continuous f) : Continuous fun t => (γ t).extend (f t) :=
   Continuous.IccExtend hγ hf
 #align continuous.path_extend Continuous.path_extend
+-/
 
 #print Path.continuous_extend /-
 /-- A useful special case of `continuous.path_extend`. -/
@@ -260,36 +268,48 @@ theorem continuous_extend : Continuous γ.extend :=
 #align path.continuous_extend Path.continuous_extend
 -/
 
+#print Filter.Tendsto.path_extend /-
 theorem Filter.Tendsto.path_extend {X Y : Type _} [TopologicalSpace X] [TopologicalSpace Y]
     {l r : Y → X} {y : Y} {l₁ : Filter ℝ} {l₂ : Filter X} {γ : ∀ y, Path (l y) (r y)}
     (hγ : Tendsto (↿γ) (𝓝 y ×ᶠ l₁.map (projIcc 0 1 zero_le_one)) l₂) :
     Tendsto (↿fun x => (γ x).extend) (𝓝 y ×ᶠ l₁) l₂ :=
   Filter.Tendsto.IccExtend' _ hγ
 #align filter.tendsto.path_extend Filter.Tendsto.path_extend
+-/
 
+#print ContinuousAt.path_extend /-
 theorem ContinuousAt.path_extend {g : Y → ℝ} {l r : Y → X} (γ : ∀ y, Path (l y) (r y)) {y : Y}
     (hγ : ContinuousAt (↿γ) (y, projIcc 0 1 zero_le_one (g y))) (hg : ContinuousAt g y) :
     ContinuousAt (fun i => (γ i).extend (g i)) y :=
   hγ.IccExtend (fun x => γ x) hg
 #align continuous_at.path_extend ContinuousAt.path_extend
+-/
 
+#print Path.extend_extends /-
 @[simp]
 theorem extend_extends {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) {t : ℝ}
     (ht : t ∈ (Icc 0 1 : Set ℝ)) : γ.extend t = γ ⟨t, ht⟩ :=
   IccExtend_of_mem _ γ ht
 #align path.extend_extends Path.extend_extends
+-/
 
+#print Path.extend_zero /-
 theorem extend_zero : γ.extend 0 = x := by simp
 #align path.extend_zero Path.extend_zero
+-/
 
+#print Path.extend_one /-
 theorem extend_one : γ.extend 1 = y := by simp
 #align path.extend_one Path.extend_one
+-/
 
+#print Path.extend_extends' /-
 @[simp]
 theorem extend_extends' {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b)
     (t : (Icc 0 1 : Set ℝ)) : γ.extend t = γ t :=
   IccExtend_val _ γ t
 #align path.extend_extends' Path.extend_extends'
+-/
 
 #print Path.extend_range /-
 @[simp]
@@ -299,15 +319,19 @@ theorem extend_range {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b)
 #align path.extend_range Path.extend_range
 -/
 
+#print Path.extend_of_le_zero /-
 theorem extend_of_le_zero {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) {t : ℝ}
     (ht : t ≤ 0) : γ.extend t = a :=
   (IccExtend_of_le_left _ _ ht).trans γ.source
 #align path.extend_of_le_zero Path.extend_of_le_zero
+-/
 
+#print Path.extend_of_one_le /-
 theorem extend_of_one_le {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) {t : ℝ}
     (ht : 1 ≤ t) : γ.extend t = b :=
   (IccExtend_of_right_le _ _ ht).trans γ.target
 #align path.extend_of_one_le Path.extend_of_one_le
+-/
 
 #print Path.refl_extend /-
 @[simp]
@@ -316,6 +340,7 @@ theorem refl_extend {X : Type _} [TopologicalSpace X] {a : X} : (Path.refl a).ex
 #align path.refl_extend Path.refl_extend
 -/
 
+#print Path.ofLine /-
 /-- The path obtained from a map defined on `ℝ` by restriction to the unit interval. -/
 def ofLine {f : ℝ → X} (hf : ContinuousOn f I) (h₀ : f 0 = x) (h₁ : f 1 = y) : Path x y
     where
@@ -324,10 +349,13 @@ def ofLine {f : ℝ → X} (hf : ContinuousOn f I) (h₀ : f 0 = x) (h₁ : f 1
   source' := h₀
   target' := h₁
 #align path.of_line Path.ofLine
+-/
 
+#print Path.ofLine_mem /-
 theorem ofLine_mem {f : ℝ → X} (hf : ContinuousOn f I) (h₀ : f 0 = x) (h₁ : f 1 = y) :
     ∀ t, ofLine hf h₀ h₁ t ∈ f '' I := fun ⟨t, t_in⟩ => ⟨t, t_in, rfl⟩
 #align path.of_line_mem Path.ofLine_mem
+-/
 
 attribute [local simp] Iic_def
 
@@ -351,12 +379,14 @@ def trans (γ : Path x y) (γ' : Path y z) : Path x z
 #align path.trans Path.trans
 -/
 
+#print Path.trans_apply /-
 theorem trans_apply (γ : Path x y) (γ' : Path y z) (t : I) :
     (γ.trans γ') t =
       if h : (t : ℝ) ≤ 1 / 2 then γ ⟨2 * t, (mul_pos_mem_iff zero_lt_two).2 ⟨t.2.1, h⟩⟩
       else γ' ⟨2 * t - 1, two_mul_sub_one_mem_iff.2 ⟨(not_le.1 h).le, t.2.2⟩⟩ :=
   show ite _ _ _ = _ by split_ifs <;> rw [extend_extends]
 #align path.trans_apply Path.trans_apply
+-/
 
 #print Path.trans_symm /-
 @[simp]
@@ -387,6 +417,7 @@ theorem refl_trans_refl {X : Type _} [TopologicalSpace X] {a : X} :
 #align path.refl_trans_refl Path.refl_trans_refl
 -/
 
+#print Path.trans_range /-
 theorem trans_range {X : Type _} [TopologicalSpace X] {a b c : X} (γ₁ : Path a b) (γ₂ : Path b c) :
     range (γ₁.trans γ₂) = range γ₁ ∪ range γ₂ :=
   by
@@ -428,6 +459,7 @@ theorem trans_range {X : Type _} [TopologicalSpace X] {a b c : X} (γ₁ : Path
         ring_nf
         rwa [γ₂.extend_extends]
 #align path.trans_range Path.trans_range
+-/
 
 #print Path.map /-
 /-- Image of a path from `x` to `y` by a continuous map -/
@@ -440,22 +472,28 @@ def map (γ : Path x y) {Y : Type _} [TopologicalSpace Y] {f : X → Y} (h : Con
 #align path.map Path.map
 -/
 
+#print Path.map_coe /-
 @[simp]
 theorem map_coe (γ : Path x y) {Y : Type _} [TopologicalSpace Y] {f : X → Y} (h : Continuous f) :
     (γ.map h : I → Y) = f ∘ γ := by ext t; rfl
 #align path.map_coe Path.map_coe
+-/
 
+#print Path.map_symm /-
 @[simp]
 theorem map_symm (γ : Path x y) {Y : Type _} [TopologicalSpace Y] {f : X → Y} (h : Continuous f) :
     (γ.map h).symm = γ.symm.map h :=
   rfl
 #align path.map_symm Path.map_symm
+-/
 
+#print Path.map_trans /-
 @[simp]
 theorem map_trans (γ : Path x y) (γ' : Path y z) {Y : Type _} [TopologicalSpace Y] {f : X → Y}
     (h : Continuous f) : (γ.trans γ').map h = (γ.map h).trans (γ'.map h) := by ext t;
   rw [trans_apply, map_coe, comp_app, trans_apply]; split_ifs <;> rfl
 #align path.map_trans Path.map_trans
+-/
 
 #print Path.map_id /-
 @[simp]
@@ -463,11 +501,13 @@ theorem map_id (γ : Path x y) : γ.map continuous_id = γ := by ext; rfl
 #align path.map_id Path.map_id
 -/
 
+#print Path.map_map /-
 @[simp]
 theorem map_map (γ : Path x y) {Y : Type _} [TopologicalSpace Y] {Z : Type _} [TopologicalSpace Z]
     {f : X → Y} (hf : Continuous f) {g : Y → Z} (hg : Continuous g) :
     (γ.map hf).map hg = γ.map (hg.comp hf) := by ext; rfl
 #align path.map_map Path.map_map
+-/
 
 #print Path.cast /-
 /-- Casting a path from `x` to `y` to a path from `x'` to `y'` when `x' = x` and `y' = y` -/
@@ -504,12 +544,14 @@ theorem cast_coe (γ : Path x y) {x' y'} (hx : x' = x) (hy : y' = y) : (γ.cast
 #align path.cast_coe Path.cast_coe
 -/
 
+#print Path.symm_continuous_family /-
 @[continuity]
 theorem symm_continuous_family {X ι : Type _} [TopologicalSpace X] [TopologicalSpace ι]
     {a b : ι → X} (γ : ∀ t : ι, Path (a t) (b t)) (h : Continuous ↿γ) :
     Continuous ↿fun t => (γ t).symm :=
   h.comp (continuous_id.Prod_map continuous_symm)
 #align path.symm_continuous_family Path.symm_continuous_family
+-/
 
 #print Path.continuous_symm /-
 @[continuity]
@@ -518,13 +560,16 @@ theorem continuous_symm : Continuous (symm : Path x y → Path y x) :=
 #align path.continuous_symm Path.continuous_symm
 -/
 
+#print Path.continuous_uncurry_extend_of_continuous_family /-
 @[continuity]
 theorem continuous_uncurry_extend_of_continuous_family {X ι : Type _} [TopologicalSpace X]
     [TopologicalSpace ι] {a b : ι → X} (γ : ∀ t : ι, Path (a t) (b t)) (h : Continuous ↿γ) :
     Continuous ↿fun t => (γ t).extend :=
   h.comp (continuous_id.Prod_map continuous_projIcc)
 #align path.continuous_uncurry_extend_of_continuous_family Path.continuous_uncurry_extend_of_continuous_family
+-/
 
+#print Path.trans_continuous_family /-
 @[continuity]
 theorem trans_continuous_family {X ι : Type _} [TopologicalSpace X] [TopologicalSpace ι]
     {a b c : ι → X} (γ₁ : ∀ t : ι, Path (a t) (b t)) (h₁ : Continuous ↿γ₁)
@@ -547,7 +592,9 @@ theorem trans_continuous_family {X ι : Type _} [TopologicalSpace X] [Topologica
   · rintro st hst
     simp [hst, mul_inv_cancel (two_ne_zero' ℝ)]
 #align path.trans_continuous_family Path.trans_continuous_family
+-/
 
+#print Continuous.path_trans /-
 @[continuity]
 theorem Continuous.path_trans {f : Y → Path x y} {g : Y → Path y z} :
     Continuous f → Continuous g → Continuous fun t => (f t).trans (g t) :=
@@ -556,11 +603,14 @@ theorem Continuous.path_trans {f : Y → Path x y} {g : Y → Path y z} :
   apply continuous_uncurry_iff.mp
   exact trans_continuous_family _ (continuous_uncurry_iff.mpr hf) _ (continuous_uncurry_iff.mpr hg)
 #align continuous.path_trans Continuous.path_trans
+-/
 
+#print Path.continuous_trans /-
 @[continuity]
 theorem continuous_trans {x y z : X} : Continuous fun ρ : Path x y × Path y z => ρ.1.trans ρ.2 :=
   continuous_fst.path_trans continuous_snd
 #align path.continuous_trans Path.continuous_trans
+-/
 
 /-! #### Product of paths -/
 
@@ -569,6 +619,7 @@ section Prod
 
 variable {a₁ a₂ a₃ : X} {b₁ b₂ b₃ : Y}
 
+#print Path.prod /-
 /-- Given a path in `X` and a path in `Y`, we can take their pointwise product to get a path in
 `X × Y`. -/
 protected def prod (γ₁ : Path a₁ a₂) (γ₂ : Path b₁ b₂) : Path (a₁, b₁) (a₂, b₂)
@@ -577,12 +628,16 @@ protected def prod (γ₁ : Path a₁ a₂) (γ₂ : Path b₁ b₂) : Path (a
   source' := by simp
   target' := by simp
 #align path.prod Path.prod
+-/
 
+#print Path.prod_coe /-
 @[simp]
 theorem prod_coe (γ₁ : Path a₁ a₂) (γ₂ : Path b₁ b₂) : coeFn (γ₁.Prod γ₂) = fun t => (γ₁ t, γ₂ t) :=
   rfl
 #align path.prod_coe_fn Path.prod_coe
+-/
 
+#print Path.trans_prod_eq_prod_trans /-
 /-- Path composition commutes with products -/
 theorem trans_prod_eq_prod_trans (γ₁ : Path a₁ a₂) (δ₁ : Path a₂ a₃) (γ₂ : Path b₁ b₂)
     (δ₂ : Path b₂ b₃) : (γ₁.Prod γ₂).trans (δ₁.Prod δ₂) = (γ₁.trans δ₁).Prod (γ₂.trans δ₂) := by
@@ -590,6 +645,7 @@ theorem trans_prod_eq_prod_trans (γ₁ : Path a₁ a₂) (δ₁ : Path a₂ a
       split_ifs <;>
     rfl
 #align path.trans_prod_eq_prod_trans Path.trans_prod_eq_prod_trans
+-/
 
 end Prod
 
@@ -655,6 +711,7 @@ protected theorem mul_apply [Mul X] [ContinuousMul X] {a₁ b₁ a₂ b₂ : X}
 /-! #### Truncating a path -/
 
 
+#print Path.truncate /-
 /-- `γ.truncate t₀ t₁` is the path which follows the path `γ` on the
   time interval `[t₀, t₁]` and stays still otherwise. -/
 def truncate {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) (t₀ t₁ : ℝ) :
@@ -682,13 +739,16 @@ def truncate {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) (t₀ t
       simp [γ.extend_of_one_le h₄, γ.extend_of_one_le (h₄.trans h₃)]
     · rfl
 #align path.truncate Path.truncate
+-/
 
+#print Path.truncateOfLE /-
 /-- `γ.truncate_of_le t₀ t₁ h`, where `h : t₀ ≤ t₁` is `γ.truncate t₀ t₁`
   casted as a path from `γ.extend t₀` to `γ.extend t₁`. -/
 def truncateOfLE {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) {t₀ t₁ : ℝ}
     (h : t₀ ≤ t₁) : Path (γ.extend t₀) (γ.extend t₁) :=
   (γ.truncate t₀ t₁).cast (by rw [min_eq_left h]) rfl
 #align path.truncate_of_le Path.truncateOfLE
+-/
 
 #print Path.truncate_range /-
 theorem truncate_range {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) {t₀ t₁ : ℝ} :
@@ -701,6 +761,7 @@ theorem truncate_range {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a
 #align path.truncate_range Path.truncate_range
 -/
 
+#print Path.truncate_continuous_family /-
 /-- For a path `γ`, `γ.truncate` gives a "continuous family of paths", by which we
   mean the uncurried function which maps `(t₀, t₁, s)` to `γ.truncate t₀ t₁ s` is continuous. -/
 @[continuity]
@@ -710,7 +771,9 @@ theorem truncate_continuous_family {X : Type _} [TopologicalSpace X] {a b : X} (
     (((continuous_subtype_val.comp (continuous_snd.comp continuous_snd)).max continuous_fst).min
       (continuous_fst.comp continuous_snd))
 #align path.truncate_continuous_family Path.truncate_continuous_family
+-/
 
+#print Path.truncate_const_continuous_family /-
 /- TODO : When `continuity` gets quicker, change the proof back to :
     `begin`
       `simp only [has_coe_to_fun.coe, coe_fn, path.truncate],`
@@ -725,7 +788,9 @@ theorem truncate_const_continuous_family {X : Type _} [TopologicalSpace X] {a b
     continuous_const.prod_mk continuous_id
   convert γ.truncate_continuous_family.comp key
 #align path.truncate_const_continuous_family Path.truncate_const_continuous_family
+-/
 
+#print Path.truncate_self /-
 @[simp]
 theorem truncate_self {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) (t : ℝ) :
     γ.truncate t t = (Path.refl <| γ.extend t).cast (by rw [min_self]) rfl :=
@@ -735,19 +800,25 @@ theorem truncate_self {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b
   simp only [truncate, CoeFun.coe, coeFn, refl, min_def, max_def]
   split_ifs with h₁ h₂ <;> congr
 #align path.truncate_self Path.truncate_self
+-/
 
+#print Path.truncate_zero_zero /-
 @[simp]
 theorem truncate_zero_zero {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) :
     γ.truncate 0 0 = (Path.refl a).cast (by rw [min_self, γ.extend_zero]) γ.extend_zero := by
   convert γ.truncate_self 0 <;> exact γ.extend_zero.symm
 #align path.truncate_zero_zero Path.truncate_zero_zero
+-/
 
+#print Path.truncate_one_one /-
 @[simp]
 theorem truncate_one_one {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) :
     γ.truncate 1 1 = (Path.refl b).cast (by rw [min_self, γ.extend_one]) γ.extend_one := by
   convert γ.truncate_self 1 <;> exact γ.extend_one.symm
 #align path.truncate_one_one Path.truncate_one_one
+-/
 
+#print Path.truncate_zero_one /-
 @[simp]
 theorem truncate_zero_one {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) :
     γ.truncate 0 1 = γ.cast (by simp [zero_le_one, extend_zero]) (by simp) :=
@@ -757,6 +828,7 @@ theorem truncate_zero_one {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path
   have : ↑x ∈ (Icc 0 1 : Set ℝ) := x.2
   rw [truncate, coe_mk, max_eq_left this.1, min_eq_left this.2, extend_extends']
 #align path.truncate_zero_one Path.truncate_zero_one
+-/
 
 /-! #### Reparametrising a path -/
 
@@ -937,10 +1009,12 @@ theorem JoinedIn.joined_subtype (h : JoinedIn F x y) :
 #align joined_in.joined_subtype JoinedIn.joined_subtype
 -/
 
+#print JoinedIn.ofLine /-
 theorem JoinedIn.ofLine {f : ℝ → X} (hf : ContinuousOn f I) (h₀ : f 0 = x) (h₁ : f 1 = y)
     (hF : f '' I ⊆ F) : JoinedIn F x y :=
   ⟨Path.ofLine hf h₀ h₁, fun t => hF <| Path.ofLine_mem hf h₀ h₁ t⟩
 #align joined_in.of_line JoinedIn.ofLine
+-/
 
 #print JoinedIn.joined /-
 theorem JoinedIn.joined (h : JoinedIn F x y) : Joined x y :=
@@ -1082,6 +1156,7 @@ def IsPathConnected (F : Set X) : Prop :=
 #align is_path_connected IsPathConnected
 -/
 
+#print isPathConnected_iff_eq /-
 theorem isPathConnected_iff_eq : IsPathConnected F ↔ ∃ x ∈ F, pathComponentIn x F = F :=
   by
   constructor <;> rintro ⟨x, x_in, h⟩ <;> use x, x_in
@@ -1090,6 +1165,7 @@ theorem isPathConnected_iff_eq : IsPathConnected F ↔ ∃ x ∈ F, pathComponen
   · intro y y_in
     rwa [← h] at y_in 
 #align is_path_connected_iff_eq isPathConnected_iff_eq
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » F) -/
 #print IsPathConnected.joinedIn /-
@@ -1136,6 +1212,7 @@ theorem IsPathConnected.subset_pathComponent (h : IsPathConnected F) (x_in : x 
 #align is_path_connected.subset_path_component IsPathConnected.subset_pathComponent
 -/
 
+#print IsPathConnected.union /-
 theorem IsPathConnected.union {U V : Set X} (hU : IsPathConnected U) (hV : IsPathConnected V)
     (hUV : (U ∩ V).Nonempty) : IsPathConnected (U ∪ V) :=
   by
@@ -1145,6 +1222,7 @@ theorem IsPathConnected.union {U V : Set X} (hU : IsPathConnected U) (hV : IsPat
   · exact (hU.joined_in x xU y yU).mono (subset_union_left U V)
   · exact (hV.joined_in x xV y yV).mono (subset_union_right U V)
 #align is_path_connected.union IsPathConnected.union
+-/
 
 #print IsPathConnected.preimage_coe /-
 /-- If a set `W` is path-connected, then it is also path-connected when seen as a set in a smaller
@@ -1159,6 +1237,7 @@ theorem IsPathConnected.preimage_coe {U W : Set X} (hW : IsPathConnected W) (hWU
 #align is_path_connected.preimage_coe IsPathConnected.preimage_coe
 -/
 
+#print IsPathConnected.exists_path_through_family /-
 theorem IsPathConnected.exists_path_through_family {X : Type _} [TopologicalSpace X] {n : ℕ}
     {s : Set X} (h : IsPathConnected s) (p : Fin (n + 1) → X) (hp : ∀ i, p i ∈ s) :
     ∃ γ : Path (p 0) (p n), range γ ⊆ s ∧ ∀ i, p i ∈ range γ :=
@@ -1208,7 +1287,9 @@ theorem IsPathConnected.exists_path_through_family {X : Type _} [TopologicalSpac
   suffices i = i % n.succ by congr; assumption
   rw [Nat.mod_eq_of_lt hi]
 #align is_path_connected.exists_path_through_family IsPathConnected.exists_path_through_family
+-/
 
+#print IsPathConnected.exists_path_through_family' /-
 theorem IsPathConnected.exists_path_through_family' {X : Type _} [TopologicalSpace X] {n : ℕ}
     {s : Set X} (h : IsPathConnected s) (p : Fin (n + 1) → X) (hp : ∀ i, p i ∈ s) :
     ∃ (γ : Path (p 0) (p n)) (t : Fin (n + 1) → I), (∀ t, γ t ∈ s) ∧ ∀ i, γ (t i) = p i :=
@@ -1220,6 +1301,7 @@ theorem IsPathConnected.exists_path_through_family' {X : Type _} [TopologicalSpa
   choose! t ht using h₂
   exact ⟨γ, t, h₁, ht⟩
 #align is_path_connected.exists_path_through_family' IsPathConnected.exists_path_through_family'
+-/
 
 /-! ### Path connected spaces -/
 
@@ -1327,6 +1409,7 @@ namespace PathConnectedSpace
 
 variable [PathConnectedSpace X]
 
+#print PathConnectedSpace.exists_path_through_family /-
 theorem exists_path_through_family {n : ℕ} (p : Fin (n + 1) → X) :
     ∃ γ : Path (p 0) (p n), ∀ i, p i ∈ range γ :=
   by
@@ -1334,7 +1417,9 @@ theorem exists_path_through_family {n : ℕ} (p : Fin (n + 1) → X) :
   rcases this.exists_path_through_family p fun i => True.intro with ⟨γ, -, h⟩
   exact ⟨γ, h⟩
 #align path_connected_space.exists_path_through_family PathConnectedSpace.exists_path_through_family
+-/
 
+#print PathConnectedSpace.exists_path_through_family' /-
 theorem exists_path_through_family' {n : ℕ} (p : Fin (n + 1) → X) :
     ∃ (γ : Path (p 0) (p n)) (t : Fin (n + 1) → I), ∀ i, γ (t i) = p i :=
   by
@@ -1342,6 +1427,7 @@ theorem exists_path_through_family' {n : ℕ} (p : Fin (n + 1) → X) :
   rcases this.exists_path_through_family' p fun i => True.intro with ⟨γ, t, -, h⟩
   exact ⟨γ, t, h⟩
 #align path_connected_space.exists_path_through_family' PathConnectedSpace.exists_path_through_family'
+-/
 
 end PathConnectedSpace
 
@@ -1358,6 +1444,7 @@ class LocPathConnectedSpace (X : Type _) [TopologicalSpace X] : Prop where
 
 export LocPathConnectedSpace (path_connected_basis)
 
+#print locPathConnected_of_bases /-
 theorem locPathConnected_of_bases {p : ι → Prop} {s : X → ι → Set X}
     (h : ∀ x, (𝓝 x).HasBasis p (s x)) (h' : ∀ x i, p i → IsPathConnected (s x i)) :
     LocPathConnectedSpace X := by
@@ -1370,6 +1457,7 @@ theorem locPathConnected_of_bases {p : ι → Prop} {s : X → ι → Set X}
     rcases(h x).mem_iff.mp U_in with ⟨i, pi, hi⟩
     tauto
 #align loc_path_connected_of_bases locPathConnected_of_bases
+-/
 
 #print pathConnectedSpace_iff_connectedSpace /-
 theorem pathConnectedSpace_iff_connectedSpace [LocPathConnectedSpace X] :

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

@@ -1091,7 +1091,7 @@ theorem isPathConnected_iff_eq : IsPathConnected F ↔ ∃ x ∈ F, pathComponen
     rwa [← h] at y_in 
 #align is_path_connected_iff_eq isPathConnected_iff_eq
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » F) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » F) -/
 #print IsPathConnected.joinedIn /-
 theorem IsPathConnected.joinedIn (h : IsPathConnected F) :
     ∀ (x) (_ : x ∈ F) (y) (_ : y ∈ F), JoinedIn F x y := fun x x_in x y_in =>
@@ -1100,7 +1100,7 @@ theorem IsPathConnected.joinedIn (h : IsPathConnected F) :
 #align is_path_connected.joined_in IsPathConnected.joinedIn
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » F) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » F) -/
 #print isPathConnected_iff /-
 theorem isPathConnected_iff :
     IsPathConnected F ↔ F.Nonempty ∧ ∀ (x) (_ : x ∈ F) (y) (_ : y ∈ F), JoinedIn F x y :=

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

@@ -397,13 +397,13 @@ theorem trans_range {X : Type _} [TopologicalSpace X] {a b c : X} (γ₁ : Path
     · left
       use 2 * t, ⟨by linarith, by linarith⟩
       rw [← γ₁.extend_extends]
-      unfold_coes  at hxt 
+      unfold_coes at hxt 
       simp only [h, comp_app, if_true] at hxt 
       exact hxt
     · right
       use 2 * t - 1, ⟨by linarith, by linarith⟩
       rw [← γ₂.extend_extends]
-      unfold_coes  at hxt 
+      unfold_coes at hxt 
       simp only [h, comp_app, if_false] at hxt 
       exact hxt
   · rintro x (⟨⟨t, ht0, ht1⟩, hxt⟩ | ⟨⟨t, ht0, ht1⟩, hxt⟩)
@@ -1000,7 +1000,7 @@ theorem JoinedIn.trans (hxy : JoinedIn F x y) (hyz : JoinedIn F y z) : JoinedIn
 #print pathComponent /-
 /-- The path component of `x` is the set of points that can be joined to `x`. -/
 def pathComponent (x : X) :=
-  { y | Joined x y }
+  {y | Joined x y}
 #align path_component pathComponent
 -/
 
@@ -1054,7 +1054,7 @@ theorem pathComponent_subset_component (x : X) : pathComponent x ⊆ connectedCo
 #print pathComponentIn /-
 /-- The path component of `x` in `F` is the set of points that can be joined to `x` in `F`. -/
 def pathComponentIn (x : X) (F : Set X) :=
-  { y | JoinedIn F x y }
+  {y | JoinedIn F x y}
 #align path_component_in pathComponentIn
 -/
 

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

@@ -344,7 +344,7 @@ def trans (γ : Path x y) (γ' : Path y z) : Path x z
       (Continuous.if_le _ _ continuous_id continuous_const (by norm_num)).comp
         continuous_subtype_val
     -- TODO: the following are provable by `continuity` but it is too slow
-    exacts[γ.continuous_extend.comp (continuous_const.mul continuous_id),
+    exacts [γ.continuous_extend.comp (continuous_const.mul continuous_id),
       γ'.continuous_extend.comp ((continuous_const.mul continuous_id).sub continuous_const)]
   source' := by norm_num
   target' := by norm_num
@@ -364,7 +364,7 @@ theorem trans_symm (γ : Path x y) (γ' : Path y z) : (γ.trans γ').symm = γ'.
   by
   ext t
   simp only [trans_apply, ← one_div, symm_apply, not_le, comp_app]
-  split_ifs with h h₁ h₂ h₃ h₄ <;> rw [coe_symm_eq] at h
+  split_ifs with h h₁ h₂ h₃ h₄ <;> rw [coe_symm_eq] at h 
   · have ht : (t : ℝ) = 1 / 2 := by linarith [unitInterval.nonneg t, unitInterval.le_one t]
     norm_num [ht]
   · refine' congr_arg _ (Subtype.ext _)
@@ -397,14 +397,14 @@ theorem trans_range {X : Type _} [TopologicalSpace X] {a b c : X} (γ₁ : Path
     · left
       use 2 * t, ⟨by linarith, by linarith⟩
       rw [← γ₁.extend_extends]
-      unfold_coes  at hxt
-      simp only [h, comp_app, if_true] at hxt
+      unfold_coes  at hxt 
+      simp only [h, comp_app, if_true] at hxt 
       exact hxt
     · right
       use 2 * t - 1, ⟨by linarith, by linarith⟩
       rw [← γ₂.extend_extends]
-      unfold_coes  at hxt
-      simp only [h, comp_app, if_false] at hxt
+      unfold_coes  at hxt 
+      simp only [h, comp_app, if_false] at hxt 
       exact hxt
   · rintro x (⟨⟨t, ht0, ht1⟩, hxt⟩ | ⟨⟨t, ht0, ht1⟩, hxt⟩)
     · use ⟨t / 2, ⟨by linarith, by linarith⟩⟩
@@ -418,10 +418,10 @@ theorem trans_range {X : Type _} [TopologicalSpace X] {a b c : X} (γ₁ : Path
         unfold_coes
         simp only [h, comp_app, if_true, le_refl, mul_one_div_cancel (two_ne_zero' ℝ)]
         rw [γ₁.extend_one]
-        rwa [← γ₂.extend_extends, h, γ₂.extend_zero] at hxt
+        rwa [← γ₂.extend_extends, h, γ₂.extend_zero] at hxt 
       · use ⟨(t + 1) / 2, ⟨by linarith, by linarith⟩⟩
         unfold_coes
-        change t ≠ 0 at h
+        change t ≠ 0 at h 
         have ht0 := lt_of_le_of_ne ht0 h.symm
         have : ¬(t + 1) / 2 ≤ 1 / 2 := by rw [not_le]; linarith
         simp only [comp_app, if_false, this]
@@ -668,7 +668,7 @@ def truncate {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) (t₀ t
     norm_cast
     split_ifs with h₁ h₂ h₃ h₄
     · simp [γ.extend_of_le_zero h₁]
-    · congr ; linarith
+    · congr; linarith
     · have h₄ : t₁ ≤ 0 := le_of_lt (by simpa using h₂)
       simp [γ.extend_of_le_zero h₄, γ.extend_of_le_zero h₁]
     all_goals rfl
@@ -798,11 +798,11 @@ theorem range_reparam (γ : Path x y) {f : I → I} (hfcont : Continuous f) (hf
     intro t
     have h₁ : Continuous (Icc_extend (zero_le_one' ℝ) f) := by continuity
     have := intermediate_value_Icc (zero_le_one' ℝ) h₁.continuous_on
-    · rw [Icc_extend_left, Icc_extend_right] at this
-      change Icc (f 0) (f 1) ⊆ _ at this
-      rw [hf₀, hf₁] at this
+    · rw [Icc_extend_left, Icc_extend_right] at this 
+      change Icc (f 0) (f 1) ⊆ _ at this 
+      rw [hf₀, hf₁] at this 
       rcases this t.2 with ⟨w, hw₁, hw₂⟩
-      rw [Icc_extend_of_mem _ _ hw₁] at hw₂
+      rw [Icc_extend_of_mem _ _ hw₁] at hw₂ 
       use ⟨w, hw₁⟩, hw₂
   rw [range_comp, this, image_univ]
 #align path.range_reparam Path.range_reparam
@@ -1039,7 +1039,7 @@ theorem pathComponent_congr (h : x ∈ pathComponent y) : pathComponent x = path
     rw [pathComponent_symm]
     exact (h.trans h').symm
   · intro h'
-    rw [pathComponent_symm] at h'⊢
+    rw [pathComponent_symm] at h' ⊢
     exact h'.trans h
 #align path_component_congr pathComponent_congr
 -/
@@ -1088,7 +1088,7 @@ theorem isPathConnected_iff_eq : IsPathConnected F ↔ ∃ x ∈ F, pathComponen
   · ext y
     exact ⟨fun hy => hy.Mem.2, h⟩
   · intro y y_in
-    rwa [← h] at y_in
+    rwa [← h] at y_in 
 #align is_path_connected_iff_eq isPathConnected_iff_eq
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » F) -/
@@ -1188,7 +1188,7 @@ theorem IsPathConnected.exists_path_through_family {X : Type _} [TopologicalSpac
         · rw [range_eq]
           left
           exact hγ₀.1 i hi'
-        · rw [not_le, ← Nat.succ_le_iff] at hi'
+        · rw [not_le, ← Nat.succ_le_iff] at hi' 
           have : i = n.succ := by linarith
           rw [this]
           use 1
@@ -1197,7 +1197,7 @@ theorem IsPathConnected.exists_path_through_family {X : Type _} [TopologicalSpac
         apply union_subset hγ₀.2
         rw [range_subset_iff]
         exact hγ₁
-  have hpp' : ∀ k < n + 1, p k = p' k := by intro k hk; simp only [p', hk, dif_pos]; congr ; ext;
+  have hpp' : ∀ k < n + 1, p k = p' k := by intro k hk; simp only [p', hk, dif_pos]; congr; ext;
     rw [Fin.val_cast_of_lt hk]; norm_cast
   use γ.cast (hpp' 0 n.zero_lt_succ) (hpp' n n.lt_succ_self)
   simp only [γ.cast_coe]
@@ -1205,18 +1205,18 @@ theorem IsPathConnected.exists_path_through_family {X : Type _} [TopologicalSpac
   rintro ⟨i, hi⟩
   suffices p ⟨i, hi⟩ = p' i by convert hγ.1 i (Nat.le_of_lt_succ hi)
   rw [← hpp' i hi]
-  suffices i = i % n.succ by congr ; assumption
+  suffices i = i % n.succ by congr; assumption
   rw [Nat.mod_eq_of_lt hi]
 #align is_path_connected.exists_path_through_family IsPathConnected.exists_path_through_family
 
 theorem IsPathConnected.exists_path_through_family' {X : Type _} [TopologicalSpace X] {n : ℕ}
     {s : Set X} (h : IsPathConnected s) (p : Fin (n + 1) → X) (hp : ∀ i, p i ∈ s) :
-    ∃ (γ : Path (p 0) (p n))(t : Fin (n + 1) → I), (∀ t, γ t ∈ s) ∧ ∀ i, γ (t i) = p i :=
+    ∃ (γ : Path (p 0) (p n)) (t : Fin (n + 1) → I), (∀ t, γ t ∈ s) ∧ ∀ i, γ (t i) = p i :=
   by
   rcases h.exists_path_through_family p hp with ⟨γ, hγ⟩
   rcases hγ with ⟨h₁, h₂⟩
-  simp only [range, mem_set_of_eq] at h₂
-  rw [range_subset_iff] at h₁
+  simp only [range, mem_set_of_eq] at h₂ 
+  rw [range_subset_iff] at h₁ 
   choose! t ht using h₂
   exact ⟨γ, t, h₁, ht⟩
 #align is_path_connected.exists_path_through_family' IsPathConnected.exists_path_through_family'
@@ -1272,7 +1272,7 @@ theorem isPathConnected_iff_pathConnectedSpace : IsPathConnected F ↔ PathConne
     refine' ⟨⟨⟨x, x_in⟩⟩, _⟩
     rintro ⟨y, y_in⟩ ⟨z, z_in⟩
     have H := h y y_in z z_in
-    rwa [joinedIn_iff_joined y_in z_in] at H
+    rwa [joinedIn_iff_joined y_in z_in] at H 
   · rintro ⟨⟨x, x_in⟩, H⟩
     refine' ⟨⟨x, x_in⟩, fun y y_in z z_in => _⟩
     rw [joinedIn_iff_joined y_in z_in]
@@ -1318,7 +1318,7 @@ instance (priority := 100) PathConnectedSpace.connectedSpace [PathConnectedSpace
 theorem IsPathConnected.isConnected (hF : IsPathConnected F) : IsConnected F :=
   by
   rw [isConnected_iff_connectedSpace]
-  rw [isPathConnected_iff_pathConnectedSpace] at hF
+  rw [isPathConnected_iff_pathConnectedSpace] at hF 
   exact @PathConnectedSpace.connectedSpace _ _ hF
 #align is_path_connected.is_connected IsPathConnected.isConnected
 -/
@@ -1336,7 +1336,7 @@ theorem exists_path_through_family {n : ℕ} (p : Fin (n + 1) → X) :
 #align path_connected_space.exists_path_through_family PathConnectedSpace.exists_path_through_family
 
 theorem exists_path_through_family' {n : ℕ} (p : Fin (n + 1) → X) :
-    ∃ (γ : Path (p 0) (p n))(t : Fin (n + 1) → I), ∀ i, γ (t i) = p i :=
+    ∃ (γ : Path (p 0) (p n)) (t : Fin (n + 1) → I), ∀ i, γ (t i) = p i :=
   by
   have : IsPathConnected (univ : Set X) := path_connected_space_iff_univ.mp (by infer_instance)
   rcases this.exists_path_through_family' p fun i => True.intro with ⟨γ, t, -, h⟩

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

@@ -288,7 +288,7 @@ theorem extend_one : γ.extend 1 = y := by simp
 @[simp]
 theorem extend_extends' {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b)
     (t : (Icc 0 1 : Set ℝ)) : γ.extend t = γ t :=
-  Icc_extend_coe _ γ t
+  IccExtend_val _ γ t
 #align path.extend_extends' Path.extend_extends'
 
 #print Path.extend_range /-

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

@@ -70,7 +70,7 @@ on `(-∞, 0]` and to `y` on `[1, +∞)`.
 
 noncomputable section
 
-open Classical Topology Filter unitInterval
+open scoped Classical Topology Filter unitInterval
 
 open Filter Set Function unitInterval
 

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

@@ -140,12 +140,6 @@ def simps.apply : I → X :=
 
 initialize_simps_projections Path (to_continuous_map_to_fun → simps.apply, -toContinuousMap)
 
-/- warning: path.coe_to_continuous_map -> Path.coe_toContinuousMap 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.coe_to_continuous_map Path.coe_toContinuousMapₓ'. -/
 @[simp]
 theorem coe_toContinuousMap : ⇑γ.toContinuousMap = γ :=
   rfl
@@ -226,12 +220,6 @@ compact-open topology on the space `C(I,X)` of continuous maps from `I` to `X`.
 instance : TopologicalSpace (Path x y) :=
   TopologicalSpace.induced (coe : _ → C(I, X)) ContinuousMap.compactOpen
 
-/- warning: path.continuous_eval -> Path.continuous_eval is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x : X} {y : X}, Continuous.{u1, u1} (Prod.{u1, 0} (Path.{u1} X _inst_1 x y) (Set.Elem.{0} Real unitInterval)) X (instTopologicalSpaceProd.{u1, 0} (Path.{u1} X _inst_1 x y) (Set.Elem.{0} Real unitInterval) (Path.topologicalSpace.{u1} X _inst_1 x y) (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 (fun (p : Prod.{u1, 0} (Path.{u1} X _inst_1 x y) (Set.Elem.{0} Real unitInterval)) => FunLike.coe.{succ u1, 1, succ u1} (Path.{u1} X _inst_1 x y) (Set.Elem.{0} Real unitInterval) (fun (_x : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) _x) (ContinuousMapClass.toFunLike.{u1, 0, u1} (Path.{u1} X _inst_1 x y) (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.continuousMapClass.{u1} X _inst_1 x y)) (Prod.fst.{u1, 0} (Path.{u1} X _inst_1 x y) (Set.Elem.{0} Real unitInterval) p) (Prod.snd.{u1, 0} (Path.{u1} X _inst_1 x y) (Set.Elem.{0} Real unitInterval) p))
-Case conversion may be inaccurate. Consider using '#align path.continuous_eval Path.continuous_evalₓ'. -/
 theorem continuous_eval : Continuous fun p : Path x y × I => p.1 p.2 :=
   continuous_eval'.comp <| continuous_induced_dom.Prod_map continuous_id
 #align path.continuous_eval Path.continuous_eval
@@ -244,12 +232,6 @@ theorem Continuous.path_eval {Y} [TopologicalSpace Y] {f : Y → Path x y} {g :
 #align continuous.path_eval Continuous.path_eval
 -/
 
-/- warning: path.continuous_uncurry_iff -> Path.continuous_uncurry_iff is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x : X} {y : X} {Y : Type.{u2}} [_inst_3 : TopologicalSpace.{u2} Y] {g : Y -> (Path.{u1} X _inst_1 x y)}, Iff (Continuous.{u2, u1} (Prod.{u2, 0} Y (Set.Elem.{0} Real unitInterval)) X (instTopologicalSpaceProd.{u2, 0} Y (Set.Elem.{0} Real unitInterval) _inst_3 (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 (Function.HasUncurry.uncurry.{max u1 u2, u2, u1} (Y -> (Path.{u1} X _inst_1 x y)) (Prod.{u2, 0} Y (Set.Elem.{0} Real unitInterval)) X (Path.hasUncurryPath.{u1, u2} X Y _inst_1 (fun (ᾰ : Y) => x) (fun (ᾰ : Y) => y)) g)) (Continuous.{u2, u1} Y (Path.{u1} X _inst_1 x y) _inst_3 (Path.topologicalSpace.{u1} X _inst_1 x y) g)
-Case conversion may be inaccurate. Consider using '#align path.continuous_uncurry_iff Path.continuous_uncurry_iffₓ'. -/
 theorem continuous_uncurry_iff {Y} [TopologicalSpace Y] {g : Y → Path x y} :
     Continuous ↿g ↔ Continuous g :=
   Iff.symm <|
@@ -264,12 +246,6 @@ def extend : ℝ → X :=
 #align path.extend Path.extend
 -/
 
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-Case conversion may be inaccurate. Consider using '#align continuous.path_extend Continuous.path_extendₓ'. -/
 /-- See Note [continuity lemma statement]. -/
 theorem Continuous.path_extend {γ : Y → Path x y} {f : Y → ℝ} (hγ : Continuous ↿γ)
     (hf : Continuous f) : Continuous fun t => (γ t).extend (f t) :=
@@ -284,12 +260,6 @@ theorem continuous_extend : Continuous γ.extend :=
 #align path.continuous_extend Path.continuous_extend
 -/
 
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 theorem Filter.Tendsto.path_extend {X Y : Type _} [TopologicalSpace X] [TopologicalSpace Y]
     {l r : Y → X} {y : Y} {l₁ : Filter ℝ} {l₂ : Filter X} {γ : ∀ y, Path (l y) (r y)}
     (hγ : Tendsto (↿γ) (𝓝 y ×ᶠ l₁.map (projIcc 0 1 zero_le_one)) l₂) :
@@ -297,54 +267,24 @@ theorem Filter.Tendsto.path_extend {X Y : Type _} [TopologicalSpace X] [Topologi
   Filter.Tendsto.IccExtend' _ hγ
 #align filter.tendsto.path_extend Filter.Tendsto.path_extend
 
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 theorem ContinuousAt.path_extend {g : Y → ℝ} {l r : Y → X} (γ : ∀ y, Path (l y) (r y)) {y : Y}
     (hγ : ContinuousAt (↿γ) (y, projIcc 0 1 zero_le_one (g y))) (hg : ContinuousAt g y) :
     ContinuousAt (fun i => (γ i).extend (g i)) y :=
   hγ.IccExtend (fun x => γ x) hg
 #align continuous_at.path_extend ContinuousAt.path_extend
 
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 @[simp]
 theorem extend_extends {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) {t : ℝ}
     (ht : t ∈ (Icc 0 1 : Set ℝ)) : γ.extend t = γ ⟨t, ht⟩ :=
   IccExtend_of_mem _ γ ht
 #align path.extend_extends Path.extend_extends
 
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 theorem extend_zero : γ.extend 0 = x := by simp
 #align path.extend_zero Path.extend_zero
 
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 theorem extend_one : γ.extend 1 = y := by simp
 #align path.extend_one Path.extend_one
 
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-Case conversion may be inaccurate. Consider using '#align path.extend_extends' Path.extend_extends'ₓ'. -/
 @[simp]
 theorem extend_extends' {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b)
     (t : (Icc 0 1 : Set ℝ)) : γ.extend t = γ t :=
@@ -359,23 +299,11 @@ theorem extend_range {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b)
 #align path.extend_range Path.extend_range
 -/
 
-/- warning: path.extend_of_le_zero -> Path.extend_of_le_zero is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align path.extend_of_le_zero Path.extend_of_le_zeroₓ'. -/
 theorem extend_of_le_zero {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) {t : ℝ}
     (ht : t ≤ 0) : γ.extend t = a :=
   (IccExtend_of_le_left _ _ ht).trans γ.source
 #align path.extend_of_le_zero Path.extend_of_le_zero
 
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-Case conversion may be inaccurate. Consider using '#align path.extend_of_one_le Path.extend_of_one_leₓ'. -/
 theorem extend_of_one_le {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) {t : ℝ}
     (ht : 1 ≤ t) : γ.extend t = b :=
   (IccExtend_of_right_le _ _ ht).trans γ.target
@@ -388,12 +316,6 @@ theorem refl_extend {X : Type _} [TopologicalSpace X] {a : X} : (Path.refl a).ex
 #align path.refl_extend Path.refl_extend
 -/
 
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-Case conversion may be inaccurate. Consider using '#align path.of_line Path.ofLineₓ'. -/
 /-- The path obtained from a map defined on `ℝ` by restriction to the unit interval. -/
 def ofLine {f : ℝ → X} (hf : ContinuousOn f I) (h₀ : f 0 = x) (h₁ : f 1 = y) : Path x y
     where
@@ -403,12 +325,6 @@ def ofLine {f : ℝ → X} (hf : ContinuousOn f I) (h₀ : f 0 = x) (h₁ : f 1
   target' := h₁
 #align path.of_line Path.ofLine
 
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 theorem ofLine_mem {f : ℝ → X} (hf : ContinuousOn f I) (h₀ : f 0 = x) (h₁ : f 1 = y) :
     ∀ t, ofLine hf h₀ h₁ t ∈ f '' I := fun ⟨t, t_in⟩ => ⟨t, t_in, rfl⟩
 #align path.of_line_mem Path.ofLine_mem
@@ -435,9 +351,6 @@ def trans (γ : Path x y) (γ' : Path y z) : Path x z
 #align path.trans Path.trans
 -/
 
-/- warning: path.trans_apply -> Path.trans_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align path.trans_apply Path.trans_applyₓ'. -/
 theorem trans_apply (γ : Path x y) (γ' : Path y z) (t : I) :
     (γ.trans γ') t =
       if h : (t : ℝ) ≤ 1 / 2 then γ ⟨2 * t, (mul_pos_mem_iff zero_lt_two).2 ⟨t.2.1, h⟩⟩
@@ -474,12 +387,6 @@ theorem refl_trans_refl {X : Type _} [TopologicalSpace X] {a : X} :
 #align path.refl_trans_refl Path.refl_trans_refl
 -/
 
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-Case conversion may be inaccurate. Consider using '#align path.trans_range Path.trans_rangeₓ'. -/
 theorem trans_range {X : Type _} [TopologicalSpace X] {a b c : X} (γ₁ : Path a b) (γ₂ : Path b c) :
     range (γ₁.trans γ₂) = range γ₁ ∪ range γ₂ :=
   by
@@ -533,35 +440,17 @@ def map (γ : Path x y) {Y : Type _} [TopologicalSpace Y] {f : X → Y} (h : Con
 #align path.map Path.map
 -/
 
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-Case conversion may be inaccurate. Consider using '#align path.map_coe Path.map_coeₓ'. -/
 @[simp]
 theorem map_coe (γ : Path x y) {Y : Type _} [TopologicalSpace Y] {f : X → Y} (h : Continuous f) :
     (γ.map h : I → Y) = f ∘ γ := by ext t; rfl
 #align path.map_coe Path.map_coe
 
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-Case conversion may be inaccurate. Consider using '#align path.map_symm Path.map_symmₓ'. -/
 @[simp]
 theorem map_symm (γ : Path x y) {Y : Type _} [TopologicalSpace Y] {f : X → Y} (h : Continuous f) :
     (γ.map h).symm = γ.symm.map h :=
   rfl
 #align path.map_symm Path.map_symm
 
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-Case conversion may be inaccurate. Consider using '#align path.map_trans Path.map_transₓ'. -/
 @[simp]
 theorem map_trans (γ : Path x y) (γ' : Path y z) {Y : Type _} [TopologicalSpace Y] {f : X → Y}
     (h : Continuous f) : (γ.trans γ').map h = (γ.map h).trans (γ'.map h) := by ext t;
@@ -574,12 +463,6 @@ theorem map_id (γ : Path x y) : γ.map continuous_id = γ := by ext; rfl
 #align path.map_id Path.map_id
 -/
 
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-Case conversion may be inaccurate. Consider using '#align path.map_map Path.map_mapₓ'. -/
 @[simp]
 theorem map_map (γ : Path x y) {Y : Type _} [TopologicalSpace Y] {Z : Type _} [TopologicalSpace Z]
     {f : X → Y} (hf : Continuous f) {g : Y → Z} (hg : Continuous g) :
@@ -621,12 +504,6 @@ theorem cast_coe (γ : Path x y) {x' y'} (hx : x' = x) (hy : y' = y) : (γ.cast
 #align path.cast_coe Path.cast_coe
 -/
 
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-Case conversion may be inaccurate. Consider using '#align path.symm_continuous_family Path.symm_continuous_familyₓ'. -/
 @[continuity]
 theorem symm_continuous_family {X ι : Type _} [TopologicalSpace X] [TopologicalSpace ι]
     {a b : ι → X} (γ : ∀ t : ι, Path (a t) (b t)) (h : Continuous ↿γ) :
@@ -641,12 +518,6 @@ theorem continuous_symm : Continuous (symm : Path x y → Path y x) :=
 #align path.continuous_symm Path.continuous_symm
 -/
 
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-Case conversion may be inaccurate. Consider using '#align path.continuous_uncurry_extend_of_continuous_family Path.continuous_uncurry_extend_of_continuous_familyₓ'. -/
 @[continuity]
 theorem continuous_uncurry_extend_of_continuous_family {X ι : Type _} [TopologicalSpace X]
     [TopologicalSpace ι] {a b : ι → X} (γ : ∀ t : ι, Path (a t) (b t)) (h : Continuous ↿γ) :
@@ -654,12 +525,6 @@ theorem continuous_uncurry_extend_of_continuous_family {X ι : Type _} [Topologi
   h.comp (continuous_id.Prod_map continuous_projIcc)
 #align path.continuous_uncurry_extend_of_continuous_family Path.continuous_uncurry_extend_of_continuous_family
 
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-Case conversion may be inaccurate. Consider using '#align path.trans_continuous_family Path.trans_continuous_familyₓ'. -/
 @[continuity]
 theorem trans_continuous_family {X ι : Type _} [TopologicalSpace X] [TopologicalSpace ι]
     {a b c : ι → X} (γ₁ : ∀ t : ι, Path (a t) (b t)) (h₁ : Continuous ↿γ₁)
@@ -683,12 +548,6 @@ theorem trans_continuous_family {X ι : Type _} [TopologicalSpace X] [Topologica
     simp [hst, mul_inv_cancel (two_ne_zero' ℝ)]
 #align path.trans_continuous_family Path.trans_continuous_family
 
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 @[continuity]
 theorem Continuous.path_trans {f : Y → Path x y} {g : Y → Path y z} :
     Continuous f → Continuous g → Continuous fun t => (f t).trans (g t) :=
@@ -698,12 +557,6 @@ theorem Continuous.path_trans {f : Y → Path x y} {g : Y → Path y z} :
   exact trans_continuous_family _ (continuous_uncurry_iff.mpr hf) _ (continuous_uncurry_iff.mpr hg)
 #align continuous.path_trans Continuous.path_trans
 
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 @[continuity]
 theorem continuous_trans {x y z : X} : Continuous fun ρ : Path x y × Path y z => ρ.1.trans ρ.2 :=
   continuous_fst.path_trans continuous_snd
@@ -716,12 +569,6 @@ section Prod
 
 variable {a₁ a₂ a₃ : X} {b₁ b₂ b₃ : Y}
 
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 /-- Given a path in `X` and a path in `Y`, we can take their pointwise product to get a path in
 `X × Y`. -/
 protected def prod (γ₁ : Path a₁ a₂) (γ₂ : Path b₁ b₂) : Path (a₁, b₁) (a₂, b₂)
@@ -731,23 +578,11 @@ protected def prod (γ₁ : Path a₁ a₂) (γ₂ : Path b₁ b₂) : Path (a
   target' := by simp
 #align path.prod Path.prod
 
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 @[simp]
 theorem prod_coe (γ₁ : Path a₁ a₂) (γ₂ : Path b₁ b₂) : coeFn (γ₁.Prod γ₂) = fun t => (γ₁ t, γ₂ t) :=
   rfl
 #align path.prod_coe_fn Path.prod_coe
 
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 /-- Path composition commutes with products -/
 theorem trans_prod_eq_prod_trans (γ₁ : Path a₁ a₂) (δ₁ : Path a₂ a₃) (γ₂ : Path b₁ b₂)
     (δ₂ : Path b₂ b₃) : (γ₁.Prod γ₂).trans (δ₁.Prod δ₂) = (γ₁.trans δ₁).Prod (γ₂.trans δ₂) := by
@@ -820,12 +655,6 @@ protected theorem mul_apply [Mul X] [ContinuousMul X] {a₁ b₁ a₂ b₂ : X}
 /-! #### Truncating a path -/
 
 
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 /-- `γ.truncate t₀ t₁` is the path which follows the path `γ` on the
   time interval `[t₀, t₁]` and stays still otherwise. -/
 def truncate {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) (t₀ t₁ : ℝ) :
@@ -854,12 +683,6 @@ def truncate {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) (t₀ t
     · rfl
 #align path.truncate Path.truncate
 
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 /-- `γ.truncate_of_le t₀ t₁ h`, where `h : t₀ ≤ t₁` is `γ.truncate t₀ t₁`
   casted as a path from `γ.extend t₀` to `γ.extend t₁`. -/
 def truncateOfLE {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) {t₀ t₁ : ℝ}
@@ -878,12 +701,6 @@ theorem truncate_range {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a
 #align path.truncate_range Path.truncate_range
 -/
 
-/- warning: path.truncate_continuous_family -> Path.truncate_continuous_family is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align path.truncate_continuous_family Path.truncate_continuous_familyₓ'. -/
 /-- For a path `γ`, `γ.truncate` gives a "continuous family of paths", by which we
   mean the uncurried function which maps `(t₀, t₁, s)` to `γ.truncate t₀ t₁ s` is continuous. -/
 @[continuity]
@@ -894,12 +711,6 @@ theorem truncate_continuous_family {X : Type _} [TopologicalSpace X] {a b : X} (
       (continuous_fst.comp continuous_snd))
 #align path.truncate_continuous_family Path.truncate_continuous_family
 
-/- warning: path.truncate_const_continuous_family -> Path.truncate_const_continuous_family is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align path.truncate_const_continuous_family Path.truncate_const_continuous_familyₓ'. -/
 /- TODO : When `continuity` gets quicker, change the proof back to :
     `begin`
       `simp only [has_coe_to_fun.coe, coe_fn, path.truncate],`
@@ -915,12 +726,6 @@ theorem truncate_const_continuous_family {X : Type _} [TopologicalSpace X] {a b
   convert γ.truncate_continuous_family.comp key
 #align path.truncate_const_continuous_family Path.truncate_const_continuous_family
 
-/- warning: path.truncate_self -> Path.truncate_self is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align path.truncate_self Path.truncate_selfₓ'. -/
 @[simp]
 theorem truncate_self {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) (t : ℝ) :
     γ.truncate t t = (Path.refl <| γ.extend t).cast (by rw [min_self]) rfl :=
@@ -931,33 +736,18 @@ theorem truncate_self {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b
   split_ifs with h₁ h₂ <;> congr
 #align path.truncate_self Path.truncate_self
 
-/- warning: path.truncate_zero_zero -> Path.truncate_zero_zero is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align path.truncate_zero_zero Path.truncate_zero_zeroₓ'. -/
 @[simp]
 theorem truncate_zero_zero {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) :
     γ.truncate 0 0 = (Path.refl a).cast (by rw [min_self, γ.extend_zero]) γ.extend_zero := by
   convert γ.truncate_self 0 <;> exact γ.extend_zero.symm
 #align path.truncate_zero_zero Path.truncate_zero_zero
 
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-Case conversion may be inaccurate. Consider using '#align path.truncate_one_one Path.truncate_one_oneₓ'. -/
 @[simp]
 theorem truncate_one_one {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) :
     γ.truncate 1 1 = (Path.refl b).cast (by rw [min_self, γ.extend_one]) γ.extend_one := by
   convert γ.truncate_self 1 <;> exact γ.extend_one.symm
 #align path.truncate_one_one Path.truncate_one_one
 
-/- warning: path.truncate_zero_one -> Path.truncate_zero_one is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align path.truncate_zero_one Path.truncate_zero_oneₓ'. -/
 @[simp]
 theorem truncate_zero_one {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) :
     γ.truncate 0 1 = γ.cast (by simp [zero_le_one, extend_zero]) (by simp) :=
@@ -1147,12 +937,6 @@ theorem JoinedIn.joined_subtype (h : JoinedIn F x y) :
 #align joined_in.joined_subtype JoinedIn.joined_subtype
 -/
 
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-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x : X} {y : X} {F : Set.{u1} X} {f : Real -> X}, (ContinuousOn.{0, u1} Real X (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_1 f unitInterval) -> (Eq.{succ u1} X (f (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) x) -> (Eq.{succ u1} X (f (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) y) -> (HasSubset.Subset.{u1} (Set.{u1} X) (Set.hasSubset.{u1} X) (Set.image.{0, u1} Real X f unitInterval) F) -> (JoinedIn.{u1} X _inst_1 F x y)
-but is expected to have type
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x : X} {y : X} {F : Set.{u1} X} {f : Real -> X}, (ContinuousOn.{0, u1} Real X (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_1 f unitInterval) -> (Eq.{succ u1} X (f (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) x) -> (Eq.{succ u1} X (f (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) y) -> (HasSubset.Subset.{u1} (Set.{u1} X) (Set.instHasSubsetSet.{u1} X) (Set.image.{0, u1} Real X f unitInterval) F) -> (JoinedIn.{u1} X _inst_1 F x y)
-Case conversion may be inaccurate. Consider using '#align joined_in.of_line JoinedIn.ofLineₓ'. -/
 theorem JoinedIn.ofLine {f : ℝ → X} (hf : ContinuousOn f I) (h₀ : f 0 = x) (h₁ : f 1 = y)
     (hF : f '' I ⊆ F) : JoinedIn F x y :=
   ⟨Path.ofLine hf h₀ h₁, fun t => hF <| Path.ofLine_mem hf h₀ h₁ t⟩
@@ -1298,12 +1082,6 @@ def IsPathConnected (F : Set X) : Prop :=
 #align is_path_connected IsPathConnected
 -/
 
-/- warning: is_path_connected_iff_eq -> isPathConnected_iff_eq is a dubious translation:
-lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {F : Set.{u1} X}, Iff (IsPathConnected.{u1} X _inst_1 F) (Exists.{succ u1} X (fun (x : X) => Exists.{0} (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) x F) (fun (H : Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) x F) => Eq.{succ u1} (Set.{u1} X) (pathComponentIn.{u1} X _inst_1 x F) F)))
-but is expected to have type
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {F : Set.{u1} X}, Iff (IsPathConnected.{u1} X _inst_1 F) (Exists.{succ u1} X (fun (x : X) => And (Membership.mem.{u1, u1} X (Set.{u1} X) (Set.instMembershipSet.{u1} X) x F) (Eq.{succ u1} (Set.{u1} X) (pathComponentIn.{u1} X _inst_1 x F) F)))
-Case conversion may be inaccurate. Consider using '#align is_path_connected_iff_eq isPathConnected_iff_eqₓ'. -/
 theorem isPathConnected_iff_eq : IsPathConnected F ↔ ∃ x ∈ F, pathComponentIn x F = F :=
   by
   constructor <;> rintro ⟨x, x_in, h⟩ <;> use x, x_in
@@ -1358,12 +1136,6 @@ theorem IsPathConnected.subset_pathComponent (h : IsPathConnected F) (x_in : x 
 #align is_path_connected.subset_path_component IsPathConnected.subset_pathComponent
 -/
 
-/- warning: is_path_connected.union -> IsPathConnected.union is a dubious translation:
-lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {U : Set.{u1} X} {V : Set.{u1} X}, (IsPathConnected.{u1} X _inst_1 U) -> (IsPathConnected.{u1} X _inst_1 V) -> (Set.Nonempty.{u1} X (Inter.inter.{u1} (Set.{u1} X) (Set.hasInter.{u1} X) U V)) -> (IsPathConnected.{u1} X _inst_1 (Union.union.{u1} (Set.{u1} X) (Set.hasUnion.{u1} X) U V))
-but is expected to have type
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {U : Set.{u1} X} {V : Set.{u1} X}, (IsPathConnected.{u1} X _inst_1 U) -> (IsPathConnected.{u1} X _inst_1 V) -> (Set.Nonempty.{u1} X (Inter.inter.{u1} (Set.{u1} X) (Set.instInterSet.{u1} X) U V)) -> (IsPathConnected.{u1} X _inst_1 (Union.union.{u1} (Set.{u1} X) (Set.instUnionSet.{u1} X) U V))
-Case conversion may be inaccurate. Consider using '#align is_path_connected.union IsPathConnected.unionₓ'. -/
 theorem IsPathConnected.union {U V : Set X} (hU : IsPathConnected U) (hV : IsPathConnected V)
     (hUV : (U ∩ V).Nonempty) : IsPathConnected (U ∪ V) :=
   by
@@ -1387,9 +1159,6 @@ theorem IsPathConnected.preimage_coe {U W : Set X} (hW : IsPathConnected W) (hWU
 #align is_path_connected.preimage_coe IsPathConnected.preimage_coe
 -/
 
-/- warning: is_path_connected.exists_path_through_family -> IsPathConnected.exists_path_through_family is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_path_connected.exists_path_through_family IsPathConnected.exists_path_through_familyₓ'. -/
 theorem IsPathConnected.exists_path_through_family {X : Type _} [TopologicalSpace X] {n : ℕ}
     {s : Set X} (h : IsPathConnected s) (p : Fin (n + 1) → X) (hp : ∀ i, p i ∈ s) :
     ∃ γ : Path (p 0) (p n), range γ ⊆ s ∧ ∀ i, p i ∈ range γ :=
@@ -1440,9 +1209,6 @@ theorem IsPathConnected.exists_path_through_family {X : Type _} [TopologicalSpac
   rw [Nat.mod_eq_of_lt hi]
 #align is_path_connected.exists_path_through_family IsPathConnected.exists_path_through_family
 
-/- warning: is_path_connected.exists_path_through_family' -> IsPathConnected.exists_path_through_family' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_path_connected.exists_path_through_family' IsPathConnected.exists_path_through_family'ₓ'. -/
 theorem IsPathConnected.exists_path_through_family' {X : Type _} [TopologicalSpace X] {n : ℕ}
     {s : Set X} (h : IsPathConnected s) (p : Fin (n + 1) → X) (hp : ∀ i, p i ∈ s) :
     ∃ (γ : Path (p 0) (p n))(t : Fin (n + 1) → I), (∀ t, γ t ∈ s) ∧ ∀ i, γ (t i) = p i :=
@@ -1561,9 +1327,6 @@ namespace PathConnectedSpace
 
 variable [PathConnectedSpace X]
 
-/- warning: path_connected_space.exists_path_through_family -> PathConnectedSpace.exists_path_through_family is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align path_connected_space.exists_path_through_family PathConnectedSpace.exists_path_through_familyₓ'. -/
 theorem exists_path_through_family {n : ℕ} (p : Fin (n + 1) → X) :
     ∃ γ : Path (p 0) (p n), ∀ i, p i ∈ range γ :=
   by
@@ -1572,9 +1335,6 @@ theorem exists_path_through_family {n : ℕ} (p : Fin (n + 1) → X) :
   exact ⟨γ, h⟩
 #align path_connected_space.exists_path_through_family PathConnectedSpace.exists_path_through_family
 
-/- warning: path_connected_space.exists_path_through_family' -> PathConnectedSpace.exists_path_through_family' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align path_connected_space.exists_path_through_family' PathConnectedSpace.exists_path_through_family'ₓ'. -/
 theorem exists_path_through_family' {n : ℕ} (p : Fin (n + 1) → X) :
     ∃ (γ : Path (p 0) (p n))(t : Fin (n + 1) → I), ∀ i, γ (t i) = p i :=
   by
@@ -1598,12 +1358,6 @@ class LocPathConnectedSpace (X : Type _) [TopologicalSpace X] : Prop where
 
 export LocPathConnectedSpace (path_connected_basis)
 
-/- warning: loc_path_connected_of_bases -> locPathConnected_of_bases is a dubious translation:
-lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {ι : Type.{u2}} {p : ι -> Prop} {s : X -> ι -> (Set.{u1} X)}, (forall (x : X), Filter.HasBasis.{u1, succ u2} X ι (nhds.{u1} X _inst_1 x) p (s x)) -> (forall (x : X) (i : ι), (p i) -> (IsPathConnected.{u1} X _inst_1 (s x i))) -> (LocPathConnectedSpace.{u1} X _inst_1)
-but is expected to have type
-  forall {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] {ι : Type.{u1}} {p : ι -> Prop} {s : X -> ι -> (Set.{u2} X)}, (forall (x : X), Filter.HasBasis.{u2, succ u1} X ι (nhds.{u2} X _inst_1 x) p (s x)) -> (forall (x : X) (i : ι), (p i) -> (IsPathConnected.{u2} X _inst_1 (s x i))) -> (LocPathConnectedSpace.{u2} X _inst_1)
-Case conversion may be inaccurate. Consider using '#align loc_path_connected_of_bases locPathConnected_of_basesₓ'. -/
 theorem locPathConnected_of_bases {p : ι → Prop} {s : X → ι → Set X}
     (h : ∀ x, (𝓝 x).HasBasis p (s x)) (h' : ∀ x i, p i → IsPathConnected (s x i)) :
     LocPathConnectedSpace X := by

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

@@ -189,19 +189,13 @@ def symm (γ : Path x y) : Path y x where
 
 #print Path.symm_symm /-
 @[simp]
-theorem symm_symm {γ : Path x y} : γ.symm.symm = γ :=
-  by
-  ext
-  simp
+theorem symm_symm {γ : Path x y} : γ.symm.symm = γ := by ext; simp
 #align path.symm_symm Path.symm_symm
 -/
 
 #print Path.refl_symm /-
 @[simp]
-theorem refl_symm {a : X} : (Path.refl a).symm = Path.refl a :=
-  by
-  ext
-  rfl
+theorem refl_symm {a : X} : (Path.refl a).symm = Path.refl a := by ext; rfl
 #align path.refl_symm Path.refl_symm
 -/
 
@@ -465,8 +459,7 @@ theorem trans_symm (γ : Path x y) (γ' : Path y z) : (γ.trans γ').symm = γ'.
   · refine' congr_arg _ (Subtype.ext _)
     have h : 2 - 2 * (t : ℝ) - 1 = 1 - 2 * t := by linarith
     norm_num [mul_sub, h]
-  · exfalso
-    linarith [unitInterval.nonneg t, unitInterval.le_one t]
+  · exfalso; linarith [unitInterval.nonneg t, unitInterval.le_one t]
 #align path.trans_symm Path.trans_symm
 -/
 
@@ -523,9 +516,7 @@ theorem trans_range {X : Type _} [TopologicalSpace X] {a b c : X} (γ₁ : Path
         unfold_coes
         change t ≠ 0 at h
         have ht0 := lt_of_le_of_ne ht0 h.symm
-        have : ¬(t + 1) / 2 ≤ 1 / 2 := by
-          rw [not_le]
-          linarith
+        have : ¬(t + 1) / 2 ≤ 1 / 2 := by rw [not_le]; linarith
         simp only [comp_app, if_false, this]
         ring_nf
         rwa [γ₂.extend_extends]
@@ -550,9 +541,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align path.map_coe Path.map_coeₓ'. -/
 @[simp]
 theorem map_coe (γ : Path x y) {Y : Type _} [TopologicalSpace Y] {f : X → Y} (h : Continuous f) :
-    (γ.map h : I → Y) = f ∘ γ := by
-  ext t
-  rfl
+    (γ.map h : I → Y) = f ∘ γ := by ext t; rfl
 #align path.map_coe Path.map_coe
 
 /- warning: path.map_symm -> Path.map_symm is a dubious translation:
@@ -575,19 +564,13 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align path.map_trans Path.map_transₓ'. -/
 @[simp]
 theorem map_trans (γ : Path x y) (γ' : Path y z) {Y : Type _} [TopologicalSpace Y] {f : X → Y}
-    (h : Continuous f) : (γ.trans γ').map h = (γ.map h).trans (γ'.map h) :=
-  by
-  ext t
-  rw [trans_apply, map_coe, comp_app, trans_apply]
-  split_ifs <;> rfl
+    (h : Continuous f) : (γ.trans γ').map h = (γ.map h).trans (γ'.map h) := by ext t;
+  rw [trans_apply, map_coe, comp_app, trans_apply]; split_ifs <;> rfl
 #align path.map_trans Path.map_trans
 
 #print Path.map_id /-
 @[simp]
-theorem map_id (γ : Path x y) : γ.map continuous_id = γ :=
-  by
-  ext
-  rfl
+theorem map_id (γ : Path x y) : γ.map continuous_id = γ := by ext; rfl
 #align path.map_id Path.map_id
 -/
 
@@ -600,9 +583,7 @@ Case conversion may be inaccurate. Consider using '#align path.map_map Path.map_
 @[simp]
 theorem map_map (γ : Path x y) {Y : Type _} [TopologicalSpace Y] {Z : Type _} [TopologicalSpace Z]
     {f : X → Y} (hf : Continuous f) {g : Y → Z} (hg : Continuous g) :
-    (γ.map hf).map hg = γ.map (hg.comp hf) := by
-  ext
-  rfl
+    (γ.map hf).map hg = γ.map (hg.comp hf) := by ext; rfl
 #align path.map_map Path.map_map
 
 #print Path.cast /-
@@ -858,8 +839,7 @@ def truncate {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) (t₀ t
     norm_cast
     split_ifs with h₁ h₂ h₃ h₄
     · simp [γ.extend_of_le_zero h₁]
-    · congr
-      linarith
+    · congr ; linarith
     · have h₄ : t₁ ≤ 0 := le_of_lt (by simpa using h₂)
       simp [γ.extend_of_le_zero h₄, γ.extend_of_le_zero h₁]
     all_goals rfl
@@ -1014,10 +994,7 @@ theorem coe_reparam (γ : Path x y) {f : I → I} (hfcont : Continuous f) (hf₀
 
 #print Path.reparam_id /-
 @[simp]
-theorem reparam_id (γ : Path x y) : γ.reparam id continuous_id rfl rfl = γ :=
-  by
-  ext
-  rfl
+theorem reparam_id (γ : Path x y) : γ.reparam id continuous_id rfl rfl = γ := by ext; rfl
 #align path.reparam_id Path.reparam_id
 -/
 
@@ -1428,12 +1405,8 @@ theorem IsPathConnected.exists_path_through_family {X : Type _} [TopologicalSpac
     induction' n with n hn
     · use Path.refl (p' 0)
       · constructor
-        · rintro i hi
-          rw [le_zero_iff.mp hi]
-          exact ⟨0, rfl⟩
-        · rw [range_subset_iff]
-          rintro x
-          exact hp' 0 le_rfl
+        · rintro i hi; rw [le_zero_iff.mp hi]; exact ⟨0, rfl⟩
+        · rw [range_subset_iff]; rintro x; exact hp' 0 le_rfl
     · rcases hn fun i hi => hp' i <| Nat.le_succ_of_le hi with ⟨γ₀, hγ₀⟩
       rcases h.joined_in (p' n) (hp' n n.le_succ) (p' <| n + 1) (hp' (n + 1) <| le_rfl) with
         ⟨γ₁, hγ₁⟩
@@ -1455,22 +1428,15 @@ theorem IsPathConnected.exists_path_through_family {X : Type _} [TopologicalSpac
         apply union_subset hγ₀.2
         rw [range_subset_iff]
         exact hγ₁
-  have hpp' : ∀ k < n + 1, p k = p' k := by
-    intro k hk
-    simp only [p', hk, dif_pos]
-    congr
-    ext
-    rw [Fin.val_cast_of_lt hk]
-    norm_cast
+  have hpp' : ∀ k < n + 1, p k = p' k := by intro k hk; simp only [p', hk, dif_pos]; congr ; ext;
+    rw [Fin.val_cast_of_lt hk]; norm_cast
   use γ.cast (hpp' 0 n.zero_lt_succ) (hpp' n n.lt_succ_self)
   simp only [γ.cast_coe]
   refine' And.intro hγ.2 _
   rintro ⟨i, hi⟩
   suffices p ⟨i, hi⟩ = p' i by convert hγ.1 i (Nat.le_of_lt_succ hi)
   rw [← hpp' i hi]
-  suffices i = i % n.succ by
-    congr
-    assumption
+  suffices i = i % n.succ by congr ; assumption
   rw [Nat.mod_eq_of_lt hi]
 #align is_path_connected.exists_path_through_family IsPathConnected.exists_path_through_family
 

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

@@ -442,10 +442,7 @@ def trans (γ : Path x y) (γ' : Path y z) : Path x z
 -/
 
 /- warning: path.trans_apply -> Path.trans_apply is a dubious translation:
-lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x : X} {y : X} {z : X} (γ : Path.{u1} X _inst_1 x y) (γ' : Path.{u1} X _inst_1 y z) (t : coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval), Eq.{succ u1} X (coeFn.{succ u1, succ u1} (Path.{u1} X _inst_1 x z) (fun (_x : Path.{u1} X _inst_1 x z) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> X) (Path.hasCoeToFun.{u1} X _inst_1 x z) (Path.trans.{u1} X _inst_1 x y z γ γ') t) (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 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+<too large>
 Case conversion may be inaccurate. Consider using '#align path.trans_apply Path.trans_applyₓ'. -/
 theorem trans_apply (γ : Path x y) (γ' : Path y z) (t : I) :
     (γ.trans γ') t =
@@ -979,10 +976,7 @@ theorem truncate_one_one {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path
 #align path.truncate_one_one Path.truncate_one_one
 
 /- warning: path.truncate_zero_one -> Path.truncate_zero_one is a dubious translation:
-lean 3 declaration is
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(Prop -> Prop) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) True And (Mathlib.Algebra.Order.ZeroLEOne._auxLemma.1.{0} Real Real.instZeroReal Real.instOneReal (Preorder.toLE.{0} Real Real.instPreorderReal) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring))) (Mathlib.Order.Basic._auxLemma.1.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))) (and_self True))))) b (Path.extend_extends.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (of_eq_true (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Eq.trans.{1} Prop (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And True True) True (Eq.trans.{1} Prop (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} 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Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) True And (Mathlib.Algebra.Order.ZeroLEOne._auxLemma.1.{0} Real Real.instZeroReal Real.instOneReal (Preorder.toLE.{0} Real Real.instPreorderReal) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring))) (Mathlib.Order.Basic._auxLemma.1.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))) (and_self True)))) (Path.target.{u1} X _inst_3 a b γ))) b) (eq_self.{succ u1} X b))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align path.truncate_zero_one Path.truncate_zero_oneₓ'. -/
 @[simp]
 theorem truncate_zero_one {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) :
@@ -1417,10 +1411,7 @@ theorem IsPathConnected.preimage_coe {U W : Set X} (hW : IsPathConnected W) (hWU
 -/
 
 /- warning: is_path_connected.exists_path_through_family -> IsPathConnected.exists_path_through_family is a dubious translation:
-lean 3 declaration is
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(HasSubset.Subset.{u1} (Set.{u1} X) (Set.instHasSubsetSet.{u1} X) (Set.range.{u1, 1} X (Set.Elem.{0} Real unitInterval) (FunLike.coe.{succ u1, 1, succ u1} (Path.{u1} X _inst_3 (p (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (p (Nat.cast.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (AddMonoidWithOne.toNatCast.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instAddMonoidWithOneFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (NeZero.succ n))) n))) (Set.Elem.{0} Real unitInterval) (fun (_x : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) _x) (ContinuousMapClass.toFunLike.{u1, 0, u1} (Path.{u1} X _inst_3 (p (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (p (Nat.cast.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (AddMonoidWithOne.toNatCast.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instAddMonoidWithOneFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (NeZero.succ n))) n))) (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_3 (Path.continuousMapClass.{u1} X _inst_3 (p (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (p (Nat.cast.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (AddMonoidWithOne.toNatCast.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instAddMonoidWithOneFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (NeZero.succ n))) n)))) γ)) s) (forall (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), Membership.mem.{u1, u1} X (Set.{u1} X) (Set.instMembershipSet.{u1} X) (p i) (Set.range.{u1, 1} X (Set.Elem.{0} Real unitInterval) (FunLike.coe.{succ u1, 1, succ u1} (Path.{u1} X _inst_3 (p (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (p (Nat.cast.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (AddMonoidWithOne.toNatCast.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instAddMonoidWithOneFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (NeZero.succ n))) n))) (Set.Elem.{0} Real unitInterval) (fun (_x : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) _x) (ContinuousMapClass.toFunLike.{u1, 0, u1} (Path.{u1} X _inst_3 (p (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (p (Nat.cast.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (AddMonoidWithOne.toNatCast.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instAddMonoidWithOneFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (NeZero.succ n))) n))) (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_3 (Path.continuousMapClass.{u1} X _inst_3 (p (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (p (Nat.cast.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (AddMonoidWithOne.toNatCast.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instAddMonoidWithOneFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (NeZero.succ n))) n)))) γ))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align is_path_connected.exists_path_through_family IsPathConnected.exists_path_through_familyₓ'. -/
 theorem IsPathConnected.exists_path_through_family {X : Type _} [TopologicalSpace X] {n : ℕ}
     {s : Set X} (h : IsPathConnected s) (p : Fin (n + 1) → X) (hp : ∀ i, p i ∈ s) :
@@ -1484,10 +1475,7 @@ theorem IsPathConnected.exists_path_through_family {X : Type _} [TopologicalSpac
 #align is_path_connected.exists_path_through_family IsPathConnected.exists_path_through_family
 
 /- warning: is_path_connected.exists_path_through_family' -> IsPathConnected.exists_path_through_family' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_path_connected.exists_path_through_family' IsPathConnected.exists_path_through_family'ₓ'. -/
 theorem IsPathConnected.exists_path_through_family' {X : Type _} [TopologicalSpace X] {n : ℕ}
     {s : Set X} (h : IsPathConnected s) (p : Fin (n + 1) → X) (hp : ∀ i, p i ∈ s) :
@@ -1608,10 +1596,7 @@ namespace PathConnectedSpace
 variable [PathConnectedSpace X]
 
 /- warning: path_connected_space.exists_path_through_family -> PathConnectedSpace.exists_path_through_family is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align path_connected_space.exists_path_through_family PathConnectedSpace.exists_path_through_familyₓ'. -/
 theorem exists_path_through_family {n : ℕ} (p : Fin (n + 1) → X) :
     ∃ γ : Path (p 0) (p n), ∀ i, p i ∈ range γ :=
@@ -1622,10 +1607,7 @@ theorem exists_path_through_family {n : ℕ} (p : Fin (n + 1) → X) :
 #align path_connected_space.exists_path_through_family PathConnectedSpace.exists_path_through_family
 
 /- warning: path_connected_space.exists_path_through_family' -> PathConnectedSpace.exists_path_through_family' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align path_connected_space.exists_path_through_family' PathConnectedSpace.exists_path_through_family'ₓ'. -/
 theorem exists_path_through_family' {n : ℕ} (p : Fin (n + 1) → X) :
     ∃ (γ : Path (p 0) (p n))(t : Fin (n + 1) → I), ∀ i, γ (t i) = p i :=

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

@@ -292,7 +292,7 @@ theorem continuous_extend : Continuous γ.extend :=
 
 /- warning: filter.tendsto.path_extend -> Filter.Tendsto.path_extend 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] {l : Y -> X} {r : Y -> X} {y : Y} {l₁ : Filter.{0} Real} {l₂ : Filter.{u1} X} {γ : forall (y : Y), Path.{u1} X _inst_3 (l y) (r y)}, (Filter.Tendsto.{u2, u1} (Prod.{u2, 0} Y (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))) X (Function.HasUncurry.uncurry.{max u2 u1, u2, u1} (forall (y : Y), Path.{u1} X _inst_3 (l y) (r y)) (Prod.{u2, 0} Y (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))) X (Path.hasUncurryPath.{u1, u2} X Y _inst_3 (fun (y : Y) => l y) (fun (y : Y) => r y)) γ) (Filter.prod.{u2, 0} Y (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (nhds.{u2} Y _inst_4 y) (Filter.map.{0, 0} Real (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Set.projIcc.{0} Real Real.linearOrder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (zero_le_one.{0} Real Real.hasZero Real.hasOne (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder))))) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring))) l₁)) l₂) -> (Filter.Tendsto.{u2, u1} (Prod.{u2, 0} Y Real) X (Function.HasUncurry.uncurry.{max u2 u1, u2, u1} (Y -> Real -> X) (Prod.{u2, 0} Y Real) X (Function.hasUncurryInduction.{u2, u1, 0, u1} Y (Real -> X) Real X (Function.hasUncurryBase.{0, u1} Real X)) (fun (x : Y) => Path.extend.{u1} X _inst_3 (l x) (r x) (γ x))) (Filter.prod.{u2, 0} Y Real (nhds.{u2} Y _inst_4 y) l₁) l₂)
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_3 : TopologicalSpace.{u1} X] [_inst_4 : TopologicalSpace.{u2} Y] {l : Y -> X} {r : Y -> X} {y : Y} {l₁ : Filter.{0} Real} {l₂ : Filter.{u1} X} {γ : forall (y : Y), Path.{u1} X _inst_3 (l y) (r y)}, (Filter.Tendsto.{u2, u1} (Prod.{u2, 0} Y (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))) X (Function.HasUncurry.uncurry.{max u2 u1, u2, u1} (forall (y : Y), Path.{u1} X _inst_3 (l y) (r y)) (Prod.{u2, 0} Y (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))) X (Path.hasUncurryPath.{u1, u2} X Y _inst_3 (fun (y : Y) => l y) (fun (y : Y) => r y)) γ) (Filter.prod.{u2, 0} Y (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (nhds.{u2} Y _inst_4 y) (Filter.map.{0, 0} Real (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Set.projIcc.{0} Real Real.linearOrder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (zero_le_one.{0} Real Real.hasZero Real.hasOne (Preorder.toHasLe.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder))))) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring))) l₁)) l₂) -> (Filter.Tendsto.{u2, u1} (Prod.{u2, 0} Y Real) X (Function.HasUncurry.uncurry.{max u2 u1, u2, u1} (Y -> Real -> X) (Prod.{u2, 0} Y Real) X (Function.hasUncurryInduction.{u2, u1, 0, u1} Y (Real -> X) Real X (Function.hasUncurryBase.{0, u1} Real X)) (fun (x : Y) => Path.extend.{u1} X _inst_3 (l x) (r x) (γ x))) (Filter.prod.{u2, 0} Y Real (nhds.{u2} Y _inst_4 y) l₁) l₂)
 but is expected to have type
   forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_3 : TopologicalSpace.{u2} X] [_inst_4 : TopologicalSpace.{u1} Y] {l : Y -> X} {r : Y -> X} {y : Y} {l₁ : Filter.{0} Real} {l₂ : Filter.{u2} X} {γ : forall (y : Y), Path.{u2} X _inst_3 (l y) (r y)}, (Filter.Tendsto.{u1, u2} (Prod.{u1, 0} Y (Set.Elem.{0} Real unitInterval)) X (Function.HasUncurry.uncurry.{max u2 u1, u1, u2} (forall (y : Y), Path.{u2} X _inst_3 (l y) (r y)) (Prod.{u1, 0} Y (Set.Elem.{0} Real unitInterval)) X (Path.hasUncurryPath.{u2, u1} X Y _inst_3 (fun (y : Y) => l y) (fun (y : Y) => r y)) γ) (Filter.prod.{u1, 0} Y (Set.Elem.{0} Real unitInterval) (nhds.{u1} Y _inst_4 y) (Filter.map.{0, 0} Real (Set.Elem.{0} Real unitInterval) (Set.projIcc.{0} Real Real.linearOrder (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (zero_le_one.{0} Real Real.instZeroReal Real.instOneReal (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (DistribLattice.toLattice.{0} Real (instDistribLattice.{0} Real Real.linearOrder)))))) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring))) l₁)) l₂) -> (Filter.Tendsto.{u1, u2} (Prod.{u1, 0} Y Real) X (Function.HasUncurry.uncurry.{max u2 u1, u1, u2} (Y -> Real -> X) (Prod.{u1, 0} Y Real) X (Function.hasUncurryInduction.{u1, u2, 0, u2} Y (Real -> X) Real X (Function.hasUncurryBase.{0, u2} Real X)) (fun (x : Y) => Path.extend.{u2} X _inst_3 (l x) (r x) (γ x))) (Filter.prod.{u1, 0} Y Real (nhds.{u1} Y _inst_4 y) l₁) l₂)
 Case conversion may be inaccurate. Consider using '#align filter.tendsto.path_extend Filter.Tendsto.path_extendₓ'. -/
@@ -305,7 +305,7 @@ theorem Filter.Tendsto.path_extend {X Y : Type _} [TopologicalSpace X] [Topologi
 
 /- warning: continuous_at.path_extend -> ContinuousAt.path_extend is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {g : Y -> Real} {l : Y -> X} {r : Y -> X} (γ : forall (y : Y), Path.{u1} X _inst_1 (l y) (r y)) {y : Y}, (ContinuousAt.{u2, u1} (Prod.{u2, 0} Y (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))) X (Prod.topologicalSpace.{u2, 0} Y (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) _inst_2 (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)))) _inst_1 (Function.HasUncurry.uncurry.{max u2 u1, u2, u1} (forall (y : Y), Path.{u1} X _inst_1 (l y) (r y)) (Prod.{u2, 0} Y (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))) X (Path.hasUncurryPath.{u1, u2} X Y _inst_1 (fun (y : Y) => l y) (fun (y : Y) => r y)) γ) (Prod.mk.{u2, 0} Y (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) y (Set.projIcc.{0} Real Real.linearOrder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (zero_le_one.{0} Real Real.hasZero Real.hasOne (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder))))) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring)) (g y)))) -> (ContinuousAt.{u2, 0} Y Real _inst_2 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) g y) -> (ContinuousAt.{u2, u1} Y X _inst_2 _inst_1 (fun (i : Y) => Path.extend.{u1} X _inst_1 (l i) (r i) (γ i) (g i)) y)
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {g : Y -> Real} {l : Y -> X} {r : Y -> X} (γ : forall (y : Y), Path.{u1} X _inst_1 (l y) (r y)) {y : Y}, (ContinuousAt.{u2, u1} (Prod.{u2, 0} Y (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))) X (Prod.topologicalSpace.{u2, 0} Y (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) _inst_2 (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)))) _inst_1 (Function.HasUncurry.uncurry.{max u2 u1, u2, u1} (forall (y : Y), Path.{u1} X _inst_1 (l y) (r y)) (Prod.{u2, 0} Y (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))) X (Path.hasUncurryPath.{u1, u2} X Y _inst_1 (fun (y : Y) => l y) (fun (y : Y) => r y)) γ) (Prod.mk.{u2, 0} Y (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) y (Set.projIcc.{0} Real Real.linearOrder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (zero_le_one.{0} Real Real.hasZero Real.hasOne (Preorder.toHasLe.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder))))) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring)) (g y)))) -> (ContinuousAt.{u2, 0} Y Real _inst_2 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) g y) -> (ContinuousAt.{u2, u1} Y X _inst_2 _inst_1 (fun (i : Y) => Path.extend.{u1} X _inst_1 (l i) (r i) (γ i) (g i)) y)
 but is expected to have type
   forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : TopologicalSpace.{u1} Y] {g : Y -> Real} {l : Y -> X} {r : Y -> X} (γ : forall (y : Y), Path.{u2} X _inst_1 (l y) (r y)) {y : Y}, (ContinuousAt.{u1, u2} (Prod.{u1, 0} Y (Set.Elem.{0} Real unitInterval)) X (instTopologicalSpaceProd.{u1, 0} Y (Set.Elem.{0} Real unitInterval) _inst_2 (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 (Function.HasUncurry.uncurry.{max u2 u1, u1, u2} (forall (y : Y), Path.{u2} X _inst_1 (l y) (r y)) (Prod.{u1, 0} Y (Set.Elem.{0} Real unitInterval)) X (Path.hasUncurryPath.{u2, u1} X Y _inst_1 (fun (y : Y) => l y) (fun (y : Y) => r y)) γ) (Prod.mk.{u1, 0} Y (Set.Elem.{0} Real unitInterval) y (Set.projIcc.{0} Real Real.linearOrder (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (zero_le_one.{0} Real Real.instZeroReal Real.instOneReal (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (DistribLattice.toLattice.{0} Real (instDistribLattice.{0} Real Real.linearOrder)))))) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring)) (g y)))) -> (ContinuousAt.{u1, 0} Y Real _inst_2 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) g y) -> (ContinuousAt.{u1, u2} Y X _inst_2 _inst_1 (fun (i : Y) => Path.extend.{u2} X _inst_1 (l i) (r i) (γ i) (g i)) y)
 Case conversion may be inaccurate. Consider using '#align continuous_at.path_extend ContinuousAt.path_extendₓ'. -/
@@ -443,7 +443,7 @@ def trans (γ : Path x y) (γ' : Path y z) : Path x z
 
 /- warning: path.trans_apply -> Path.trans_apply is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x : X} {y : X} {z : X} (γ : Path.{u1} X _inst_1 x y) (γ' : Path.{u1} X _inst_1 y z) (t : coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval), Eq.{succ u1} X (coeFn.{succ u1, succ u1} (Path.{u1} X _inst_1 x z) (fun (_x : Path.{u1} X _inst_1 x z) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> X) (Path.hasCoeToFun.{u1} X _inst_1 x z) (Path.trans.{u1} X _inst_1 x y z γ γ') t) (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 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unitInterval))))) t) (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)))))) => coeFn.{succ u1, succ u1} (Path.{u1} X _inst_1 x y) (fun (_x : Path.{u1} X _inst_1 x y) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> X) (Path.hasCoeToFun.{u1} X _inst_1 x y) γ (Subtype.mk.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (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) 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(DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) (LT.lt.{0} Real (Preorder.toLT.{0} Real (PartialOrder.toPreorder.{0} Real (LinearOrder.toPartialOrder.{0} Real Real.linearOrder))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} 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+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x : X} {y : X} {z : X} (γ : Path.{u1} X _inst_1 x y) (γ' : Path.{u1} X _inst_1 y z) (t : coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval), Eq.{succ u1} X (coeFn.{succ u1, succ u1} (Path.{u1} X _inst_1 x z) (fun (_x : Path.{u1} X _inst_1 x z) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> X) (Path.hasCoeToFun.{u1} X _inst_1 x z) (Path.trans.{u1} X _inst_1 x y z γ γ') t) (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 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(Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval))))) t) (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 (h : 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))))) t) (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)))))) => coeFn.{succ u1, succ u1} (Path.{u1} X _inst_1 x y) (fun (_x : Path.{u1} X _inst_1 x y) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> X) (Path.hasCoeToFun.{u1} X _inst_1 x y) γ (Subtype.mk.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (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) 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(One.one.{0} Real (AddMonoidWithOne.toOne.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (AddCommGroupWithOne.toAddGroupWithOne.{0} Real (Ring.toAddCommGroupWithOne.{0} Real Real.ring))))))))))) (unitInterval.mul_pos_mem_iff (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real (AddZeroClass.toHasAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddMonoidWithOne.toAddMonoid.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (AddCommGroupWithOne.toAddGroupWithOne.{0} Real (Ring.toAddCommGroupWithOne.{0} Real Real.ring)))))) (One.one.{0} Real (AddMonoidWithOne.toOne.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (AddCommGroupWithOne.toAddGroupWithOne.{0} Real (Ring.toAddCommGroupWithOne.{0} Real Real.ring)))))))) ((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))))) t) (zero_lt_two.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (AddCommGroupWithOne.toAddGroupWithOne.{0} Real (Ring.toAddCommGroupWithOne.{0} Real Real.ring))) Real.partialOrder (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring) (NeZero.one.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) Real.nontrivial) (OrderedAddCommGroup.to_covariantClass_left_le.{0} Real Real.orderedAddCommGroup))) (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))) ((fun (a : Type) (b : 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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) unitInterval) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval))))) t)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (Iff.mpr (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) (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) unitInterval) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval))))) t)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) unitInterval) (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} Real) Type 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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))))) t)) (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))))) t) (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))))) t) (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))))) t) (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))))) t)) (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))))) t) (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) t)) (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) t) (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) t)))))))
 but is expected to have type
   forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x : X} {y : X} {z : X} (γ : Path.{u1} X _inst_1 x y) (γ' : Path.{u1} X _inst_1 y z) (t : Set.Elem.{0} Real unitInterval), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) t) (FunLike.coe.{succ u1, 1, succ u1} (Path.{u1} X _inst_1 x z) (Set.Elem.{0} Real unitInterval) (fun (_x : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) _x) (ContinuousMapClass.toFunLike.{u1, 0, u1} (Path.{u1} X _inst_1 x z) (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.continuousMapClass.{u1} X _inst_1 x z)) (Path.trans.{u1} X _inst_1 x y z γ γ') t) (dite.{succ u1} X (LE.le.{0} Real Real.instLEReal (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) t) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (Real.decidableLE (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) t) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (fun (h : LE.le.{0} Real Real.instLEReal (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) t) (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.{u1} X _inst_1 x y) (Set.Elem.{0} Real unitInterval) (fun (_x : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) _x) (ContinuousMapClass.toFunLike.{u1, 0, u1} (Path.{u1} X _inst_1 x y) (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.continuousMapClass.{u1} X _inst_1 x y)) γ (Subtype.mk.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 (AddMonoidWithOne.toNatCast.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) t)) (Iff.mpr (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 (AddMonoidWithOne.toNatCast.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) t)) 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) t) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 (AddMonoidWithOne.toNatCast.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (unitInterval.mul_pos_mem_iff (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 (AddMonoidWithOne.toNatCast.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) t) (zero_lt_two.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal)) Real.partialOrder (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring) (NeZero.one.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real.nontrivial) (OrderedAddCommGroup.to_covariantClass_left_le.{0} Real Real.orderedAddCommGroup))) (And.intro (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) t)) (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) t) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 (AddMonoidWithOne.toNatCast.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (And.left (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) t)) (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) t) (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) t)) h)))) (fun (h : Not (LE.le.{0} Real Real.instLEReal (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) t) (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.{u1} X _inst_1 y z) (Set.Elem.{0} Real unitInterval) (fun (_x : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) _x) (ContinuousMapClass.toFunLike.{u1, 0, u1} (Path.{u1} X _inst_1 y z) (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.continuousMapClass.{u1} X _inst_1 y z)) γ' (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) t)) (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) t)) (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) t) (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) t)) (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) t)) (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) t) (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) t) (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) t) (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) t)) (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) t) (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) t)) (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) t) (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) t)))))))
 Case conversion may be inaccurate. Consider using '#align path.trans_apply Path.trans_applyₓ'. -/
@@ -980,9 +980,9 @@ theorem truncate_one_one {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path
 
 /- warning: path.truncate_zero_one -> Path.truncate_zero_one is a dubious translation:
 lean 3 declaration is
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X a a_1) (ᾰ : X) (ᾰ_1 : X) (e_2 : Eq.{succ u1} X ᾰ ᾰ_1) => congr.{succ u1, 1} X Prop (Eq.{succ u1} X a) (Eq.{succ u1} X a_1) ᾰ ᾰ_1 (congr_arg.{succ u1, succ u1} X (X -> Prop) a a_1 (Eq.{succ u1} X) e_1) e_2) (Path.extend.{u1} X _inst_3 a b γ (LinearOrder.min.{0} Real Real.linearOrder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) a (Eq.trans.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (LinearOrder.min.{0} Real Real.linearOrder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) a ((fun (γ : Path.{u1} X _inst_3 a b) (γ_1 : Path.{u1} X _inst_3 a b) (e_1 : Eq.{succ u1} (Path.{u1} X _inst_3 a b) γ γ_1) (ᾰ : Real) (ᾰ_1 : Real) (e_2 : Eq.{1} Real ᾰ ᾰ_1) => congr.{1, succ u1} Real X (Path.extend.{u1} X _inst_3 a b γ) (Path.extend.{u1} X _inst_3 a b γ_1) ᾰ ᾰ_1 (congr_arg.{succ u1, succ u1} (Path.{u1} X _inst_3 a b) (Real -> X) γ γ_1 (Path.extend.{u1} X _inst_3 a b) e_1) e_2) γ γ (rfl.{succ u1} (Path.{u1} X _inst_3 a b) γ) (LinearOrder.min.{0} Real Real.linearOrder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (min_eq_left.{0} Real Real.linearOrder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (Iff.mpr (LE.le.{0} Real (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (LinearOrder.toPartialOrder.{0} Real Real.linearOrder))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) True ((fun {α : Type} [_inst_1 : Zero.{0} α] [_inst_2 : One.{0} α] [_inst_3 : LE.{0} α] [_inst_4 : ZeroLEOneClass.{0} α _inst_1 _inst_2 _inst_3] => iff_true_intro (LE.le.{0} α _inst_3 (OfNat.ofNat.{0} α 0 (OfNat.mk.{0} α 0 (Zero.zero.{0} α _inst_1))) (OfNat.ofNat.{0} α 1 (OfNat.mk.{0} α 1 (One.one.{0} α _inst_2)))) (zero_le_one.{0} α _inst_1 _inst_2 _inst_3 _inst_4)) Real Real.hasZero Real.hasOne (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (LinearOrder.toPartialOrder.{0} Real Real.linearOrder))) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring)) True.intro))) (Path.extend_zero.{u1} X _inst_3 a b γ)) a a (rfl.{succ u1} X a)) (propext (Eq.{succ u1} X a a) True (eq_self_iff_true.{succ u1} X a)))) trivial) (Eq.mpr.{0} (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) b) True (id_tag Tactic.IdTag.simp (Eq.{1} Prop (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) b) True) (Eq.trans.{1} Prop (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) b) (Eq.{succ u1} X b b) True ((fun (a : X) (a_1 : X) (e_1 : Eq.{succ u1} X a a_1) (ᾰ : X) (ᾰ_1 : X) (e_2 : Eq.{succ u1} X ᾰ ᾰ_1) => congr.{succ u1, 1} X Prop (Eq.{succ u1} X a) (Eq.{succ u1} X a_1) ᾰ ᾰ_1 (congr_arg.{succ u1, succ u1} X (X -> Prop) a a_1 (Eq.{succ u1} X) e_1) e_2) (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) b (Eq.trans.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (coeFn.{succ u1, succ u1} (Path.{u1} X _inst_3 a b) (fun (_x : Path.{u1} X _inst_3 a b) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> X) (Path.hasCoeToFun.{u1} X _inst_3 a b) γ (OfNat.ofNat.{0} (Subtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommMonoid.toPartialOrder.{0} Real (OrderedSemiring.toOrderedAddCommMonoid.{0} Real Real.orderedSemiring))) (Zero.zero.{0} Real (MulZeroClass.toHasZero.{0} Real (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring)))))) (One.one.{0} Real (AddMonoidWithOne.toOne.{0} Real (AddCommMonoidWithOne.toAddMonoidWithOne.{0} Real (NonAssocSemiring.toAddCommMonoidWithOne.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))))))) 1 (OfNat.mk.{0} (Subtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real 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Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) ((fun {α : Type} [_inst_1 : Zero.{0} α] [_inst_2 : One.{0} α] [_inst_3 : LE.{0} α] [_inst_4 : ZeroLEOneClass.{0} α _inst_1 _inst_2 _inst_3] => iff_true_intro (LE.le.{0} α _inst_3 (OfNat.ofNat.{0} α 0 (OfNat.mk.{0} α 0 (Zero.zero.{0} α _inst_1))) (OfNat.ofNat.{0} α 1 (OfNat.mk.{0} α 1 (One.one.{0} α _inst_2)))) (zero_le_one.{0} α _inst_1 _inst_2 _inst_3 _inst_4)) Real Real.hasZero Real.hasOne (Preorder.toLE.{0} Real Real.preorder) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring))) True.intro))) (coeFn.{succ u1, succ u1} (Path.{u1} X _inst_3 a b) (fun (_x : Path.{u1} X _inst_3 a b) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> X) (Path.hasCoeToFun.{u1} X _inst_3 a b) γ (OfNat.ofNat.{0} (Subtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} 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(One.one.{0} Real Real.hasOne))) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (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))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) True (Set.right_mem_Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) ((fun {α : Type} [_inst_1 : Zero.{0} α] [_inst_2 : One.{0} α] [_inst_3 : LE.{0} α] [_inst_4 : ZeroLEOneClass.{0} α _inst_1 _inst_2 _inst_3] => iff_true_intro (LE.le.{0} α _inst_3 (OfNat.ofNat.{0} α 0 (OfNat.mk.{0} α 0 (Zero.zero.{0} α _inst_1))) (OfNat.ofNat.{0} α 1 (OfNat.mk.{0} α 1 (One.one.{0} α _inst_2)))) (zero_le_one.{0} α _inst_1 _inst_2 _inst_3 _inst_4)) Real Real.hasZero Real.hasOne (Preorder.toLE.{0} Real Real.preorder) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring))) True.intro)) ((fun [_inst_1 : CoeFun.{succ u1, succ u1} (Path.{u1} X _inst_3 a b) (fun (_x : Path.{u1} X _inst_3 a b) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> X)] (x : Path.{u1} X _inst_3 a b) (x_1 : Path.{u1} X _inst_3 a b) (e_2 : Eq.{succ u1} (Path.{u1} X _inst_3 a b) x x_1) (ᾰ : coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (ᾰ_1 : coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (e_3 : Eq.{1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) ᾰ ᾰ_1) => congr.{1, succ u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X (coeFn.{succ u1, succ u1} (Path.{u1} X _inst_3 a b) (fun (_x : Path.{u1} X _inst_3 a b) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> X) _inst_1 x) (coeFn.{succ u1, succ u1} (Path.{u1} X _inst_3 a b) (fun (_x : Path.{u1} X _inst_3 a b) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> X) _inst_1 x_1) ᾰ ᾰ_1 (congr_arg.{succ u1, succ u1} (Path.{u1} X _inst_3 a b) ((fun (_x : Path.{u1} X _inst_3 a b) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> X) x) x x_1 (coeFn.{succ u1, succ u1} (Path.{u1} X _inst_3 a b) (fun (_x : Path.{u1} X _inst_3 a b) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> X) _inst_1) e_2) e_3) (Path.hasCoeToFun.{u1} X _inst_3 a b) γ γ (rfl.{succ u1} (Path.{u1} X _inst_3 a b) γ) (Subtype.mk.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (Iff.mpr (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) (OfNat.ofNat.{0} Real 1 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Real Real.hasOne)))) ((fun {α : Type} [_inst_1 : Zero.{0} α] [_inst_2 : One.{0} α] [_inst_3 : LE.{0} α] [_inst_4 : ZeroLEOneClass.{0} α _inst_1 _inst_2 _inst_3] => iff_true_intro (LE.le.{0} α _inst_3 (OfNat.ofNat.{0} α 0 (OfNat.mk.{0} α 0 (Zero.zero.{0} α _inst_1))) (OfNat.ofNat.{0} α 1 (OfNat.mk.{0} α 1 (One.one.{0} α _inst_2)))) (zero_le_one.{0} α _inst_1 _inst_2 _inst_3 _inst_4)) Real Real.hasZero Real.hasOne (Preorder.toLE.{0} Real Real.preorder) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring))) True.intro)) (OfNat.ofNat.{0} (Subtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommMonoid.toPartialOrder.{0} Real (OrderedSemiring.toOrderedAddCommMonoid.{0} Real Real.orderedSemiring))) (Zero.zero.{0} Real (MulZeroClass.toHasZero.{0} Real (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring)))))) (One.one.{0} Real (AddMonoidWithOne.toOne.{0} Real (AddCommMonoidWithOne.toAddMonoidWithOne.{0} Real (NonAssocSemiring.toAddCommMonoidWithOne.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))))))) 1 (OfNat.mk.{0} (Subtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommMonoid.toPartialOrder.{0} Real (OrderedSemiring.toOrderedAddCommMonoid.{0} Real Real.orderedSemiring))) (Zero.zero.{0} Real (MulZeroClass.toHasZero.{0} Real (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring)))))) (One.one.{0} Real (AddMonoidWithOne.toOne.{0} Real (AddCommMonoidWithOne.toAddMonoidWithOne.{0} Real (NonAssocSemiring.toAddCommMonoidWithOne.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))))))) 1 (One.one.{0} (Subtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommMonoid.toPartialOrder.{0} Real (OrderedSemiring.toOrderedAddCommMonoid.{0} Real Real.orderedSemiring))) (Zero.zero.{0} Real (MulZeroClass.toHasZero.{0} Real (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring)))))) (One.one.{0} Real (AddMonoidWithOne.toOne.{0} Real (AddCommMonoidWithOne.toAddMonoidWithOne.{0} Real (NonAssocSemiring.toAddCommMonoidWithOne.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))))))) (Set.Icc.one.{0} Real Real.orderedSemiring)))) (Set.Icc.mk_one.{0} Real Real.orderedSemiring (Iff.mpr (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) True (Iff.trans (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (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))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) True (Set.right_mem_Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) ((fun {α : Type} [_inst_1 : Zero.{0} α] [_inst_2 : One.{0} α] [_inst_3 : LE.{0} α] [_inst_4 : ZeroLEOneClass.{0} α _inst_1 _inst_2 _inst_3] => iff_true_intro (LE.le.{0} α _inst_3 (OfNat.ofNat.{0} α 0 (OfNat.mk.{0} α 0 (Zero.zero.{0} α _inst_1))) (OfNat.ofNat.{0} α 1 (OfNat.mk.{0} α 1 (One.one.{0} α _inst_2)))) (zero_le_one.{0} α _inst_1 _inst_2 _inst_3 _inst_4)) Real Real.hasZero Real.hasOne (Preorder.toLE.{0} Real Real.preorder) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring))) True.intro)))) (Path.target.{u1} X _inst_3 a b γ)) b b (rfl.{succ u1} X b)) (propext (Eq.{succ u1} X b b) True (eq_self_iff_true.{succ u1} X b)))) trivial))
+  forall {X : Type.{u1}} [_inst_3 : TopologicalSpace.{u1} X] {a : X} {b : X} (γ : Path.{u1} X _inst_3 a b), Eq.{succ u1} (Path.{u1} X _inst_3 (Path.extend.{u1} X _inst_3 a b γ (LinearOrder.min.{0} Real Real.linearOrder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Path.truncate.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (Path.cast.{u1} X _inst_3 a b γ (Path.extend.{u1} X _inst_3 a b γ (LinearOrder.min.{0} Real Real.linearOrder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (Eq.mpr.{0} (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (LinearOrder.min.{0} Real Real.linearOrder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) a) True (id_tag Tactic.IdTag.simp (Eq.{1} Prop (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (LinearOrder.min.{0} Real Real.linearOrder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) a) True) (Eq.trans.{1} Prop (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (LinearOrder.min.{0} Real Real.linearOrder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) a) (Eq.{succ u1} X a a) True ((fun (a : X) (a_1 : X) (e_1 : Eq.{succ u1} X a a_1) (ᾰ : X) (ᾰ_1 : X) (e_2 : Eq.{succ u1} X ᾰ ᾰ_1) => congr.{succ u1, 1} X Prop (Eq.{succ u1} X a) (Eq.{succ u1} X a_1) ᾰ ᾰ_1 (congr_arg.{succ u1, succ u1} X (X -> Prop) a a_1 (Eq.{succ u1} X) e_1) e_2) (Path.extend.{u1} X _inst_3 a b γ (LinearOrder.min.{0} Real Real.linearOrder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) a (Eq.trans.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (LinearOrder.min.{0} Real Real.linearOrder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) a ((fun (γ : Path.{u1} X _inst_3 a b) (γ_1 : Path.{u1} X _inst_3 a b) (e_1 : Eq.{succ u1} (Path.{u1} X _inst_3 a b) γ γ_1) (ᾰ : Real) (ᾰ_1 : Real) (e_2 : Eq.{1} Real ᾰ ᾰ_1) => congr.{1, succ u1} Real X (Path.extend.{u1} X _inst_3 a b γ) (Path.extend.{u1} X _inst_3 a b γ_1) ᾰ ᾰ_1 (congr_arg.{succ u1, succ u1} (Path.{u1} X _inst_3 a b) (Real -> X) γ γ_1 (Path.extend.{u1} X _inst_3 a b) e_1) e_2) γ γ (rfl.{succ u1} (Path.{u1} X _inst_3 a b) γ) (LinearOrder.min.{0} Real Real.linearOrder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (min_eq_left.{0} Real Real.linearOrder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (Iff.mpr (LE.le.{0} Real (Preorder.toHasLe.{0} Real (PartialOrder.toPreorder.{0} Real (LinearOrder.toPartialOrder.{0} Real Real.linearOrder))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) True ((fun {α : Type} [_inst_1 : Zero.{0} α] [_inst_2 : One.{0} α] [_inst_3 : LE.{0} α] [_inst_4 : ZeroLEOneClass.{0} α _inst_1 _inst_2 _inst_3] => iff_true_intro (LE.le.{0} α _inst_3 (OfNat.ofNat.{0} α 0 (OfNat.mk.{0} α 0 (Zero.zero.{0} α _inst_1))) (OfNat.ofNat.{0} α 1 (OfNat.mk.{0} α 1 (One.one.{0} α _inst_2)))) (zero_le_one.{0} α _inst_1 _inst_2 _inst_3 _inst_4)) Real Real.hasZero Real.hasOne (Preorder.toHasLe.{0} Real (PartialOrder.toPreorder.{0} Real (LinearOrder.toPartialOrder.{0} Real Real.linearOrder))) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring)) True.intro))) (Path.extend_zero.{u1} X _inst_3 a b γ)) a a (rfl.{succ u1} X a)) (propext (Eq.{succ u1} X a a) True (eq_self_iff_true.{succ u1} X a)))) trivial) (Eq.mpr.{0} (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) b) True (id_tag Tactic.IdTag.simp (Eq.{1} Prop (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) b) True) (Eq.trans.{1} Prop (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) b) (Eq.{succ u1} X b b) True ((fun (a : X) (a_1 : X) (e_1 : Eq.{succ u1} X a a_1) (ᾰ : X) (ᾰ_1 : X) (e_2 : Eq.{succ u1} X ᾰ ᾰ_1) => congr.{succ u1, 1} X Prop (Eq.{succ u1} X a) (Eq.{succ u1} X a_1) ᾰ ᾰ_1 (congr_arg.{succ u1, succ u1} X (X -> Prop) a a_1 (Eq.{succ u1} X) e_1) e_2) (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) b (Eq.trans.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (coeFn.{succ u1, succ u1} (Path.{u1} X _inst_3 a b) (fun (_x : Path.{u1} X _inst_3 a b) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> X) (Path.hasCoeToFun.{u1} X _inst_3 a b) γ (OfNat.ofNat.{0} (Subtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommMonoid.toPartialOrder.{0} Real (OrderedSemiring.toOrderedAddCommMonoid.{0} Real Real.orderedSemiring))) (Zero.zero.{0} Real (MulZeroClass.toHasZero.{0} Real (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring)))))) (One.one.{0} Real (AddMonoidWithOne.toOne.{0} Real (AddCommMonoidWithOne.toAddMonoidWithOne.{0} Real (NonAssocSemiring.toAddCommMonoidWithOne.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))))))) 1 (OfNat.mk.{0} (Subtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommMonoid.toPartialOrder.{0} Real (OrderedSemiring.toOrderedAddCommMonoid.{0} Real Real.orderedSemiring))) (Zero.zero.{0} Real (MulZeroClass.toHasZero.{0} Real (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring)))))) (One.one.{0} Real (AddMonoidWithOne.toOne.{0} Real (AddCommMonoidWithOne.toAddMonoidWithOne.{0} Real (NonAssocSemiring.toAddCommMonoidWithOne.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))))))) 1 (One.one.{0} (Subtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommMonoid.toPartialOrder.{0} Real (OrderedSemiring.toOrderedAddCommMonoid.{0} Real Real.orderedSemiring))) (Zero.zero.{0} Real (MulZeroClass.toHasZero.{0} Real (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring)))))) (One.one.{0} Real (AddMonoidWithOne.toOne.{0} Real (AddCommMonoidWithOne.toAddMonoidWithOne.{0} Real (NonAssocSemiring.toAddCommMonoidWithOne.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))))))) (Set.Icc.one.{0} Real Real.orderedSemiring))))) b (Eq.trans.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (coeFn.{succ u1, succ u1} (Path.{u1} X _inst_3 a b) (fun (_x : Path.{u1} X _inst_3 a b) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> X) (Path.hasCoeToFun.{u1} X _inst_3 a b) γ (Subtype.mk.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (Iff.mpr (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) True (Iff.trans (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (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))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) True (Set.right_mem_Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) ((fun {α : Type} [_inst_1 : Zero.{0} α] [_inst_2 : One.{0} α] [_inst_3 : LE.{0} α] [_inst_4 : ZeroLEOneClass.{0} α _inst_1 _inst_2 _inst_3] => iff_true_intro (LE.le.{0} α _inst_3 (OfNat.ofNat.{0} α 0 (OfNat.mk.{0} α 0 (Zero.zero.{0} α _inst_1))) (OfNat.ofNat.{0} α 1 (OfNat.mk.{0} α 1 (One.one.{0} α _inst_2)))) (zero_le_one.{0} α _inst_1 _inst_2 _inst_3 _inst_4)) Real Real.hasZero Real.hasOne (Preorder.toHasLe.{0} Real Real.preorder) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring))) True.intro))) (coeFn.{succ u1, succ u1} (Path.{u1} X _inst_3 a b) (fun (_x : Path.{u1} X _inst_3 a b) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> X) (Path.hasCoeToFun.{u1} X _inst_3 a b) γ (OfNat.ofNat.{0} (Subtype.{1} Real (fun (x : Real) => 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(OrderedSemiring.toOrderedAddCommMonoid.{0} Real Real.orderedSemiring))) (Zero.zero.{0} Real (MulZeroClass.toHasZero.{0} Real (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring)))))) (One.one.{0} Real (AddMonoidWithOne.toOne.{0} Real (AddCommMonoidWithOne.toAddMonoidWithOne.{0} Real (NonAssocSemiring.toAddCommMonoidWithOne.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))))))) 1 (One.one.{0} (Subtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommMonoid.toPartialOrder.{0} Real (OrderedSemiring.toOrderedAddCommMonoid.{0} Real Real.orderedSemiring))) (Zero.zero.{0} Real (MulZeroClass.toHasZero.{0} Real (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring)))))) (One.one.{0} Real (AddMonoidWithOne.toOne.{0} Real (AddCommMonoidWithOne.toAddMonoidWithOne.{0} Real (NonAssocSemiring.toAddCommMonoidWithOne.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))))))) (Set.Icc.one.{0} Real Real.orderedSemiring))))) (Path.extend_extends.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (Iff.mpr (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) True (Iff.trans (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (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))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) True (Set.right_mem_Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) ((fun {α : Type} [_inst_1 : Zero.{0} α] [_inst_2 : One.{0} α] [_inst_3 : LE.{0} α] [_inst_4 : ZeroLEOneClass.{0} α _inst_1 _inst_2 _inst_3] => iff_true_intro (LE.le.{0} α _inst_3 (OfNat.ofNat.{0} α 0 (OfNat.mk.{0} α 0 (Zero.zero.{0} α _inst_1))) (OfNat.ofNat.{0} α 1 (OfNat.mk.{0} α 1 (One.one.{0} α _inst_2)))) (zero_le_one.{0} α _inst_1 _inst_2 _inst_3 _inst_4)) Real Real.hasZero Real.hasOne (Preorder.toHasLe.{0} Real Real.preorder) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring))) True.intro)) ((fun [_inst_1 : CoeFun.{succ u1, succ u1} (Path.{u1} X _inst_3 a b) (fun (_x : Path.{u1} X _inst_3 a b) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> X)] (x : Path.{u1} X _inst_3 a b) (x_1 : Path.{u1} X _inst_3 a b) (e_2 : Eq.{succ u1} (Path.{u1} X _inst_3 a b) x x_1) (ᾰ : coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (ᾰ_1 : coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (e_3 : Eq.{1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) ᾰ ᾰ_1) => congr.{1, succ u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X (coeFn.{succ u1, succ u1} (Path.{u1} X _inst_3 a b) (fun (_x : Path.{u1} X _inst_3 a b) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> X) _inst_1 x) (coeFn.{succ u1, succ u1} (Path.{u1} X _inst_3 a b) (fun (_x : Path.{u1} X _inst_3 a b) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> X) _inst_1 x_1) ᾰ ᾰ_1 (congr_arg.{succ u1, succ u1} (Path.{u1} X _inst_3 a b) ((fun (_x : Path.{u1} X _inst_3 a b) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> X) x) x x_1 (coeFn.{succ u1, succ u1} (Path.{u1} X _inst_3 a b) (fun (_x : Path.{u1} X _inst_3 a b) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> X) _inst_1) e_2) e_3) (Path.hasCoeToFun.{u1} X _inst_3 a b) γ γ (rfl.{succ u1} (Path.{u1} X _inst_3 a b) γ) (Subtype.mk.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (Iff.mpr (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) True (Iff.trans (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (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))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) True (Set.right_mem_Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) ((fun {α : Type} [_inst_1 : Zero.{0} α] [_inst_2 : One.{0} α] [_inst_3 : LE.{0} α] [_inst_4 : ZeroLEOneClass.{0} α _inst_1 _inst_2 _inst_3] => iff_true_intro (LE.le.{0} α _inst_3 (OfNat.ofNat.{0} α 0 (OfNat.mk.{0} α 0 (Zero.zero.{0} α _inst_1))) (OfNat.ofNat.{0} α 1 (OfNat.mk.{0} α 1 (One.one.{0} α _inst_2)))) (zero_le_one.{0} α _inst_1 _inst_2 _inst_3 _inst_4)) Real Real.hasZero Real.hasOne (Preorder.toHasLe.{0} Real Real.preorder) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring))) True.intro)) (OfNat.ofNat.{0} (Subtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommMonoid.toPartialOrder.{0} Real (OrderedSemiring.toOrderedAddCommMonoid.{0} Real Real.orderedSemiring))) (Zero.zero.{0} Real (MulZeroClass.toHasZero.{0} Real (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring)))))) (One.one.{0} Real (AddMonoidWithOne.toOne.{0} Real (AddCommMonoidWithOne.toAddMonoidWithOne.{0} Real (NonAssocSemiring.toAddCommMonoidWithOne.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))))))) 1 (OfNat.mk.{0} (Subtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommMonoid.toPartialOrder.{0} Real (OrderedSemiring.toOrderedAddCommMonoid.{0} Real Real.orderedSemiring))) (Zero.zero.{0} Real (MulZeroClass.toHasZero.{0} Real (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring)))))) (One.one.{0} Real (AddMonoidWithOne.toOne.{0} Real (AddCommMonoidWithOne.toAddMonoidWithOne.{0} Real (NonAssocSemiring.toAddCommMonoidWithOne.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))))))) 1 (One.one.{0} (Subtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedAddCommMonoid.toPartialOrder.{0} Real (OrderedSemiring.toOrderedAddCommMonoid.{0} Real Real.orderedSemiring))) (Zero.zero.{0} Real (MulZeroClass.toHasZero.{0} Real (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring)))))) (One.one.{0} Real (AddMonoidWithOne.toOne.{0} Real (AddCommMonoidWithOne.toAddMonoidWithOne.{0} Real (NonAssocSemiring.toAddCommMonoidWithOne.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))))))) (Set.Icc.one.{0} Real Real.orderedSemiring)))) (Set.Icc.mk_one.{0} Real Real.orderedSemiring (Iff.mpr (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) True (Iff.trans (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (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))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) True (Set.right_mem_Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) ((fun {α : Type} [_inst_1 : Zero.{0} α] [_inst_2 : One.{0} α] [_inst_3 : LE.{0} α] [_inst_4 : ZeroLEOneClass.{0} α _inst_1 _inst_2 _inst_3] => iff_true_intro (LE.le.{0} α _inst_3 (OfNat.ofNat.{0} α 0 (OfNat.mk.{0} α 0 (Zero.zero.{0} α _inst_1))) (OfNat.ofNat.{0} α 1 (OfNat.mk.{0} α 1 (One.one.{0} α _inst_2)))) (zero_le_one.{0} α _inst_1 _inst_2 _inst_3 _inst_4)) Real Real.hasZero Real.hasOne (Preorder.toHasLe.{0} Real Real.preorder) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring))) True.intro)))) (Path.target.{u1} X _inst_3 a b γ)) b b (rfl.{succ u1} X b)) (propext (Eq.{succ u1} X b b) True (eq_self_iff_true.{succ u1} X b)))) trivial))
 but is expected to have type
-  forall {X : Type.{u1}} [_inst_3 : TopologicalSpace.{u1} X] {a : X} {b : X} (γ : Path.{u1} X _inst_3 a b), Eq.{succ u1} (Path.{u1} X _inst_3 (Path.extend.{u1} X _inst_3 a b γ (Min.min.{0} Real (LinearOrderedRing.toMin.{0} Real Real.instLinearOrderedRingReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Path.truncate.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (Path.cast.{u1} X _inst_3 a b γ (Path.extend.{u1} X _inst_3 a b γ (Min.min.{0} Real (LinearOrderedRing.toMin.{0} Real Real.instLinearOrderedRingReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (of_eq_true (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (Min.min.{0} Real (LinearOrder.toMin.{0} Real Real.linearOrder) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) a) (Eq.trans.{1} Prop (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (Min.min.{0} Real (LinearOrder.toMin.{0} Real Real.linearOrder) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) a) (Eq.{succ u1} X a a) True (congrFun.{succ u1, 1} X (fun (a._@.Init.Prelude._hyg.170 : X) => Prop) (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (Min.min.{0} Real (LinearOrder.toMin.{0} Real Real.linearOrder) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))) (Eq.{succ u1} X a) (congrArg.{succ u1, succ u1} X (X -> Prop) (Path.extend.{u1} X _inst_3 a b γ (Min.min.{0} Real (LinearOrder.toMin.{0} Real Real.linearOrder) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) a (Eq.{succ u1} X) (Eq.trans.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (Min.min.{0} Real (LinearOrder.toMin.{0} Real Real.linearOrder) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (FunLike.coe.{succ u1, 1, succ u1} (Path.{u1} X _inst_3 a b) (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} (Path.{u1} X _inst_3 a b) (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_3 (Path.continuousMapClass.{u1} X _inst_3 a b)) γ (Subtype.mk.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (of_eq_true (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Eq.trans.{1} Prop (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And True True) True (Eq.trans.{1} Prop (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And True True) (Mathlib.Data.Set.Intervals.Basic._auxLemma.4.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (congr.{1, 1} Prop Prop (And (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (And True) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) True (congrArg.{1, 1} Prop (Prop -> Prop) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) True And (Mathlib.Init.Algebra.Order._auxLemma.1.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (Mathlib.Algebra.Order.ZeroLEOne._auxLemma.1.{0} Real Real.instZeroReal Real.instOneReal (Preorder.toLE.{0} Real Real.instPreorderReal) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring)))) (and_self True))))) a (Eq.trans.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (Min.min.{0} Real (LinearOrder.toMin.{0} Real Real.linearOrder) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (FunLike.coe.{succ u1, 1, succ u1} (Path.{u1} X _inst_3 a b) (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} (Path.{u1} X _inst_3 a b) (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_3 (Path.continuousMapClass.{u1} X _inst_3 a b)) γ (Subtype.mk.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (of_eq_true (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Eq.trans.{1} Prop (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And True True) True (Eq.trans.{1} Prop (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And True True) (Mathlib.Data.Set.Intervals.Basic._auxLemma.4.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (congr.{1, 1} Prop Prop (And (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (And True) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) True (congrArg.{1, 1} Prop (Prop -> Prop) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) True And (Mathlib.Init.Algebra.Order._auxLemma.1.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (Mathlib.Algebra.Order.ZeroLEOne._auxLemma.1.{0} Real Real.instZeroReal Real.instOneReal (Preorder.toLE.{0} Real Real.instPreorderReal) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring)))) (and_self True))))) (congrArg.{1, succ u1} Real X (Min.min.{0} Real (LinearOrder.toMin.{0} Real Real.linearOrder) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Path.extend.{u1} X _inst_3 a b γ) (min_eq_left.{0} Real Real.linearOrder (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (of_eq_true (GE.ge.{0} Real (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (LinearOrder.toPartialOrder.{0} Real Real.linearOrder))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (Eq.trans.{1} Prop (GE.ge.{0} Real (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (LinearOrder.toPartialOrder.{0} Real Real.linearOrder))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (LE.le.{0} Real (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (LinearOrder.toPartialOrder.{0} Real Real.linearOrder))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) True (Mathlib.Order.Basic._auxLemma.3.{0} Real (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (LinearOrder.toPartialOrder.{0} Real Real.linearOrder))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (Mathlib.Algebra.Order.ZeroLEOne._auxLemma.1.{0} Real Real.instZeroReal Real.instOneReal (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (LinearOrder.toPartialOrder.{0} Real Real.linearOrder))) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring)))))) (Path.extend_extends.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (of_eq_true (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Eq.trans.{1} Prop (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And True True) True (Eq.trans.{1} Prop (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And True True) (Mathlib.Data.Set.Intervals.Basic._auxLemma.4.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (congr.{1, 1} Prop Prop (And (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (And True) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) True (congrArg.{1, 1} Prop (Prop -> Prop) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) True And (Mathlib.Init.Algebra.Order._auxLemma.1.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (Mathlib.Algebra.Order.ZeroLEOne._auxLemma.1.{0} Real Real.instZeroReal Real.instOneReal (Preorder.toLE.{0} Real Real.instPreorderReal) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring)))) (and_self True))))) (Path.source.{u1} X _inst_3 a b γ))) a) (eq_self.{succ u1} X a))) (of_eq_true (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) b) (Eq.trans.{1} Prop (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) b) (Eq.{succ u1} X b b) True (congrFun.{succ u1, 1} X (fun (a._@.Init.Prelude._hyg.170 : X) => Prop) (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Eq.{succ u1} X b) (congrArg.{succ u1, succ u1} X (X -> Prop) (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) b (Eq.{succ u1} X) (Eq.trans.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (FunLike.coe.{succ u1, 1, succ u1} (Path.{u1} X _inst_3 a b) (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} (Path.{u1} X _inst_3 a b) (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_3 (Path.continuousMapClass.{u1} X _inst_3 a b)) γ (Subtype.mk.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (of_eq_true (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Eq.trans.{1} Prop (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And True True) True (Eq.trans.{1} Prop (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And True True) (Mathlib.Data.Set.Intervals.Basic._auxLemma.4.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (congr.{1, 1} Prop Prop (And (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And True) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) True (congrArg.{1, 1} Prop (Prop -> Prop) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) True And (Mathlib.Algebra.Order.ZeroLEOne._auxLemma.1.{0} Real Real.instZeroReal Real.instOneReal (Preorder.toLE.{0} Real Real.instPreorderReal) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring))) (Mathlib.Init.Algebra.Order._auxLemma.1.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))) (and_self True))))) b (Path.extend_extends.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (of_eq_true (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Eq.trans.{1} Prop (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And True True) True (Eq.trans.{1} Prop (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And True True) (Mathlib.Data.Set.Intervals.Basic._auxLemma.4.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (congr.{1, 1} Prop Prop (And (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And True) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) True (congrArg.{1, 1} Prop (Prop -> Prop) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) True And (Mathlib.Algebra.Order.ZeroLEOne._auxLemma.1.{0} Real Real.instZeroReal Real.instOneReal (Preorder.toLE.{0} Real Real.instPreorderReal) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring))) (Mathlib.Init.Algebra.Order._auxLemma.1.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))) (and_self True)))) (Path.target.{u1} X _inst_3 a b γ))) b) (eq_self.{succ u1} X b))))
+  forall {X : Type.{u1}} [_inst_3 : TopologicalSpace.{u1} X] {a : X} {b : X} (γ : Path.{u1} X _inst_3 a b), Eq.{succ u1} (Path.{u1} X _inst_3 (Path.extend.{u1} X _inst_3 a b γ (Min.min.{0} Real (LinearOrderedRing.toMin.{0} Real Real.instLinearOrderedRingReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Path.truncate.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (Path.cast.{u1} X _inst_3 a b γ (Path.extend.{u1} X _inst_3 a b γ (Min.min.{0} Real (LinearOrderedRing.toMin.{0} Real Real.instLinearOrderedRingReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (of_eq_true (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (Min.min.{0} Real (LinearOrder.toMin.{0} Real Real.linearOrder) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) a) (Eq.trans.{1} Prop (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (Min.min.{0} Real (LinearOrder.toMin.{0} Real Real.linearOrder) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) a) (Eq.{succ u1} X a a) True (congrFun.{succ u1, 1} X (fun (a._@.Init.Prelude._hyg.170 : X) => Prop) (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (Min.min.{0} Real (LinearOrder.toMin.{0} Real Real.linearOrder) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))) (Eq.{succ u1} X a) (congrArg.{succ u1, succ u1} X (X -> Prop) (Path.extend.{u1} X _inst_3 a b γ (Min.min.{0} Real (LinearOrder.toMin.{0} Real Real.linearOrder) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) a (Eq.{succ u1} X) (Eq.trans.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (Min.min.{0} Real (LinearOrder.toMin.{0} Real Real.linearOrder) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (FunLike.coe.{succ u1, 1, succ u1} (Path.{u1} X _inst_3 a b) (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} (Path.{u1} X _inst_3 a b) (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_3 (Path.continuousMapClass.{u1} X _inst_3 a b)) γ (Subtype.mk.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (of_eq_true (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Eq.trans.{1} Prop (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And True True) True (Eq.trans.{1} Prop (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And True True) (Mathlib.Data.Set.Intervals.Basic._auxLemma.4.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (congr.{1, 1} Prop Prop (And (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (And True) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) True (congrArg.{1, 1} Prop (Prop -> Prop) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) True And (Mathlib.Order.Basic._auxLemma.1.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (Mathlib.Algebra.Order.ZeroLEOne._auxLemma.1.{0} Real Real.instZeroReal Real.instOneReal (Preorder.toLE.{0} Real Real.instPreorderReal) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring)))) (and_self True))))) a (Eq.trans.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (Min.min.{0} Real (LinearOrder.toMin.{0} Real Real.linearOrder) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (FunLike.coe.{succ u1, 1, succ u1} (Path.{u1} X _inst_3 a b) (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} (Path.{u1} X _inst_3 a b) (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_3 (Path.continuousMapClass.{u1} X _inst_3 a b)) γ (Subtype.mk.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (of_eq_true (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Eq.trans.{1} Prop (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And True True) True (Eq.trans.{1} Prop (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And True True) (Mathlib.Data.Set.Intervals.Basic._auxLemma.4.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (congr.{1, 1} Prop Prop (And (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (And True) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) True (congrArg.{1, 1} Prop (Prop -> Prop) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) True And (Mathlib.Order.Basic._auxLemma.1.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (Mathlib.Algebra.Order.ZeroLEOne._auxLemma.1.{0} Real Real.instZeroReal Real.instOneReal (Preorder.toLE.{0} Real Real.instPreorderReal) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring)))) (and_self True))))) (congrArg.{1, succ u1} Real X (Min.min.{0} Real (LinearOrder.toMin.{0} Real Real.linearOrder) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Path.extend.{u1} X _inst_3 a b γ) (min_eq_left.{0} Real Real.linearOrder (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (of_eq_true (GE.ge.{0} Real (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (LinearOrder.toPartialOrder.{0} Real Real.linearOrder))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (Eq.trans.{1} Prop (GE.ge.{0} Real (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (LinearOrder.toPartialOrder.{0} Real Real.linearOrder))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (LE.le.{0} Real (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (LinearOrder.toPartialOrder.{0} Real Real.linearOrder))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) True (Mathlib.Order.Basic._auxLemma.3.{0} Real (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (LinearOrder.toPartialOrder.{0} Real Real.linearOrder))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (Mathlib.Algebra.Order.ZeroLEOne._auxLemma.1.{0} Real Real.instZeroReal Real.instOneReal (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (LinearOrder.toPartialOrder.{0} Real Real.linearOrder))) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring)))))) (Path.extend_extends.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (of_eq_true (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Eq.trans.{1} Prop (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And True True) True (Eq.trans.{1} Prop (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And True True) (Mathlib.Data.Set.Intervals.Basic._auxLemma.4.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (congr.{1, 1} Prop Prop (And (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (And True) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) True (congrArg.{1, 1} Prop (Prop -> Prop) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) True And (Mathlib.Order.Basic._auxLemma.1.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (Mathlib.Algebra.Order.ZeroLEOne._auxLemma.1.{0} Real Real.instZeroReal Real.instOneReal (Preorder.toLE.{0} Real Real.instPreorderReal) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring)))) (and_self True))))) (Path.source.{u1} X _inst_3 a b γ))) a) (eq_self.{succ u1} X a))) (of_eq_true (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) b) (Eq.trans.{1} Prop (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) b) (Eq.{succ u1} X b b) True (congrFun.{succ u1, 1} X (fun (a._@.Init.Prelude._hyg.170 : X) => Prop) (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Eq.{succ u1} X b) (congrArg.{succ u1, succ u1} X (X -> Prop) (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) b (Eq.{succ u1} X) (Eq.trans.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (FunLike.coe.{succ u1, 1, succ u1} (Path.{u1} X _inst_3 a b) (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} (Path.{u1} X _inst_3 a b) (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_3 (Path.continuousMapClass.{u1} X _inst_3 a b)) γ (Subtype.mk.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (of_eq_true (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Eq.trans.{1} Prop (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And True True) True (Eq.trans.{1} Prop (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And True True) (Mathlib.Data.Set.Intervals.Basic._auxLemma.4.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (congr.{1, 1} Prop Prop (And (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And True) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) True (congrArg.{1, 1} Prop (Prop -> Prop) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) True And (Mathlib.Algebra.Order.ZeroLEOne._auxLemma.1.{0} Real Real.instZeroReal Real.instOneReal (Preorder.toLE.{0} Real Real.instPreorderReal) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring))) (Mathlib.Order.Basic._auxLemma.1.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))) (and_self True))))) b (Path.extend_extends.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (of_eq_true (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Eq.trans.{1} Prop (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And True True) True (Eq.trans.{1} Prop (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And True True) (Mathlib.Data.Set.Intervals.Basic._auxLemma.4.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (congr.{1, 1} Prop Prop (And (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And True) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) True (congrArg.{1, 1} Prop (Prop -> Prop) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) True And (Mathlib.Algebra.Order.ZeroLEOne._auxLemma.1.{0} Real Real.instZeroReal Real.instOneReal (Preorder.toLE.{0} Real Real.instPreorderReal) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring))) (Mathlib.Order.Basic._auxLemma.1.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))) (and_self True)))) (Path.target.{u1} X _inst_3 a b γ))) b) (eq_self.{succ u1} X b))))
 Case conversion may be inaccurate. Consider using '#align path.truncate_zero_one Path.truncate_zero_oneₓ'. -/
 @[simp]
 theorem truncate_zero_one {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) :

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

@@ -445,7 +445,7 @@ def trans (γ : Path x y) (γ' : Path y z) : Path x z
 lean 3 declaration is
   forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x : X} {y : X} {z : X} (γ : Path.{u1} X _inst_1 x y) (γ' : Path.{u1} X _inst_1 y z) (t : coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval), Eq.{succ u1} X (coeFn.{succ u1, succ u1} (Path.{u1} X _inst_1 x z) (fun (_x : Path.{u1} X _inst_1 x z) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> X) (Path.hasCoeToFun.{u1} X _inst_1 x z) (Path.trans.{u1} X _inst_1 x y z γ γ') t) (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))))) t) (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)))))) (Real.decidableLE ((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))))) t) (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 (h : 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))))) t) (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)))))) => coeFn.{succ u1, succ u1} (Path.{u1} X _inst_1 x y) (fun (_x : Path.{u1} X _inst_1 x y) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> X) (Path.hasCoeToFun.{u1} X _inst_1 x y) γ (Subtype.mk.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (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) unitInterval) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval))))) t)) (Iff.mpr (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) (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 (AddZeroClass.toHasAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddMonoidWithOne.toAddMonoid.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (AddCommGroupWithOne.toAddGroupWithOne.{0} Real (Ring.toAddCommGroupWithOne.{0} Real Real.ring)))))) (One.one.{0} Real (AddMonoidWithOne.toOne.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (AddCommGroupWithOne.toAddGroupWithOne.{0} Real (Ring.toAddCommGroupWithOne.{0} Real Real.ring)))))))) ((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))))) t)) unitInterval) (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) ((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))))) t) (Set.Icc.{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 (AddZeroClass.toHasAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddMonoidWithOne.toAddMonoid.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (AddCommGroupWithOne.toAddGroupWithOne.{0} Real (Ring.toAddCommGroupWithOne.{0} Real Real.ring)))))) (One.one.{0} Real (AddMonoidWithOne.toOne.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (AddCommGroupWithOne.toAddGroupWithOne.{0} Real (Ring.toAddCommGroupWithOne.{0} Real Real.ring))))))))))) (unitInterval.mul_pos_mem_iff (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real (AddZeroClass.toHasAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddMonoidWithOne.toAddMonoid.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (AddCommGroupWithOne.toAddGroupWithOne.{0} Real (Ring.toAddCommGroupWithOne.{0} Real Real.ring)))))) (One.one.{0} Real (AddMonoidWithOne.toOne.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (AddCommGroupWithOne.toAddGroupWithOne.{0} Real (Ring.toAddCommGroupWithOne.{0} Real Real.ring)))))))) ((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))))) t) (zero_lt_two.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (AddCommGroupWithOne.toAddGroupWithOne.{0} Real (Ring.toAddCommGroupWithOne.{0} Real Real.ring))) Real.partialOrder (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring) (NeZero.one.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) Real.nontrivial) (OrderedAddCommGroup.to_covariantClass_left_le.{0} Real Real.orderedAddCommGroup))) (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))) ((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))))) t)) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.preorder) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeBase.{1, 1} (coeSort.{1, 2} 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(DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) (LT.lt.{0} Real (Preorder.toLT.{0} Real (PartialOrder.toPreorder.{0} Real (LinearOrder.toPartialOrder.{0} Real Real.linearOrder))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} 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(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) t)) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.preorder) (Subtype.val.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) t) (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) t)))))))
 but is expected to have type
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γ') t) (dite.{succ u1} X (LE.le.{0} Real Real.instLEReal (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) t) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (Real.decidableLE (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) t) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (fun (h : LE.le.{0} Real Real.instLEReal (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) t) (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.{u1} X _inst_1 x y) (Set.Elem.{0} Real unitInterval) (fun (_x : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) _x) (ContinuousMapClass.toFunLike.{u1, 0, u1} (Path.{u1} X _inst_1 x y) (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.continuousMapClass.{u1} X _inst_1 x y)) γ (Subtype.mk.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 (AddMonoidWithOne.toNatCast.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) t)) (Iff.mpr (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 (AddMonoidWithOne.toNatCast.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) t)) 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) t) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 (AddMonoidWithOne.toNatCast.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (unitInterval.mul_pos_mem_iff (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 (AddMonoidWithOne.toNatCast.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) t) (zero_lt_two.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal)) Real.partialOrder (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring) (NeZero.one.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) Real.nontrivial) (OrderedAddCommGroup.to_covariantClass_left_le.{0} Real Real.orderedAddCommGroup))) (And.intro (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) t)) (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) t) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 (AddMonoidWithOne.toNatCast.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (And.left (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) t)) (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) t) (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) t)) h)))) (fun (h : Not (LE.le.{0} Real Real.instLEReal (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) t) (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.{u1} X _inst_1 y z) (Set.Elem.{0} Real unitInterval) (fun (_x : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) _x) (ContinuousMapClass.toFunLike.{u1, 0, u1} (Path.{u1} X _inst_1 y z) (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.continuousMapClass.{u1} X _inst_1 y z)) γ' (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) t)) (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) t)) (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) t) (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) t)) (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) t)) (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) t) (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) t) (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) t) (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) t)) (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) t) (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) t)) (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) t) (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) t)))))))
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x : X} {y : X} {z : X} (γ : Path.{u1} X _inst_1 x y) (γ' : Path.{u1} X _inst_1 y z) (t : Set.Elem.{0} Real unitInterval), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) t) (FunLike.coe.{succ u1, 1, succ u1} (Path.{u1} X _inst_1 x z) (Set.Elem.{0} Real unitInterval) (fun (_x : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) _x) (ContinuousMapClass.toFunLike.{u1, 0, u1} (Path.{u1} X _inst_1 x z) (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.continuousMapClass.{u1} X _inst_1 x z)) (Path.trans.{u1} X _inst_1 x y z γ γ') t) (dite.{succ u1} X (LE.le.{0} Real Real.instLEReal (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) t) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (Real.decidableLE (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) t) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (fun (h : LE.le.{0} Real Real.instLEReal (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) t) (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.{u1} X _inst_1 x y) (Set.Elem.{0} Real unitInterval) (fun (_x : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) _x) (ContinuousMapClass.toFunLike.{u1, 0, u1} (Path.{u1} X _inst_1 x y) (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.continuousMapClass.{u1} X _inst_1 x y)) γ (Subtype.mk.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 (AddMonoidWithOne.toNatCast.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) t)) (Iff.mpr (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 (AddMonoidWithOne.toNatCast.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) t)) 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) t) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 (AddMonoidWithOne.toNatCast.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (unitInterval.mul_pos_mem_iff (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 (AddMonoidWithOne.toNatCast.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) t) (zero_lt_two.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal)) Real.partialOrder (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring) (NeZero.one.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Real.nontrivial) (OrderedAddCommGroup.to_covariantClass_left_le.{0} Real Real.orderedAddCommGroup))) (And.intro (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) t)) (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) t) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 (AddMonoidWithOne.toNatCast.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat 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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.{u1} X _inst_1 y z) (Set.Elem.{0} Real unitInterval) (fun (_x : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) _x) (ContinuousMapClass.toFunLike.{u1, 0, u1} (Path.{u1} X _inst_1 y z) (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.continuousMapClass.{u1} X _inst_1 y z)) γ' (Subtype.mk.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} 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(Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) t)) (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) t) (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) t)) (And.intro 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(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) t)) (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) t) (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) t)) (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) t) (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) t)))))))
 Case conversion may be inaccurate. Consider using '#align path.trans_apply Path.trans_applyₓ'. -/
 theorem trans_apply (γ : Path x y) (γ' : Path y z) (t : I) :
     (γ.trans γ') t =

mathlib commit https://github.com/leanprover-community/mathlib/commit/e05ead7993520a432bec94ac504842d90707ad63

@@ -877,18 +877,18 @@ def truncate {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) (t₀ t
     · rfl
 #align path.truncate Path.truncate
 
-/- warning: path.truncate_of_le -> Path.truncateOfLe is a dubious translation:
+/- warning: path.truncate_of_le -> Path.truncateOfLE is a dubious translation:
 lean 3 declaration is
   forall {X : Type.{u1}} [_inst_3 : TopologicalSpace.{u1} X] {a : X} {b : X} (γ : Path.{u1} X _inst_3 a b) {t₀ : Real} {t₁ : Real}, (LE.le.{0} Real Real.hasLe t₀ t₁) -> (Path.{u1} X _inst_3 (Path.extend.{u1} X _inst_3 a b γ t₀) (Path.extend.{u1} X _inst_3 a b γ t₁))
 but is expected to have type
   forall {X : Type.{u1}} [_inst_3 : TopologicalSpace.{u1} X] {a : X} {b : X} (γ : Path.{u1} X _inst_3 a b) {t₀ : Real} {t₁ : Real}, (LE.le.{0} Real Real.instLEReal t₀ t₁) -> (Path.{u1} X _inst_3 (Path.extend.{u1} X _inst_3 a b γ t₀) (Path.extend.{u1} X _inst_3 a b γ t₁))
-Case conversion may be inaccurate. Consider using '#align path.truncate_of_le Path.truncateOfLeₓ'. -/
+Case conversion may be inaccurate. Consider using '#align path.truncate_of_le Path.truncateOfLEₓ'. -/
 /-- `γ.truncate_of_le t₀ t₁ h`, where `h : t₀ ≤ t₁` is `γ.truncate t₀ t₁`
   casted as a path from `γ.extend t₀` to `γ.extend t₁`. -/
-def truncateOfLe {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) {t₀ t₁ : ℝ}
+def truncateOfLE {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) {t₀ t₁ : ℝ}
     (h : t₀ ≤ t₁) : Path (γ.extend t₀) (γ.extend t₁) :=
   (γ.truncate t₀ t₁).cast (by rw [min_eq_left h]) rfl
-#align path.truncate_of_le Path.truncateOfLe
+#align path.truncate_of_le Path.truncateOfLE
 
 #print Path.truncate_range /-
 theorem truncate_range {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) {t₀ t₁ : ℝ} :

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

@@ -443,7 +443,7 @@ def trans (γ : Path x y) (γ' : Path y z) : Path x z
 
 /- warning: path.trans_apply -> Path.trans_apply is a dubious translation:
 lean 3 declaration is
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(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) t)) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.preorder) (Subtype.val.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) t) (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) t)))))))
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x : X} {y : X} {z : X} (γ : Path.{u1} X _inst_1 x y) (γ' : Path.{u1} X _inst_1 y z) (t : coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval), Eq.{succ u1} X (coeFn.{succ u1, succ u1} (Path.{u1} X _inst_1 x z) (fun (_x : Path.{u1} X _inst_1 x z) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> X) (Path.hasCoeToFun.{u1} X _inst_1 x z) (Path.trans.{u1} X _inst_1 x y z γ γ') t) (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))))) t) (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)))))) (Real.decidableLE ((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))))) t) (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 (h : 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))))) t) (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)))))) => coeFn.{succ u1, succ u1} (Path.{u1} X _inst_1 x y) (fun (_x : Path.{u1} X _inst_1 x y) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> X) (Path.hasCoeToFun.{u1} X _inst_1 x y) γ (Subtype.mk.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (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) 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(One.one.{0} Real (AddMonoidWithOne.toOne.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (AddCommGroupWithOne.toAddGroupWithOne.{0} Real (Ring.toAddCommGroupWithOne.{0} Real Real.ring))))))))))) (unitInterval.mul_pos_mem_iff (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real (AddZeroClass.toHasAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddMonoidWithOne.toAddMonoid.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (AddCommGroupWithOne.toAddGroupWithOne.{0} Real (Ring.toAddCommGroupWithOne.{0} Real Real.ring)))))) (One.one.{0} Real (AddMonoidWithOne.toOne.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (AddCommGroupWithOne.toAddGroupWithOne.{0} Real (Ring.toAddCommGroupWithOne.{0} Real Real.ring)))))))) ((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))))) t) (zero_lt_two.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (AddCommGroupWithOne.toAddGroupWithOne.{0} Real (Ring.toAddCommGroupWithOne.{0} Real Real.ring))) Real.partialOrder (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring) (NeZero.one.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) Real.nontrivial) (OrderedAddCommGroup.to_covariantClass_left_le.{0} Real Real.orderedAddCommGroup))) (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))) ((fun (a : Type) (b : Type) 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(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))))) t) (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 (AddZeroClass.toHasAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddMonoidWithOne.toAddMonoid.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (AddCommGroupWithOne.toAddGroupWithOne.{0} Real (Ring.toAddCommGroupWithOne.{0} Real Real.ring)))))) (One.one.{0} Real (AddMonoidWithOne.toOne.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (AddCommGroupWithOne.toAddGroupWithOne.{0} Real (Ring.toAddCommGroupWithOne.{0} Real Real.ring)))))))))) (And.left (LE.le.{0} Real (Preorder.toLE.{0} Real Real.preorder) 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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))))) t) (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))))))) => coeFn.{succ u1, succ u1} (Path.{u1} X _inst_1 y z) (fun (_x : Path.{u1} X _inst_1 y z) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> X) (Path.hasCoeToFun.{u1} X _inst_1 y z) γ' (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 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(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))))) t)) (And.intro (LE.le.{0} Real (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))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} 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unitInterval) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval))))) t) (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 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(DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) (LT.lt.{0} Real (Preorder.toLT.{0} Real (PartialOrder.toPreorder.{0} Real (LinearOrder.toPartialOrder.{0} Real Real.linearOrder))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} 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(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) t)) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.preorder) (Subtype.val.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) t) (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) t)))))))
 but is expected to have type
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γ') t) (dite.{succ u1} X (LE.le.{0} Real Real.instLEReal (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) t) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (Real.decidableLE (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) t) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (fun (h : LE.le.{0} Real Real.instLEReal (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) t) (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.{u1} X _inst_1 x y) (Set.Elem.{0} Real unitInterval) (fun (_x : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) _x) (ContinuousMapClass.toFunLike.{u1, 0, u1} (Path.{u1} X _inst_1 x y) (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.continuousMapClass.{u1} X _inst_1 x y)) γ (Subtype.mk.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 (AddMonoidWithOne.toNatCast.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) t)) (Iff.mpr (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 (AddMonoidWithOne.toNatCast.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) t)) 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) t) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 (AddMonoidWithOne.toNatCast.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (unitInterval.mul_pos_mem_iff (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 (AddMonoidWithOne.toNatCast.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) t) (zero_lt_two.{0} Real (AddGroupWithOne.toAddMonoidWithOne.{0} Real (Ring.toAddGroupWithOne.{0} Real Real.instRingReal)) Real.partialOrder (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring) (NeZero.one.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} 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(instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (And.left (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) t)) (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) t) (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) t)) h)))) (fun (h : Not (LE.le.{0} Real Real.instLEReal (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) t) (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.{u1} X _inst_1 y z) (Set.Elem.{0} Real unitInterval) (fun (_x : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) _x) (ContinuousMapClass.toFunLike.{u1, 0, u1} (Path.{u1} X _inst_1 y z) (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.continuousMapClass.{u1} X _inst_1 y z)) γ' (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) t)) (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) t)) (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) t) (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) t)) (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) t)) (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) t) (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) t) (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) t) (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) t)) (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) t) (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) t)) (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) t) (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) t)))))))
 Case conversion may be inaccurate. Consider using '#align path.trans_apply Path.trans_applyₓ'. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/d11893b411025250c8e61ff2f12ccbd7ee35ab15

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Patrick Massot
 
 ! This file was ported from Lean 3 source module topology.path_connected
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 97eab48559068f3d6313da387714ef25768fb730
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.Topology.UnitInterval
 /-!
 # Path connectedness
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 ## Main definitions
 
 In the file the unit interval `[0, 1]` in `ℝ` is denoted by `I`, and `X` is a topological space.

mathlib commit https://github.com/leanprover-community/mathlib/commit/57e09a1296bfb4330ddf6624f1028ba186117d82

@@ -76,64 +76,87 @@ variable {X Y : Type _} [TopologicalSpace X] [TopologicalSpace Y] {x y z : X} {
 /-! ### Paths -/
 
 
+#print Path /-
 /-- Continuous path connecting two points `x` and `y` in a topological space -/
 @[nolint has_nonempty_instance]
 structure Path (x y : X) extends C(I, X) where
   source' : to_fun 0 = x
   target' : to_fun 1 = y
 #align path Path
+-/
 
 instance : CoeFun (Path x y) fun _ => I → X :=
   ⟨fun p => p.toFun⟩
 
+#print Path.ext /-
 @[ext]
 protected theorem Path.ext : ∀ {γ₁ γ₂ : Path x y}, (γ₁ : I → X) = γ₂ → γ₁ = γ₂
   | ⟨⟨x, h11⟩, h12, h13⟩, ⟨⟨x, h21⟩, h22, h23⟩, rfl => rfl
 #align path.ext Path.ext
+-/
 
 namespace Path
 
+#print Path.coe_mk_mk /-
 @[simp]
-theorem coe_mk (f : I → X) (h₁ h₂ h₃) : ⇑(mk ⟨f, h₁⟩ h₂ h₃ : Path x y) = f :=
+theorem coe_mk_mk (f : I → X) (h₁ h₂ h₃) : ⇑(mk ⟨f, h₁⟩ h₂ h₃ : Path x y) = f :=
   rfl
-#align path.coe_mk Path.coe_mk
+#align path.coe_mk Path.coe_mk_mk
+-/
 
 variable (γ : Path x y)
 
+#print Path.continuous /-
 @[continuity]
 protected theorem continuous : Continuous γ :=
   γ.continuous_toFun
 #align path.continuous Path.continuous
+-/
 
+#print Path.source /-
 @[simp]
 protected theorem source : γ 0 = x :=
   γ.source'
 #align path.source Path.source
+-/
 
+#print Path.target /-
 @[simp]
 protected theorem target : γ 1 = y :=
   γ.target'
 #align path.target Path.target
+-/
 
+#print Path.simps.apply /-
 /-- See Note [custom simps projection]. We need to specify this projection explicitly in this case,
 because it is a composition of multiple projections. -/
-def Simps.apply : I → X :=
+def simps.apply : I → X :=
   γ
-#align path.simps.apply Path.Simps.apply
+#align path.simps.apply Path.simps.apply
+-/
 
 initialize_simps_projections Path (to_continuous_map_to_fun → simps.apply, -toContinuousMap)
 
+/- warning: path.coe_to_continuous_map -> Path.coe_toContinuousMap is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x : X} {y : X} (γ : Path.{u1} X _inst_1 x y), Eq.{succ u1} ((coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> X) (coeFn.{succ u1, succ u1} (ContinuousMap.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) (fun (_x : ContinuousMap.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> X) (ContinuousMap.hasCoeToFun.{0, u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_1) (Path.toContinuousMap.{u1} X _inst_1 x y γ)) (coeFn.{succ u1, succ u1} (Path.{u1} X _inst_1 x y) (fun (_x : Path.{u1} X _inst_1 x y) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> X) (Path.hasCoeToFun.{u1} X _inst_1 x y) γ)
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x : X} {y : X} (γ : Path.{u1} X _inst_1 x y), Eq.{succ u1} (forall (ᾰ : Set.Elem.{0} Real unitInterval), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) ᾰ) (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 (_x : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) _x) (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 x y γ)) (FunLike.coe.{succ u1, 1, succ u1} (Path.{u1} X _inst_1 x y) (Set.Elem.{0} Real unitInterval) (fun (_x : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) _x) (ContinuousMapClass.toFunLike.{u1, 0, u1} (Path.{u1} X _inst_1 x y) (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.continuousMapClass.{u1} X _inst_1 x y)) γ)
+Case conversion may be inaccurate. Consider using '#align path.coe_to_continuous_map Path.coe_toContinuousMapₓ'. -/
 @[simp]
 theorem coe_toContinuousMap : ⇑γ.toContinuousMap = γ :=
   rfl
 #align path.coe_to_continuous_map Path.coe_toContinuousMap
 
+#print Path.hasUncurryPath /-
 /-- Any function `φ : Π (a : α), path (x a) (y a)` can be seen as a function `α × I → X`. -/
 instance hasUncurryPath {X α : Type _} [TopologicalSpace X] {x y : α → X} :
     HasUncurry (∀ a : α, Path (x a) (y a)) (α × I) X :=
   ⟨fun φ p => φ p.1 p.2⟩
 #align path.has_uncurry_path Path.hasUncurryPath
+-/
 
+#print Path.refl /-
 /-- The constant path from a point to itself -/
 @[refl, simps]
 def refl (x : X) : Path x x where
@@ -142,11 +165,15 @@ def refl (x : X) : Path x x where
   source' := rfl
   target' := rfl
 #align path.refl Path.refl
+-/
 
+#print Path.refl_range /-
 @[simp]
 theorem refl_range {a : X} : range (Path.refl a) = {a} := by simp [Path.refl, CoeFun.coe, coeFn]
 #align path.refl_range Path.refl_range
+-/
 
+#print Path.symm /-
 /-- The reverse of a path from `x` to `y`, as a path from `y` to `x` -/
 @[symm, simps]
 def symm (γ : Path x y) : Path y x where
@@ -155,21 +182,27 @@ def symm (γ : Path x y) : Path y x where
   source' := by simpa [-Path.target] using γ.target
   target' := by simpa [-Path.source] using γ.source
 #align path.symm Path.symm
+-/
 
+#print Path.symm_symm /-
 @[simp]
 theorem symm_symm {γ : Path x y} : γ.symm.symm = γ :=
   by
   ext
   simp
 #align path.symm_symm Path.symm_symm
+-/
 
+#print Path.refl_symm /-
 @[simp]
 theorem refl_symm {a : X} : (Path.refl a).symm = Path.refl a :=
   by
   ext
   rfl
 #align path.refl_symm Path.refl_symm
+-/
 
+#print Path.symm_range /-
 @[simp]
 theorem symm_range {a b : X} (γ : Path a b) : range γ.symm = range γ :=
   by
@@ -180,6 +213,7 @@ theorem symm_range {a b : X} (γ : Path a b) : range γ.symm = range γ :=
     convert hxy
   simp
 #align path.symm_range Path.symm_range
+-/
 
 /-! #### Space of paths -/
 
@@ -195,16 +229,30 @@ compact-open topology on the space `C(I,X)` of continuous maps from `I` to `X`.
 instance : TopologicalSpace (Path x y) :=
   TopologicalSpace.induced (coe : _ → C(I, X)) ContinuousMap.compactOpen
 
+/- warning: path.continuous_eval -> Path.continuous_eval is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x : X} {y : X}, Continuous.{u1, u1} (Prod.{u1, 0} (Path.{u1} X _inst_1 x y) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)) X (Prod.topologicalSpace.{u1, 0} (Path.{u1} X _inst_1 x y) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (Path.topologicalSpace.{u1} X _inst_1 x y) (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)))) _inst_1 (fun (p : Prod.{u1, 0} (Path.{u1} X _inst_1 x y) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)) => coeFn.{succ u1, succ u1} (Path.{u1} X _inst_1 x y) (fun (_x : Path.{u1} X _inst_1 x y) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> X) (Path.hasCoeToFun.{u1} X _inst_1 x y) (Prod.fst.{u1, 0} (Path.{u1} X _inst_1 x y) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) p) (Prod.snd.{u1, 0} (Path.{u1} X _inst_1 x y) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) p))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x : X} {y : X}, Continuous.{u1, u1} (Prod.{u1, 0} (Path.{u1} X _inst_1 x y) (Set.Elem.{0} Real unitInterval)) X (instTopologicalSpaceProd.{u1, 0} (Path.{u1} X _inst_1 x y) (Set.Elem.{0} Real unitInterval) (Path.topologicalSpace.{u1} X _inst_1 x y) (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 (fun (p : Prod.{u1, 0} (Path.{u1} X _inst_1 x y) (Set.Elem.{0} Real unitInterval)) => FunLike.coe.{succ u1, 1, succ u1} (Path.{u1} X _inst_1 x y) (Set.Elem.{0} Real unitInterval) (fun (_x : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) _x) (ContinuousMapClass.toFunLike.{u1, 0, u1} (Path.{u1} X _inst_1 x y) (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.continuousMapClass.{u1} X _inst_1 x y)) (Prod.fst.{u1, 0} (Path.{u1} X _inst_1 x y) (Set.Elem.{0} Real unitInterval) p) (Prod.snd.{u1, 0} (Path.{u1} X _inst_1 x y) (Set.Elem.{0} Real unitInterval) p))
+Case conversion may be inaccurate. Consider using '#align path.continuous_eval Path.continuous_evalₓ'. -/
 theorem continuous_eval : Continuous fun p : Path x y × I => p.1 p.2 :=
   continuous_eval'.comp <| continuous_induced_dom.Prod_map continuous_id
 #align path.continuous_eval Path.continuous_eval
 
+#print Continuous.path_eval /-
 @[continuity]
 theorem Continuous.path_eval {Y} [TopologicalSpace Y] {f : Y → Path x y} {g : Y → I}
     (hf : Continuous f) (hg : Continuous g) : Continuous fun y => f y (g y) :=
   Continuous.comp continuous_eval (hf.prod_mk hg)
 #align continuous.path_eval Continuous.path_eval
+-/
 
+/- warning: path.continuous_uncurry_iff -> Path.continuous_uncurry_iff is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x : X} {y : X} {Y : Type.{u2}} [_inst_3 : TopologicalSpace.{u2} Y] {g : Y -> (Path.{u1} X _inst_1 x y)}, Iff (Continuous.{u2, u1} (Prod.{u2, 0} Y (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)) X (Prod.topologicalSpace.{u2, 0} Y (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) _inst_3 (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)))) _inst_1 (Function.HasUncurry.uncurry.{max u2 u1, u2, u1} (Y -> (Path.{u1} X _inst_1 x y)) (Prod.{u2, 0} Y (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)) X (Path.hasUncurryPath.{u1, u2} X Y _inst_1 (fun (ᾰ : Y) => x) (fun (ᾰ : Y) => y)) g)) (Continuous.{u2, u1} Y (Path.{u1} X _inst_1 x y) _inst_3 (Path.topologicalSpace.{u1} X _inst_1 x y) g)
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x : X} {y : X} {Y : Type.{u2}} [_inst_3 : TopologicalSpace.{u2} Y] {g : Y -> (Path.{u1} X _inst_1 x y)}, Iff (Continuous.{u2, u1} (Prod.{u2, 0} Y (Set.Elem.{0} Real unitInterval)) X (instTopologicalSpaceProd.{u2, 0} Y (Set.Elem.{0} Real unitInterval) _inst_3 (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 (Function.HasUncurry.uncurry.{max u1 u2, u2, u1} (Y -> (Path.{u1} X _inst_1 x y)) (Prod.{u2, 0} Y (Set.Elem.{0} Real unitInterval)) X (Path.hasUncurryPath.{u1, u2} X Y _inst_1 (fun (ᾰ : Y) => x) (fun (ᾰ : Y) => y)) g)) (Continuous.{u2, u1} Y (Path.{u1} X _inst_1 x y) _inst_3 (Path.topologicalSpace.{u1} X _inst_1 x y) g)
+Case conversion may be inaccurate. Consider using '#align path.continuous_uncurry_iff Path.continuous_uncurry_iffₓ'. -/
 theorem continuous_uncurry_iff {Y} [TopologicalSpace Y] {g : Y → Path x y} :
     Continuous ↿g ↔ Continuous g :=
   Iff.symm <|
@@ -212,23 +260,39 @@ theorem continuous_uncurry_iff {Y} [TopologicalSpace Y] {g : Y → Path x y} :
       ⟨fun h => continuous_uncurry_of_continuous ⟨_, h⟩, continuous_of_continuous_uncurry ↑g⟩
 #align path.continuous_uncurry_iff Path.continuous_uncurry_iff
 
+#print Path.extend /-
 /-- A continuous map extending a path to `ℝ`, constant before `0` and after `1`. -/
 def extend : ℝ → X :=
   IccExtend zero_le_one γ
 #align path.extend Path.extend
+-/
 
+/- warning: continuous.path_extend -> Continuous.path_extend is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {x : X} {y : X} {γ : Y -> (Path.{u1} X _inst_1 x y)} {f : Y -> Real}, (Continuous.{u2, u1} (Prod.{u2, 0} Y (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)) X (Prod.topologicalSpace.{u2, 0} Y (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) _inst_2 (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)))) _inst_1 (Function.HasUncurry.uncurry.{max u2 u1, u2, u1} (Y -> (Path.{u1} X _inst_1 x y)) (Prod.{u2, 0} Y (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)) X (Path.hasUncurryPath.{u1, u2} X Y _inst_1 (fun (ᾰ : Y) => x) (fun (ᾰ : Y) => y)) γ)) -> (Continuous.{u2, 0} Y Real _inst_2 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f) -> (Continuous.{u2, u1} Y X _inst_2 _inst_1 (fun (t : Y) => Path.extend.{u1} X _inst_1 x y (γ t) (f t)))
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : TopologicalSpace.{u1} Y] {x : X} {y : X} {γ : Y -> (Path.{u2} X _inst_1 x y)} {f : Y -> Real}, (Continuous.{u1, u2} (Prod.{u1, 0} Y (Set.Elem.{0} Real unitInterval)) X (instTopologicalSpaceProd.{u1, 0} Y (Set.Elem.{0} Real unitInterval) _inst_2 (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 (Function.HasUncurry.uncurry.{max u2 u1, u1, u2} (Y -> (Path.{u2} X _inst_1 x y)) (Prod.{u1, 0} Y (Set.Elem.{0} Real unitInterval)) X (Path.hasUncurryPath.{u2, u1} X Y _inst_1 (fun (ᾰ : Y) => x) (fun (ᾰ : Y) => y)) γ)) -> (Continuous.{u1, 0} Y Real _inst_2 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f) -> (Continuous.{u1, u2} Y X _inst_2 _inst_1 (fun (t : Y) => Path.extend.{u2} X _inst_1 x y (γ t) (f t)))
+Case conversion may be inaccurate. Consider using '#align continuous.path_extend Continuous.path_extendₓ'. -/
 /-- See Note [continuity lemma statement]. -/
 theorem Continuous.path_extend {γ : Y → Path x y} {f : Y → ℝ} (hγ : Continuous ↿γ)
     (hf : Continuous f) : Continuous fun t => (γ t).extend (f t) :=
   Continuous.IccExtend hγ hf
 #align continuous.path_extend Continuous.path_extend
 
+#print Path.continuous_extend /-
 /-- A useful special case of `continuous.path_extend`. -/
 @[continuity]
 theorem continuous_extend : Continuous γ.extend :=
   γ.Continuous.Icc_extend'
 #align path.continuous_extend Path.continuous_extend
+-/
 
+/- warning: filter.tendsto.path_extend -> Filter.Tendsto.path_extend 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] {l : Y -> X} {r : Y -> X} {y : Y} {l₁ : Filter.{0} Real} {l₂ : Filter.{u1} X} {γ : forall (y : Y), Path.{u1} X _inst_3 (l y) (r y)}, (Filter.Tendsto.{u2, u1} (Prod.{u2, 0} Y (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))) X (Function.HasUncurry.uncurry.{max u2 u1, u2, u1} (forall (y : Y), Path.{u1} X _inst_3 (l y) (r y)) (Prod.{u2, 0} Y (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))) X (Path.hasUncurryPath.{u1, u2} X Y _inst_3 (fun (y : Y) => l y) (fun (y : Y) => r y)) γ) (Filter.prod.{u2, 0} Y (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (nhds.{u2} Y _inst_4 y) (Filter.map.{0, 0} Real (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Set.projIcc.{0} Real Real.linearOrder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (zero_le_one.{0} Real Real.hasZero Real.hasOne (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder))))) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring))) l₁)) l₂) -> (Filter.Tendsto.{u2, u1} (Prod.{u2, 0} Y Real) X (Function.HasUncurry.uncurry.{max u2 u1, u2, u1} (Y -> Real -> X) (Prod.{u2, 0} Y Real) X (Function.hasUncurryInduction.{u2, u1, 0, u1} Y (Real -> X) Real X (Function.hasUncurryBase.{0, u1} Real X)) (fun (x : Y) => Path.extend.{u1} X _inst_3 (l x) (r x) (γ x))) (Filter.prod.{u2, 0} Y Real (nhds.{u2} Y _inst_4 y) l₁) l₂)
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_3 : TopologicalSpace.{u2} X] [_inst_4 : TopologicalSpace.{u1} Y] {l : Y -> X} {r : Y -> X} {y : Y} {l₁ : Filter.{0} Real} {l₂ : Filter.{u2} X} {γ : forall (y : Y), Path.{u2} X _inst_3 (l y) (r y)}, (Filter.Tendsto.{u1, u2} (Prod.{u1, 0} Y (Set.Elem.{0} Real unitInterval)) X (Function.HasUncurry.uncurry.{max u2 u1, u1, u2} (forall (y : Y), Path.{u2} X _inst_3 (l y) (r y)) (Prod.{u1, 0} Y (Set.Elem.{0} Real unitInterval)) X (Path.hasUncurryPath.{u2, u1} X Y _inst_3 (fun (y : Y) => l y) (fun (y : Y) => r y)) γ) (Filter.prod.{u1, 0} Y (Set.Elem.{0} Real unitInterval) (nhds.{u1} Y _inst_4 y) (Filter.map.{0, 0} Real (Set.Elem.{0} Real unitInterval) (Set.projIcc.{0} Real Real.linearOrder (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (zero_le_one.{0} Real Real.instZeroReal Real.instOneReal (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (DistribLattice.toLattice.{0} Real (instDistribLattice.{0} Real Real.linearOrder)))))) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring))) l₁)) l₂) -> (Filter.Tendsto.{u1, u2} (Prod.{u1, 0} Y Real) X (Function.HasUncurry.uncurry.{max u2 u1, u1, u2} (Y -> Real -> X) (Prod.{u1, 0} Y Real) X (Function.hasUncurryInduction.{u1, u2, 0, u2} Y (Real -> X) Real X (Function.hasUncurryBase.{0, u2} Real X)) (fun (x : Y) => Path.extend.{u2} X _inst_3 (l x) (r x) (γ x))) (Filter.prod.{u1, 0} Y Real (nhds.{u1} Y _inst_4 y) l₁) l₂)
+Case conversion may be inaccurate. Consider using '#align filter.tendsto.path_extend Filter.Tendsto.path_extendₓ'. -/
 theorem Filter.Tendsto.path_extend {X Y : Type _} [TopologicalSpace X] [TopologicalSpace Y]
     {l r : Y → X} {y : Y} {l₁ : Filter ℝ} {l₂ : Filter X} {γ : ∀ y, Path (l y) (r y)}
     (hγ : Tendsto (↿γ) (𝓝 y ×ᶠ l₁.map (projIcc 0 1 zero_le_one)) l₂) :
@@ -236,51 +300,103 @@ theorem Filter.Tendsto.path_extend {X Y : Type _} [TopologicalSpace X] [Topologi
   Filter.Tendsto.IccExtend' _ hγ
 #align filter.tendsto.path_extend Filter.Tendsto.path_extend
 
+/- warning: continuous_at.path_extend -> ContinuousAt.path_extend is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {g : Y -> Real} {l : Y -> X} {r : Y -> X} (γ : forall (y : Y), Path.{u1} X _inst_1 (l y) (r y)) {y : Y}, (ContinuousAt.{u2, u1} (Prod.{u2, 0} Y (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))) X (Prod.topologicalSpace.{u2, 0} Y (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) _inst_2 (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)))) _inst_1 (Function.HasUncurry.uncurry.{max u2 u1, u2, u1} (forall (y : Y), Path.{u1} X _inst_1 (l y) (r y)) (Prod.{u2, 0} Y (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))) X (Path.hasUncurryPath.{u1, u2} X Y _inst_1 (fun (y : Y) => l y) (fun (y : Y) => r y)) γ) (Prod.mk.{u2, 0} Y (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) y (Set.projIcc.{0} Real Real.linearOrder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (zero_le_one.{0} Real Real.hasZero Real.hasOne (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder))))) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring)) (g y)))) -> (ContinuousAt.{u2, 0} Y Real _inst_2 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) g y) -> (ContinuousAt.{u2, u1} Y X _inst_2 _inst_1 (fun (i : Y) => Path.extend.{u1} X _inst_1 (l i) (r i) (γ i) (g i)) y)
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : TopologicalSpace.{u1} Y] {g : Y -> Real} {l : Y -> X} {r : Y -> X} (γ : forall (y : Y), Path.{u2} X _inst_1 (l y) (r y)) {y : Y}, (ContinuousAt.{u1, u2} (Prod.{u1, 0} Y (Set.Elem.{0} Real unitInterval)) X (instTopologicalSpaceProd.{u1, 0} Y (Set.Elem.{0} Real unitInterval) _inst_2 (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 (Function.HasUncurry.uncurry.{max u2 u1, u1, u2} (forall (y : Y), Path.{u2} X _inst_1 (l y) (r y)) (Prod.{u1, 0} Y (Set.Elem.{0} Real unitInterval)) X (Path.hasUncurryPath.{u2, u1} X Y _inst_1 (fun (y : Y) => l y) (fun (y : Y) => r y)) γ) (Prod.mk.{u1, 0} Y (Set.Elem.{0} Real unitInterval) y (Set.projIcc.{0} Real Real.linearOrder (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (zero_le_one.{0} Real Real.instZeroReal Real.instOneReal (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (DistribLattice.toLattice.{0} Real (instDistribLattice.{0} Real Real.linearOrder)))))) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring)) (g y)))) -> (ContinuousAt.{u1, 0} Y Real _inst_2 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) g y) -> (ContinuousAt.{u1, u2} Y X _inst_2 _inst_1 (fun (i : Y) => Path.extend.{u2} X _inst_1 (l i) (r i) (γ i) (g i)) y)
+Case conversion may be inaccurate. Consider using '#align continuous_at.path_extend ContinuousAt.path_extendₓ'. -/
 theorem ContinuousAt.path_extend {g : Y → ℝ} {l r : Y → X} (γ : ∀ y, Path (l y) (r y)) {y : Y}
     (hγ : ContinuousAt (↿γ) (y, projIcc 0 1 zero_le_one (g y))) (hg : ContinuousAt g y) :
     ContinuousAt (fun i => (γ i).extend (g i)) y :=
   hγ.IccExtend (fun x => γ x) hg
 #align continuous_at.path_extend ContinuousAt.path_extend
 
+/- warning: path.extend_extends -> Path.extend_extends is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_3 : TopologicalSpace.{u1} X] {a : X} {b : X} (γ : Path.{u1} X _inst_3 a b) {t : Real} (ht : Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) t (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))), Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ t) (coeFn.{succ u1, succ u1} (Path.{u1} X _inst_3 a b) (fun (_x : Path.{u1} X _inst_3 a b) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> X) (Path.hasCoeToFun.{u1} X _inst_3 a b) γ (Subtype.mk.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) t ht))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_3 : TopologicalSpace.{u1} X] {a : X} {b : X} (γ : Path.{u1} X _inst_3 a b) {t : Real} (ht : Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) t (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))), Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ t) (FunLike.coe.{succ u1, 1, succ u1} (Path.{u1} X _inst_3 a b) (Set.Elem.{0} Real unitInterval) (fun (_x : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) _x) (ContinuousMapClass.toFunLike.{u1, 0, u1} (Path.{u1} X _inst_3 a b) (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_3 (Path.continuousMapClass.{u1} X _inst_3 a b)) γ (Subtype.mk.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) t ht))
+Case conversion may be inaccurate. Consider using '#align path.extend_extends Path.extend_extendsₓ'. -/
 @[simp]
 theorem extend_extends {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) {t : ℝ}
     (ht : t ∈ (Icc 0 1 : Set ℝ)) : γ.extend t = γ ⟨t, ht⟩ :=
   IccExtend_of_mem _ γ ht
 #align path.extend_extends Path.extend_extends
 
+/- warning: path.extend_zero -> Path.extend_zero is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x : X} {y : X} (γ : Path.{u1} X _inst_1 x y), Eq.{succ u1} X (Path.extend.{u1} X _inst_1 x y γ (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) x
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x : X} {y : X} (γ : Path.{u1} X _inst_1 x y), Eq.{succ u1} X (Path.extend.{u1} X _inst_1 x y γ (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) x
+Case conversion may be inaccurate. Consider using '#align path.extend_zero Path.extend_zeroₓ'. -/
 theorem extend_zero : γ.extend 0 = x := by simp
 #align path.extend_zero Path.extend_zero
 
+/- warning: path.extend_one -> Path.extend_one is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x : X} {y : X} (γ : Path.{u1} X _inst_1 x y), Eq.{succ u1} X (Path.extend.{u1} X _inst_1 x y γ (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) y
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x : X} {y : X} (γ : Path.{u1} X _inst_1 x y), Eq.{succ u1} X (Path.extend.{u1} X _inst_1 x y γ (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) y
+Case conversion may be inaccurate. Consider using '#align path.extend_one Path.extend_oneₓ'. -/
 theorem extend_one : γ.extend 1 = y := by simp
 #align path.extend_one Path.extend_one
 
+/- warning: path.extend_extends' -> Path.extend_extends' is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_3 : TopologicalSpace.{u1} X] {a : X} {b : X} (γ : Path.{u1} X _inst_3 a b) (t : coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))), Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))))))) t)) (coeFn.{succ u1, succ u1} (Path.{u1} X _inst_3 a b) (fun (_x : Path.{u1} X _inst_3 a b) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> X) (Path.hasCoeToFun.{u1} X _inst_3 a b) γ t)
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_3 : TopologicalSpace.{u1} X] {a : X} {b : X} (γ : Path.{u1} X _inst_3 a b) (t : Set.Elem.{0} Real (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))), Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) t)) (FunLike.coe.{succ u1, 1, succ u1} (Path.{u1} X _inst_3 a b) (Set.Elem.{0} Real unitInterval) (fun (_x : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) _x) (ContinuousMapClass.toFunLike.{u1, 0, u1} (Path.{u1} X _inst_3 a b) (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_3 (Path.continuousMapClass.{u1} X _inst_3 a b)) γ t)
+Case conversion may be inaccurate. Consider using '#align path.extend_extends' Path.extend_extends'ₓ'. -/
 @[simp]
 theorem extend_extends' {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b)
     (t : (Icc 0 1 : Set ℝ)) : γ.extend t = γ t :=
   Icc_extend_coe _ γ t
 #align path.extend_extends' Path.extend_extends'
 
+#print Path.extend_range /-
 @[simp]
 theorem extend_range {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) :
     range γ.extend = range γ :=
   IccExtend_range _ γ
 #align path.extend_range Path.extend_range
+-/
 
+/- warning: path.extend_of_le_zero -> Path.extend_of_le_zero is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_3 : TopologicalSpace.{u1} X] {a : X} {b : X} (γ : Path.{u1} X _inst_3 a b) {t : Real}, (LE.le.{0} Real Real.hasLe t (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ t) a)
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_3 : TopologicalSpace.{u1} X] {a : X} {b : X} (γ : Path.{u1} X _inst_3 a b) {t : Real}, (LE.le.{0} Real Real.instLEReal t (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ t) a)
+Case conversion may be inaccurate. Consider using '#align path.extend_of_le_zero Path.extend_of_le_zeroₓ'. -/
 theorem extend_of_le_zero {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) {t : ℝ}
     (ht : t ≤ 0) : γ.extend t = a :=
   (IccExtend_of_le_left _ _ ht).trans γ.source
 #align path.extend_of_le_zero Path.extend_of_le_zero
 
+/- warning: path.extend_of_one_le -> Path.extend_of_one_le is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_3 : TopologicalSpace.{u1} X] {a : X} {b : X} (γ : Path.{u1} X _inst_3 a b) {t : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) t) -> (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ t) b)
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_3 : TopologicalSpace.{u1} X] {a : X} {b : X} (γ : Path.{u1} X _inst_3 a b) {t : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) t) -> (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ t) b)
+Case conversion may be inaccurate. Consider using '#align path.extend_of_one_le Path.extend_of_one_leₓ'. -/
 theorem extend_of_one_le {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) {t : ℝ}
     (ht : 1 ≤ t) : γ.extend t = b :=
   (IccExtend_of_right_le _ _ ht).trans γ.target
 #align path.extend_of_one_le Path.extend_of_one_le
 
+#print Path.refl_extend /-
 @[simp]
 theorem refl_extend {X : Type _} [TopologicalSpace X] {a : X} : (Path.refl a).extend = fun _ => a :=
   rfl
 #align path.refl_extend Path.refl_extend
+-/
 
+/- warning: path.of_line -> Path.ofLine is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x : X} {y : X} {f : Real -> X}, (ContinuousOn.{0, u1} Real X (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_1 f unitInterval) -> (Eq.{succ u1} X (f (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) x) -> (Eq.{succ u1} X (f (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) y) -> (Path.{u1} X _inst_1 x y)
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x : X} {y : X} {f : Real -> X}, (ContinuousOn.{0, u1} Real X (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_1 f unitInterval) -> (Eq.{succ u1} X (f (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) x) -> (Eq.{succ u1} X (f (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) y) -> (Path.{u1} X _inst_1 x y)
+Case conversion may be inaccurate. Consider using '#align path.of_line Path.ofLineₓ'. -/
 /-- The path obtained from a map defined on `ℝ` by restriction to the unit interval. -/
 def ofLine {f : ℝ → X} (hf : ContinuousOn f I) (h₀ : f 0 = x) (h₁ : f 1 = y) : Path x y
     where
@@ -290,12 +406,19 @@ def ofLine {f : ℝ → X} (hf : ContinuousOn f I) (h₀ : f 0 = x) (h₁ : f 1
   target' := h₁
 #align path.of_line Path.ofLine
 
+/- warning: path.of_line_mem -> Path.ofLine_mem is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x : X} {y : X} {f : Real -> X} (hf : ContinuousOn.{0, u1} Real X (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_1 f unitInterval) (h₀ : Eq.{succ u1} X (f (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) x) (h₁ : Eq.{succ u1} X (f (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) y) (t : coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval), Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) (coeFn.{succ u1, succ u1} (Path.{u1} X _inst_1 x y) (fun (_x : Path.{u1} X _inst_1 x y) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> X) (Path.hasCoeToFun.{u1} X _inst_1 x y) (Path.ofLine.{u1} X _inst_1 x y f hf h₀ h₁) t) (Set.image.{0, u1} Real X f unitInterval)
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x : X} {y : X} {f : Real -> X} (hf : ContinuousOn.{0, u1} Real X (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_1 f unitInterval) (h₀ : Eq.{succ u1} X (f (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) x) (h₁ : Eq.{succ u1} X (f (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) y) (t : Set.Elem.{0} Real unitInterval), Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) t) (Set.{u1} X) (Set.instMembershipSet.{u1} X) (FunLike.coe.{succ u1, 1, succ u1} (Path.{u1} X _inst_1 x y) (Set.Elem.{0} Real unitInterval) (fun (_x : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) _x) (ContinuousMapClass.toFunLike.{u1, 0, u1} (Path.{u1} X _inst_1 x y) (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.continuousMapClass.{u1} X _inst_1 x y)) (Path.ofLine.{u1} X _inst_1 x y f hf h₀ h₁) t) (Set.image.{0, u1} Real X f unitInterval)
+Case conversion may be inaccurate. Consider using '#align path.of_line_mem Path.ofLine_memₓ'. -/
 theorem ofLine_mem {f : ℝ → X} (hf : ContinuousOn f I) (h₀ : f 0 = x) (h₁ : f 1 = y) :
     ∀ t, ofLine hf h₀ h₁ t ∈ f '' I := fun ⟨t, t_in⟩ => ⟨t, t_in, rfl⟩
 #align path.of_line_mem Path.ofLine_mem
 
 attribute [local simp] Iic_def
 
+#print Path.trans /-
 /-- Concatenation of two paths from `x` to `y` and from `y` to `z`, putting the first
 path on `[0, 1/2]` and the second one on `[1/2, 1]`. -/
 @[trans]
@@ -313,7 +436,14 @@ def trans (γ : Path x y) (γ' : Path y z) : Path x z
   source' := by norm_num
   target' := by norm_num
 #align path.trans Path.trans
+-/
 
+/- warning: path.trans_apply -> Path.trans_apply is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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γ') t) (dite.{succ u1} X (LE.le.{0} Real Real.instLEReal (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) t) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (Real.decidableLE (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) t) (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} 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(instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (And.left (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) t)) (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) t) (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) t)) h)))) (fun (h : Not (LE.le.{0} Real Real.instLEReal (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) t) (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.{u1} X _inst_1 y z) (Set.Elem.{0} Real unitInterval) (fun (_x : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) _x) (ContinuousMapClass.toFunLike.{u1, 0, u1} (Path.{u1} X _inst_1 y z) (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.continuousMapClass.{u1} X _inst_1 y z)) γ' (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) t)) (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) t)) (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) t) (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) t)) (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) t)) (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) t) (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) t) (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) t) (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) t)) (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) t) (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) t)) (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) t) (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) t)))))))
+Case conversion may be inaccurate. Consider using '#align path.trans_apply Path.trans_applyₓ'. -/
 theorem trans_apply (γ : Path x y) (γ' : Path y z) (t : I) :
     (γ.trans γ') t =
       if h : (t : ℝ) ≤ 1 / 2 then γ ⟨2 * t, (mul_pos_mem_iff zero_lt_two).2 ⟨t.2.1, h⟩⟩
@@ -321,6 +451,7 @@ theorem trans_apply (γ : Path x y) (γ' : Path y z) (t : I) :
   show ite _ _ _ = _ by split_ifs <;> rw [extend_extends]
 #align path.trans_apply Path.trans_apply
 
+#print Path.trans_symm /-
 @[simp]
 theorem trans_symm (γ : Path x y) (γ' : Path y z) : (γ.trans γ').symm = γ'.symm.trans γ.symm :=
   by
@@ -337,7 +468,9 @@ theorem trans_symm (γ : Path x y) (γ' : Path y z) : (γ.trans γ').symm = γ'.
   · exfalso
     linarith [unitInterval.nonneg t, unitInterval.le_one t]
 #align path.trans_symm Path.trans_symm
+-/
 
+#print Path.refl_trans_refl /-
 @[simp]
 theorem refl_trans_refl {X : Type _} [TopologicalSpace X] {a : X} :
     (Path.refl a).trans (Path.refl a) = Path.refl a :=
@@ -346,7 +479,14 @@ theorem refl_trans_refl {X : Type _} [TopologicalSpace X] {a : X} :
   simp only [Path.trans, if_t_t, one_div, Path.refl_extend]
   rfl
 #align path.refl_trans_refl Path.refl_trans_refl
+-/
 
+/- warning: path.trans_range -> Path.trans_range is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_3 : TopologicalSpace.{u1} X] {a : X} {b : X} {c : X} (γ₁ : Path.{u1} X _inst_3 a b) (γ₂ : Path.{u1} X _inst_3 b c), Eq.{succ u1} (Set.{u1} X) (Set.range.{u1, 1} X (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeFn.{succ u1, succ u1} (Path.{u1} X _inst_3 a c) (fun (_x : Path.{u1} X _inst_3 a c) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> X) (Path.hasCoeToFun.{u1} X _inst_3 a c) (Path.trans.{u1} X _inst_3 a b c γ₁ γ₂))) (Union.union.{u1} (Set.{u1} X) (Set.hasUnion.{u1} X) (Set.range.{u1, 1} X (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeFn.{succ u1, succ u1} (Path.{u1} X _inst_3 a b) (fun (_x : Path.{u1} X _inst_3 a b) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> X) (Path.hasCoeToFun.{u1} X _inst_3 a b) γ₁)) (Set.range.{u1, 1} X (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeFn.{succ u1, succ u1} (Path.{u1} X _inst_3 b c) (fun (_x : Path.{u1} X _inst_3 b c) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> X) (Path.hasCoeToFun.{u1} X _inst_3 b c) γ₂)))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_3 : TopologicalSpace.{u1} X] {a : X} {b : X} {c : X} (γ₁ : Path.{u1} X _inst_3 a b) (γ₂ : Path.{u1} X _inst_3 b c), Eq.{succ u1} (Set.{u1} X) (Set.range.{u1, 1} X (Set.Elem.{0} Real unitInterval) (FunLike.coe.{succ u1, 1, succ u1} (Path.{u1} X _inst_3 a c) (Set.Elem.{0} Real unitInterval) (fun (_x : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) _x) (ContinuousMapClass.toFunLike.{u1, 0, u1} (Path.{u1} X _inst_3 a c) (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_3 (Path.continuousMapClass.{u1} X _inst_3 a c)) (Path.trans.{u1} X _inst_3 a b c γ₁ γ₂))) (Union.union.{u1} (Set.{u1} X) (Set.instUnionSet.{u1} X) (Set.range.{u1, 1} X (Set.Elem.{0} Real unitInterval) (FunLike.coe.{succ u1, 1, succ u1} (Path.{u1} X _inst_3 a b) (Set.Elem.{0} Real unitInterval) (fun (_x : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) _x) (ContinuousMapClass.toFunLike.{u1, 0, u1} (Path.{u1} X _inst_3 a b) (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_3 (Path.continuousMapClass.{u1} X _inst_3 a b)) γ₁)) (Set.range.{u1, 1} X (Set.Elem.{0} Real unitInterval) (FunLike.coe.{succ u1, 1, succ u1} (Path.{u1} X _inst_3 b c) (Set.Elem.{0} Real unitInterval) (fun (_x : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) _x) (ContinuousMapClass.toFunLike.{u1, 0, u1} (Path.{u1} X _inst_3 b c) (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_3 (Path.continuousMapClass.{u1} X _inst_3 b c)) γ₂)))
+Case conversion may be inaccurate. Consider using '#align path.trans_range Path.trans_rangeₓ'. -/
 theorem trans_range {X : Type _} [TopologicalSpace X] {a b c : X} (γ₁ : Path a b) (γ₂ : Path b c) :
     range (γ₁.trans γ₂) = range γ₁ ∪ range γ₂ :=
   by
@@ -391,6 +531,7 @@ theorem trans_range {X : Type _} [TopologicalSpace X] {a b c : X} (γ₁ : Path
         rwa [γ₂.extend_extends]
 #align path.trans_range Path.trans_range
 
+#print Path.map /-
 /-- Image of a path from `x` to `y` by a continuous map -/
 def map (γ : Path x y) {Y : Type _} [TopologicalSpace Y] {f : X → Y} (h : Continuous f) :
     Path (f x) (f y) where
@@ -399,7 +540,14 @@ def map (γ : Path x y) {Y : Type _} [TopologicalSpace Y] {f : X → Y} (h : Con
   source' := by simp
   target' := by simp
 #align path.map Path.map
+-/
 
+/- warning: path.map_coe -> Path.map_coe is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x : X} {y : X} (γ : Path.{u1} X _inst_1 x y) {Y : Type.{u2}} [_inst_3 : TopologicalSpace.{u2} Y] {f : X -> Y} (h : Continuous.{u1, u2} X Y _inst_1 _inst_3 f), Eq.{succ u2} ((fun (_x : Path.{u2} Y _inst_3 (f x) (f y)) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> Y) (Path.map.{u1, u2} X _inst_1 x y γ Y _inst_3 f h)) (coeFn.{succ u2, succ u2} (Path.{u2} Y _inst_3 (f x) (f y)) (fun (_x : Path.{u2} Y _inst_3 (f x) (f y)) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> Y) (Path.hasCoeToFun.{u2} Y _inst_3 (f x) (f y)) (Path.map.{u1, u2} X _inst_1 x y γ Y _inst_3 f h)) (Function.comp.{1, succ u1, succ u2} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X Y f (coeFn.{succ u1, succ u1} (Path.{u1} X _inst_1 x y) (fun (_x : Path.{u1} X _inst_1 x y) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> X) (Path.hasCoeToFun.{u1} X _inst_1 x y) γ))
+but is expected to have type
+  forall {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] {x : X} {y : X} (γ : Path.{u2} X _inst_1 x y) {Y : Type.{u1}} [_inst_3 : TopologicalSpace.{u1} Y] {f : X -> Y} (h : Continuous.{u2, u1} X Y _inst_1 _inst_3 f), Eq.{succ u1} (forall (a : Set.Elem.{0} Real unitInterval), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => Y) a) (FunLike.coe.{succ u1, 1, succ u1} (Path.{u1} Y _inst_3 (f x) (f y)) (Set.Elem.{0} Real unitInterval) (fun (_x : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => Y) _x) (ContinuousMapClass.toFunLike.{u1, 0, u1} (Path.{u1} Y _inst_3 (f x) (f y)) (Set.Elem.{0} Real unitInterval) Y (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_3 (Path.continuousMapClass.{u1} Y _inst_3 (f x) (f y))) (Path.map.{u2, u1} X _inst_1 x y γ Y _inst_3 f h)) (Function.comp.{1, succ u2, succ u1} (Set.Elem.{0} Real unitInterval) X Y f (FunLike.coe.{succ u2, 1, succ u2} (Path.{u2} X _inst_1 x y) (Set.Elem.{0} Real unitInterval) (fun (_x : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) _x) (ContinuousMapClass.toFunLike.{u2, 0, u2} (Path.{u2} X _inst_1 x y) (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.continuousMapClass.{u2} X _inst_1 x y)) γ))
+Case conversion may be inaccurate. Consider using '#align path.map_coe Path.map_coeₓ'. -/
 @[simp]
 theorem map_coe (γ : Path x y) {Y : Type _} [TopologicalSpace Y] {f : X → Y} (h : Continuous f) :
     (γ.map h : I → Y) = f ∘ γ := by
@@ -407,12 +555,24 @@ theorem map_coe (γ : Path x y) {Y : Type _} [TopologicalSpace Y] {f : X → Y}
   rfl
 #align path.map_coe Path.map_coe
 
+/- warning: path.map_symm -> Path.map_symm is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x : X} {y : X} (γ : Path.{u1} X _inst_1 x y) {Y : Type.{u2}} [_inst_3 : TopologicalSpace.{u2} Y] {f : X -> Y} (h : Continuous.{u1, u2} X Y _inst_1 _inst_3 f), Eq.{succ u2} (Path.{u2} Y _inst_3 (f y) (f x)) (Path.symm.{u2} Y _inst_3 (f x) (f y) (Path.map.{u1, u2} X _inst_1 x y γ Y _inst_3 f h)) (Path.map.{u1, u2} X _inst_1 y x (Path.symm.{u1} X _inst_1 x y γ) Y _inst_3 (fun {y : X} => f y) h)
+but is expected to have type
+  forall {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] {x : X} {y : X} (γ : Path.{u2} X _inst_1 x y) {Y : Type.{u1}} [_inst_3 : TopologicalSpace.{u1} Y] {f : X -> Y} (h : Continuous.{u2, u1} X Y _inst_1 _inst_3 f), Eq.{succ u1} (Path.{u1} Y _inst_3 (f y) (f x)) (Path.symm.{u1} Y _inst_3 (f x) (f y) (Path.map.{u2, u1} X _inst_1 x y γ Y _inst_3 f h)) (Path.map.{u2, u1} X _inst_1 y x (Path.symm.{u2} X _inst_1 x y γ) Y _inst_3 f h)
+Case conversion may be inaccurate. Consider using '#align path.map_symm Path.map_symmₓ'. -/
 @[simp]
 theorem map_symm (γ : Path x y) {Y : Type _} [TopologicalSpace Y] {f : X → Y} (h : Continuous f) :
     (γ.map h).symm = γ.symm.map h :=
   rfl
 #align path.map_symm Path.map_symm
 
+/- warning: path.map_trans -> Path.map_trans is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x : X} {y : X} {z : X} (γ : Path.{u1} X _inst_1 x y) (γ' : Path.{u1} X _inst_1 y z) {Y : Type.{u2}} [_inst_3 : TopologicalSpace.{u2} Y] {f : X -> Y} (h : Continuous.{u1, u2} X Y _inst_1 _inst_3 f), Eq.{succ u2} (Path.{u2} Y _inst_3 (f x) (f z)) (Path.map.{u1, u2} X _inst_1 x z (Path.trans.{u1} X _inst_1 x y z γ γ') Y _inst_3 f h) (Path.trans.{u2} Y _inst_3 (f x) (f y) (f z) (Path.map.{u1, u2} X _inst_1 x y γ Y _inst_3 f h) (Path.map.{u1, u2} X _inst_1 y z γ' Y _inst_3 (fun {y : X} => f y) h))
+but is expected to have type
+  forall {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] {x : X} {y : X} {z : X} (γ : Path.{u2} X _inst_1 x y) (γ' : Path.{u2} X _inst_1 y z) {Y : Type.{u1}} [_inst_3 : TopologicalSpace.{u1} Y] {f : X -> Y} (h : Continuous.{u2, u1} X Y _inst_1 _inst_3 f), Eq.{succ u1} (Path.{u1} Y _inst_3 (f x) (f z)) (Path.map.{u2, u1} X _inst_1 x z (Path.trans.{u2} X _inst_1 x y z γ γ') Y _inst_3 f h) (Path.trans.{u1} Y _inst_3 (f x) (f y) (f z) (Path.map.{u2, u1} X _inst_1 x y γ Y _inst_3 f h) (Path.map.{u2, u1} X _inst_1 y z γ' Y _inst_3 f h))
+Case conversion may be inaccurate. Consider using '#align path.map_trans Path.map_transₓ'. -/
 @[simp]
 theorem map_trans (γ : Path x y) (γ' : Path y z) {Y : Type _} [TopologicalSpace Y] {f : X → Y}
     (h : Continuous f) : (γ.trans γ').map h = (γ.map h).trans (γ'.map h) :=
@@ -422,13 +582,21 @@ theorem map_trans (γ : Path x y) (γ' : Path y z) {Y : Type _} [TopologicalSpac
   split_ifs <;> rfl
 #align path.map_trans Path.map_trans
 
+#print Path.map_id /-
 @[simp]
 theorem map_id (γ : Path x y) : γ.map continuous_id = γ :=
   by
   ext
   rfl
 #align path.map_id Path.map_id
+-/
 
+/- warning: path.map_map -> Path.map_map is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x : X} {y : X} (γ : Path.{u1} X _inst_1 x y) {Y : Type.{u2}} [_inst_3 : TopologicalSpace.{u2} Y] {Z : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} Z] {f : X -> Y} (hf : Continuous.{u1, u2} X Y _inst_1 _inst_3 f) {g : Y -> Z} (hg : Continuous.{u2, u3} Y Z _inst_3 _inst_4 g), Eq.{succ u3} (Path.{u3} Z _inst_4 (g (f x)) (g (f y))) (Path.map.{u2, u3} Y _inst_3 (f x) (f y) (Path.map.{u1, u2} X _inst_1 x y γ Y _inst_3 f hf) Z _inst_4 g hg) (Path.map.{u1, u3} X _inst_1 x y γ Z _inst_4 (fun {x : X} => g (f x)) (Continuous.comp.{u1, u2, u3} X Y Z _inst_1 _inst_3 _inst_4 g (fun (x : X) => f x) hg hf))
+but is expected to have type
+  forall {X : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} X] {x : X} {y : X} (γ : Path.{u3} X _inst_1 x y) {Y : Type.{u2}} [_inst_3 : TopologicalSpace.{u2} Y] {Z : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} Z] {f : X -> Y} (hf : Continuous.{u3, u2} X Y _inst_1 _inst_3 f) {g : Y -> Z} (hg : Continuous.{u2, u1} Y Z _inst_3 _inst_4 g), Eq.{succ u1} (Path.{u1} Z _inst_4 (g (f x)) (g (f y))) (Path.map.{u2, u1} Y _inst_3 (f x) (f y) (Path.map.{u3, u2} X _inst_1 x y γ Y _inst_3 f hf) Z _inst_4 g hg) (Path.map.{u3, u1} X _inst_1 x y γ Z _inst_4 (Function.comp.{succ u3, succ u2, succ u1} X Y Z g f) (Continuous.comp.{u3, u1, u2} X Y Z _inst_1 _inst_3 _inst_4 g f hg hf))
+Case conversion may be inaccurate. Consider using '#align path.map_map Path.map_mapₓ'. -/
 @[simp]
 theorem map_map (γ : Path x y) {Y : Type _} [TopologicalSpace Y] {Z : Type _} [TopologicalSpace Z]
     {f : X → Y} (hf : Continuous f) {g : Y → Z} (hg : Continuous g) :
@@ -437,6 +605,7 @@ theorem map_map (γ : Path x y) {Y : Type _} [TopologicalSpace Y] {Z : Type _} [
   rfl
 #align path.map_map Path.map_map
 
+#print Path.cast /-
 /-- Casting a path from `x` to `y` to a path from `x'` to `y'` when `x' = x` and `y' = y` -/
 def cast (γ : Path x y) {x' y'} (hx : x' = x) (hy : y' = y) : Path x' y'
     where
@@ -445,25 +614,38 @@ def cast (γ : Path x y) {x' y'} (hx : x' = x) (hy : y' = y) : Path x' y'
   source' := by simp [hx]
   target' := by simp [hy]
 #align path.cast Path.cast
+-/
 
+#print Path.symm_cast /-
 @[simp]
 theorem symm_cast {X : Type _} [TopologicalSpace X] {a₁ a₂ b₁ b₂ : X} (γ : Path a₂ b₂)
     (ha : a₁ = a₂) (hb : b₁ = b₂) : (γ.cast ha hb).symm = γ.symm.cast hb ha :=
   rfl
 #align path.symm_cast Path.symm_cast
+-/
 
+#print Path.trans_cast /-
 @[simp]
 theorem trans_cast {X : Type _} [TopologicalSpace X] {a₁ a₂ b₁ b₂ c₁ c₂ : X} (γ : Path a₂ b₂)
     (γ' : Path b₂ c₂) (ha : a₁ = a₂) (hb : b₁ = b₂) (hc : c₁ = c₂) :
     (γ.cast ha hb).trans (γ'.cast hb hc) = (γ.trans γ').cast ha hc :=
   rfl
 #align path.trans_cast Path.trans_cast
+-/
 
+#print Path.cast_coe /-
 @[simp]
 theorem cast_coe (γ : Path x y) {x' y'} (hx : x' = x) (hy : y' = y) : (γ.cast hx hy : I → X) = γ :=
   rfl
 #align path.cast_coe Path.cast_coe
+-/
 
+/- warning: path.symm_continuous_family -> Path.symm_continuous_family is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {ι : Type.{u2}} [_inst_3 : TopologicalSpace.{u1} X] [_inst_4 : TopologicalSpace.{u2} ι] {a : ι -> X} {b : ι -> X} (γ : forall (t : ι), Path.{u1} X _inst_3 (a t) (b t)), (Continuous.{u2, u1} (Prod.{u2, 0} ι (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)) X (Prod.topologicalSpace.{u2, 0} ι (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) _inst_4 (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)))) _inst_3 (Function.HasUncurry.uncurry.{max u2 u1, u2, u1} (forall (t : ι), Path.{u1} X _inst_3 (a t) (b t)) (Prod.{u2, 0} ι (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)) X (Path.hasUncurryPath.{u1, u2} X ι _inst_3 (fun (t : ι) => a t) (fun (t : ι) => b t)) γ)) -> (Continuous.{u2, u1} (Prod.{u2, 0} ι (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)) X (Prod.topologicalSpace.{u2, 0} ι (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) _inst_4 (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)))) _inst_3 (Function.HasUncurry.uncurry.{max u2 u1, u2, u1} (forall (t : ι), Path.{u1} X _inst_3 (b t) (a t)) (Prod.{u2, 0} ι (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)) X (Path.hasUncurryPath.{u1, u2} X ι _inst_3 (fun (t : ι) => b t) (fun (t : ι) => a t)) (fun (t : ι) => Path.symm.{u1} X _inst_3 (a t) (b t) (γ t))))
+but is expected to have type
+  forall {X : Type.{u2}} {ι : Type.{u1}} [_inst_3 : TopologicalSpace.{u2} X] [_inst_4 : TopologicalSpace.{u1} ι] {a : ι -> X} {b : ι -> X} (γ : forall (t : ι), Path.{u2} X _inst_3 (a t) (b t)), (Continuous.{u1, u2} (Prod.{u1, 0} ι (Set.Elem.{0} Real unitInterval)) X (instTopologicalSpaceProd.{u1, 0} ι (Set.Elem.{0} Real unitInterval) _inst_4 (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_3 (Function.HasUncurry.uncurry.{max u2 u1, u1, u2} (forall (t : ι), Path.{u2} X _inst_3 (a t) (b t)) (Prod.{u1, 0} ι (Set.Elem.{0} Real unitInterval)) X (Path.hasUncurryPath.{u2, u1} X ι _inst_3 (fun (t : ι) => a t) (fun (t : ι) => b t)) γ)) -> (Continuous.{u1, u2} (Prod.{u1, 0} ι (Set.Elem.{0} Real unitInterval)) X (instTopologicalSpaceProd.{u1, 0} ι (Set.Elem.{0} Real unitInterval) _inst_4 (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_3 (Function.HasUncurry.uncurry.{max u2 u1, u1, u2} (forall (t : ι), Path.{u2} X _inst_3 (b t) (a t)) (Prod.{u1, 0} ι (Set.Elem.{0} Real unitInterval)) X (Path.hasUncurryPath.{u2, u1} X ι _inst_3 (fun (t : ι) => b t) (fun (t : ι) => a t)) (fun (t : ι) => Path.symm.{u2} X _inst_3 (a t) (b t) (γ t))))
+Case conversion may be inaccurate. Consider using '#align path.symm_continuous_family Path.symm_continuous_familyₓ'. -/
 @[continuity]
 theorem symm_continuous_family {X ι : Type _} [TopologicalSpace X] [TopologicalSpace ι]
     {a b : ι → X} (γ : ∀ t : ι, Path (a t) (b t)) (h : Continuous ↿γ) :
@@ -471,11 +653,19 @@ theorem symm_continuous_family {X ι : Type _} [TopologicalSpace X] [Topological
   h.comp (continuous_id.Prod_map continuous_symm)
 #align path.symm_continuous_family Path.symm_continuous_family
 
+#print Path.continuous_symm /-
 @[continuity]
 theorem continuous_symm : Continuous (symm : Path x y → Path y x) :=
   continuous_uncurry_iff.mp <| symm_continuous_family _ (continuous_fst.path_eval continuous_snd)
 #align path.continuous_symm Path.continuous_symm
+-/
 
+/- warning: path.continuous_uncurry_extend_of_continuous_family -> Path.continuous_uncurry_extend_of_continuous_family is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {ι : Type.{u2}} [_inst_3 : TopologicalSpace.{u1} X] [_inst_4 : TopologicalSpace.{u2} ι] {a : ι -> X} {b : ι -> X} (γ : forall (t : ι), Path.{u1} X _inst_3 (a t) (b t)), (Continuous.{u2, u1} (Prod.{u2, 0} ι (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)) X (Prod.topologicalSpace.{u2, 0} ι (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) _inst_4 (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)))) _inst_3 (Function.HasUncurry.uncurry.{max u2 u1, u2, u1} (forall (t : ι), Path.{u1} X _inst_3 (a t) (b t)) (Prod.{u2, 0} ι (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)) X (Path.hasUncurryPath.{u1, u2} X ι _inst_3 (fun (t : ι) => a t) (fun (t : ι) => b t)) γ)) -> (Continuous.{u2, u1} (Prod.{u2, 0} ι Real) X (Prod.topologicalSpace.{u2, 0} ι Real _inst_4 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_3 (Function.HasUncurry.uncurry.{max u2 u1, u2, u1} (ι -> Real -> X) (Prod.{u2, 0} ι Real) X (Function.hasUncurryInduction.{u2, u1, 0, u1} ι (Real -> X) Real X (Function.hasUncurryBase.{0, u1} Real X)) (fun (t : ι) => Path.extend.{u1} X _inst_3 (a t) (b t) (γ t))))
+but is expected to have type
+  forall {X : Type.{u2}} {ι : Type.{u1}} [_inst_3 : TopologicalSpace.{u2} X] [_inst_4 : TopologicalSpace.{u1} ι] {a : ι -> X} {b : ι -> X} (γ : forall (t : ι), Path.{u2} X _inst_3 (a t) (b t)), (Continuous.{u1, u2} (Prod.{u1, 0} ι (Set.Elem.{0} Real unitInterval)) X (instTopologicalSpaceProd.{u1, 0} ι (Set.Elem.{0} Real unitInterval) _inst_4 (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_3 (Function.HasUncurry.uncurry.{max u2 u1, u1, u2} (forall (t : ι), Path.{u2} X _inst_3 (a t) (b t)) (Prod.{u1, 0} ι (Set.Elem.{0} Real unitInterval)) X (Path.hasUncurryPath.{u2, u1} X ι _inst_3 (fun (t : ι) => a t) (fun (t : ι) => b t)) γ)) -> (Continuous.{u1, u2} (Prod.{u1, 0} ι Real) X (instTopologicalSpaceProd.{u1, 0} ι Real _inst_4 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) _inst_3 (Function.HasUncurry.uncurry.{max u2 u1, u1, u2} (ι -> Real -> X) (Prod.{u1, 0} ι Real) X (Function.hasUncurryInduction.{u1, u2, 0, u2} ι (Real -> X) Real X (Function.hasUncurryBase.{0, u2} Real X)) (fun (t : ι) => Path.extend.{u2} X _inst_3 (a t) (b t) (γ t))))
+Case conversion may be inaccurate. Consider using '#align path.continuous_uncurry_extend_of_continuous_family Path.continuous_uncurry_extend_of_continuous_familyₓ'. -/
 @[continuity]
 theorem continuous_uncurry_extend_of_continuous_family {X ι : Type _} [TopologicalSpace X]
     [TopologicalSpace ι] {a b : ι → X} (γ : ∀ t : ι, Path (a t) (b t)) (h : Continuous ↿γ) :
@@ -483,6 +673,12 @@ theorem continuous_uncurry_extend_of_continuous_family {X ι : Type _} [Topologi
   h.comp (continuous_id.Prod_map continuous_projIcc)
 #align path.continuous_uncurry_extend_of_continuous_family Path.continuous_uncurry_extend_of_continuous_family
 
+/- warning: path.trans_continuous_family -> Path.trans_continuous_family is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {ι : Type.{u2}} [_inst_3 : TopologicalSpace.{u1} X] [_inst_4 : TopologicalSpace.{u2} ι] {a : ι -> X} {b : ι -> X} {c : ι -> X} (γ₁ : forall (t : ι), Path.{u1} X _inst_3 (a t) (b t)), (Continuous.{u2, u1} (Prod.{u2, 0} ι (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)) X (Prod.topologicalSpace.{u2, 0} ι (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) _inst_4 (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)))) _inst_3 (Function.HasUncurry.uncurry.{max u2 u1, u2, u1} (forall (t : ι), Path.{u1} X _inst_3 (a t) (b t)) (Prod.{u2, 0} ι (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)) X (Path.hasUncurryPath.{u1, u2} X ι _inst_3 (fun (t : ι) => a t) (fun (t : ι) => b t)) γ₁)) -> (forall (γ₂ : forall (t : ι), Path.{u1} X _inst_3 (b t) (c t)), (Continuous.{u2, u1} (Prod.{u2, 0} ι (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)) X (Prod.topologicalSpace.{u2, 0} ι (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) _inst_4 (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)))) _inst_3 (Function.HasUncurry.uncurry.{max u2 u1, u2, u1} (forall (t : ι), Path.{u1} X _inst_3 (b t) (c t)) (Prod.{u2, 0} ι (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)) X (Path.hasUncurryPath.{u1, u2} X ι _inst_3 (fun (t : ι) => b t) (fun (t : ι) => c t)) γ₂)) -> (Continuous.{u2, u1} (Prod.{u2, 0} ι (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)) X (Prod.topologicalSpace.{u2, 0} ι (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) _inst_4 (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)))) _inst_3 (Function.HasUncurry.uncurry.{max u2 u1, u2, u1} (forall (t : ι), Path.{u1} X _inst_3 (a t) (c t)) (Prod.{u2, 0} ι (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)) X (Path.hasUncurryPath.{u1, u2} X ι _inst_3 (fun (t : ι) => a t) (fun (t : ι) => c t)) (fun (t : ι) => Path.trans.{u1} X _inst_3 (a t) (b t) (c t) (γ₁ t) (γ₂ t)))))
+but is expected to have type
+  forall {X : Type.{u2}} {ι : Type.{u1}} [_inst_3 : TopologicalSpace.{u2} X] [_inst_4 : TopologicalSpace.{u1} ι] {a : ι -> X} {b : ι -> X} {c : ι -> X} (γ₁ : forall (t : ι), Path.{u2} X _inst_3 (a t) (b t)), (Continuous.{u1, u2} (Prod.{u1, 0} ι (Set.Elem.{0} Real unitInterval)) X (instTopologicalSpaceProd.{u1, 0} ι (Set.Elem.{0} Real unitInterval) _inst_4 (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_3 (Function.HasUncurry.uncurry.{max u2 u1, u1, u2} (forall (t : ι), Path.{u2} X _inst_3 (a t) (b t)) (Prod.{u1, 0} ι (Set.Elem.{0} Real unitInterval)) X (Path.hasUncurryPath.{u2, u1} X ι _inst_3 (fun (t : ι) => a t) (fun (t : ι) => b t)) γ₁)) -> (forall (γ₂ : forall (t : ι), Path.{u2} X _inst_3 (b t) (c t)), (Continuous.{u1, u2} (Prod.{u1, 0} ι (Set.Elem.{0} Real unitInterval)) X (instTopologicalSpaceProd.{u1, 0} ι (Set.Elem.{0} Real unitInterval) _inst_4 (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_3 (Function.HasUncurry.uncurry.{max u2 u1, u1, u2} (forall (t : ι), Path.{u2} X _inst_3 (b t) (c t)) (Prod.{u1, 0} ι (Set.Elem.{0} Real unitInterval)) X (Path.hasUncurryPath.{u2, u1} X ι _inst_3 (fun (t : ι) => b t) (fun (t : ι) => c t)) γ₂)) -> (Continuous.{u1, u2} (Prod.{u1, 0} ι (Set.Elem.{0} Real unitInterval)) X (instTopologicalSpaceProd.{u1, 0} ι (Set.Elem.{0} Real unitInterval) _inst_4 (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_3 (Function.HasUncurry.uncurry.{max u2 u1, u1, u2} (forall (t : ι), Path.{u2} X _inst_3 (a t) (c t)) (Prod.{u1, 0} ι (Set.Elem.{0} Real unitInterval)) X (Path.hasUncurryPath.{u2, u1} X ι _inst_3 (fun (t : ι) => a t) (fun (t : ι) => c t)) (fun (t : ι) => Path.trans.{u2} X _inst_3 (a t) (b t) (c t) (γ₁ t) (γ₂ t)))))
+Case conversion may be inaccurate. Consider using '#align path.trans_continuous_family Path.trans_continuous_familyₓ'. -/
 @[continuity]
 theorem trans_continuous_family {X ι : Type _} [TopologicalSpace X] [TopologicalSpace ι]
     {a b c : ι → X} (γ₁ : ∀ t : ι, Path (a t) (b t)) (h₁ : Continuous ↿γ₁)
@@ -506,6 +702,12 @@ theorem trans_continuous_family {X ι : Type _} [TopologicalSpace X] [Topologica
     simp [hst, mul_inv_cancel (two_ne_zero' ℝ)]
 #align path.trans_continuous_family Path.trans_continuous_family
 
+/- warning: continuous.path_trans -> Continuous.path_trans is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {x : X} {y : X} {z : X} {f : Y -> (Path.{u1} X _inst_1 x y)} {g : Y -> (Path.{u1} X _inst_1 y z)}, (Continuous.{u2, u1} Y (Path.{u1} X _inst_1 x y) _inst_2 (Path.topologicalSpace.{u1} X _inst_1 x y) f) -> (Continuous.{u2, u1} Y (Path.{u1} X _inst_1 y z) _inst_2 (Path.topologicalSpace.{u1} X _inst_1 y z) g) -> (Continuous.{u2, u1} Y (Path.{u1} X _inst_1 x z) _inst_2 (Path.topologicalSpace.{u1} X _inst_1 x z) (fun (t : Y) => Path.trans.{u1} X _inst_1 x y z (f t) (g t)))
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : TopologicalSpace.{u1} Y] {x : X} {y : X} {z : X} {f : Y -> (Path.{u2} X _inst_1 x y)} {g : Y -> (Path.{u2} X _inst_1 y z)}, (Continuous.{u1, u2} Y (Path.{u2} X _inst_1 x y) _inst_2 (Path.topologicalSpace.{u2} X _inst_1 x y) f) -> (Continuous.{u1, u2} Y (Path.{u2} X _inst_1 y z) _inst_2 (Path.topologicalSpace.{u2} X _inst_1 y z) g) -> (Continuous.{u1, u2} Y (Path.{u2} X _inst_1 x z) _inst_2 (Path.topologicalSpace.{u2} X _inst_1 x z) (fun (t : Y) => Path.trans.{u2} X _inst_1 x y z (f t) (g t)))
+Case conversion may be inaccurate. Consider using '#align continuous.path_trans Continuous.path_transₓ'. -/
 @[continuity]
 theorem Continuous.path_trans {f : Y → Path x y} {g : Y → Path y z} :
     Continuous f → Continuous g → Continuous fun t => (f t).trans (g t) :=
@@ -515,6 +717,12 @@ theorem Continuous.path_trans {f : Y → Path x y} {g : Y → Path y z} :
   exact trans_continuous_family _ (continuous_uncurry_iff.mpr hf) _ (continuous_uncurry_iff.mpr hg)
 #align continuous.path_trans Continuous.path_trans
 
+/- warning: path.continuous_trans -> Path.continuous_trans is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x : X} {y : X} {z : X}, Continuous.{u1, u1} (Prod.{u1, u1} (Path.{u1} X _inst_1 x y) (Path.{u1} X _inst_1 y z)) (Path.{u1} X _inst_1 x z) (Prod.topologicalSpace.{u1, u1} (Path.{u1} X _inst_1 x y) (Path.{u1} X _inst_1 y z) (Path.topologicalSpace.{u1} X _inst_1 x y) (Path.topologicalSpace.{u1} X _inst_1 y z)) (Path.topologicalSpace.{u1} X _inst_1 x z) (fun (ρ : Prod.{u1, u1} (Path.{u1} X _inst_1 x y) (Path.{u1} X _inst_1 y z)) => Path.trans.{u1} X _inst_1 x y z (Prod.fst.{u1, u1} (Path.{u1} X _inst_1 x y) (Path.{u1} X _inst_1 y z) ρ) (Prod.snd.{u1, u1} (Path.{u1} X _inst_1 x y) (Path.{u1} X _inst_1 y z) ρ))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x : X} {y : X} {z : X}, Continuous.{u1, u1} (Prod.{u1, u1} (Path.{u1} X _inst_1 x y) (Path.{u1} X _inst_1 y z)) (Path.{u1} X _inst_1 x z) (instTopologicalSpaceProd.{u1, u1} (Path.{u1} X _inst_1 x y) (Path.{u1} X _inst_1 y z) (Path.topologicalSpace.{u1} X _inst_1 x y) (Path.topologicalSpace.{u1} X _inst_1 y z)) (Path.topologicalSpace.{u1} X _inst_1 x z) (fun (ρ : Prod.{u1, u1} (Path.{u1} X _inst_1 x y) (Path.{u1} X _inst_1 y z)) => Path.trans.{u1} X _inst_1 x y z (Prod.fst.{u1, u1} (Path.{u1} X _inst_1 x y) (Path.{u1} X _inst_1 y z) ρ) (Prod.snd.{u1, u1} (Path.{u1} X _inst_1 x y) (Path.{u1} X _inst_1 y z) ρ))
+Case conversion may be inaccurate. Consider using '#align path.continuous_trans Path.continuous_transₓ'. -/
 @[continuity]
 theorem continuous_trans {x y z : X} : Continuous fun ρ : Path x y × Path y z => ρ.1.trans ρ.2 :=
   continuous_fst.path_trans continuous_snd
@@ -527,6 +735,12 @@ section Prod
 
 variable {a₁ a₂ a₃ : X} {b₁ b₂ b₃ : Y}
 
+/- warning: path.prod -> Path.prod is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {a₁ : X} {a₂ : X} {b₁ : Y} {b₂ : Y}, (Path.{u1} X _inst_1 a₁ a₂) -> (Path.{u2} Y _inst_2 b₁ b₂) -> (Path.{max u1 u2} (Prod.{u1, u2} X Y) (Prod.topologicalSpace.{u1, u2} X Y _inst_1 _inst_2) (Prod.mk.{u1, u2} X Y a₁ b₁) (Prod.mk.{u1, u2} X Y a₂ b₂))
+but is expected to have type
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {a₁ : X} {a₂ : X} {b₁ : Y} {b₂ : Y}, (Path.{u1} X _inst_1 a₁ a₂) -> (Path.{u2} Y _inst_2 b₁ b₂) -> (Path.{max u2 u1} (Prod.{u1, u2} X Y) (instTopologicalSpaceProd.{u1, u2} X Y _inst_1 _inst_2) (Prod.mk.{u1, u2} X Y a₁ b₁) (Prod.mk.{u1, u2} X Y a₂ b₂))
+Case conversion may be inaccurate. Consider using '#align path.prod Path.prodₓ'. -/
 /-- Given a path in `X` and a path in `Y`, we can take their pointwise product to get a path in
 `X × Y`. -/
 protected def prod (γ₁ : Path a₁ a₂) (γ₂ : Path b₁ b₂) : Path (a₁, b₁) (a₂, b₂)
@@ -536,16 +750,27 @@ protected def prod (γ₁ : Path a₁ a₂) (γ₂ : Path b₁ b₂) : Path (a
   target' := by simp
 #align path.prod Path.prod
 
+/- warning: path.prod_coe_fn -> Path.prod_coe is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {a₁ : X} {a₂ : X} {b₁ : Y} {b₂ : Y} (γ₁ : Path.{u1} X _inst_1 a₁ a₂) (γ₂ : Path.{u2} Y _inst_2 b₁ b₂), Eq.{succ (max u1 u2)} ((coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> (Prod.{u1, u2} X Y)) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (Path.{max u1 u2} (Prod.{u1, u2} X Y) (Prod.topologicalSpace.{u1, u2} X Y _inst_1 _inst_2) (Prod.mk.{u1, u2} X Y a₁ b₁) (Prod.mk.{u1, u2} X Y a₂ b₂)) (fun (_x : Path.{max u1 u2} (Prod.{u1, u2} X Y) (Prod.topologicalSpace.{u1, u2} X Y _inst_1 _inst_2) (Prod.mk.{u1, u2} X Y a₁ b₁) (Prod.mk.{u1, u2} X Y a₂ b₂)) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> (Prod.{u1, u2} X Y)) (Path.hasCoeToFun.{max u1 u2} (Prod.{u1, u2} X Y) (Prod.topologicalSpace.{u1, u2} X Y _inst_1 _inst_2) (Prod.mk.{u1, u2} X Y a₁ b₁) (Prod.mk.{u1, u2} X Y a₂ b₂)) (Path.prod.{u1, u2} X Y _inst_1 _inst_2 a₁ a₂ b₁ b₂ γ₁ γ₂)) (fun (t : coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) => Prod.mk.{u1, u2} X Y (coeFn.{succ u1, succ u1} (Path.{u1} X _inst_1 a₁ a₂) (fun (_x : Path.{u1} X _inst_1 a₁ a₂) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> X) (Path.hasCoeToFun.{u1} X _inst_1 a₁ a₂) γ₁ t) (coeFn.{succ u2, succ u2} (Path.{u2} Y _inst_2 b₁ b₂) (fun (_x : Path.{u2} Y _inst_2 b₁ b₂) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> Y) (Path.hasCoeToFun.{u2} Y _inst_2 b₁ b₂) γ₂ t))
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : TopologicalSpace.{u1} Y] {a₁ : X} {a₂ : X} {b₁ : Y} {b₂ : Y} (γ₁ : Path.{u2} X _inst_1 a₁ a₂) (γ₂ : Path.{u1} Y _inst_2 b₁ b₂), Eq.{max (succ u2) (succ u1)} (forall (ᾰ : Set.Elem.{0} Real unitInterval), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => Prod.{u2, u1} X Y) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), 1, max (succ u2) (succ u1)} (Path.{max u1 u2} (Prod.{u2, u1} X Y) (instTopologicalSpaceProd.{u2, u1} X Y _inst_1 _inst_2) (Prod.mk.{u2, u1} X Y a₁ b₁) (Prod.mk.{u2, u1} X Y a₂ b₂)) (Set.Elem.{0} Real unitInterval) (fun (_x : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => Prod.{u2, u1} X Y) _x) (ContinuousMapClass.toFunLike.{max u2 u1, 0, max u2 u1} (Path.{max u1 u2} (Prod.{u2, u1} X Y) (instTopologicalSpaceProd.{u2, u1} X Y _inst_1 _inst_2) (Prod.mk.{u2, u1} X Y a₁ b₁) (Prod.mk.{u2, u1} X Y a₂ b₂)) (Set.Elem.{0} Real unitInterval) (Prod.{u2, u1} X Y) (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))) (instTopologicalSpaceProd.{u2, u1} X Y _inst_1 _inst_2) (Path.continuousMapClass.{max u2 u1} (Prod.{u2, u1} X Y) (instTopologicalSpaceProd.{u2, u1} X Y _inst_1 _inst_2) (Prod.mk.{u2, u1} X Y a₁ b₁) (Prod.mk.{u2, u1} X Y a₂ b₂))) (Path.prod.{u2, u1} X Y _inst_1 _inst_2 a₁ a₂ b₁ b₂ γ₁ γ₂)) (fun (t : Set.Elem.{0} Real unitInterval) => Prod.mk.{u2, u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) t) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => Y) t) (FunLike.coe.{succ u2, 1, succ u2} (Path.{u2} X _inst_1 a₁ a₂) (Set.Elem.{0} Real unitInterval) (fun (_x : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) _x) (ContinuousMapClass.toFunLike.{u2, 0, u2} (Path.{u2} X _inst_1 a₁ a₂) (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.continuousMapClass.{u2} X _inst_1 a₁ a₂)) γ₁ t) (FunLike.coe.{succ u1, 1, succ u1} (Path.{u1} Y _inst_2 b₁ b₂) (Set.Elem.{0} Real unitInterval) (fun (_x : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => Y) _x) (ContinuousMapClass.toFunLike.{u1, 0, u1} (Path.{u1} Y _inst_2 b₁ b₂) (Set.Elem.{0} Real unitInterval) Y (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_2 (Path.continuousMapClass.{u1} Y _inst_2 b₁ b₂)) γ₂ t))
+Case conversion may be inaccurate. Consider using '#align path.prod_coe_fn Path.prod_coeₓ'. -/
 @[simp]
-theorem prod_coeFn (γ₁ : Path a₁ a₂) (γ₂ : Path b₁ b₂) :
-    coeFn (γ₁.Prod γ₂) = fun t => (γ₁ t, γ₂ t) :=
+theorem prod_coe (γ₁ : Path a₁ a₂) (γ₂ : Path b₁ b₂) : coeFn (γ₁.Prod γ₂) = fun t => (γ₁ t, γ₂ t) :=
   rfl
-#align path.prod_coe_fn Path.prod_coeFn
-
+#align path.prod_coe_fn Path.prod_coe
+
+/- warning: path.trans_prod_eq_prod_trans -> Path.trans_prod_eq_prod_trans is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {a₁ : X} {a₂ : X} {a₃ : X} {b₁ : Y} {b₂ : Y} {b₃ : Y} (γ₁ : Path.{u1} X _inst_1 a₁ a₂) (δ₁ : Path.{u1} X _inst_1 a₂ a₃) (γ₂ : Path.{u2} Y _inst_2 b₁ b₂) (δ₂ : Path.{u2} Y _inst_2 b₂ b₃), Eq.{succ (max u1 u2)} (Path.{max u1 u2} (Prod.{u1, u2} X Y) (Prod.topologicalSpace.{u1, u2} X Y _inst_1 _inst_2) (Prod.mk.{u1, u2} X Y a₁ b₁) (Prod.mk.{u1, u2} X Y a₃ b₃)) (Path.trans.{max u1 u2} (Prod.{u1, u2} X Y) (Prod.topologicalSpace.{u1, u2} X Y _inst_1 _inst_2) (Prod.mk.{u1, u2} X Y a₁ b₁) (Prod.mk.{u1, u2} X Y a₂ b₂) (Prod.mk.{u1, u2} X Y a₃ b₃) (Path.prod.{u1, u2} X Y _inst_1 _inst_2 a₁ a₂ b₁ b₂ γ₁ γ₂) (Path.prod.{u1, u2} X Y _inst_1 _inst_2 a₂ a₃ b₂ b₃ δ₁ δ₂)) (Path.prod.{u1, u2} X Y _inst_1 _inst_2 a₁ a₃ b₁ b₃ (Path.trans.{u1} X _inst_1 a₁ a₂ a₃ γ₁ δ₁) (Path.trans.{u2} Y _inst_2 b₁ b₂ b₃ γ₂ δ₂))
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : TopologicalSpace.{u1} Y] {a₁ : X} {a₂ : X} {a₃ : X} {b₁ : Y} {b₂ : Y} {b₃ : Y} (γ₁ : Path.{u2} X _inst_1 a₁ a₂) (δ₁ : Path.{u2} X _inst_1 a₂ a₃) (γ₂ : Path.{u1} Y _inst_2 b₁ b₂) (δ₂ : Path.{u1} Y _inst_2 b₂ b₃), Eq.{max (succ u2) (succ u1)} (Path.{max u2 u1} (Prod.{u2, u1} X Y) (instTopologicalSpaceProd.{u2, u1} X Y _inst_1 _inst_2) (Prod.mk.{u2, u1} X Y a₁ b₁) (Prod.mk.{u2, u1} X Y a₃ b₃)) (Path.trans.{max u2 u1} (Prod.{u2, u1} X Y) (instTopologicalSpaceProd.{u2, u1} X Y _inst_1 _inst_2) (Prod.mk.{u2, u1} X Y a₁ b₁) (Prod.mk.{u2, u1} X Y a₂ b₂) (Prod.mk.{u2, u1} X Y a₃ b₃) (Path.prod.{u2, u1} X Y _inst_1 _inst_2 a₁ a₂ b₁ b₂ γ₁ γ₂) (Path.prod.{u2, u1} X Y _inst_1 _inst_2 a₂ a₃ b₂ b₃ δ₁ δ₂)) (Path.prod.{u2, u1} X Y _inst_1 _inst_2 a₁ a₃ b₁ b₃ (Path.trans.{u2} X _inst_1 a₁ a₂ a₃ γ₁ δ₁) (Path.trans.{u1} Y _inst_2 b₁ b₂ b₃ γ₂ δ₂))
+Case conversion may be inaccurate. Consider using '#align path.trans_prod_eq_prod_trans Path.trans_prod_eq_prod_transₓ'. -/
 /-- Path composition commutes with products -/
 theorem trans_prod_eq_prod_trans (γ₁ : Path a₁ a₂) (δ₁ : Path a₂ a₃) (γ₂ : Path b₁ b₂)
     (δ₂ : Path b₂ b₃) : (γ₁.Prod γ₂).trans (δ₁.Prod δ₂) = (γ₁.trans δ₁).Prod (γ₂.trans δ₂) := by
-  ext t <;> unfold Path.trans <;> simp only [Path.coe_mk, Path.prod_coeFn, Function.comp_apply] <;>
+  ext t <;> unfold Path.trans <;> simp only [Path.coe_mk_mk, Path.prod_coe, Function.comp_apply] <;>
       split_ifs <;>
     rfl
 #align path.trans_prod_eq_prod_trans Path.trans_prod_eq_prod_trans
@@ -556,6 +781,7 @@ section Pi
 
 variable {χ : ι → Type _} [∀ i, TopologicalSpace (χ i)] {as bs cs : ∀ i, χ i}
 
+#print Path.pi /-
 /-- Given a family of paths, one in each Xᵢ, we take their pointwise product to get a path in
 Π i, Xᵢ. -/
 protected def pi (γ : ∀ i, Path (as i) (bs i)) : Path as bs
@@ -564,27 +790,33 @@ protected def pi (γ : ∀ i, Path (as i) (bs i)) : Path as bs
   source' := by simp
   target' := by simp
 #align path.pi Path.pi
+-/
 
+#print Path.pi_coe /-
 @[simp]
-theorem pi_coeFn (γ : ∀ i, Path (as i) (bs i)) : coeFn (Path.pi γ) = fun t i => γ i t :=
+theorem pi_coe (γ : ∀ i, Path (as i) (bs i)) : coeFn (Path.pi γ) = fun t i => γ i t :=
   rfl
-#align path.pi_coe_fn Path.pi_coeFn
+#align path.pi_coe_fn Path.pi_coe
+-/
 
+#print Path.trans_pi_eq_pi_trans /-
 /-- Path composition commutes with products -/
 theorem trans_pi_eq_pi_trans (γ₀ : ∀ i, Path (as i) (bs i)) (γ₁ : ∀ i, Path (bs i) (cs i)) :
     (Path.pi γ₀).trans (Path.pi γ₁) = Path.pi fun i => (γ₀ i).trans (γ₁ i) :=
   by
   ext (t i)
   unfold Path.trans
-  simp only [Path.coe_mk, Function.comp_apply, pi_coe_fn]
+  simp only [Path.coe_mk_mk, Function.comp_apply, pi_coe_fn]
   split_ifs <;> rfl
 #align path.trans_pi_eq_pi_trans Path.trans_pi_eq_pi_trans
+-/
 
 end Pi
 
 /-! #### Pointwise multiplication/addition of two paths in a topological (additive) group -/
 
 
+#print Path.mul /-
 /-- Pointwise multiplication of paths in a topological group. The additive version is probably more
 useful. -/
 @[to_additive "Pointwise addition of paths in a topological additive group."]
@@ -593,17 +825,26 @@ protected def mul [Mul X] [ContinuousMul X] {a₁ b₁ a₂ b₂ : X} (γ₁ : P
   (γ₁.Prod γ₂).map continuous_mul
 #align path.mul Path.mul
 #align path.add Path.add
+-/
 
+#print Path.mul_apply /-
 @[to_additive]
 protected theorem mul_apply [Mul X] [ContinuousMul X] {a₁ b₁ a₂ b₂ : X} (γ₁ : Path a₁ b₁)
     (γ₂ : Path a₂ b₂) (t : unitInterval) : (γ₁.mul γ₂) t = γ₁ t * γ₂ t :=
   rfl
 #align path.mul_apply Path.mul_apply
 #align path.add_apply Path.add_apply
+-/
 
 /-! #### Truncating a path -/
 
 
+/- warning: path.truncate -> Path.truncate is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_3 : TopologicalSpace.{u1} X] {a : X} {b : X} (γ : Path.{u1} X _inst_3 a b) (t₀ : Real) (t₁ : Real), Path.{u1} X _inst_3 (Path.extend.{u1} X _inst_3 a b γ (LinearOrder.min.{0} Real Real.linearOrder t₀ t₁)) (Path.extend.{u1} X _inst_3 a b γ t₁)
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_3 : TopologicalSpace.{u1} X] {a : X} {b : X} (γ : Path.{u1} X _inst_3 a b) (t₀ : Real) (t₁ : Real), Path.{u1} X _inst_3 (Path.extend.{u1} X _inst_3 a b γ (Min.min.{0} Real (LinearOrderedRing.toMin.{0} Real Real.instLinearOrderedRingReal) t₀ t₁)) (Path.extend.{u1} X _inst_3 a b γ t₁)
+Case conversion may be inaccurate. Consider using '#align path.truncate Path.truncateₓ'. -/
 /-- `γ.truncate t₀ t₁` is the path which follows the path `γ` on the
   time interval `[t₀, t₁]` and stays still otherwise. -/
 def truncate {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) (t₀ t₁ : ℝ) :
@@ -633,6 +874,12 @@ def truncate {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) (t₀ t
     · rfl
 #align path.truncate Path.truncate
 
+/- warning: path.truncate_of_le -> Path.truncateOfLe is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_3 : TopologicalSpace.{u1} X] {a : X} {b : X} (γ : Path.{u1} X _inst_3 a b) {t₀ : Real} {t₁ : Real}, (LE.le.{0} Real Real.hasLe t₀ t₁) -> (Path.{u1} X _inst_3 (Path.extend.{u1} X _inst_3 a b γ t₀) (Path.extend.{u1} X _inst_3 a b γ t₁))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_3 : TopologicalSpace.{u1} X] {a : X} {b : X} (γ : Path.{u1} X _inst_3 a b) {t₀ : Real} {t₁ : Real}, (LE.le.{0} Real Real.instLEReal t₀ t₁) -> (Path.{u1} X _inst_3 (Path.extend.{u1} X _inst_3 a b γ t₀) (Path.extend.{u1} X _inst_3 a b γ t₁))
+Case conversion may be inaccurate. Consider using '#align path.truncate_of_le Path.truncateOfLeₓ'. -/
 /-- `γ.truncate_of_le t₀ t₁ h`, where `h : t₀ ≤ t₁` is `γ.truncate t₀ t₁`
   casted as a path from `γ.extend t₀` to `γ.extend t₁`. -/
 def truncateOfLe {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) {t₀ t₁ : ℝ}
@@ -640,6 +887,7 @@ def truncateOfLe {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) {t
   (γ.truncate t₀ t₁).cast (by rw [min_eq_left h]) rfl
 #align path.truncate_of_le Path.truncateOfLe
 
+#print Path.truncate_range /-
 theorem truncate_range {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) {t₀ t₁ : ℝ} :
     range (γ.truncate t₀ t₁) ⊆ range γ :=
   by
@@ -648,7 +896,14 @@ theorem truncate_range {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a
   intro x hx
   simp only [CoeFun.coe, coeFn, Path.truncate, mem_range_self]
 #align path.truncate_range Path.truncate_range
+-/
 
+/- warning: path.truncate_continuous_family -> Path.truncate_continuous_family is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_3 : TopologicalSpace.{u1} X] {a : X} {b : X} (γ : Path.{u1} X _inst_3 a b), Continuous.{0, u1} (Prod.{0, 0} Real (Prod.{0, 0} Real (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval))) X (Prod.topologicalSpace.{0, 0} Real (Prod.{0, 0} Real (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Prod.topologicalSpace.{0, 0} Real (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))))) _inst_3 (fun (x : Prod.{0, 0} Real (Prod.{0, 0} Real (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval))) => coeFn.{succ u1, succ u1} (Path.{u1} X _inst_3 (Path.extend.{u1} X _inst_3 a b γ (LinearOrder.min.{0} Real Real.linearOrder (Prod.fst.{0, 0} Real (Prod.{0, 0} Real (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)) x) (Prod.fst.{0, 0} Real (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (Prod.snd.{0, 0} Real (Prod.{0, 0} Real (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)) x)))) (Path.extend.{u1} X _inst_3 a b γ (Prod.fst.{0, 0} Real (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (Prod.snd.{0, 0} Real (Prod.{0, 0} Real (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)) x)))) (fun (_x : Path.{u1} X _inst_3 (Path.extend.{u1} X _inst_3 a b γ (LinearOrder.min.{0} Real Real.linearOrder (Prod.fst.{0, 0} Real (Prod.{0, 0} Real (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)) x) (Prod.fst.{0, 0} Real (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (Prod.snd.{0, 0} Real (Prod.{0, 0} Real (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)) x)))) (Path.extend.{u1} X _inst_3 a b γ (Prod.fst.{0, 0} Real (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (Prod.snd.{0, 0} Real (Prod.{0, 0} Real (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)) x)))) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> X) (Path.hasCoeToFun.{u1} X _inst_3 (Path.extend.{u1} X _inst_3 a b γ (LinearOrder.min.{0} Real Real.linearOrder (Prod.fst.{0, 0} Real (Prod.{0, 0} Real (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)) x) (Prod.fst.{0, 0} Real (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (Prod.snd.{0, 0} Real (Prod.{0, 0} Real (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)) x)))) (Path.extend.{u1} X _inst_3 a b γ (Prod.fst.{0, 0} Real (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (Prod.snd.{0, 0} Real (Prod.{0, 0} Real (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)) x)))) (Path.truncate.{u1} X _inst_3 a b γ (Prod.fst.{0, 0} Real (Prod.{0, 0} Real (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)) x) (Prod.fst.{0, 0} Real (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (Prod.snd.{0, 0} Real (Prod.{0, 0} Real (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)) x))) (Prod.snd.{0, 0} Real (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (Prod.snd.{0, 0} Real (Prod.{0, 0} Real (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)) x)))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_3 : TopologicalSpace.{u1} X] {a : X} {b : X} (γ : Path.{u1} X _inst_3 a b), Continuous.{0, u1} (Prod.{0, 0} Real (Prod.{0, 0} Real (Set.Elem.{0} Real unitInterval))) X (instTopologicalSpaceProd.{0, 0} Real (Prod.{0, 0} Real (Set.Elem.{0} Real unitInterval)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceProd.{0, 0} Real (Set.Elem.{0} Real 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_3 (fun (x : Prod.{0, 0} Real (Prod.{0, 0} Real (Set.Elem.{0} Real unitInterval))) => FunLike.coe.{succ u1, 1, succ u1} (Path.{u1} X _inst_3 (Path.extend.{u1} X _inst_3 a b γ (Min.min.{0} Real (LinearOrderedRing.toMin.{0} Real Real.instLinearOrderedRingReal) (Prod.fst.{0, 0} Real (Prod.{0, 0} Real (Set.Elem.{0} Real unitInterval)) x) (Prod.fst.{0, 0} Real (Set.Elem.{0} Real unitInterval) (Prod.snd.{0, 0} Real (Prod.{0, 0} Real (Set.Elem.{0} Real unitInterval)) x)))) (Path.extend.{u1} X _inst_3 a b γ (Prod.fst.{0, 0} Real (Set.Elem.{0} Real unitInterval) (Prod.snd.{0, 0} Real (Prod.{0, 0} Real (Set.Elem.{0} Real unitInterval)) x)))) (Set.Elem.{0} Real unitInterval) (fun (_x : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) _x) (ContinuousMapClass.toFunLike.{u1, 0, u1} (Path.{u1} X _inst_3 (Path.extend.{u1} X _inst_3 a b γ (Min.min.{0} Real (LinearOrderedRing.toMin.{0} Real Real.instLinearOrderedRingReal) (Prod.fst.{0, 0} Real (Prod.{0, 0} Real (Set.Elem.{0} Real unitInterval)) x) (Prod.fst.{0, 0} Real (Set.Elem.{0} Real unitInterval) (Prod.snd.{0, 0} Real (Prod.{0, 0} Real (Set.Elem.{0} Real unitInterval)) x)))) (Path.extend.{u1} X _inst_3 a b γ (Prod.fst.{0, 0} Real (Set.Elem.{0} Real unitInterval) (Prod.snd.{0, 0} Real (Prod.{0, 0} Real (Set.Elem.{0} Real unitInterval)) x)))) (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_3 (Path.continuousMapClass.{u1} X _inst_3 (Path.extend.{u1} X _inst_3 a b γ (Min.min.{0} Real (LinearOrderedRing.toMin.{0} Real Real.instLinearOrderedRingReal) (Prod.fst.{0, 0} Real (Prod.{0, 0} Real (Set.Elem.{0} Real unitInterval)) x) (Prod.fst.{0, 0} Real (Set.Elem.{0} Real unitInterval) (Prod.snd.{0, 0} Real (Prod.{0, 0} Real (Set.Elem.{0} Real unitInterval)) x)))) (Path.extend.{u1} X _inst_3 a b γ (Prod.fst.{0, 0} Real (Set.Elem.{0} Real unitInterval) (Prod.snd.{0, 0} Real (Prod.{0, 0} Real (Set.Elem.{0} Real unitInterval)) x))))) (Path.truncate.{u1} X _inst_3 a b γ (Prod.fst.{0, 0} Real (Prod.{0, 0} Real (Set.Elem.{0} Real unitInterval)) x) (Prod.fst.{0, 0} Real (Set.Elem.{0} Real unitInterval) (Prod.snd.{0, 0} Real (Prod.{0, 0} Real (Set.Elem.{0} Real unitInterval)) x))) (Prod.snd.{0, 0} Real (Set.Elem.{0} Real unitInterval) (Prod.snd.{0, 0} Real (Prod.{0, 0} Real (Set.Elem.{0} Real unitInterval)) x)))
+Case conversion may be inaccurate. Consider using '#align path.truncate_continuous_family Path.truncate_continuous_familyₓ'. -/
 /-- For a path `γ`, `γ.truncate` gives a "continuous family of paths", by which we
   mean the uncurried function which maps `(t₀, t₁, s)` to `γ.truncate t₀ t₁ s` is continuous. -/
 @[continuity]
@@ -659,6 +914,12 @@ theorem truncate_continuous_family {X : Type _} [TopologicalSpace X] {a b : X} (
       (continuous_fst.comp continuous_snd))
 #align path.truncate_continuous_family Path.truncate_continuous_family
 
+/- warning: path.truncate_const_continuous_family -> Path.truncate_const_continuous_family is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_3 : TopologicalSpace.{u1} X] {a : X} {b : X} (γ : Path.{u1} X _inst_3 a b) (t : Real), Continuous.{0, u1} (Prod.{0, 0} Real (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)) X (Prod.topologicalSpace.{0, 0} Real (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)))) _inst_3 (Function.HasUncurry.uncurry.{u1, 0, u1} (forall (t₁ : Real), Path.{u1} X _inst_3 (Path.extend.{u1} X _inst_3 a b γ (LinearOrder.min.{0} Real Real.linearOrder t t₁)) (Path.extend.{u1} X _inst_3 a b γ t₁)) (Prod.{0, 0} Real (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval)) X (Path.hasUncurryPath.{u1, 0} X Real _inst_3 (fun (t₁ : Real) => Path.extend.{u1} X _inst_3 a b γ (LinearOrder.min.{0} Real Real.linearOrder t t₁)) (fun (t₁ : Real) => Path.extend.{u1} X _inst_3 a b γ t₁)) (Path.truncate.{u1} X _inst_3 a b γ t))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_3 : TopologicalSpace.{u1} X] {a : X} {b : X} (γ : Path.{u1} X _inst_3 a b) (t : Real), Continuous.{0, u1} (Prod.{0, 0} Real (Set.Elem.{0} Real unitInterval)) X (instTopologicalSpaceProd.{0, 0} Real (Set.Elem.{0} Real 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_3 (Function.HasUncurry.uncurry.{u1, 0, u1} (forall (t₁ : Real), Path.{u1} X _inst_3 (Path.extend.{u1} X _inst_3 a b γ (Min.min.{0} Real (LinearOrderedRing.toMin.{0} Real Real.instLinearOrderedRingReal) t t₁)) (Path.extend.{u1} X _inst_3 a b γ t₁)) (Prod.{0, 0} Real (Set.Elem.{0} Real unitInterval)) X (Path.hasUncurryPath.{u1, 0} X Real _inst_3 (fun (t₁ : Real) => Path.extend.{u1} X _inst_3 a b γ (Min.min.{0} Real (LinearOrderedRing.toMin.{0} Real Real.instLinearOrderedRingReal) t t₁)) (fun (t₁ : Real) => Path.extend.{u1} X _inst_3 a b γ t₁)) (Path.truncate.{u1} X _inst_3 a b γ t))
+Case conversion may be inaccurate. Consider using '#align path.truncate_const_continuous_family Path.truncate_const_continuous_familyₓ'. -/
 /- TODO : When `continuity` gets quicker, change the proof back to :
     `begin`
       `simp only [has_coe_to_fun.coe, coe_fn, path.truncate],`
@@ -674,6 +935,12 @@ theorem truncate_const_continuous_family {X : Type _} [TopologicalSpace X] {a b
   convert γ.truncate_continuous_family.comp key
 #align path.truncate_const_continuous_family Path.truncate_const_continuous_family
 
+/- warning: path.truncate_self -> Path.truncate_self is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_3 : TopologicalSpace.{u1} X] {a : X} {b : X} (γ : Path.{u1} X _inst_3 a b) (t : Real), Eq.{succ u1} (Path.{u1} X _inst_3 (Path.extend.{u1} X _inst_3 a b γ (LinearOrder.min.{0} Real Real.linearOrder t t)) (Path.extend.{u1} X _inst_3 a b γ t)) (Path.truncate.{u1} X _inst_3 a b γ t t) (Path.cast.{u1} X _inst_3 (Path.extend.{u1} X _inst_3 a b γ t) (Path.extend.{u1} X _inst_3 a b γ t) (Path.refl.{u1} X _inst_3 (Path.extend.{u1} X _inst_3 a b γ t)) (Path.extend.{u1} X _inst_3 a b γ (LinearOrder.min.{0} Real Real.linearOrder t t)) (Path.extend.{u1} X _inst_3 a b γ t) (Eq.mpr.{0} (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (LinearOrder.min.{0} Real Real.linearOrder t t)) (Path.extend.{u1} X _inst_3 a b γ t)) (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ t) (Path.extend.{u1} X _inst_3 a b γ t)) (id_tag Tactic.IdTag.rw (Eq.{1} Prop (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (LinearOrder.min.{0} Real Real.linearOrder t t)) (Path.extend.{u1} X _inst_3 a b γ t)) (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ t) (Path.extend.{u1} X _inst_3 a b γ t))) (Eq.ndrec.{0, 1} Real (LinearOrder.min.{0} Real Real.linearOrder t t) (fun (_a : Real) => Eq.{1} Prop (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (LinearOrder.min.{0} Real Real.linearOrder t t)) (Path.extend.{u1} X _inst_3 a b γ t)) (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ _a) (Path.extend.{u1} X _inst_3 a b γ t))) (rfl.{1} Prop (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (LinearOrder.min.{0} Real Real.linearOrder t t)) (Path.extend.{u1} X _inst_3 a b γ t))) t (min_self.{0} Real Real.linearOrder t))) (rfl.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ t))) (rfl.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ t)))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_3 : TopologicalSpace.{u1} X] {a : X} {b : X} (γ : Path.{u1} X _inst_3 a b) (t : Real), Eq.{succ u1} (Path.{u1} X _inst_3 (Path.extend.{u1} X _inst_3 a b γ (Min.min.{0} Real (LinearOrderedRing.toMin.{0} Real Real.instLinearOrderedRingReal) t t)) (Path.extend.{u1} X _inst_3 a b γ t)) (Path.truncate.{u1} X _inst_3 a b γ t t) (Path.cast.{u1} X _inst_3 (Path.extend.{u1} X _inst_3 a b γ t) (Path.extend.{u1} X _inst_3 a b γ t) (Path.refl.{u1} X _inst_3 (Path.extend.{u1} X _inst_3 a b γ t)) (Path.extend.{u1} X _inst_3 a b γ (Min.min.{0} Real (LinearOrderedRing.toMin.{0} Real Real.instLinearOrderedRingReal) t t)) (Path.extend.{u1} X _inst_3 a b γ t) (Eq.mpr.{0} (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (Min.min.{0} Real (LinearOrderedRing.toMin.{0} Real Real.instLinearOrderedRingReal) t t)) (Path.extend.{u1} X _inst_3 a b γ t)) (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ t) (Path.extend.{u1} X _inst_3 a b γ t)) (id.{0} (Eq.{1} Prop (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (Min.min.{0} Real (LinearOrderedRing.toMin.{0} Real Real.instLinearOrderedRingReal) t t)) (Path.extend.{u1} X _inst_3 a b γ t)) (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ t) (Path.extend.{u1} X _inst_3 a b γ t))) (Eq.ndrec.{0, 1} Real (Min.min.{0} Real (LinearOrder.toMin.{0} Real Real.linearOrder) t t) (fun (_a : Real) => Eq.{1} Prop (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (Min.min.{0} Real (LinearOrderedRing.toMin.{0} Real Real.instLinearOrderedRingReal) t t)) (Path.extend.{u1} X _inst_3 a b γ t)) (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ _a) (Path.extend.{u1} X _inst_3 a b γ t))) (Eq.refl.{1} Prop (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (Min.min.{0} Real (LinearOrderedRing.toMin.{0} Real Real.instLinearOrderedRingReal) t t)) (Path.extend.{u1} X _inst_3 a b γ t))) t (min_self.{0} Real Real.linearOrder t))) (Eq.refl.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ t))) (rfl.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ t)))
+Case conversion may be inaccurate. Consider using '#align path.truncate_self Path.truncate_selfₓ'. -/
 @[simp]
 theorem truncate_self {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) (t : ℝ) :
     γ.truncate t t = (Path.refl <| γ.extend t).cast (by rw [min_self]) rfl :=
@@ -684,18 +951,36 @@ theorem truncate_self {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b
   split_ifs with h₁ h₂ <;> congr
 #align path.truncate_self Path.truncate_self
 
+/- warning: path.truncate_zero_zero -> Path.truncate_zero_zero is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {X : Type.{u1}} [_inst_3 : TopologicalSpace.{u1} X] {a : X} {b : X} (γ : Path.{u1} X _inst_3 a b), Eq.{succ u1} (Path.{u1} X _inst_3 (Path.extend.{u1} X _inst_3 a b γ (Min.min.{0} Real (LinearOrderedRing.toMin.{0} Real Real.instLinearOrderedRingReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (Path.truncate.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (Path.cast.{u1} X _inst_3 a a (Path.refl.{u1} X _inst_3 a) (Path.extend.{u1} X _inst_3 a b γ (Min.min.{0} Real (LinearOrderedRing.toMin.{0} Real Real.instLinearOrderedRingReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (Eq.mpr.{0} (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (Min.min.{0} Real (LinearOrderedRing.toMin.{0} Real Real.instLinearOrderedRingReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) a) (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) a) (id.{0} (Eq.{1} Prop (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (Min.min.{0} Real (LinearOrderedRing.toMin.{0} Real Real.instLinearOrderedRingReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) a) (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) a)) (Eq.ndrec.{0, 1} Real (Min.min.{0} Real (LinearOrder.toMin.{0} Real Real.linearOrder) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (fun (_a : Real) => Eq.{1} Prop (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (Min.min.{0} Real (LinearOrderedRing.toMin.{0} Real Real.instLinearOrderedRingReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) a) (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ _a) a)) (Eq.refl.{1} Prop (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (Min.min.{0} Real (LinearOrderedRing.toMin.{0} Real Real.instLinearOrderedRingReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) a)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (min_self.{0} Real Real.linearOrder (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))) (Eq.mpr.{0} (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) a) (Eq.{succ u1} X a a) (id.{0} (Eq.{1} Prop (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) a) (Eq.{succ u1} X a a)) (Eq.ndrec.{0, succ u1} X (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (fun (_a : X) => Eq.{1} Prop (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) a) (Eq.{succ u1} X _a a)) (Eq.refl.{1} Prop (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) a)) a (Path.extend_zero.{u1} X _inst_3 a b γ))) (Eq.refl.{succ u1} X a))) (Path.extend_zero.{u1} X _inst_3 a b γ))
+Case conversion may be inaccurate. Consider using '#align path.truncate_zero_zero Path.truncate_zero_zeroₓ'. -/
 @[simp]
 theorem truncate_zero_zero {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) :
     γ.truncate 0 0 = (Path.refl a).cast (by rw [min_self, γ.extend_zero]) γ.extend_zero := by
   convert γ.truncate_self 0 <;> exact γ.extend_zero.symm
 #align path.truncate_zero_zero Path.truncate_zero_zero
 
+/- warning: path.truncate_one_one -> Path.truncate_one_one 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.truncate_one_one Path.truncate_one_oneₓ'. -/
 @[simp]
 theorem truncate_one_one {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) :
     γ.truncate 1 1 = (Path.refl b).cast (by rw [min_self, γ.extend_one]) γ.extend_one := by
   convert γ.truncate_self 1 <;> exact γ.extend_one.symm
 #align path.truncate_one_one Path.truncate_one_one
 
+/- warning: path.truncate_zero_one -> Path.truncate_zero_one is a dubious translation:
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Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) ((fun {α : Type} [_inst_1 : Zero.{0} α] [_inst_2 : One.{0} α] [_inst_3 : LE.{0} α] [_inst_4 : ZeroLEOneClass.{0} α _inst_1 _inst_2 _inst_3] => iff_true_intro (LE.le.{0} α _inst_3 (OfNat.ofNat.{0} α 0 (OfNat.mk.{0} α 0 (Zero.zero.{0} α _inst_1))) (OfNat.ofNat.{0} α 1 (OfNat.mk.{0} α 1 (One.one.{0} α _inst_2)))) (zero_le_one.{0} α _inst_1 _inst_2 _inst_3 _inst_4)) Real Real.hasZero Real.hasOne (Preorder.toLE.{0} Real Real.preorder) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring))) True.intro))) (coeFn.{succ u1, succ u1} (Path.{u1} X _inst_3 a b) (fun (_x : Path.{u1} X _inst_3 a b) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> X) (Path.hasCoeToFun.{u1} X _inst_3 a b) γ (OfNat.ofNat.{0} (Subtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} 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(One.one.{0} Real Real.hasOne))) (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (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))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) True (Set.right_mem_Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) ((fun {α : Type} [_inst_1 : Zero.{0} α] [_inst_2 : One.{0} α] [_inst_3 : LE.{0} α] [_inst_4 : ZeroLEOneClass.{0} α _inst_1 _inst_2 _inst_3] => iff_true_intro (LE.le.{0} α _inst_3 (OfNat.ofNat.{0} α 0 (OfNat.mk.{0} α 0 (Zero.zero.{0} α _inst_1))) (OfNat.ofNat.{0} α 1 (OfNat.mk.{0} α 1 (One.one.{0} α _inst_2)))) (zero_le_one.{0} α _inst_1 _inst_2 _inst_3 _inst_4)) Real Real.hasZero Real.hasOne (Preorder.toLE.{0} Real Real.preorder) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring))) True.intro)) ((fun [_inst_1 : CoeFun.{succ u1, succ u1} (Path.{u1} X _inst_3 a b) (fun (_x : Path.{u1} X _inst_3 a b) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) -> X)] (x : Path.{u1} X _inst_3 a b) (x_1 : Path.{u1} X _inst_3 a b) (e_2 : Eq.{succ u1} (Path.{u1} X _inst_3 a b) x x_1) (ᾰ : coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (ᾰ_1 : coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (e_3 : Eq.{1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) ᾰ ᾰ_1) => congr.{1, succ u1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) X (coeFn.{succ u1, succ u1} (Path.{u1} X _inst_3 a b) (fun (_x : Path.{u1} X _inst_3 a b) => (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) 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+but is expected to have type
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(OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (of_eq_true (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (Min.min.{0} Real (LinearOrder.toMin.{0} Real Real.linearOrder) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) a) (Eq.trans.{1} Prop (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (Min.min.{0} Real (LinearOrder.toMin.{0} Real Real.linearOrder) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) a) (Eq.{succ u1} X a a) True (congrFun.{succ u1, 1} X (fun (a._@.Init.Prelude._hyg.170 : X) => Prop) (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (Min.min.{0} Real (LinearOrder.toMin.{0} Real Real.linearOrder) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))) (Eq.{succ u1} X a) (congrArg.{succ u1, succ u1} X (X -> Prop) (Path.extend.{u1} X _inst_3 a b γ (Min.min.{0} Real (LinearOrder.toMin.{0} Real Real.linearOrder) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) a (Eq.{succ u1} X) (Eq.trans.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (Min.min.{0} Real (LinearOrder.toMin.{0} Real Real.linearOrder) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (FunLike.coe.{succ u1, 1, succ u1} (Path.{u1} X _inst_3 a b) (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} (Path.{u1} X _inst_3 a b) (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_3 (Path.continuousMapClass.{u1} X _inst_3 a b)) γ (Subtype.mk.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (of_eq_true (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Eq.trans.{1} Prop (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And True True) True (Eq.trans.{1} Prop (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And True True) (Mathlib.Data.Set.Intervals.Basic._auxLemma.4.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (congr.{1, 1} Prop Prop (And (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (And True) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) True (congrArg.{1, 1} Prop (Prop -> Prop) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) True And (Mathlib.Init.Algebra.Order._auxLemma.1.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (Mathlib.Algebra.Order.ZeroLEOne._auxLemma.1.{0} Real Real.instZeroReal Real.instOneReal (Preorder.toLE.{0} Real Real.instPreorderReal) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring)))) (and_self True))))) a (Eq.trans.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (Min.min.{0} Real (LinearOrder.toMin.{0} Real Real.linearOrder) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (FunLike.coe.{succ u1, 1, succ u1} (Path.{u1} X _inst_3 a b) (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} (Path.{u1} X _inst_3 a b) (Set.Elem.{0} Real unitInterval) X (instTopologicalSpaceSubtype.{0} Real (fun (x : Real) => 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(OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And True True) True (Eq.trans.{1} Prop (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And True True) (Mathlib.Data.Set.Intervals.Basic._auxLemma.4.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (congr.{1, 1} Prop Prop (And (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (And True) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) True (congrArg.{1, 1} Prop (Prop -> Prop) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) True And (Mathlib.Init.Algebra.Order._auxLemma.1.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (Mathlib.Algebra.Order.ZeroLEOne._auxLemma.1.{0} Real Real.instZeroReal Real.instOneReal (Preorder.toLE.{0} Real Real.instPreorderReal) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring)))) (and_self True))))) (congrArg.{1, succ u1} Real X (Min.min.{0} Real (LinearOrder.toMin.{0} Real Real.linearOrder) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Path.extend.{u1} X _inst_3 a b γ) (min_eq_left.{0} Real Real.linearOrder (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (of_eq_true (GE.ge.{0} Real (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (LinearOrder.toPartialOrder.{0} Real Real.linearOrder))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} 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(Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (LinearOrder.toPartialOrder.{0} Real Real.linearOrder))) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring)))))) (Path.extend_extends.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (of_eq_true (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Eq.trans.{1} Prop (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And True True) True (Eq.trans.{1} Prop (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And True True) (Mathlib.Data.Set.Intervals.Basic._auxLemma.4.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} 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(OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring)))) (and_self True))))) (Path.source.{u1} X _inst_3 a b γ))) a) (eq_self.{succ u1} X a))) (of_eq_true (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) b) (Eq.trans.{1} Prop (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) b) (Eq.{succ u1} X b b) True (congrFun.{succ u1, 1} X (fun (a._@.Init.Prelude._hyg.170 : X) => Prop) (Eq.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Eq.{succ u1} X b) (congrArg.{succ u1, succ u1} X (X -> Prop) (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) b (Eq.{succ u1} X) (Eq.trans.{succ u1} X (Path.extend.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (FunLike.coe.{succ u1, 1, succ u1} (Path.{u1} X _inst_3 a b) (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} (Path.{u1} X _inst_3 a b) (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_3 (Path.continuousMapClass.{u1} X _inst_3 a b)) γ (Subtype.mk.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (of_eq_true (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Eq.trans.{1} Prop (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And True True) True (Eq.trans.{1} Prop (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And True True) (Mathlib.Data.Set.Intervals.Basic._auxLemma.4.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (congr.{1, 1} Prop Prop (And (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And True) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) True (congrArg.{1, 1} Prop (Prop -> Prop) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) True And (Mathlib.Algebra.Order.ZeroLEOne._auxLemma.1.{0} Real Real.instZeroReal Real.instOneReal (Preorder.toLE.{0} Real Real.instPreorderReal) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring))) (Mathlib.Init.Algebra.Order._auxLemma.1.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))) (and_self True))))) b (Path.extend_extends.{u1} X _inst_3 a b γ (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (of_eq_true (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Eq.trans.{1} Prop (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And True True) True (Eq.trans.{1} Prop (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And True True) (Mathlib.Data.Set.Intervals.Basic._auxLemma.4.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (congr.{1, 1} Prop Prop (And (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (And True) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) True (congrArg.{1, 1} Prop (Prop -> Prop) (LE.le.{0} Real (Preorder.toLE.{0} Real Real.instPreorderReal) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) True And (Mathlib.Algebra.Order.ZeroLEOne._auxLemma.1.{0} Real Real.instZeroReal Real.instOneReal (Preorder.toLE.{0} Real Real.instPreorderReal) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring))) (Mathlib.Init.Algebra.Order._auxLemma.1.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))) (and_self True)))) (Path.target.{u1} X _inst_3 a b γ))) b) (eq_self.{succ u1} X b))))
+Case conversion may be inaccurate. Consider using '#align path.truncate_zero_one Path.truncate_zero_oneₓ'. -/
 @[simp]
 theorem truncate_zero_one {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) :
     γ.truncate 0 1 = γ.cast (by simp [zero_le_one, extend_zero]) (by simp) :=
@@ -709,6 +994,7 @@ theorem truncate_zero_one {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path
 /-! #### Reparametrising a path -/
 
 
+#print Path.reparam /-
 /-- Given a path `γ` and a function `f : I → I` where `f 0 = 0` and `f 1 = 1`, `γ.reparam f` is the
 path defined by `γ ∘ f`.
 -/
@@ -719,20 +1005,26 @@ def reparam (γ : Path x y) (f : I → I) (hfcont : Continuous f) (hf₀ : f 0 =
   source' := by simp [hf₀]
   target' := by simp [hf₁]
 #align path.reparam Path.reparam
+-/
 
+#print Path.coe_reparam /-
 @[simp]
-theorem coe_to_fun (γ : Path x y) {f : I → I} (hfcont : Continuous f) (hf₀ : f 0 = 0)
+theorem coe_reparam (γ : Path x y) {f : I → I} (hfcont : Continuous f) (hf₀ : f 0 = 0)
     (hf₁ : f 1 = 1) : ⇑(γ.reparam f hfcont hf₀ hf₁) = γ ∘ f :=
   rfl
-#align path.coe_to_fun Path.coe_to_fun
+#align path.coe_to_fun Path.coe_reparam
+-/
 
+#print Path.reparam_id /-
 @[simp]
 theorem reparam_id (γ : Path x y) : γ.reparam id continuous_id rfl rfl = γ :=
   by
   ext
   rfl
 #align path.reparam_id Path.reparam_id
+-/
 
+#print Path.range_reparam /-
 theorem range_reparam (γ : Path x y) {f : I → I} (hfcont : Continuous f) (hf₀ : f 0 = 0)
     (hf₁ : f 1 = 1) : range ⇑(γ.reparam f hfcont hf₀ hf₁) = range γ :=
   by
@@ -750,56 +1042,73 @@ theorem range_reparam (γ : Path x y) {f : I → I} (hfcont : Continuous f) (hf
       use ⟨w, hw₁⟩, hw₂
   rw [range_comp, this, image_univ]
 #align path.range_reparam Path.range_reparam
+-/
 
+#print Path.refl_reparam /-
 theorem refl_reparam {f : I → I} (hfcont : Continuous f) (hf₀ : f 0 = 0) (hf₁ : f 1 = 1) :
     (refl x).reparam f hfcont hf₀ hf₁ = refl x :=
   by
   ext
   simp
 #align path.refl_reparam Path.refl_reparam
+-/
 
 end Path
 
 /-! ### Being joined by a path -/
 
 
+#print Joined /-
 /-- The relation "being joined by a path". This is an equivalence relation. -/
 def Joined (x y : X) : Prop :=
   Nonempty (Path x y)
 #align joined Joined
+-/
 
+#print Joined.refl /-
 @[refl]
 theorem Joined.refl (x : X) : Joined x x :=
   ⟨Path.refl x⟩
 #align joined.refl Joined.refl
+-/
 
+#print Joined.somePath /-
 /-- When two points are joined, choose some path from `x` to `y`. -/
 def Joined.somePath (h : Joined x y) : Path x y :=
   Nonempty.some h
 #align joined.some_path Joined.somePath
+-/
 
+#print Joined.symm /-
 @[symm]
 theorem Joined.symm {x y : X} (h : Joined x y) : Joined y x :=
   ⟨h.somePath.symm⟩
 #align joined.symm Joined.symm
+-/
 
+#print Joined.trans /-
 @[trans]
 theorem Joined.trans {x y z : X} (hxy : Joined x y) (hyz : Joined y z) : Joined x z :=
   ⟨hxy.somePath.trans hyz.somePath⟩
 #align joined.trans Joined.trans
+-/
 
 variable (X)
 
+#print pathSetoid /-
 /-- The setoid corresponding the equivalence relation of being joined by a continuous path. -/
 def pathSetoid : Setoid X where
   R := Joined
   iseqv := Equivalence.mk _ Joined.refl (fun x y => Joined.symm) fun x y z => Joined.trans
 #align path_setoid pathSetoid
+-/
 
+#print ZerothHomotopy /-
 /-- The quotient type of points of a topological space modulo being joined by a continuous path. -/
 def ZerothHomotopy :=
   Quotient (pathSetoid X)
 #align zeroth_homotopy ZerothHomotopy
+-/
 
 instance : Inhabited (ZerothHomotopy ℝ) :=
   ⟨@Quotient.mk' ℝ (pathSetoid ℝ) 0⟩
@@ -809,38 +1118,51 @@ variable {X}
 /-! ### Being joined by a path inside a set -/
 
 
+#print JoinedIn /-
 /-- The relation "being joined by a path in `F`". Not quite an equivalence relation since it's not
 reflexive for points that do not belong to `F`. -/
 def JoinedIn (F : Set X) (x y : X) : Prop :=
   ∃ γ : Path x y, ∀ t, γ t ∈ F
 #align joined_in JoinedIn
+-/
 
 variable {F : Set X}
 
+#print JoinedIn.mem /-
 theorem JoinedIn.mem (h : JoinedIn F x y) : x ∈ F ∧ y ∈ F :=
   by
   rcases h with ⟨γ, γ_in⟩
   have : γ 0 ∈ F ∧ γ 1 ∈ F := by constructor <;> apply γ_in
   simpa using this
 #align joined_in.mem JoinedIn.mem
+-/
 
+#print JoinedIn.source_mem /-
 theorem JoinedIn.source_mem (h : JoinedIn F x y) : x ∈ F :=
   h.Mem.1
 #align joined_in.source_mem JoinedIn.source_mem
+-/
 
+#print JoinedIn.target_mem /-
 theorem JoinedIn.target_mem (h : JoinedIn F x y) : y ∈ F :=
   h.Mem.2
 #align joined_in.target_mem JoinedIn.target_mem
+-/
 
+#print JoinedIn.somePath /-
 /-- When `x` and `y` are joined in `F`, choose a path from `x` to `y` inside `F` -/
 def JoinedIn.somePath (h : JoinedIn F x y) : Path x y :=
   Classical.choose h
 #align joined_in.some_path JoinedIn.somePath
+-/
 
+#print JoinedIn.somePath_mem /-
 theorem JoinedIn.somePath_mem (h : JoinedIn F x y) (t : I) : h.somePath t ∈ F :=
   Classical.choose_spec h t
 #align joined_in.some_path_mem JoinedIn.somePath_mem
+-/
 
+#print JoinedIn.joined_subtype /-
 /-- If `x` and `y` are joined in the set `F`, then they are joined in the subtype `F`. -/
 theorem JoinedIn.joined_subtype (h : JoinedIn F x y) :
     Joined (⟨x, h.source_mem⟩ : F) (⟨y, h.target_mem⟩ : F) :=
@@ -849,34 +1171,52 @@ theorem JoinedIn.joined_subtype (h : JoinedIn F x y) :
       source' := by simp
       target' := by simp }⟩
 #align joined_in.joined_subtype JoinedIn.joined_subtype
+-/
 
-theorem JoinedIn.of_line {f : ℝ → X} (hf : ContinuousOn f I) (h₀ : f 0 = x) (h₁ : f 1 = y)
+/- warning: joined_in.of_line -> JoinedIn.ofLine is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x : X} {y : X} {F : Set.{u1} X} {f : Real -> X}, (ContinuousOn.{0, u1} Real X (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_1 f unitInterval) -> (Eq.{succ u1} X (f (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) x) -> (Eq.{succ u1} X (f (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) y) -> (HasSubset.Subset.{u1} (Set.{u1} X) (Set.hasSubset.{u1} X) (Set.image.{0, u1} Real X f unitInterval) F) -> (JoinedIn.{u1} X _inst_1 F x y)
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {x : X} {y : X} {F : Set.{u1} X} {f : Real -> X}, (ContinuousOn.{0, u1} Real X (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_1 f unitInterval) -> (Eq.{succ u1} X (f (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) x) -> (Eq.{succ u1} X (f (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) y) -> (HasSubset.Subset.{u1} (Set.{u1} X) (Set.instHasSubsetSet.{u1} X) (Set.image.{0, u1} Real X f unitInterval) F) -> (JoinedIn.{u1} X _inst_1 F x y)
+Case conversion may be inaccurate. Consider using '#align joined_in.of_line JoinedIn.ofLineₓ'. -/
+theorem JoinedIn.ofLine {f : ℝ → X} (hf : ContinuousOn f I) (h₀ : f 0 = x) (h₁ : f 1 = y)
     (hF : f '' I ⊆ F) : JoinedIn F x y :=
   ⟨Path.ofLine hf h₀ h₁, fun t => hF <| Path.ofLine_mem hf h₀ h₁ t⟩
-#align joined_in.of_line JoinedIn.of_line
+#align joined_in.of_line JoinedIn.ofLine
 
+#print JoinedIn.joined /-
 theorem JoinedIn.joined (h : JoinedIn F x y) : Joined x y :=
   ⟨h.somePath⟩
 #align joined_in.joined JoinedIn.joined
+-/
 
+#print joinedIn_iff_joined /-
 theorem joinedIn_iff_joined (x_in : x ∈ F) (y_in : y ∈ F) :
     JoinedIn F x y ↔ Joined (⟨x, x_in⟩ : F) (⟨y, y_in⟩ : F) :=
   ⟨fun h => h.joined_subtype, fun h => ⟨h.somePath.map continuous_subtype_val, by simp⟩⟩
 #align joined_in_iff_joined joinedIn_iff_joined
+-/
 
+#print joinedIn_univ /-
 @[simp]
 theorem joinedIn_univ : JoinedIn univ x y ↔ Joined x y := by
   simp [JoinedIn, Joined, exists_true_iff_nonempty]
 #align joined_in_univ joinedIn_univ
+-/
 
+#print JoinedIn.mono /-
 theorem JoinedIn.mono {U V : Set X} (h : JoinedIn U x y) (hUV : U ⊆ V) : JoinedIn V x y :=
   ⟨h.somePath, fun t => hUV (h.somePath_mem t)⟩
 #align joined_in.mono JoinedIn.mono
+-/
 
+#print JoinedIn.refl /-
 theorem JoinedIn.refl (h : x ∈ F) : JoinedIn F x x :=
   ⟨Path.refl x, fun t => h⟩
 #align joined_in.refl JoinedIn.refl
+-/
 
+#print JoinedIn.symm /-
 @[symm]
 theorem JoinedIn.symm (h : JoinedIn F x y) : JoinedIn F y x :=
   by
@@ -884,7 +1224,9 @@ theorem JoinedIn.symm (h : JoinedIn F x y) : JoinedIn F y x :=
   simp_all [joinedIn_iff_joined]
   exact h.symm
 #align joined_in.symm JoinedIn.symm
+-/
 
+#print JoinedIn.trans /-
 theorem JoinedIn.trans (hxy : JoinedIn F x y) (hyz : JoinedIn F y z) : JoinedIn F x z :=
   by
   cases' hxy.mem with hx hy
@@ -892,33 +1234,45 @@ theorem JoinedIn.trans (hxy : JoinedIn F x y) (hyz : JoinedIn F y z) : JoinedIn
   simp_all [joinedIn_iff_joined]
   exact hxy.trans hyz
 #align joined_in.trans JoinedIn.trans
+-/
 
 /-! ### Path component -/
 
 
+#print pathComponent /-
 /-- The path component of `x` is the set of points that can be joined to `x`. -/
 def pathComponent (x : X) :=
   { y | Joined x y }
 #align path_component pathComponent
+-/
 
+#print mem_pathComponent_self /-
 @[simp]
 theorem mem_pathComponent_self (x : X) : x ∈ pathComponent x :=
   Joined.refl x
 #align mem_path_component_self mem_pathComponent_self
+-/
 
+#print pathComponent.nonempty /-
 @[simp]
 theorem pathComponent.nonempty (x : X) : (pathComponent x).Nonempty :=
   ⟨x, mem_pathComponent_self x⟩
 #align path_component.nonempty pathComponent.nonempty
+-/
 
+#print mem_pathComponent_of_mem /-
 theorem mem_pathComponent_of_mem (h : x ∈ pathComponent y) : y ∈ pathComponent x :=
   Joined.symm h
 #align mem_path_component_of_mem mem_pathComponent_of_mem
+-/
 
+#print pathComponent_symm /-
 theorem pathComponent_symm : x ∈ pathComponent y ↔ y ∈ pathComponent x :=
   ⟨fun h => mem_pathComponent_of_mem h, fun h => mem_pathComponent_of_mem h⟩
 #align path_component_symm pathComponent_symm
+-/
 
+#print pathComponent_congr /-
 theorem pathComponent_congr (h : x ∈ pathComponent y) : pathComponent x = pathComponent y :=
   by
   ext z
@@ -930,35 +1284,52 @@ theorem pathComponent_congr (h : x ∈ pathComponent y) : pathComponent x = path
     rw [pathComponent_symm] at h'⊢
     exact h'.trans h
 #align path_component_congr pathComponent_congr
+-/
 
+#print pathComponent_subset_component /-
 theorem pathComponent_subset_component (x : X) : pathComponent x ⊆ connectedComponent x :=
   fun y h =>
   (isConnected_range h.somePath.Continuous).subset_connectedComponent ⟨0, by simp⟩ ⟨1, by simp⟩
 #align path_component_subset_component pathComponent_subset_component
+-/
 
+#print pathComponentIn /-
 /-- The path component of `x` in `F` is the set of points that can be joined to `x` in `F`. -/
 def pathComponentIn (x : X) (F : Set X) :=
   { y | JoinedIn F x y }
 #align path_component_in pathComponentIn
+-/
 
+#print pathComponentIn_univ /-
 @[simp]
 theorem pathComponentIn_univ (x : X) : pathComponentIn x univ = pathComponent x := by
   simp [pathComponentIn, pathComponent, JoinedIn, Joined, exists_true_iff_nonempty]
 #align path_component_in_univ pathComponentIn_univ
+-/
 
+#print Joined.mem_pathComponent /-
 theorem Joined.mem_pathComponent (hyz : Joined y z) (hxy : y ∈ pathComponent x) :
     z ∈ pathComponent x :=
   hxy.trans hyz
 #align joined.mem_path_component Joined.mem_pathComponent
+-/
 
 /-! ### Path connected sets -/
 
 
+#print IsPathConnected /-
 /-- A set `F` is path connected if it contains a point that can be joined to all other in `F`. -/
 def IsPathConnected (F : Set X) : Prop :=
   ∃ x ∈ F, ∀ {y}, y ∈ F → JoinedIn F x y
 #align is_path_connected IsPathConnected
+-/
 
+/- warning: is_path_connected_iff_eq -> isPathConnected_iff_eq is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {F : Set.{u1} X}, Iff (IsPathConnected.{u1} X _inst_1 F) (Exists.{succ u1} X (fun (x : X) => Exists.{0} (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) x F) (fun (H : Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) x F) => Eq.{succ u1} (Set.{u1} X) (pathComponentIn.{u1} X _inst_1 x F) F)))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {F : Set.{u1} X}, Iff (IsPathConnected.{u1} X _inst_1 F) (Exists.{succ u1} X (fun (x : X) => And (Membership.mem.{u1, u1} X (Set.{u1} X) (Set.instMembershipSet.{u1} X) x F) (Eq.{succ u1} (Set.{u1} X) (pathComponentIn.{u1} X _inst_1 x F) F)))
+Case conversion may be inaccurate. Consider using '#align is_path_connected_iff_eq isPathConnected_iff_eqₓ'. -/
 theorem isPathConnected_iff_eq : IsPathConnected F ↔ ∃ x ∈ F, pathComponentIn x F = F :=
   by
   constructor <;> rintro ⟨x, x_in, h⟩ <;> use x, x_in
@@ -969,13 +1340,16 @@ theorem isPathConnected_iff_eq : IsPathConnected F ↔ ∃ x ∈ F, pathComponen
 #align is_path_connected_iff_eq isPathConnected_iff_eq
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » F) -/
+#print IsPathConnected.joinedIn /-
 theorem IsPathConnected.joinedIn (h : IsPathConnected F) :
     ∀ (x) (_ : x ∈ F) (y) (_ : y ∈ F), JoinedIn F x y := fun x x_in x y_in =>
   let ⟨b, b_in, hb⟩ := h
   (hb x_in).symm.trans (hb y_in)
 #align is_path_connected.joined_in IsPathConnected.joinedIn
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » F) -/
+#print isPathConnected_iff /-
 theorem isPathConnected_iff :
     IsPathConnected F ↔ F.Nonempty ∧ ∀ (x) (_ : x ∈ F) (y) (_ : y ∈ F), JoinedIn F x y :=
   ⟨fun h =>
@@ -984,7 +1358,9 @@ theorem isPathConnected_iff :
       h.JoinedIn⟩,
     fun ⟨⟨b, b_in⟩, h⟩ => ⟨b, b_in, fun x x_in => h b b_in x x_in⟩⟩
 #align is_path_connected_iff isPathConnected_iff
+-/
 
+#print IsPathConnected.image /-
 theorem IsPathConnected.image {Y : Type _} [TopologicalSpace Y] (hF : IsPathConnected F) {f : X → Y}
     (hf : Continuous f) : IsPathConnected (f '' F) :=
   by
@@ -993,16 +1369,27 @@ theorem IsPathConnected.image {Y : Type _} [TopologicalSpace Y] (hF : IsPathConn
   rintro _ ⟨y, y_in, rfl⟩
   exact ⟨(hx y_in).somePath.map hf, fun t => ⟨_, (hx y_in).somePath_mem t, rfl⟩⟩
 #align is_path_connected.image IsPathConnected.image
+-/
 
+#print IsPathConnected.mem_pathComponent /-
 theorem IsPathConnected.mem_pathComponent (h : IsPathConnected F) (x_in : x ∈ F) (y_in : y ∈ F) :
     y ∈ pathComponent x :=
   (h.JoinedIn x x_in y y_in).Joined
 #align is_path_connected.mem_path_component IsPathConnected.mem_pathComponent
+-/
 
+#print IsPathConnected.subset_pathComponent /-
 theorem IsPathConnected.subset_pathComponent (h : IsPathConnected F) (x_in : x ∈ F) :
     F ⊆ pathComponent x := fun y y_in => h.mem_pathComponent x_in y_in
 #align is_path_connected.subset_path_component IsPathConnected.subset_pathComponent
+-/
 
+/- warning: is_path_connected.union -> IsPathConnected.union is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {U : Set.{u1} X} {V : Set.{u1} X}, (IsPathConnected.{u1} X _inst_1 U) -> (IsPathConnected.{u1} X _inst_1 V) -> (Set.Nonempty.{u1} X (Inter.inter.{u1} (Set.{u1} X) (Set.hasInter.{u1} X) U V)) -> (IsPathConnected.{u1} X _inst_1 (Union.union.{u1} (Set.{u1} X) (Set.hasUnion.{u1} X) U V))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {U : Set.{u1} X} {V : Set.{u1} X}, (IsPathConnected.{u1} X _inst_1 U) -> (IsPathConnected.{u1} X _inst_1 V) -> (Set.Nonempty.{u1} X (Inter.inter.{u1} (Set.{u1} X) (Set.instInterSet.{u1} X) U V)) -> (IsPathConnected.{u1} X _inst_1 (Union.union.{u1} (Set.{u1} X) (Set.instUnionSet.{u1} X) U V))
+Case conversion may be inaccurate. Consider using '#align is_path_connected.union IsPathConnected.unionₓ'. -/
 theorem IsPathConnected.union {U V : Set X} (hU : IsPathConnected U) (hV : IsPathConnected V)
     (hUV : (U ∩ V).Nonempty) : IsPathConnected (U ∪ V) :=
   by
@@ -1013,6 +1400,7 @@ theorem IsPathConnected.union {U V : Set X} (hU : IsPathConnected U) (hV : IsPat
   · exact (hV.joined_in x xV y yV).mono (subset_union_right U V)
 #align is_path_connected.union IsPathConnected.union
 
+#print IsPathConnected.preimage_coe /-
 /-- If a set `W` is path-connected, then it is also path-connected when seen as a set in a smaller
 ambient type `U` (when `U` contains `W`). -/
 theorem IsPathConnected.preimage_coe {U W : Set X} (hW : IsPathConnected W) (hWU : W ⊆ U) :
@@ -1023,7 +1411,14 @@ theorem IsPathConnected.preimage_coe {U W : Set X} (hW : IsPathConnected W) (hWU
   rintro ⟨y, hyU⟩ hyW
   exact ⟨(hx hyW).joined_subtype.somePath.map (continuous_inclusion hWU), by simp⟩
 #align is_path_connected.preimage_coe IsPathConnected.preimage_coe
+-/
 
+/- warning: is_path_connected.exists_path_through_family -> IsPathConnected.exists_path_through_family is a dubious translation:
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+but is expected to have type
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(NeZero.succ n))) n)))) γ))))))
+Case conversion may be inaccurate. Consider using '#align is_path_connected.exists_path_through_family IsPathConnected.exists_path_through_familyₓ'. -/
 theorem IsPathConnected.exists_path_through_family {X : Type _} [TopologicalSpace X] {n : ℕ}
     {s : Set X} (h : IsPathConnected s) (p : Fin (n + 1) → X) (hp : ∀ i, p i ∈ s) :
     ∃ γ : Path (p 0) (p n), range γ ⊆ s ∧ ∀ i, p i ∈ range γ :=
@@ -1085,6 +1480,12 @@ theorem IsPathConnected.exists_path_through_family {X : Type _} [TopologicalSpac
   rw [Nat.mod_eq_of_lt hi]
 #align is_path_connected.exists_path_through_family IsPathConnected.exists_path_through_family
 
+/- warning: is_path_connected.exists_path_through_family' -> IsPathConnected.exists_path_through_family' is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align is_path_connected.exists_path_through_family' IsPathConnected.exists_path_through_family'ₓ'. -/
 theorem IsPathConnected.exists_path_through_family' {X : Type _} [TopologicalSpace X] {n : ℕ}
     {s : Set X} (h : IsPathConnected s) (p : Fin (n + 1) → X) (hp : ∀ i, p i ∈ s) :
     ∃ (γ : Path (p 0) (p n))(t : Fin (n + 1) → I), (∀ t, γ t ∈ s) ∧ ∀ i, γ (t i) = p i :=
@@ -1100,13 +1501,16 @@ theorem IsPathConnected.exists_path_through_family' {X : Type _} [TopologicalSpa
 /-! ### Path connected spaces -/
 
 
+#print PathConnectedSpace /-
 /-- A topological space is path-connected if it is non-empty and every two points can be
 joined by a continuous path. -/
 class PathConnectedSpace (X : Type _) [TopologicalSpace X] : Prop where
   Nonempty : Nonempty X
   Joined : ∀ x y : X, Joined x y
 #align path_connected_space PathConnectedSpace
+-/
 
+#print pathConnectedSpace_iff_zerothHomotopy /-
 theorem pathConnectedSpace_iff_zerothHomotopy :
     PathConnectedSpace X ↔ Nonempty (ZerothHomotopy X) ∧ Subsingleton (ZerothHomotopy X) :=
   by
@@ -1121,18 +1525,22 @@ theorem pathConnectedSpace_iff_zerothHomotopy :
     skip
     exact ⟨(nonempty_quotient_iff _).mp h, fun x y => Quotient.exact <| Subsingleton.elim ⟦x⟧ ⟦y⟧⟩
 #align path_connected_space_iff_zeroth_homotopy pathConnectedSpace_iff_zerothHomotopy
+-/
 
 namespace PathConnectedSpace
 
 variable [PathConnectedSpace X]
 
+#print PathConnectedSpace.somePath /-
 /-- Use path-connectedness to build a path between two points. -/
 def somePath (x y : X) : Path x y :=
   Nonempty.some (joined x y)
 #align path_connected_space.some_path PathConnectedSpace.somePath
+-/
 
 end PathConnectedSpace
 
+#print isPathConnected_iff_pathConnectedSpace /-
 theorem isPathConnected_iff_pathConnectedSpace : IsPathConnected F ↔ PathConnectedSpace F :=
   by
   rw [isPathConnected_iff]
@@ -1147,7 +1555,9 @@ theorem isPathConnected_iff_pathConnectedSpace : IsPathConnected F ↔ PathConne
     rw [joinedIn_iff_joined y_in z_in]
     apply H
 #align is_path_connected_iff_path_connected_space isPathConnected_iff_pathConnectedSpace
+-/
 
+#print pathConnectedSpace_iff_univ /-
 theorem pathConnectedSpace_iff_univ : PathConnectedSpace X ↔ IsPathConnected (univ : Set X) :=
   by
   constructor
@@ -1161,11 +1571,15 @@ theorem pathConnectedSpace_iff_univ : PathConnectedSpace X ↔ IsPathConnected (
     cases' h with x h
     exact ⟨⟨x⟩, by simpa using h'⟩
 #align path_connected_space_iff_univ pathConnectedSpace_iff_univ
+-/
 
+#print pathConnectedSpace_iff_eq /-
 theorem pathConnectedSpace_iff_eq : PathConnectedSpace X ↔ ∃ x : X, pathComponent x = univ := by
   simp [pathConnectedSpace_iff_univ, isPathConnected_iff_eq]
 #align path_connected_space_iff_eq pathConnectedSpace_iff_eq
+-/
 
+#print PathConnectedSpace.connectedSpace /-
 -- see Note [lower instance priority]
 instance (priority := 100) PathConnectedSpace.connectedSpace [PathConnectedSpace X] :
     ConnectedSpace X := by
@@ -1175,18 +1589,27 @@ instance (priority := 100) PathConnectedSpace.connectedSpace [PathConnectedSpace
   rw [← univ_subset_iff]
   exact (by simpa using hx : pathComponent x = univ) ▸ pathComponent_subset_component x
 #align path_connected_space.connected_space PathConnectedSpace.connectedSpace
+-/
 
+#print IsPathConnected.isConnected /-
 theorem IsPathConnected.isConnected (hF : IsPathConnected F) : IsConnected F :=
   by
   rw [isConnected_iff_connectedSpace]
   rw [isPathConnected_iff_pathConnectedSpace] at hF
   exact @PathConnectedSpace.connectedSpace _ _ hF
 #align is_path_connected.is_connected IsPathConnected.isConnected
+-/
 
 namespace PathConnectedSpace
 
 variable [PathConnectedSpace X]
 
+/- warning: path_connected_space.exists_path_through_family -> PathConnectedSpace.exists_path_through_family is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align path_connected_space.exists_path_through_family PathConnectedSpace.exists_path_through_familyₓ'. -/
 theorem exists_path_through_family {n : ℕ} (p : Fin (n + 1) → X) :
     ∃ γ : Path (p 0) (p n), ∀ i, p i ∈ range γ :=
   by
@@ -1195,6 +1618,12 @@ theorem exists_path_through_family {n : ℕ} (p : Fin (n + 1) → X) :
   exact ⟨γ, h⟩
 #align path_connected_space.exists_path_through_family PathConnectedSpace.exists_path_through_family
 
+/- warning: path_connected_space.exists_path_through_family' -> PathConnectedSpace.exists_path_through_family' is a dubious translation:
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+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_3 : PathConnectedSpace.{u1} X _inst_1] {n : Nat} (p : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> X), Exists.{succ u1} (Path.{u1} X _inst_1 (p (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (p (Nat.cast.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (AddMonoidWithOne.toNatCast.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instAddMonoidWithOneFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (NeZero.succ n))) n))) (fun (γ : Path.{u1} X _inst_1 (p (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (p (Nat.cast.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (AddMonoidWithOne.toNatCast.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instAddMonoidWithOneFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (NeZero.succ n))) n))) => Exists.{1} ((Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> (Set.Elem.{0} Real unitInterval)) (fun (t : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> (Set.Elem.{0} Real unitInterval)) => forall (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) (t i)) (FunLike.coe.{succ u1, 1, succ u1} (Path.{u1} X _inst_1 (p (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (p (Nat.cast.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (AddMonoidWithOne.toNatCast.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instAddMonoidWithOneFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (NeZero.succ n))) n))) (Set.Elem.{0} Real unitInterval) (fun (_x : Set.Elem.{0} Real unitInterval) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Set.Elem.{0} Real unitInterval) => X) _x) (ContinuousMapClass.toFunLike.{u1, 0, u1} (Path.{u1} X _inst_1 (p (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (p (Nat.cast.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (AddMonoidWithOne.toNatCast.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instAddMonoidWithOneFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (NeZero.succ n))) n))) (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.continuousMapClass.{u1} X _inst_1 (p (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (p (Nat.cast.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (AddMonoidWithOne.toNatCast.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instAddMonoidWithOneFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (NeZero.succ n))) n)))) γ (t i)) (p i)))
+Case conversion may be inaccurate. Consider using '#align path_connected_space.exists_path_through_family' PathConnectedSpace.exists_path_through_family'ₓ'. -/
 theorem exists_path_through_family' {n : ℕ} (p : Fin (n + 1) → X) :
     ∃ (γ : Path (p 0) (p n))(t : Fin (n + 1) → I), ∀ i, γ (t i) = p i :=
   by
@@ -1208,15 +1637,23 @@ end PathConnectedSpace
 /-! ### Locally path connected spaces -/
 
 
+#print LocPathConnectedSpace /-
 /-- A topological space is locally path connected, at every point, path connected
 neighborhoods form a neighborhood basis. -/
 class LocPathConnectedSpace (X : Type _) [TopologicalSpace X] : Prop where
   path_connected_basis : ∀ x : X, (𝓝 x).HasBasis (fun s : Set X => s ∈ 𝓝 x ∧ IsPathConnected s) id
 #align loc_path_connected_space LocPathConnectedSpace
+-/
 
 export LocPathConnectedSpace (path_connected_basis)
 
-theorem loc_path_connected_of_bases {p : ι → Prop} {s : X → ι → Set X}
+/- warning: loc_path_connected_of_bases -> locPathConnected_of_bases is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {ι : Type.{u2}} {p : ι -> Prop} {s : X -> ι -> (Set.{u1} X)}, (forall (x : X), Filter.HasBasis.{u1, succ u2} X ι (nhds.{u1} X _inst_1 x) p (s x)) -> (forall (x : X) (i : ι), (p i) -> (IsPathConnected.{u1} X _inst_1 (s x i))) -> (LocPathConnectedSpace.{u1} X _inst_1)
+but is expected to have type
+  forall {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] {ι : Type.{u1}} {p : ι -> Prop} {s : X -> ι -> (Set.{u2} X)}, (forall (x : X), Filter.HasBasis.{u2, succ u1} X ι (nhds.{u2} X _inst_1 x) p (s x)) -> (forall (x : X) (i : ι), (p i) -> (IsPathConnected.{u2} X _inst_1 (s x i))) -> (LocPathConnectedSpace.{u2} X _inst_1)
+Case conversion may be inaccurate. Consider using '#align loc_path_connected_of_bases locPathConnected_of_basesₓ'. -/
+theorem locPathConnected_of_bases {p : ι → Prop} {s : X → ι → Set X}
     (h : ∀ x, (𝓝 x).HasBasis p (s x)) (h' : ∀ x i, p i → IsPathConnected (s x i)) :
     LocPathConnectedSpace X := by
   constructor
@@ -1227,8 +1664,9 @@ theorem loc_path_connected_of_bases {p : ι → Prop} {s : X → ι → Set X}
   · rintro U ⟨U_in, hU⟩
     rcases(h x).mem_iff.mp U_in with ⟨i, pi, hi⟩
     tauto
-#align loc_path_connected_of_bases loc_path_connected_of_bases
+#align loc_path_connected_of_bases locPathConnected_of_bases
 
+#print pathConnectedSpace_iff_connectedSpace /-
 theorem pathConnectedSpace_iff_connectedSpace [LocPathConnectedSpace X] :
     PathConnectedSpace X ↔ ConnectedSpace X :=
   by
@@ -1251,20 +1689,24 @@ theorem pathConnectedSpace_iff_connectedSpace [LocPathConnectedSpace X] :
       rcases H U U_in with ⟨z, hz, hz'⟩
       exact (hU.joined_in z hz y <| mem_of_mem_nhds U_in).Joined.mem_pathComponent hz'
 #align path_connected_space_iff_connected_space pathConnectedSpace_iff_connectedSpace
+-/
 
-theorem path_connected_subset_basis [LocPathConnectedSpace X] {U : Set X} (h : IsOpen U)
+#print pathConnected_subset_basis /-
+theorem pathConnected_subset_basis [LocPathConnectedSpace X] {U : Set X} (h : IsOpen U)
     (hx : x ∈ U) : (𝓝 x).HasBasis (fun s : Set X => s ∈ 𝓝 x ∧ IsPathConnected s ∧ s ⊆ U) id :=
   (path_connected_basis x).hasBasis_self_subset (IsOpen.mem_nhds h hx)
-#align path_connected_subset_basis path_connected_subset_basis
+#align path_connected_subset_basis pathConnected_subset_basis
+-/
 
-theorem loc_path_connected_of_isOpen [LocPathConnectedSpace X] {U : Set X} (h : IsOpen U) :
+#print locPathConnected_of_isOpen /-
+theorem locPathConnected_of_isOpen [LocPathConnectedSpace X] {U : Set X} (h : IsOpen U) :
     LocPathConnectedSpace U :=
   ⟨by
     rintro ⟨x, x_in⟩
     rw [nhds_subtype_eq_comap]
     constructor
     intro V
-    rw [(has_basis.comap (coe : U → X) (path_connected_subset_basis h x_in)).mem_iff]
+    rw [(has_basis.comap (coe : U → X) (pathConnected_subset_basis h x_in)).mem_iff]
     constructor
     · rintro ⟨W, ⟨W_in, hW, hWU⟩, hWV⟩
       exact ⟨coe ⁻¹' W, ⟨⟨preimage_mem_comap W_in, hW.preimage_coe hWU⟩, hWV⟩⟩
@@ -1277,13 +1719,16 @@ theorem loc_path_connected_of_isOpen [LocPathConnectedSpace X] {U : Set X} (h :
       rintro x ⟨y, ⟨y_in, hy⟩⟩
       rw [← Subtype.coe_injective hy]
       tauto⟩
-#align loc_path_connected_of_is_open loc_path_connected_of_isOpen
+#align loc_path_connected_of_is_open locPathConnected_of_isOpen
+-/
 
+#print IsOpen.isConnected_iff_isPathConnected /-
 theorem IsOpen.isConnected_iff_isPathConnected [LocPathConnectedSpace X] {U : Set X}
     (U_op : IsOpen U) : IsPathConnected U ↔ IsConnected U :=
   by
   rw [isConnected_iff_connectedSpace, isPathConnected_iff_pathConnectedSpace]
-  haveI := loc_path_connected_of_isOpen U_op
+  haveI := locPathConnected_of_isOpen U_op
   exact pathConnectedSpace_iff_connectedSpace
 #align is_open.is_connected_iff_is_path_connected IsOpen.isConnected_iff_isPathConnected
+-/
 

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

@@ -968,14 +968,14 @@ theorem isPathConnected_iff_eq : IsPathConnected F ↔ ∃ x ∈ F, pathComponen
     rwa [← h] at y_in
 #align is_path_connected_iff_eq isPathConnected_iff_eq
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x y «expr ∈ » F) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » F) -/
 theorem IsPathConnected.joinedIn (h : IsPathConnected F) :
     ∀ (x) (_ : x ∈ F) (y) (_ : y ∈ F), JoinedIn F x y := fun x x_in x y_in =>
   let ⟨b, b_in, hb⟩ := h
   (hb x_in).symm.trans (hb y_in)
 #align is_path_connected.joined_in IsPathConnected.joinedIn
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x y «expr ∈ » F) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » F) -/
 theorem isPathConnected_iff :
     IsPathConnected F ↔ F.Nonempty ∧ ∀ (x) (_ : x ∈ F) (y) (_ : y ∈ F), JoinedIn F x y :=
   ⟨fun h =>

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

Reference the newly created issues #12094 and #12096, as well as the pre-existing #5171. Change all references to #10927 to #5171. Some of these changes were not labelled as "porting note"; change this for good measure.

@@ -71,7 +71,7 @@ variable {X Y : Type*} [TopologicalSpace X] [TopologicalSpace Y] {x y z : X} {ι
 /-! ### Paths -/
 
 /-- Continuous path connecting two points `x` and `y` in a topological space -/
--- porting note (#10927): removed @[nolint has_nonempty_instance]
+-- porting note (#5171): removed @[nolint has_nonempty_instance]
 structure Path (x y : X) extends C(I, X) where
   /-- The start point of a `Path`. -/
   source' : toFun 0 = x

Reconstitute the file Algebra.Order.Monoid.WithZero from three files:

• Algebra.Order.Monoid.WithZero.Defs
• Algebra.Order.Monoid.WithZero.Basic
• Algebra.Order.WithZero

Avoid importing it in many files. Most uses were just to get le_zero_iff to work on Nat.

Before

After

@@ -1065,7 +1065,7 @@ theorem IsPathConnected.exists_path_through_family {n : ℕ}
     · use Path.refl (p' 0)
       · constructor
         · rintro i hi
-          rw [le_zero_iff.mp hi]
+          rw [Nat.le_zero.mp hi]
           exact ⟨0, rfl⟩
         · rw [range_subset_iff]
           rintro _x

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

According to git, the moves are:

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

@@ -3,7 +3,7 @@ Copyright (c) 2020 Patrick Massot. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Patrick Massot
 -/
-import Mathlib.Topology.Algebra.Order.ProjIcc
+import Mathlib.Topology.Order.ProjIcc
 import Mathlib.Topology.CompactOpen
 import Mathlib.Topology.UnitInterval
 

More tactics that are not used, found using the linter at #11308.

The PR consists of tactic removals, whitespace changes and replacing a porting note by an explanation.

@@ -1140,7 +1140,6 @@ theorem pathConnectedSpace_iff_zerothHomotopy :
     exact Quotient.sound (PathConnectedSpace.joined x y)
   · unfold ZerothHomotopy
     rintro ⟨h, h'⟩
-    skip
     exact ⟨(nonempty_quotient_iff _).mp h, fun x y => Quotient.exact <| Subsingleton.elim ⟦x⟧ ⟦y⟧⟩
 #align path_connected_space_iff_zeroth_homotopy pathConnectedSpace_iff_zerothHomotopy
 

We remove all but one open Classicals, instead preferring to use open scoped Classical. The only real side-effect this led to is moving a couple declarations to use Exists.choose instead of Classical.choose.

The first few commits are explicitly labelled regex replaces for ease of review.

@@ -63,7 +63,8 @@ on `(-∞, 0]` and to `y` on `[1, +∞)`.
 
 noncomputable section
 
-open Classical Topology Filter unitInterval Set Function
+open scoped Classical
+open Topology Filter unitInterval Set Function
 
 variable {X Y : Type*} [TopologicalSpace X] [TopologicalSpace Y] {x y z : X} {ι : Type*}
 

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>

@@ -315,6 +315,7 @@ theorem ofLine_mem {f : ℝ → X} (hf : ContinuousOn f I) (h₀ : f 0 = x) (h
 
 attribute [local simp] Iic_def
 
+set_option tactic.skipAssignedInstances false in
 /-- Concatenation of two paths from `x` to `y` and from `y` to `z`, putting the first
 path on `[0, 1/2]` and the second one on `[1/2, 1]`. -/
 @[trans]

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

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

@@ -89,7 +89,7 @@ instance Path.funLike : FunLike (Path x y) I X where
 instance Path.continuousMapClass : ContinuousMapClass (Path x y) I X where
   map_continuous := fun γ => show Continuous γ.toContinuousMap by continuity
 
--- porting note: not necessary in light of the instance above
+-- Porting note: not necessary in light of the instance above
 /-
 instance : CoeFun (Path x y) fun _ => I → X :=
   ⟨fun p => p.toFun⟩
@@ -108,7 +108,7 @@ theorem coe_mk_mk (f : I → X) (h₁) (h₂ : f 0 = x) (h₃ : f 1 = y) :
     ⇑(mk ⟨f, h₁⟩ h₂ h₃ : Path x y) = f :=
   rfl
 #align path.coe_mk Path.coe_mk_mk
--- porting note: the name `Path.coe_mk` better refers to a new lemma below
+-- Porting note: the name `Path.coe_mk` better refers to a new lemma below
 
 variable (γ : Path x y)
 
@@ -140,7 +140,7 @@ theorem coe_toContinuousMap : ⇑γ.toContinuousMap = γ :=
   rfl
 #align path.coe_to_continuous_map Path.coe_toContinuousMap
 
--- porting note: this is needed because of the `Path.continuousMapClass` instance
+-- Porting note: this is needed because of the `Path.continuousMapClass` instance
 @[simp]
 theorem coe_mk : ⇑(γ : C(I, X)) = γ :=
   rfl
@@ -677,13 +677,13 @@ theorem truncate_self {a b : X} (γ : Path a b) (t : ℝ) :
   split_ifs with h₁ h₂ <;> congr
 #align path.truncate_self Path.truncate_self
 
-@[simp 1001] -- porting note: increase `simp` priority so left-hand side doesn't simplify
+@[simp 1001] -- Porting note: increase `simp` priority so left-hand side doesn't simplify
 theorem truncate_zero_zero {a b : X} (γ : Path a b) :
     γ.truncate 0 0 = (Path.refl a).cast (by rw [min_self, γ.extend_zero]) γ.extend_zero := by
   convert γ.truncate_self 0
 #align path.truncate_zero_zero Path.truncate_zero_zero
 
-@[simp 1001] -- porting note: increase `simp` priority so left-hand side doesn't simplify
+@[simp 1001] -- Porting note: increase `simp` priority so left-hand side doesn't simplify
 theorem truncate_one_one {a b : X} (γ : Path a b) :
     γ.truncate 1 1 = (Path.refl b).cast (by rw [min_self, γ.extend_one]) γ.extend_one := by
   convert γ.truncate_self 1
@@ -717,7 +717,7 @@ theorem coe_reparam (γ : Path x y) {f : I → I} (hfcont : Continuous f) (hf₀
     (hf₁ : f 1 = 1) : ⇑(γ.reparam f hfcont hf₀ hf₁) = γ ∘ f :=
   rfl
 #align path.coe_to_fun Path.coe_reparam
--- porting note: this seems like it was poorly named (was: `coe_to_fun`)
+-- Porting note: this seems like it was poorly named (was: `coe_to_fun`)
 
 @[simp]
 theorem reparam_id (γ : Path x y) : γ.reparam id continuous_id rfl rfl = γ := by

Co-authored-by: Patrick Massot <patrickmassot@free.fr> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -1056,7 +1056,7 @@ theorem IsPathConnected.exists_path_through_family {n : ℕ}
   obtain ⟨γ, hγ⟩ : ∃ γ : Path (p' 0) (p' n), (∀ i ≤ n, p' i ∈ range γ) ∧ range γ ⊆ s := by
     have hp' : ∀ i ≤ n, p' i ∈ s := by
       intro i hi
-      simp [Nat.lt_succ_of_le hi, hp]
+      simp [p', Nat.lt_succ_of_le hi, hp]
     clear_value p'
     clear hp p
     induction' n with n hn
@@ -1091,7 +1091,7 @@ theorem IsPathConnected.exists_path_through_family {n : ℕ}
         exact hγ₁
   have hpp' : ∀ k < n + 1, p k = p' k := by
     intro k hk
-    simp only [hk, dif_pos]
+    simp only [p', hk, dif_pos]
     congr
     ext
     rw [Fin.val_cast_of_lt hk]

Classifies by adding issue number (#10927) to porting notes claiming removed @[nolint has_nonempty_instance].

@@ -70,7 +70,7 @@ variable {X Y : Type*} [TopologicalSpace X] [TopologicalSpace Y] {x y z : X} {ι
 /-! ### Paths -/
 
 /-- Continuous path connecting two points `x` and `y` in a topological space -/
--- porting note: removed @[nolint has_nonempty_instance]
+-- porting note (#10927): removed @[nolint has_nonempty_instance]
 structure Path (x y : X) extends C(I, X) where
   /-- The start point of a `Path`. -/
   source' : toFun 0 = x

Classifies by adding issue number (#10754) to porting notes claiming added instance.

@@ -84,7 +84,7 @@ instance Path.funLike : FunLike (Path x y) I X where
     simp only [DFunLike.coe_fn_eq] at h
     cases γ₁; cases γ₂; congr
 
--- porting note: added this instance so that we can use `FunLike.coe` for `CoeFun`
+-- Porting note (#10754): added this instance so that we can use `FunLike.coe` for `CoeFun`
 -- this also fixed very strange `simp` timeout issues
 instance Path.continuousMapClass : ContinuousMapClass (Path x y) I X where
   map_continuous := fun γ => show Continuous γ.toContinuousMap by continuity

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

Zulip thread

Important changes

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

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

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

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

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

Similarly, MyEquivClass should take EquivLike as a parameter.

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

Remaining issues

Slower (failing) search

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

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

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

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

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

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

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

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

simp not firing sometimes

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

Missing instances due to unification failing

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

Workaround for issues

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

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

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

@@ -78,14 +78,16 @@ structure Path (x y : X) extends C(I, X) where
   target' : toFun 1 = y
 #align path Path
 
--- porting note: added this instance so that we can use `DFunLike.coe` for `CoeFun`
--- this also fixed very strange `simp` timeout issues
-instance Path.continuousMapClass : ContinuousMapClass (Path x y) I X where
+instance Path.funLike : FunLike (Path x y) I X where
   coe := fun γ ↦ ⇑γ.toContinuousMap
   coe_injective' := fun γ₁ γ₂ h => by
     simp only [DFunLike.coe_fn_eq] at h
     cases γ₁; cases γ₂; congr
-  map_continuous := fun γ => by continuity
+
+-- porting note: added this instance so that we can use `FunLike.coe` for `CoeFun`
+-- this also fixed very strange `simp` timeout issues
+instance Path.continuousMapClass : ContinuousMapClass (Path x y) I X where
+  map_continuous := fun γ => show Continuous γ.toContinuousMap by continuity
 
 -- porting note: not necessary in light of the instance above
 /-

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

@@ -1276,17 +1276,17 @@ theorem pathConnectedSpace_iff_connectedSpace [LocPathConnectedSpace X] :
     rw [pathConnectedSpace_iff_eq]
     use Classical.arbitrary X
     refine' IsClopen.eq_univ ⟨_, _⟩ (by simp)
+    · rw [isClosed_iff_nhds]
+      intro y H
+      rcases (path_connected_basis y).ex_mem with ⟨U, ⟨U_in, hU⟩⟩
+      rcases H U U_in with ⟨z, hz, hz'⟩
+      exact (hU.joinedIn z hz y <| mem_of_mem_nhds U_in).joined.mem_pathComponent hz'
     · rw [isOpen_iff_mem_nhds]
       intro y y_in
       rcases (path_connected_basis y).ex_mem with ⟨U, ⟨U_in, hU⟩⟩
       apply mem_of_superset U_in
       rw [← pathComponent_congr y_in]
       exact hU.subset_pathComponent (mem_of_mem_nhds U_in)
-    · rw [isClosed_iff_nhds]
-      intro y H
-      rcases (path_connected_basis y).ex_mem with ⟨U, ⟨U_in, hU⟩⟩
-      rcases H U U_in with ⟨z, hz, hz'⟩
-      exact (hU.joinedIn z hz y <| mem_of_mem_nhds U_in).joined.mem_pathComponent hz'
 #align path_connected_space_iff_connected_space pathConnectedSpace_iff_connectedSpace
 
 theorem pathConnected_subset_basis [LocPathConnectedSpace X] {U : Set X} (h : IsOpen U)

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>

@@ -78,12 +78,12 @@ structure Path (x y : X) extends C(I, X) where
   target' : toFun 1 = y
 #align path Path
 
--- porting note: added this instance so that we can use `FunLike.coe` for `CoeFun`
+-- porting note: added this instance so that we can use `DFunLike.coe` for `CoeFun`
 -- this also fixed very strange `simp` timeout issues
 instance Path.continuousMapClass : ContinuousMapClass (Path x y) I X where
   coe := fun γ ↦ ⇑γ.toContinuousMap
   coe_injective' := fun γ₁ γ₂ h => by
-    simp only [FunLike.coe_fn_eq] at h
+    simp only [DFunLike.coe_fn_eq] at h
     cases γ₁; cases γ₂; congr
   map_continuous := fun γ => by continuity
 
@@ -190,7 +190,7 @@ theorem refl_symm {a : X} : (Path.refl a).symm = Path.refl a := by
 @[simp]
 theorem symm_range {a b : X} (γ : Path a b) : range γ.symm = range γ := by
   ext x
-  simp only [mem_range, Path.symm, FunLike.coe, unitInterval.symm, SetCoe.exists, comp_apply,
+  simp only [mem_range, Path.symm, DFunLike.coe, unitInterval.symm, SetCoe.exists, comp_apply,
     Subtype.coe_mk]
   constructor <;> rintro ⟨y, hy, hxy⟩ <;> refine' ⟨1 - y, mem_iff_one_sub_mem.mp hy, _⟩ <;>
     convert hxy
@@ -202,7 +202,7 @@ theorem symm_range {a b : X} (γ : Path a b) : range γ.symm = range γ := by
 
 open ContinuousMap
 
-/- porting note: because of the new `FunLike` instance, we already have a coercion to `C(I, X)`
+/- porting note: because of the `DFunLike` instance, we already have a coercion to `C(I, X)`
 so we avoid adding another.
 --instance : Coe (Path x y) C(I, X) :=
   --⟨fun γ => γ.1⟩
@@ -646,7 +646,7 @@ theorem truncate_range {a b : X} (γ : Path a b) {t₀ t₁ : ℝ} :
   rw [← γ.extend_range]
   simp only [range_subset_iff, SetCoe.exists, SetCoe.forall]
   intro x _hx
-  simp only [FunLike.coe, Path.truncate, mem_range_self]
+  simp only [DFunLike.coe, Path.truncate, mem_range_self]
 #align path.truncate_range Path.truncate_range
 
 /-- For a path `γ`, `γ.truncate` gives a "continuous family of paths", by which we
@@ -671,7 +671,7 @@ theorem truncate_self {a b : X} (γ : Path a b) (t : ℝ) :
     γ.truncate t t = (Path.refl <| γ.extend t).cast (by rw [min_self]) rfl := by
   ext x
   rw [cast_coe]
-  simp only [truncate, FunLike.coe, refl, min_def, max_def]
+  simp only [truncate, DFunLike.coe, refl, min_def, max_def]
   split_ifs with h₁ h₂ <;> congr
 #align path.truncate_self Path.truncate_self
 

• rename Finset.Nonempty.image_iff to Finset.image_nonempty, deprecate the old version;
• rename Set.nonempty_image_iff to Set.image_nonempty, deprecate the old version;
• drop unneeded Finset.Nonempty arguments here and there;
• add versions of some lemmas that assume Nonempty s instead of Nonempty (s.image f) or Nonempty (s.map f).

@@ -991,7 +991,7 @@ nonrec theorem Inducing.isPathConnected_iff {f : X → Y} (hf : Inducing f) :
     IsPathConnected F ↔ IsPathConnected (f '' F) := by
   refine ⟨fun hF ↦ hF.image hf.continuous, fun hF ↦ ?_⟩
   simp? [isPathConnected_iff] at hF ⊢ says
-    simp only [isPathConnected_iff, nonempty_image_iff, mem_image, forall_exists_index,
+    simp only [isPathConnected_iff, image_nonempty, mem_image, forall_exists_index,
       and_imp, forall_apply_eq_imp_iff₂] at hF ⊢
   refine ⟨hF.1, fun x hx y hy ↦ ?_⟩
   rcases hF.2 x hx y hy with ⟨γ, hγ⟩

Introduce a typeclass LocallyCompactPair that allows us to unify different versions of ContinuousMap.continuous_eval and similar lemmas.

@@ -215,7 +215,7 @@ instance topologicalSpace : TopologicalSpace (Path x y) :=
   TopologicalSpace.induced ((↑) : _ → C(I, X)) ContinuousMap.compactOpen
 
 theorem continuous_eval : Continuous fun p : Path x y × I => p.1 p.2 :=
-  continuous_eval'.comp <| (continuous_induced_dom (α := Path x y)).prod_map continuous_id
+  continuous_eval.comp <| (continuous_induced_dom (α := Path x y)).prod_map continuous_id
 #align path.continuous_eval Path.continuous_eval
 
 @[continuity]

Search for [∀∃].*(_ and manually replace some occurrences with more readable versions. In case of ∀, the new expressions are defeq to the old ones. In case of ∃, they differ by exists_prop.

In some rare cases, golf proofs that needed fixing.

@@ -960,13 +960,13 @@ theorem isPathConnected_iff_eq : IsPathConnected F ↔ ∃ x ∈ F, pathComponen
 #align is_path_connected_iff_eq isPathConnected_iff_eq
 
 theorem IsPathConnected.joinedIn (h : IsPathConnected F) :
-    ∀ (x) (_ : x ∈ F) (y) (_ : y ∈ F), JoinedIn F x y := fun _x x_in _y y_in =>
+    ∀ᵉ (x ∈ F) (y ∈ F), JoinedIn F x y := fun _x x_in _y y_in =>
   let ⟨_b, _b_in, hb⟩ := h
   (hb x_in).symm.trans (hb y_in)
 #align is_path_connected.joined_in IsPathConnected.joinedIn
 
 theorem isPathConnected_iff :
-    IsPathConnected F ↔ F.Nonempty ∧ ∀ (x) (_ : x ∈ F) (y) (_ : y ∈ F), JoinedIn F x y :=
+    IsPathConnected F ↔ F.Nonempty ∧ ∀ᵉ (x ∈ F) (y ∈ F), JoinedIn F x y :=
   ⟨fun h =>
     ⟨let ⟨b, b_in, _hb⟩ := h; ⟨b, b_in⟩, h.joinedIn⟩,
     fun ⟨⟨b, b_in⟩, h⟩ => ⟨b, b_in, fun x_in => h _ b_in _ x_in⟩⟩

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

@@ -172,12 +172,15 @@ def symm (γ : Path x y) : Path y x where
 #align path.symm Path.symm
 
 @[simp]
-theorem symm_symm {γ : Path x y} : γ.symm.symm = γ := by
+theorem symm_symm (γ : Path x y) : γ.symm.symm = γ := by
   ext t
   show γ (σ (σ t)) = γ t
   rw [unitInterval.symm_symm]
 #align path.symm_symm Path.symm_symm
 
+theorem symm_bijective : Function.Bijective (Path.symm : Path x y → Path y x) :=
+  Function.bijective_iff_has_inverse.mpr ⟨_, symm_symm, symm_symm⟩
+
 @[simp]
 theorem refl_symm {a : X} : (Path.refl a).symm = Path.refl a := by
   ext

Only Prop-values fields should be capitalized, not P-valued fields where P is Prop-valued.

Rather than fixing Nonempty := in constructors, I just deleted the line as the instance can almost always be found automatically.

@@ -1118,9 +1118,9 @@ theorem IsPathConnected.exists_path_through_family' {n : ℕ}
 joined by a continuous path. -/
 class PathConnectedSpace (X : Type*) [TopologicalSpace X] : Prop where
   /-- A path-connected space must be nonempty. -/
-  Nonempty : Nonempty X
+  nonempty : Nonempty X
   /-- Any two points in a path-connected space must be joined by a continuous path. -/
-  Joined : ∀ x y : X, Joined x y
+  joined : ∀ x y : X, Joined x y
 #align path_connected_space PathConnectedSpace
 
 theorem pathConnectedSpace_iff_zerothHomotopy :
@@ -1130,7 +1130,7 @@ theorem pathConnectedSpace_iff_zerothHomotopy :
   · intro h
     refine' ⟨(nonempty_quotient_iff _).mpr h.1, ⟨_⟩⟩
     rintro ⟨x⟩ ⟨y⟩
-    exact Quotient.sound (PathConnectedSpace.Joined x y)
+    exact Quotient.sound (PathConnectedSpace.joined x y)
   · unfold ZerothHomotopy
     rintro ⟨h, h'⟩
     skip
@@ -1143,7 +1143,7 @@ variable [PathConnectedSpace X]
 
 /-- Use path-connectedness to build a path between two points. -/
 def somePath (x y : X) : Path x y :=
-  Nonempty.some (Joined x y)
+  Nonempty.some (joined x y)
 #align path_connected_space.some_path PathConnectedSpace.somePath
 
 end PathConnectedSpace
@@ -1165,11 +1165,11 @@ theorem isPathConnected_iff_pathConnectedSpace : IsPathConnected F ↔ PathConne
 theorem pathConnectedSpace_iff_univ : PathConnectedSpace X ↔ IsPathConnected (univ : Set X) := by
   constructor
   · intro h
-    haveI := @PathConnectedSpace.Nonempty X _ _
+    haveI := @PathConnectedSpace.nonempty X _ _
     inhabit X
     refine' ⟨default, mem_univ _, _⟩
     intros y _hy
-    simpa using PathConnectedSpace.Joined default y
+    simpa using PathConnectedSpace.joined default y
   · intro h
     have h' := h.joinedIn
     cases' h with x h
@@ -1196,8 +1196,8 @@ instance Quotient.instPathConnectedSpace {s : Setoid X} [PathConnectedSpace X] :
 /-- This is a special case of `NormedSpace.instPathConnectedSpace` (and
 `TopologicalAddGroup.pathConnectedSpace`). It exists only to simplify dependencies. -/
 instance Real.instPathConnectedSpace : PathConnectedSpace ℝ where
-  Nonempty := inferInstance
-  Joined := fun x y ↦ ⟨⟨⟨fun (t : I) ↦ (1 - t) * x + t * y, by continuity⟩, by simp, by simp⟩⟩
+  joined x y := ⟨⟨⟨fun (t : I) ↦ (1 - t) * x + t * y, by continuity⟩, by simp, by simp⟩⟩
+  nonempty := inferInstance
 
 theorem pathConnectedSpace_iff_eq : PathConnectedSpace X ↔ ∃ x : X, pathComponent x = univ := by
   simp [pathConnectedSpace_iff_univ, isPathConnected_iff_eq]

@@ -983,7 +983,7 @@ theorem IsPathConnected.image (hF : IsPathConnected F) {f : X → Y}
     (hf : Continuous f) : IsPathConnected (f '' F) := hF.image' hf.continuousOn
 #align is_path_connected.image IsPathConnected.image
 
-/-- If `f : X → Y` is a `Inducing`, `F(f)` is path-connected iff `F` is. -/
+/-- If `f : X → Y` is a `Inducing`, `f(F)` is path-connected iff `F` is. -/
 nonrec theorem Inducing.isPathConnected_iff {f : X → Y} (hf : Inducing f) :
     IsPathConnected F ↔ IsPathConnected (f '' F) := by
   refine ⟨fun hF ↦ hF.image hf.continuous, fun hF ↦ ?_⟩

Generalizing one of the proofs introduced in #7878

@@ -875,13 +875,8 @@ theorem JoinedIn.trans (hxy : JoinedIn F x y) (hyz : JoinedIn F y z) : JoinedIn
 
 theorem Specializes.joinedIn (h : x ⤳ y) (hx : x ∈ F) (hy : y ∈ F) : JoinedIn F x y := by
   refine ⟨⟨⟨Set.piecewise {1} (const I y) (const I x), ?_⟩, by simp, by simp⟩, fun t ↦ ?_⟩
-  · simp only [const, continuous_def, piecewise_preimage]
-    intro U hU
-    by_cases hy' : y ∈ U
-    · simp [hy', h.mem_open hU hy']
-    · by_cases hx' : x ∈ U
-      · simpa [hx', hy'] using isOpen_univ.sdiff isClosed_singleton
-      · simp [hx', hy']
+  · exact isClosed_singleton.continuous_piecewise_of_specializes continuous_const continuous_const
+      fun _ ↦ h
   · simp only [Path.coe_mk_mk, piecewise]
     split_ifs <;> assumption
 

Mirrors the corresponding proofs for connectedness.

Co-authored-by: @ADedecker

@@ -245,7 +245,7 @@ theorem continuous_extend : Continuous γ.extend :=
   γ.continuous.Icc_extend'
 #align path.continuous_extend Path.continuous_extend
 
-theorem _root_.Filter.Tendsto.path_extend {X Y : Type*} [TopologicalSpace X] [TopologicalSpace Y]
+theorem _root_.Filter.Tendsto.path_extend
     {l r : Y → X} {y : Y} {l₁ : Filter ℝ} {l₂ : Filter X} {γ : ∀ y, Path (l y) (r y)}
     (hγ : Tendsto (↿γ) (𝓝 y ×ˢ l₁.map (projIcc 0 1 zero_le_one)) l₂) :
     Tendsto (↿fun x => (γ x).extend) (𝓝 y ×ˢ l₁) l₂ :=
@@ -259,7 +259,7 @@ theorem _root_.ContinuousAt.path_extend {g : Y → ℝ} {l r : Y → X} (γ : 
 #align continuous_at.path_extend ContinuousAt.path_extend
 
 @[simp]
-theorem extend_extends {X : Type*} [TopologicalSpace X] {a b : X} (γ : Path a b) {t : ℝ}
+theorem extend_extends {a b : X} (γ : Path a b) {t : ℝ}
     (ht : t ∈ (Icc 0 1 : Set ℝ)) : γ.extend t = γ ⟨t, ht⟩ :=
   IccExtend_of_mem _ γ ht
 #align path.extend_extends Path.extend_extends
@@ -271,29 +271,28 @@ theorem extend_one : γ.extend 1 = y := by simp
 #align path.extend_one Path.extend_one
 
 @[simp]
-theorem extend_extends' {X : Type*} [TopologicalSpace X] {a b : X} (γ : Path a b)
-    (t : (Icc 0 1 : Set ℝ)) : γ.extend t = γ t :=
+theorem extend_extends' {a b : X} (γ : Path a b) (t : (Icc 0 1 : Set ℝ)) : γ.extend t = γ t :=
   IccExtend_val _ γ t
 #align path.extend_extends' Path.extend_extends'
 
 @[simp]
-theorem extend_range {X : Type*} [TopologicalSpace X] {a b : X} (γ : Path a b) :
+theorem extend_range {a b : X} (γ : Path a b) :
     range γ.extend = range γ :=
   IccExtend_range _ γ
 #align path.extend_range Path.extend_range
 
-theorem extend_of_le_zero {X : Type*} [TopologicalSpace X] {a b : X} (γ : Path a b) {t : ℝ}
+theorem extend_of_le_zero {a b : X} (γ : Path a b) {t : ℝ}
     (ht : t ≤ 0) : γ.extend t = a :=
   (IccExtend_of_le_left _ _ ht).trans γ.source
 #align path.extend_of_le_zero Path.extend_of_le_zero
 
-theorem extend_of_one_le {X : Type*} [TopologicalSpace X] {a b : X} (γ : Path a b) {t : ℝ}
+theorem extend_of_one_le {a b : X} (γ : Path a b) {t : ℝ}
     (ht : 1 ≤ t) : γ.extend t = b :=
   (IccExtend_of_right_le _ _ ht).trans γ.target
 #align path.extend_of_one_le Path.extend_of_one_le
 
 @[simp]
-theorem refl_extend {X : Type*} [TopologicalSpace X] {a : X} : (Path.refl a).extend = fun _ => a :=
+theorem refl_extend {a : X} : (Path.refl a).extend = fun _ => a :=
   rfl
 #align path.refl_extend Path.refl_extend
 
@@ -349,14 +348,14 @@ theorem trans_symm (γ : Path x y) (γ' : Path y z) : (γ.trans γ').symm = γ'.
 #align path.trans_symm Path.trans_symm
 
 @[simp]
-theorem refl_trans_refl {X : Type*} [TopologicalSpace X] {a : X} :
+theorem refl_trans_refl {a : X} :
     (Path.refl a).trans (Path.refl a) = Path.refl a := by
   ext
   simp only [Path.trans, ite_self, one_div, Path.refl_extend]
   rfl
 #align path.refl_trans_refl Path.refl_trans_refl
 
-theorem trans_range {X : Type*} [TopologicalSpace X] {a b c : X} (γ₁ : Path a b) (γ₂ : Path b c) :
+theorem trans_range {a b c : X} (γ₁ : Path a b) (γ₂ : Path b c) :
     range (γ₁.trans γ₂) = range γ₁ ∪ range γ₂ := by
   rw [Path.trans]
   apply eq_of_subset_of_subset
@@ -394,33 +393,32 @@ theorem trans_range {X : Type*} [TopologicalSpace X] {a b c : X} (γ₁ : Path a
 #align path.trans_range Path.trans_range
 
 /-- Image of a path from `x` to `y` by a map which is continuous on the path. -/
-def map' (γ : Path x y) {Y : Type*} [TopologicalSpace Y] {f : X → Y}
-    (h : ContinuousOn f (range γ)) : Path (f x) (f y) where
+def map' (γ : Path x y) {f : X → Y} (h : ContinuousOn f (range γ)) : Path (f x) (f y) where
   toFun := f ∘ γ
   continuous_toFun := h.comp_continuous γ.continuous (fun x ↦ mem_range_self x)
   source' := by simp
   target' := by simp
 
 /-- Image of a path from `x` to `y` by a continuous map -/
-def map (γ : Path x y) {Y : Type*} [TopologicalSpace Y] {f : X → Y} (h : Continuous f) :
+def map (γ : Path x y) {f : X → Y} (h : Continuous f) :
     Path (f x) (f y) := γ.map' h.continuousOn
 #align path.map Path.map
 
 @[simp]
-theorem map_coe (γ : Path x y) {Y : Type*} [TopologicalSpace Y] {f : X → Y} (h : Continuous f) :
+theorem map_coe (γ : Path x y) {f : X → Y} (h : Continuous f) :
     (γ.map h : I → Y) = f ∘ γ := by
   ext t
   rfl
 #align path.map_coe Path.map_coe
 
 @[simp]
-theorem map_symm (γ : Path x y) {Y : Type*} [TopologicalSpace Y] {f : X → Y} (h : Continuous f) :
+theorem map_symm (γ : Path x y) {f : X → Y} (h : Continuous f) :
     (γ.map h).symm = γ.symm.map h :=
   rfl
 #align path.map_symm Path.map_symm
 
 @[simp]
-theorem map_trans (γ : Path x y) (γ' : Path y z) {Y : Type*} [TopologicalSpace Y] {f : X → Y}
+theorem map_trans (γ : Path x y) (γ' : Path y z) {f : X → Y}
     (h : Continuous f) : (γ.trans γ').map h = (γ.map h).trans (γ'.map h) := by
   ext t
   rw [trans_apply, map_coe, Function.comp_apply, trans_apply]
@@ -434,7 +432,7 @@ theorem map_id (γ : Path x y) : γ.map continuous_id = γ := by
 #align path.map_id Path.map_id
 
 @[simp]
-theorem map_map (γ : Path x y) {Y : Type*} [TopologicalSpace Y] {Z : Type*} [TopologicalSpace Z]
+theorem map_map (γ : Path x y) {Z : Type*} [TopologicalSpace Z]
     {f : X → Y} (hf : Continuous f) {g : Y → Z} (hg : Continuous g) :
     (γ.map hf).map hg = γ.map (hg.comp hf) := by
   ext
@@ -450,13 +448,13 @@ def cast (γ : Path x y) {x' y'} (hx : x' = x) (hy : y' = y) : Path x' y' where
 #align path.cast Path.cast
 
 @[simp]
-theorem symm_cast {X : Type*} [TopologicalSpace X] {a₁ a₂ b₁ b₂ : X} (γ : Path a₂ b₂)
-    (ha : a₁ = a₂) (hb : b₁ = b₂) : (γ.cast ha hb).symm = γ.symm.cast hb ha :=
+theorem symm_cast {a₁ a₂ b₁ b₂ : X} (γ : Path a₂ b₂) (ha : a₁ = a₂) (hb : b₁ = b₂) :
+    (γ.cast ha hb).symm = γ.symm.cast hb ha :=
   rfl
 #align path.symm_cast Path.symm_cast
 
 @[simp]
-theorem trans_cast {X : Type*} [TopologicalSpace X] {a₁ a₂ b₁ b₂ c₁ c₂ : X} (γ : Path a₂ b₂)
+theorem trans_cast {a₁ a₂ b₁ b₂ c₁ c₂ : X} (γ : Path a₂ b₂)
     (γ' : Path b₂ c₂) (ha : a₁ = a₂) (hb : b₁ = b₂) (hc : c₁ = c₂) :
     (γ.cast ha hb).trans (γ'.cast hb hc) = (γ.trans γ').cast ha hc :=
   rfl
@@ -468,7 +466,7 @@ theorem cast_coe (γ : Path x y) {x' y'} (hx : x' = x) (hy : y' = y) : (γ.cast
 #align path.cast_coe Path.cast_coe
 
 @[continuity]
-theorem symm_continuous_family {X ι : Type*} [TopologicalSpace X] [TopologicalSpace ι]
+theorem symm_continuous_family {ι : Type*} [TopologicalSpace ι]
     {a b : ι → X} (γ : ∀ t : ι, Path (a t) (b t)) (h : Continuous ↿γ) :
     Continuous ↿fun t => (γ t).symm :=
   h.comp (continuous_id.prod_map continuous_symm)
@@ -480,15 +478,15 @@ theorem continuous_symm : Continuous (symm : Path x y → Path y x) :=
 #align path.continuous_symm Path.continuous_symm
 
 @[continuity]
-theorem continuous_uncurry_extend_of_continuous_family {X ι : Type*} [TopologicalSpace X]
-    [TopologicalSpace ι] {a b : ι → X} (γ : ∀ t : ι, Path (a t) (b t)) (h : Continuous ↿γ) :
+theorem continuous_uncurry_extend_of_continuous_family {ι : Type*} [TopologicalSpace ι]
+    {a b : ι → X} (γ : ∀ t : ι, Path (a t) (b t)) (h : Continuous ↿γ) :
     Continuous ↿fun t => (γ t).extend := by
   refine' h.comp (continuous_id.prod_map continuous_projIcc)
   exact zero_le_one
 #align path.continuous_uncurry_extend_of_continuous_family Path.continuous_uncurry_extend_of_continuous_family
 
 @[continuity]
-theorem trans_continuous_family {X ι : Type*} [TopologicalSpace X] [TopologicalSpace ι]
+theorem trans_continuous_family {ι : Type*} [TopologicalSpace ι]
     {a b c : ι → X} (γ₁ : ∀ t : ι, Path (a t) (b t)) (h₁ : Continuous ↿γ₁)
     (γ₂ : ∀ t : ι, Path (b t) (c t)) (h₂ : Continuous ↿γ₂) :
     Continuous ↿fun t => (γ₁ t).trans (γ₂ t) := by
@@ -640,7 +638,7 @@ def truncateOfLE {X : Type*} [TopologicalSpace X] {a b : X} (γ : Path a b) {t
   (γ.truncate t₀ t₁).cast (by rw [min_eq_left h]) rfl
 #align path.truncate_of_le Path.truncateOfLE
 
-theorem truncate_range {X : Type*} [TopologicalSpace X] {a b : X} (γ : Path a b) {t₀ t₁ : ℝ} :
+theorem truncate_range {a b : X} (γ : Path a b) {t₀ t₁ : ℝ} :
     range (γ.truncate t₀ t₁) ⊆ range γ := by
   rw [← γ.extend_range]
   simp only [range_subset_iff, SetCoe.exists, SetCoe.forall]
@@ -651,7 +649,7 @@ theorem truncate_range {X : Type*} [TopologicalSpace X] {a b : X} (γ : Path a b
 /-- For a path `γ`, `γ.truncate` gives a "continuous family of paths", by which we
   mean the uncurried function which maps `(t₀, t₁, s)` to `γ.truncate t₀ t₁ s` is continuous. -/
 @[continuity]
-theorem truncate_continuous_family {X : Type*} [TopologicalSpace X] {a b : X} (γ : Path a b) :
+theorem truncate_continuous_family {a b : X} (γ : Path a b) :
     Continuous (fun x => γ.truncate x.1 x.2.1 x.2.2 : ℝ × ℝ × I → X) :=
   γ.continuous_extend.comp
     (((continuous_subtype_val.comp (continuous_snd.comp continuous_snd)).max continuous_fst).min
@@ -659,14 +657,14 @@ theorem truncate_continuous_family {X : Type*} [TopologicalSpace X] {a b : X} (
 #align path.truncate_continuous_family Path.truncate_continuous_family
 
 @[continuity]
-theorem truncate_const_continuous_family {X : Type*} [TopologicalSpace X] {a b : X} (γ : Path a b)
+theorem truncate_const_continuous_family {a b : X} (γ : Path a b)
     (t : ℝ) : Continuous ↿(γ.truncate t) := by
   have key : Continuous (fun x => (t, x) : ℝ × I → ℝ × ℝ × I) := by continuity
   exact γ.truncate_continuous_family.comp key
 #align path.truncate_const_continuous_family Path.truncate_const_continuous_family
 
 @[simp]
-theorem truncate_self {X : Type*} [TopologicalSpace X] {a b : X} (γ : Path a b) (t : ℝ) :
+theorem truncate_self {a b : X} (γ : Path a b) (t : ℝ) :
     γ.truncate t t = (Path.refl <| γ.extend t).cast (by rw [min_self]) rfl := by
   ext x
   rw [cast_coe]
@@ -675,19 +673,19 @@ theorem truncate_self {X : Type*} [TopologicalSpace X] {a b : X} (γ : Path a b)
 #align path.truncate_self Path.truncate_self
 
 @[simp 1001] -- porting note: increase `simp` priority so left-hand side doesn't simplify
-theorem truncate_zero_zero {X : Type*} [TopologicalSpace X] {a b : X} (γ : Path a b) :
+theorem truncate_zero_zero {a b : X} (γ : Path a b) :
     γ.truncate 0 0 = (Path.refl a).cast (by rw [min_self, γ.extend_zero]) γ.extend_zero := by
   convert γ.truncate_self 0
 #align path.truncate_zero_zero Path.truncate_zero_zero
 
 @[simp 1001] -- porting note: increase `simp` priority so left-hand side doesn't simplify
-theorem truncate_one_one {X : Type*} [TopologicalSpace X] {a b : X} (γ : Path a b) :
+theorem truncate_one_one {a b : X} (γ : Path a b) :
     γ.truncate 1 1 = (Path.refl b).cast (by rw [min_self, γ.extend_one]) γ.extend_one := by
   convert γ.truncate_self 1
 #align path.truncate_one_one Path.truncate_one_one
 
 @[simp]
-theorem truncate_zero_one {X : Type*} [TopologicalSpace X] {a b : X} (γ : Path a b) :
+theorem truncate_zero_one {a b : X} (γ : Path a b) :
     γ.truncate 0 1 = γ.cast (by simp [zero_le_one, extend_zero]) (by simp) := by
   ext x
   rw [cast_coe]
@@ -875,6 +873,21 @@ theorem JoinedIn.trans (hxy : JoinedIn F x y) (hyz : JoinedIn F y z) : JoinedIn
   exact hxy.trans hyz
 #align joined_in.trans JoinedIn.trans
 
+theorem Specializes.joinedIn (h : x ⤳ y) (hx : x ∈ F) (hy : y ∈ F) : JoinedIn F x y := by
+  refine ⟨⟨⟨Set.piecewise {1} (const I y) (const I x), ?_⟩, by simp, by simp⟩, fun t ↦ ?_⟩
+  · simp only [const, continuous_def, piecewise_preimage]
+    intro U hU
+    by_cases hy' : y ∈ U
+    · simp [hy', h.mem_open hU hy']
+    · by_cases hx' : x ∈ U
+      · simpa [hx', hy'] using isOpen_univ.sdiff isClosed_singleton
+      · simp [hx', hy']
+  · simp only [Path.coe_mk_mk, piecewise]
+    split_ifs <;> assumption
+
+theorem Inseparable.joinedIn (h : Inseparable x y) (hx : x ∈ F) (hy : y ∈ F) : JoinedIn F x y :=
+  h.specializes.joinedIn hx hy
+
 /-! ### Path component -/
 
 
@@ -961,7 +974,8 @@ theorem isPathConnected_iff :
     fun ⟨⟨b, b_in⟩, h⟩ => ⟨b, b_in, fun x_in => h _ b_in _ x_in⟩⟩
 #align is_path_connected_iff isPathConnected_iff
 
-theorem IsPathConnected.image' {Y : Type*} [TopologicalSpace Y] (hF : IsPathConnected F)
+/-- If `f` is continuous on `F` and `F` is path-connected, so is `f(F)`. -/
+theorem IsPathConnected.image' (hF : IsPathConnected F)
     {f : X → Y} (hf : ContinuousOn f F) : IsPathConnected (f '' F) := by
   rcases hF with ⟨x, x_in, hx⟩
   use f x, mem_image_of_mem f x_in
@@ -969,10 +983,39 @@ theorem IsPathConnected.image' {Y : Type*} [TopologicalSpace Y] (hF : IsPathConn
   refine ⟨(hx y_in).somePath.map' ?_, fun t ↦ ⟨_, (hx y_in).somePath_mem t, rfl⟩⟩
   exact hf.mono (range_subset_iff.2 (hx y_in).somePath_mem)
 
-theorem IsPathConnected.image {Y : Type*} [TopologicalSpace Y] (hF : IsPathConnected F) {f : X → Y}
+/-- If `f` is continuous and `F` is path-connected, so is `f(F)`. -/
+theorem IsPathConnected.image (hF : IsPathConnected F) {f : X → Y}
     (hf : Continuous f) : IsPathConnected (f '' F) := hF.image' hf.continuousOn
 #align is_path_connected.image IsPathConnected.image
 
+/-- If `f : X → Y` is a `Inducing`, `F(f)` is path-connected iff `F` is. -/
+nonrec theorem Inducing.isPathConnected_iff {f : X → Y} (hf : Inducing f) :
+    IsPathConnected F ↔ IsPathConnected (f '' F) := by
+  refine ⟨fun hF ↦ hF.image hf.continuous, fun hF ↦ ?_⟩
+  simp? [isPathConnected_iff] at hF ⊢ says
+    simp only [isPathConnected_iff, nonempty_image_iff, mem_image, forall_exists_index,
+      and_imp, forall_apply_eq_imp_iff₂] at hF ⊢
+  refine ⟨hF.1, fun x hx y hy ↦ ?_⟩
+  rcases hF.2 x hx y hy with ⟨γ, hγ⟩
+  choose γ' hγ' hγγ' using hγ
+  have key₁ : Inseparable x (γ' 0) := by rw [← hf.inseparable_iff, hγγ' 0, γ.source]
+  have key₂ : Inseparable (γ' 1) y := by rw [← hf.inseparable_iff, hγγ' 1, γ.target]
+  refine key₁.joinedIn hx (hγ' 0) |>.trans ⟨⟨⟨γ', ?_⟩, rfl, rfl⟩, hγ'⟩ |>.trans
+    (key₂.joinedIn (hγ' 1) hy)
+  simpa [hf.continuous_iff] using γ.continuous.congr fun t ↦ (hγγ' t).symm
+
+/-- If `h : X → Y` is a homeomorphism, `h(s)` is path-connected iff `s` is. -/
+@[simp]
+theorem Homeomorph.isPathConnected_image {s : Set X} (h : X ≃ₜ Y) :
+    IsPathConnected (h '' s) ↔ IsPathConnected s :=
+  h.inducing.isPathConnected_iff.symm
+
+/-- If `h : X → Y` is a homeomorphism, `h⁻¹(s)` is path-connected iff `s` is. -/
+@[simp]
+theorem Homeomorph.isPathConnected_preimage {s : Set Y} (h : X ≃ₜ Y) :
+    IsPathConnected (h ⁻¹' s) ↔ IsPathConnected s := by
+  rw [← Homeomorph.image_symm]; exact h.symm.isPathConnected_image
+
 theorem IsPathConnected.mem_pathComponent (h : IsPathConnected F) (x_in : x ∈ F) (y_in : y ∈ F) :
     y ∈ pathComponent x :=
   (h.joinedIn x x_in y y_in).joined
@@ -1006,7 +1049,7 @@ theorem IsPathConnected.preimage_coe {U W : Set X} (hW : IsPathConnected W) (hWU
   exact ⟨(hx hyW).joined_subtype.somePath.map (continuous_inclusion hWU), by simp⟩
 #align is_path_connected.preimage_coe IsPathConnected.preimage_coe
 
-theorem IsPathConnected.exists_path_through_family {X : Type*} [TopologicalSpace X] {n : ℕ}
+theorem IsPathConnected.exists_path_through_family {n : ℕ}
     {s : Set X} (h : IsPathConnected s) (p : Fin (n + 1) → X) (hp : ∀ i, p i ∈ s) :
     ∃ γ : Path (p 0) (p n), range γ ⊆ s ∧ ∀ i, p i ∈ range γ := by
   let p' : ℕ → X := fun k => if h : k < n + 1 then p ⟨k, h⟩ else p ⟨0, n.zero_lt_succ⟩
@@ -1062,7 +1105,7 @@ theorem IsPathConnected.exists_path_through_family {X : Type*} [TopologicalSpace
   rw [Nat.mod_eq_of_lt hi]
 #align is_path_connected.exists_path_through_family IsPathConnected.exists_path_through_family
 
-theorem IsPathConnected.exists_path_through_family' {X : Type*} [TopologicalSpace X] {n : ℕ}
+theorem IsPathConnected.exists_path_through_family' {n : ℕ}
     {s : Set X} (h : IsPathConnected s) (p : Fin (n + 1) → X) (hp : ∀ i, p i ∈ s) :
     ∃ (γ : Path (p 0) (p n)) (t : Fin (n + 1) → I), (∀ t, γ t ∈ s) ∧ ∀ i, γ (t i) = p i := by
   rcases h.exists_path_through_family p hp with ⟨γ, hγ⟩

For faster build times and clearer dependencies. No attempt at being exhaustive.

The new import in Clopen.lean had been transitively imported before.

@@ -5,7 +5,6 @@ Authors: Patrick Massot
 -/
 import Mathlib.Topology.Algebra.Order.ProjIcc
 import Mathlib.Topology.CompactOpen
-import Mathlib.Topology.ContinuousFunction.Basic
 import Mathlib.Topology.UnitInterval
 
 #align_import topology.path_connected from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"

Replace rcases( with rcases (. Same thing for convert( and congrm(. No other change.

@@ -1223,7 +1223,7 @@ theorem locPathConnected_of_bases {p : ι → Prop} {s : X → ι → Set X}
   · intro i pi
     exact ⟨s x i, ⟨(h x).mem_of_mem pi, h' x i pi⟩, by rfl⟩
   · rintro U ⟨U_in, _hU⟩
-    rcases(h x).mem_iff.mp U_in with ⟨i, pi, hi⟩
+    rcases (h x).mem_iff.mp U_in with ⟨i, pi, hi⟩
     tauto
 #align loc_path_connected_of_bases locPathConnected_of_bases
 
@@ -1238,13 +1238,13 @@ theorem pathConnectedSpace_iff_connectedSpace [LocPathConnectedSpace X] :
     refine' IsClopen.eq_univ ⟨_, _⟩ (by simp)
     · rw [isOpen_iff_mem_nhds]
       intro y y_in
-      rcases(path_connected_basis y).ex_mem with ⟨U, ⟨U_in, hU⟩⟩
+      rcases (path_connected_basis y).ex_mem with ⟨U, ⟨U_in, hU⟩⟩
       apply mem_of_superset U_in
       rw [← pathComponent_congr y_in]
       exact hU.subset_pathComponent (mem_of_mem_nhds U_in)
     · rw [isClosed_iff_nhds]
       intro y H
-      rcases(path_connected_basis y).ex_mem with ⟨U, ⟨U_in, hU⟩⟩
+      rcases (path_connected_basis y).ex_mem with ⟨U, ⟨U_in, hU⟩⟩
       rcases H U U_in with ⟨z, hz, hz'⟩
       exact (hU.joinedIn z hz y <| mem_of_mem_nhds U_in).joined.mem_pathComponent hz'
 #align path_connected_space_iff_connected_space pathConnectedSpace_iff_connectedSpace

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

@@ -1148,7 +1148,7 @@ theorem isPathConnected_range [PathConnectedSpace X] {f : X → Y} (hf : Continu
   exact isPathConnected_univ.image hf
 
 theorem Function.Surjective.pathConnectedSpace [PathConnectedSpace X]
-  {f : X → Y} (hf : Surjective f) (hf' : Continuous f) : PathConnectedSpace Y := by
+    {f : X → Y} (hf : Surjective f) (hf' : Continuous f) : PathConnectedSpace Y := by
   rw [pathConnectedSpace_iff_univ, ← hf.range_eq]
   exact isPathConnected_range hf'
 

@@ -1156,7 +1156,7 @@ instance Quotient.instPathConnectedSpace {s : Setoid X} [PathConnectedSpace X] :
     PathConnectedSpace (Quotient s) :=
   (surjective_quotient_mk' X).pathConnectedSpace continuous_coinduced_rng
 
-/-- This is a special case of `NormedSpace.path_connected` (and
+/-- This is a special case of `NormedSpace.instPathConnectedSpace` (and
 `TopologicalAddGroup.pathConnectedSpace`). It exists only to simplify dependencies. -/
 instance Real.instPathConnectedSpace : PathConnectedSpace ℝ where
   Nonempty := inferInstance

The mathlib3 lemma is about quotient.mk, which takes an instance argument and is translated into mathlib4 as Quotient.mk'.

@@ -1154,7 +1154,7 @@ theorem Function.Surjective.pathConnectedSpace [PathConnectedSpace X]
 
 instance Quotient.instPathConnectedSpace {s : Setoid X} [PathConnectedSpace X] :
     PathConnectedSpace (Quotient s) :=
-  (surjective_quotient_mk X).pathConnectedSpace continuous_coinduced_rng
+  (surjective_quotient_mk' X).pathConnectedSpace continuous_coinduced_rng
 
 /-- This is a special case of `NormedSpace.path_connected` (and
 `TopologicalAddGroup.pathConnectedSpace`). It exists only to simplify dependencies. -/

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.

@@ -338,31 +338,15 @@ theorem trans_symm (γ : Path x y) (γ' : Path y z) : (γ.trans γ').symm = γ'.
   ext t
   simp only [trans_apply, ← one_div, symm_apply, not_le, Function.comp_apply]
   split_ifs with h h₁ h₂ <;> rw [coe_symm_eq] at h
-  · have ht : (t : ℝ) = 1 / 2 := by
-      refine le_antisymm h₁ ?_
-      rw [sub_le_comm] at h
-      norm_num at h
-      exact h
-    -- porting note: was `linarith [unitInterval.nonneg t, unitInterval.le_one t]` but `linarith`
-    -- doesn't know about `ℚ` yet. https://github.com/leanprover-community/mathlib4/issues/2714
-    -- porting note: although `linarith` now knows about `ℚ`, it still fails here as it doesn't
-    -- find `LinearOrder X`.
-    simp_rw [unitInterval.symm, ht]
-    norm_num
+  · have ht : (t : ℝ) = 1 / 2 := by linarith
+    norm_num [ht]
   · refine' congr_arg _ (Subtype.ext _)
-    norm_num [unitInterval.symm, sub_sub_eq_add_sub, mul_sub]
-    ring
+    norm_num [sub_sub_eq_add_sub, mul_sub]
   · refine' congr_arg _ (Subtype.ext _)
     norm_num [mul_sub, h]
-    ring
-  · -- porting note: was `linarith [unitInterval.nonneg t, unitInterval.le_one t]` but `linarith`
-    -- doesn't know about `ℚ` yet. https://github.com/leanprover-community/mathlib4/issues/2714
-    -- porting note: although `linarith` now knows about `ℚ`, it still fails here as it doesn't
-    -- find `LinearOrder X`.
-    exfalso
-    rw [sub_le_comm] at h
-    norm_num at h h₂
-    exact (h.trans h₂).ne rfl
+    ring -- TODO norm_num should really do this
+  · exfalso
+    linarith
 #align path.trans_symm Path.trans_symm
 
 @[simp]

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

This has nice performance benefits.

@@ -66,7 +66,7 @@ noncomputable section
 
 open Classical Topology Filter unitInterval Set Function
 
-variable {X Y : Type _} [TopologicalSpace X] [TopologicalSpace Y] {x y z : X} {ι : Type _}
+variable {X Y : Type*} [TopologicalSpace X] [TopologicalSpace Y] {x y z : X} {ι : Type*}
 
 /-! ### Paths -/
 
@@ -145,7 +145,7 @@ theorem coe_mk : ⇑(γ : C(I, X)) = γ :=
   rfl
 
 /-- Any function `φ : Π (a : α), Path (x a) (y a)` can be seen as a function `α × I → X`. -/
-instance hasUncurryPath {X α : Type _} [TopologicalSpace X] {x y : α → X} :
+instance hasUncurryPath {X α : Type*} [TopologicalSpace X] {x y : α → X} :
     HasUncurry (∀ a : α, Path (x a) (y a)) (α × I) X :=
   ⟨fun φ p => φ p.1 p.2⟩
 #align path.has_uncurry_path Path.hasUncurryPath
@@ -246,7 +246,7 @@ theorem continuous_extend : Continuous γ.extend :=
   γ.continuous.Icc_extend'
 #align path.continuous_extend Path.continuous_extend
 
-theorem _root_.Filter.Tendsto.path_extend {X Y : Type _} [TopologicalSpace X] [TopologicalSpace Y]
+theorem _root_.Filter.Tendsto.path_extend {X Y : Type*} [TopologicalSpace X] [TopologicalSpace Y]
     {l r : Y → X} {y : Y} {l₁ : Filter ℝ} {l₂ : Filter X} {γ : ∀ y, Path (l y) (r y)}
     (hγ : Tendsto (↿γ) (𝓝 y ×ˢ l₁.map (projIcc 0 1 zero_le_one)) l₂) :
     Tendsto (↿fun x => (γ x).extend) (𝓝 y ×ˢ l₁) l₂ :=
@@ -260,7 +260,7 @@ theorem _root_.ContinuousAt.path_extend {g : Y → ℝ} {l r : Y → X} (γ : 
 #align continuous_at.path_extend ContinuousAt.path_extend
 
 @[simp]
-theorem extend_extends {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) {t : ℝ}
+theorem extend_extends {X : Type*} [TopologicalSpace X] {a b : X} (γ : Path a b) {t : ℝ}
     (ht : t ∈ (Icc 0 1 : Set ℝ)) : γ.extend t = γ ⟨t, ht⟩ :=
   IccExtend_of_mem _ γ ht
 #align path.extend_extends Path.extend_extends
@@ -272,29 +272,29 @@ theorem extend_one : γ.extend 1 = y := by simp
 #align path.extend_one Path.extend_one
 
 @[simp]
-theorem extend_extends' {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b)
+theorem extend_extends' {X : Type*} [TopologicalSpace X] {a b : X} (γ : Path a b)
     (t : (Icc 0 1 : Set ℝ)) : γ.extend t = γ t :=
   IccExtend_val _ γ t
 #align path.extend_extends' Path.extend_extends'
 
 @[simp]
-theorem extend_range {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) :
+theorem extend_range {X : Type*} [TopologicalSpace X] {a b : X} (γ : Path a b) :
     range γ.extend = range γ :=
   IccExtend_range _ γ
 #align path.extend_range Path.extend_range
 
-theorem extend_of_le_zero {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) {t : ℝ}
+theorem extend_of_le_zero {X : Type*} [TopologicalSpace X] {a b : X} (γ : Path a b) {t : ℝ}
     (ht : t ≤ 0) : γ.extend t = a :=
   (IccExtend_of_le_left _ _ ht).trans γ.source
 #align path.extend_of_le_zero Path.extend_of_le_zero
 
-theorem extend_of_one_le {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) {t : ℝ}
+theorem extend_of_one_le {X : Type*} [TopologicalSpace X] {a b : X} (γ : Path a b) {t : ℝ}
     (ht : 1 ≤ t) : γ.extend t = b :=
   (IccExtend_of_right_le _ _ ht).trans γ.target
 #align path.extend_of_one_le Path.extend_of_one_le
 
 @[simp]
-theorem refl_extend {X : Type _} [TopologicalSpace X] {a : X} : (Path.refl a).extend = fun _ => a :=
+theorem refl_extend {X : Type*} [TopologicalSpace X] {a : X} : (Path.refl a).extend = fun _ => a :=
   rfl
 #align path.refl_extend Path.refl_extend
 
@@ -366,14 +366,14 @@ theorem trans_symm (γ : Path x y) (γ' : Path y z) : (γ.trans γ').symm = γ'.
 #align path.trans_symm Path.trans_symm
 
 @[simp]
-theorem refl_trans_refl {X : Type _} [TopologicalSpace X] {a : X} :
+theorem refl_trans_refl {X : Type*} [TopologicalSpace X] {a : X} :
     (Path.refl a).trans (Path.refl a) = Path.refl a := by
   ext
   simp only [Path.trans, ite_self, one_div, Path.refl_extend]
   rfl
 #align path.refl_trans_refl Path.refl_trans_refl
 
-theorem trans_range {X : Type _} [TopologicalSpace X] {a b c : X} (γ₁ : Path a b) (γ₂ : Path b c) :
+theorem trans_range {X : Type*} [TopologicalSpace X] {a b c : X} (γ₁ : Path a b) (γ₂ : Path b c) :
     range (γ₁.trans γ₂) = range γ₁ ∪ range γ₂ := by
   rw [Path.trans]
   apply eq_of_subset_of_subset
@@ -411,7 +411,7 @@ theorem trans_range {X : Type _} [TopologicalSpace X] {a b c : X} (γ₁ : Path
 #align path.trans_range Path.trans_range
 
 /-- Image of a path from `x` to `y` by a map which is continuous on the path. -/
-def map' (γ : Path x y) {Y : Type _} [TopologicalSpace Y] {f : X → Y}
+def map' (γ : Path x y) {Y : Type*} [TopologicalSpace Y] {f : X → Y}
     (h : ContinuousOn f (range γ)) : Path (f x) (f y) where
   toFun := f ∘ γ
   continuous_toFun := h.comp_continuous γ.continuous (fun x ↦ mem_range_self x)
@@ -419,25 +419,25 @@ def map' (γ : Path x y) {Y : Type _} [TopologicalSpace Y] {f : X → Y}
   target' := by simp
 
 /-- Image of a path from `x` to `y` by a continuous map -/
-def map (γ : Path x y) {Y : Type _} [TopologicalSpace Y] {f : X → Y} (h : Continuous f) :
+def map (γ : Path x y) {Y : Type*} [TopologicalSpace Y] {f : X → Y} (h : Continuous f) :
     Path (f x) (f y) := γ.map' h.continuousOn
 #align path.map Path.map
 
 @[simp]
-theorem map_coe (γ : Path x y) {Y : Type _} [TopologicalSpace Y] {f : X → Y} (h : Continuous f) :
+theorem map_coe (γ : Path x y) {Y : Type*} [TopologicalSpace Y] {f : X → Y} (h : Continuous f) :
     (γ.map h : I → Y) = f ∘ γ := by
   ext t
   rfl
 #align path.map_coe Path.map_coe
 
 @[simp]
-theorem map_symm (γ : Path x y) {Y : Type _} [TopologicalSpace Y] {f : X → Y} (h : Continuous f) :
+theorem map_symm (γ : Path x y) {Y : Type*} [TopologicalSpace Y] {f : X → Y} (h : Continuous f) :
     (γ.map h).symm = γ.symm.map h :=
   rfl
 #align path.map_symm Path.map_symm
 
 @[simp]
-theorem map_trans (γ : Path x y) (γ' : Path y z) {Y : Type _} [TopologicalSpace Y] {f : X → Y}
+theorem map_trans (γ : Path x y) (γ' : Path y z) {Y : Type*} [TopologicalSpace Y] {f : X → Y}
     (h : Continuous f) : (γ.trans γ').map h = (γ.map h).trans (γ'.map h) := by
   ext t
   rw [trans_apply, map_coe, Function.comp_apply, trans_apply]
@@ -451,7 +451,7 @@ theorem map_id (γ : Path x y) : γ.map continuous_id = γ := by
 #align path.map_id Path.map_id
 
 @[simp]
-theorem map_map (γ : Path x y) {Y : Type _} [TopologicalSpace Y] {Z : Type _} [TopologicalSpace Z]
+theorem map_map (γ : Path x y) {Y : Type*} [TopologicalSpace Y] {Z : Type*} [TopologicalSpace Z]
     {f : X → Y} (hf : Continuous f) {g : Y → Z} (hg : Continuous g) :
     (γ.map hf).map hg = γ.map (hg.comp hf) := by
   ext
@@ -467,13 +467,13 @@ def cast (γ : Path x y) {x' y'} (hx : x' = x) (hy : y' = y) : Path x' y' where
 #align path.cast Path.cast
 
 @[simp]
-theorem symm_cast {X : Type _} [TopologicalSpace X] {a₁ a₂ b₁ b₂ : X} (γ : Path a₂ b₂)
+theorem symm_cast {X : Type*} [TopologicalSpace X] {a₁ a₂ b₁ b₂ : X} (γ : Path a₂ b₂)
     (ha : a₁ = a₂) (hb : b₁ = b₂) : (γ.cast ha hb).symm = γ.symm.cast hb ha :=
   rfl
 #align path.symm_cast Path.symm_cast
 
 @[simp]
-theorem trans_cast {X : Type _} [TopologicalSpace X] {a₁ a₂ b₁ b₂ c₁ c₂ : X} (γ : Path a₂ b₂)
+theorem trans_cast {X : Type*} [TopologicalSpace X] {a₁ a₂ b₁ b₂ c₁ c₂ : X} (γ : Path a₂ b₂)
     (γ' : Path b₂ c₂) (ha : a₁ = a₂) (hb : b₁ = b₂) (hc : c₁ = c₂) :
     (γ.cast ha hb).trans (γ'.cast hb hc) = (γ.trans γ').cast ha hc :=
   rfl
@@ -485,7 +485,7 @@ theorem cast_coe (γ : Path x y) {x' y'} (hx : x' = x) (hy : y' = y) : (γ.cast
 #align path.cast_coe Path.cast_coe
 
 @[continuity]
-theorem symm_continuous_family {X ι : Type _} [TopologicalSpace X] [TopologicalSpace ι]
+theorem symm_continuous_family {X ι : Type*} [TopologicalSpace X] [TopologicalSpace ι]
     {a b : ι → X} (γ : ∀ t : ι, Path (a t) (b t)) (h : Continuous ↿γ) :
     Continuous ↿fun t => (γ t).symm :=
   h.comp (continuous_id.prod_map continuous_symm)
@@ -497,7 +497,7 @@ theorem continuous_symm : Continuous (symm : Path x y → Path y x) :=
 #align path.continuous_symm Path.continuous_symm
 
 @[continuity]
-theorem continuous_uncurry_extend_of_continuous_family {X ι : Type _} [TopologicalSpace X]
+theorem continuous_uncurry_extend_of_continuous_family {X ι : Type*} [TopologicalSpace X]
     [TopologicalSpace ι] {a b : ι → X} (γ : ∀ t : ι, Path (a t) (b t)) (h : Continuous ↿γ) :
     Continuous ↿fun t => (γ t).extend := by
   refine' h.comp (continuous_id.prod_map continuous_projIcc)
@@ -505,7 +505,7 @@ theorem continuous_uncurry_extend_of_continuous_family {X ι : Type _} [Topologi
 #align path.continuous_uncurry_extend_of_continuous_family Path.continuous_uncurry_extend_of_continuous_family
 
 @[continuity]
-theorem trans_continuous_family {X ι : Type _} [TopologicalSpace X] [TopologicalSpace ι]
+theorem trans_continuous_family {X ι : Type*} [TopologicalSpace X] [TopologicalSpace ι]
     {a b c : ι → X} (γ₁ : ∀ t : ι, Path (a t) (b t)) (h₁ : Continuous ↿γ₁)
     (γ₂ : ∀ t : ι, Path (b t) (c t)) (h₂ : Continuous ↿γ₂) :
     Continuous ↿fun t => (γ₁ t).trans (γ₂ t) := by
@@ -574,7 +574,7 @@ end Prod
 
 section Pi
 
-variable {χ : ι → Type _} [∀ i, TopologicalSpace (χ i)] {as bs cs : ∀ i, χ i}
+variable {χ : ι → Type*} [∀ i, TopologicalSpace (χ i)] {as bs cs : ∀ i, χ i}
 
 /-- Given a family of paths, one in each Xᵢ, we take their pointwise product to get a path in
 Π i, Xᵢ. -/
@@ -624,7 +624,7 @@ protected theorem mul_apply [Mul X] [ContinuousMul X] {a₁ b₁ a₂ b₂ : X}
 
 /-- `γ.truncate t₀ t₁` is the path which follows the path `γ` on the
   time interval `[t₀, t₁]` and stays still otherwise. -/
-def truncate {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) (t₀ t₁ : ℝ) :
+def truncate {X : Type*} [TopologicalSpace X] {a b : X} (γ : Path a b) (t₀ t₁ : ℝ) :
     Path (γ.extend <| min t₀ t₁) (γ.extend t₁) where
   toFun s := γ.extend (min (max s t₀) t₁)
   continuous_toFun :=
@@ -652,12 +652,12 @@ def truncate {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) (t₀ t
 
 /-- `γ.truncateOfLE t₀ t₁ h`, where `h : t₀ ≤ t₁` is `γ.truncate t₀ t₁`
   casted as a path from `γ.extend t₀` to `γ.extend t₁`. -/
-def truncateOfLE {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) {t₀ t₁ : ℝ}
+def truncateOfLE {X : Type*} [TopologicalSpace X] {a b : X} (γ : Path a b) {t₀ t₁ : ℝ}
     (h : t₀ ≤ t₁) : Path (γ.extend t₀) (γ.extend t₁) :=
   (γ.truncate t₀ t₁).cast (by rw [min_eq_left h]) rfl
 #align path.truncate_of_le Path.truncateOfLE
 
-theorem truncate_range {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) {t₀ t₁ : ℝ} :
+theorem truncate_range {X : Type*} [TopologicalSpace X] {a b : X} (γ : Path a b) {t₀ t₁ : ℝ} :
     range (γ.truncate t₀ t₁) ⊆ range γ := by
   rw [← γ.extend_range]
   simp only [range_subset_iff, SetCoe.exists, SetCoe.forall]
@@ -668,7 +668,7 @@ theorem truncate_range {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a
 /-- For a path `γ`, `γ.truncate` gives a "continuous family of paths", by which we
   mean the uncurried function which maps `(t₀, t₁, s)` to `γ.truncate t₀ t₁ s` is continuous. -/
 @[continuity]
-theorem truncate_continuous_family {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) :
+theorem truncate_continuous_family {X : Type*} [TopologicalSpace X] {a b : X} (γ : Path a b) :
     Continuous (fun x => γ.truncate x.1 x.2.1 x.2.2 : ℝ × ℝ × I → X) :=
   γ.continuous_extend.comp
     (((continuous_subtype_val.comp (continuous_snd.comp continuous_snd)).max continuous_fst).min
@@ -676,14 +676,14 @@ theorem truncate_continuous_family {X : Type _} [TopologicalSpace X] {a b : X} (
 #align path.truncate_continuous_family Path.truncate_continuous_family
 
 @[continuity]
-theorem truncate_const_continuous_family {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b)
+theorem truncate_const_continuous_family {X : Type*} [TopologicalSpace X] {a b : X} (γ : Path a b)
     (t : ℝ) : Continuous ↿(γ.truncate t) := by
   have key : Continuous (fun x => (t, x) : ℝ × I → ℝ × ℝ × I) := by continuity
   exact γ.truncate_continuous_family.comp key
 #align path.truncate_const_continuous_family Path.truncate_const_continuous_family
 
 @[simp]
-theorem truncate_self {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) (t : ℝ) :
+theorem truncate_self {X : Type*} [TopologicalSpace X] {a b : X} (γ : Path a b) (t : ℝ) :
     γ.truncate t t = (Path.refl <| γ.extend t).cast (by rw [min_self]) rfl := by
   ext x
   rw [cast_coe]
@@ -692,19 +692,19 @@ theorem truncate_self {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b
 #align path.truncate_self Path.truncate_self
 
 @[simp 1001] -- porting note: increase `simp` priority so left-hand side doesn't simplify
-theorem truncate_zero_zero {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) :
+theorem truncate_zero_zero {X : Type*} [TopologicalSpace X] {a b : X} (γ : Path a b) :
     γ.truncate 0 0 = (Path.refl a).cast (by rw [min_self, γ.extend_zero]) γ.extend_zero := by
   convert γ.truncate_self 0
 #align path.truncate_zero_zero Path.truncate_zero_zero
 
 @[simp 1001] -- porting note: increase `simp` priority so left-hand side doesn't simplify
-theorem truncate_one_one {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) :
+theorem truncate_one_one {X : Type*} [TopologicalSpace X] {a b : X} (γ : Path a b) :
     γ.truncate 1 1 = (Path.refl b).cast (by rw [min_self, γ.extend_one]) γ.extend_one := by
   convert γ.truncate_self 1
 #align path.truncate_one_one Path.truncate_one_one
 
 @[simp]
-theorem truncate_zero_one {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) :
+theorem truncate_zero_one {X : Type*} [TopologicalSpace X] {a b : X} (γ : Path a b) :
     γ.truncate 0 1 = γ.cast (by simp [zero_le_one, extend_zero]) (by simp) := by
   ext x
   rw [cast_coe]
@@ -978,7 +978,7 @@ theorem isPathConnected_iff :
     fun ⟨⟨b, b_in⟩, h⟩ => ⟨b, b_in, fun x_in => h _ b_in _ x_in⟩⟩
 #align is_path_connected_iff isPathConnected_iff
 
-theorem IsPathConnected.image' {Y : Type _} [TopologicalSpace Y] (hF : IsPathConnected F)
+theorem IsPathConnected.image' {Y : Type*} [TopologicalSpace Y] (hF : IsPathConnected F)
     {f : X → Y} (hf : ContinuousOn f F) : IsPathConnected (f '' F) := by
   rcases hF with ⟨x, x_in, hx⟩
   use f x, mem_image_of_mem f x_in
@@ -986,7 +986,7 @@ theorem IsPathConnected.image' {Y : Type _} [TopologicalSpace Y] (hF : IsPathCon
   refine ⟨(hx y_in).somePath.map' ?_, fun t ↦ ⟨_, (hx y_in).somePath_mem t, rfl⟩⟩
   exact hf.mono (range_subset_iff.2 (hx y_in).somePath_mem)
 
-theorem IsPathConnected.image {Y : Type _} [TopologicalSpace Y] (hF : IsPathConnected F) {f : X → Y}
+theorem IsPathConnected.image {Y : Type*} [TopologicalSpace Y] (hF : IsPathConnected F) {f : X → Y}
     (hf : Continuous f) : IsPathConnected (f '' F) := hF.image' hf.continuousOn
 #align is_path_connected.image IsPathConnected.image
 
@@ -1023,7 +1023,7 @@ theorem IsPathConnected.preimage_coe {U W : Set X} (hW : IsPathConnected W) (hWU
   exact ⟨(hx hyW).joined_subtype.somePath.map (continuous_inclusion hWU), by simp⟩
 #align is_path_connected.preimage_coe IsPathConnected.preimage_coe
 
-theorem IsPathConnected.exists_path_through_family {X : Type _} [TopologicalSpace X] {n : ℕ}
+theorem IsPathConnected.exists_path_through_family {X : Type*} [TopologicalSpace X] {n : ℕ}
     {s : Set X} (h : IsPathConnected s) (p : Fin (n + 1) → X) (hp : ∀ i, p i ∈ s) :
     ∃ γ : Path (p 0) (p n), range γ ⊆ s ∧ ∀ i, p i ∈ range γ := by
   let p' : ℕ → X := fun k => if h : k < n + 1 then p ⟨k, h⟩ else p ⟨0, n.zero_lt_succ⟩
@@ -1079,7 +1079,7 @@ theorem IsPathConnected.exists_path_through_family {X : Type _} [TopologicalSpac
   rw [Nat.mod_eq_of_lt hi]
 #align is_path_connected.exists_path_through_family IsPathConnected.exists_path_through_family
 
-theorem IsPathConnected.exists_path_through_family' {X : Type _} [TopologicalSpace X] {n : ℕ}
+theorem IsPathConnected.exists_path_through_family' {X : Type*} [TopologicalSpace X] {n : ℕ}
     {s : Set X} (h : IsPathConnected s) (p : Fin (n + 1) → X) (hp : ∀ i, p i ∈ s) :
     ∃ (γ : Path (p 0) (p n)) (t : Fin (n + 1) → I), (∀ t, γ t ∈ s) ∧ ∀ i, γ (t i) = p i := by
   rcases h.exists_path_through_family p hp with ⟨γ, hγ⟩
@@ -1095,7 +1095,7 @@ theorem IsPathConnected.exists_path_through_family' {X : Type _} [TopologicalSpa
 
 /-- A topological space is path-connected if it is non-empty and every two points can be
 joined by a continuous path. -/
-class PathConnectedSpace (X : Type _) [TopologicalSpace X] : Prop where
+class PathConnectedSpace (X : Type*) [TopologicalSpace X] : Prop where
   /-- A path-connected space must be nonempty. -/
   Nonempty : Nonempty X
   /-- Any two points in a path-connected space must be joined by a continuous path. -/
@@ -1223,7 +1223,7 @@ end PathConnectedSpace
 
 /-- A topological space is locally path connected, at every point, path connected
 neighborhoods form a neighborhood basis. -/
-class LocPathConnectedSpace (X : Type _) [TopologicalSpace X] : Prop where
+class LocPathConnectedSpace (X : Type*) [TopologicalSpace X] : Prop where
   /-- Each neighborhood filter has a basis of path-connected neighborhoods. -/
   path_connected_basis : ∀ x : X, (𝓝 x).HasBasis (fun s : Set X => s ∈ 𝓝 x ∧ IsPathConnected s) id
 #align loc_path_connected_space LocPathConnectedSpace

@@ -410,13 +410,17 @@ theorem trans_range {X : Type _} [TopologicalSpace X] {a b c : X} (γ₁ : Path
         rwa [γ₂.extend_extends]
 #align path.trans_range Path.trans_range
 
-/-- Image of a path from `x` to `y` by a continuous map -/
-def map (γ : Path x y) {Y : Type _} [TopologicalSpace Y] {f : X → Y} (h : Continuous f) :
-    Path (f x) (f y) where
+/-- Image of a path from `x` to `y` by a map which is continuous on the path. -/
+def map' (γ : Path x y) {Y : Type _} [TopologicalSpace Y] {f : X → Y}
+    (h : ContinuousOn f (range γ)) : Path (f x) (f y) where
   toFun := f ∘ γ
-  continuous_toFun := by continuity
+  continuous_toFun := h.comp_continuous γ.continuous (fun x ↦ mem_range_self x)
   source' := by simp
   target' := by simp
+
+/-- Image of a path from `x` to `y` by a continuous map -/
+def map (γ : Path x y) {Y : Type _} [TopologicalSpace Y] {f : X → Y} (h : Continuous f) :
+    Path (f x) (f y) := γ.map' h.continuousOn
 #align path.map Path.map
 
 @[simp]
@@ -974,12 +978,16 @@ theorem isPathConnected_iff :
     fun ⟨⟨b, b_in⟩, h⟩ => ⟨b, b_in, fun x_in => h _ b_in _ x_in⟩⟩
 #align is_path_connected_iff isPathConnected_iff
 
-theorem IsPathConnected.image {Y : Type _} [TopologicalSpace Y] (hF : IsPathConnected F) {f : X → Y}
-    (hf : Continuous f) : IsPathConnected (f '' F) := by
+theorem IsPathConnected.image' {Y : Type _} [TopologicalSpace Y] (hF : IsPathConnected F)
+    {f : X → Y} (hf : ContinuousOn f F) : IsPathConnected (f '' F) := by
   rcases hF with ⟨x, x_in, hx⟩
   use f x, mem_image_of_mem f x_in
   rintro _ ⟨y, y_in, rfl⟩
-  exact ⟨(hx y_in).somePath.map hf, fun t => ⟨_, (hx y_in).somePath_mem t, rfl⟩⟩
+  refine ⟨(hx y_in).somePath.map' ?_, fun t ↦ ⟨_, (hx y_in).somePath_mem t, rfl⟩⟩
+  exact hf.mono (range_subset_iff.2 (hx y_in).somePath_mem)
+
+theorem IsPathConnected.image {Y : Type _} [TopologicalSpace Y] (hF : IsPathConnected F) {f : X → Y}
+    (hf : Continuous f) : IsPathConnected (f '' F) := hF.image' hf.continuousOn
 #align is_path_connected.image IsPathConnected.image
 
 theorem IsPathConnected.mem_pathComponent (h : IsPathConnected F) (x_in : x ∈ F) (y_in : y ∈ F) :
@@ -991,6 +999,11 @@ theorem IsPathConnected.subset_pathComponent (h : IsPathConnected F) (x_in : x 
     F ⊆ pathComponent x := fun _y y_in => h.mem_pathComponent x_in y_in
 #align is_path_connected.subset_path_component IsPathConnected.subset_pathComponent
 
+theorem isPathConnected_singleton (x : X) : IsPathConnected ({x} : Set X) := by
+  refine ⟨x, rfl, ?_⟩
+  rintro y rfl
+  exact JoinedIn.refl rfl
+
 theorem IsPathConnected.union {U V : Set X} (hU : IsPathConnected U) (hV : IsPathConnected V)
     (hUV : (U ∩ V).Nonempty) : IsPathConnected (U ∪ V) := by
   rcases hUV with ⟨x, xU, xV⟩

@@ -1142,6 +1142,29 @@ theorem pathConnectedSpace_iff_univ : PathConnectedSpace X ↔ IsPathConnected (
     exact ⟨⟨x⟩, by simpa using h'⟩
 #align path_connected_space_iff_univ pathConnectedSpace_iff_univ
 
+theorem isPathConnected_univ [PathConnectedSpace X] : IsPathConnected (univ : Set X) :=
+  pathConnectedSpace_iff_univ.mp inferInstance
+
+theorem isPathConnected_range [PathConnectedSpace X] {f : X → Y} (hf : Continuous f) :
+    IsPathConnected (range f) := by
+  rw [← image_univ]
+  exact isPathConnected_univ.image hf
+
+theorem Function.Surjective.pathConnectedSpace [PathConnectedSpace X]
+  {f : X → Y} (hf : Surjective f) (hf' : Continuous f) : PathConnectedSpace Y := by
+  rw [pathConnectedSpace_iff_univ, ← hf.range_eq]
+  exact isPathConnected_range hf'
+
+instance Quotient.instPathConnectedSpace {s : Setoid X} [PathConnectedSpace X] :
+    PathConnectedSpace (Quotient s) :=
+  (surjective_quotient_mk X).pathConnectedSpace continuous_coinduced_rng
+
+/-- This is a special case of `NormedSpace.path_connected` (and
+`TopologicalAddGroup.pathConnectedSpace`). It exists only to simplify dependencies. -/
+instance Real.instPathConnectedSpace : PathConnectedSpace ℝ where
+  Nonempty := inferInstance
+  Joined := fun x y ↦ ⟨⟨⟨fun (t : I) ↦ (1 - t) * x + t * y, by continuity⟩, by simp, by simp⟩⟩
+
 theorem pathConnectedSpace_iff_eq : PathConnectedSpace X ↔ ∃ x : X, pathComponent x = univ := by
   simp [pathConnectedSpace_iff_univ, isPathConnected_iff_eq]
 #align path_connected_space_iff_eq pathConnectedSpace_iff_eq

• depends on: #5966

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

@@ -2,17 +2,14 @@
 Copyright (c) 2020 Patrick Massot. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Patrick Massot
-
-! This file was ported from Lean 3 source module topology.path_connected
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Topology.Algebra.Order.ProjIcc
 import Mathlib.Topology.CompactOpen
 import Mathlib.Topology.ContinuousFunction.Basic
 import Mathlib.Topology.UnitInterval
 
+#align_import topology.path_connected from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
+
 /-!
 # Path connectedness
 

Changes are of the form

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

@@ -924,7 +924,7 @@ theorem pathComponent_congr (h : x ∈ pathComponent y) : pathComponent x = path
     rw [pathComponent_symm]
     exact (h.trans h').symm
   · intro h'
-    rw [pathComponent_symm] at h'⊢
+    rw [pathComponent_symm] at h' ⊢
     exact h'.trans h
 #align path_component_congr pathComponent_congr
 

Co-authored-by: Xavier Roblot <46200072+xroblot@users.noreply.github.com> Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr> Co-authored-by: Riccardo Brasca <riccardo.brasca@gmail.com> Co-authored-by: Yury G. Kudryashov <urkud@urkud.name> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Pol'tta / Miyahara Kō <pol_tta@outlook.jp> Co-authored-by: Jason Yuen <jason_yuen2007@hotmail.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com> Co-authored-by: Jireh Loreaux <loreaujy@gmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: Heather Macbeth <25316162+hrmacbeth@users.noreply.github.com> Co-authored-by: Jujian Zhang <jujian.zhang1998@outlook.com> Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

@@ -591,7 +591,7 @@ theorem pi_coe (γ : ∀ i, Path (as i) (bs i)) : ⇑(Path.pi γ) = fun t i => 
 /-- Path composition commutes with products -/
 theorem trans_pi_eq_pi_trans (γ₀ : ∀ i, Path (as i) (bs i)) (γ₁ : ∀ i, Path (bs i) (cs i)) :
     (Path.pi γ₀).trans (Path.pi γ₁) = Path.pi fun i => (γ₀ i).trans (γ₁ i) := by
-  ext (t i)
+  ext t i
   unfold Path.trans
   simp only [Path.coe_mk_mk, Function.comp_apply, pi_coe]
   split_ifs <;> rfl

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

@@ -1071,7 +1071,7 @@ theorem IsPathConnected.exists_path_through_family {X : Type _} [TopologicalSpac
 
 theorem IsPathConnected.exists_path_through_family' {X : Type _} [TopologicalSpace X] {n : ℕ}
     {s : Set X} (h : IsPathConnected s) (p : Fin (n + 1) → X) (hp : ∀ i, p i ∈ s) :
-    ∃ (γ : Path (p 0) (p n))(t : Fin (n + 1) → I), (∀ t, γ t ∈ s) ∧ ∀ i, γ (t i) = p i := by
+    ∃ (γ : Path (p 0) (p n)) (t : Fin (n + 1) → I), (∀ t, γ t ∈ s) ∧ ∀ i, γ (t i) = p i := by
   rcases h.exists_path_through_family p hp with ⟨γ, hγ⟩
   rcases hγ with ⟨h₁, h₂⟩
   simp only [range, mem_setOf_eq] at h₂
@@ -1177,7 +1177,7 @@ theorem exists_path_through_family {n : ℕ} (p : Fin (n + 1) → X) :
 #align path_connected_space.exists_path_through_family PathConnectedSpace.exists_path_through_family
 
 theorem exists_path_through_family' {n : ℕ} (p : Fin (n + 1) → X) :
-    ∃ (γ : Path (p 0) (p n))(t : Fin (n + 1) → I), ∀ i, γ (t i) = p i := by
+    ∃ (γ : Path (p 0) (p n)) (t : Fin (n + 1) → I), ∀ i, γ (t i) = p i := by
   have : IsPathConnected (univ : Set X) := pathConnectedSpace_iff_univ.mp (by infer_instance)
   rcases this.exists_path_through_family' p fun _i => True.intro with ⟨γ, t, -, h⟩
   exact ⟨γ, t, h⟩

These are all doc fixes

@@ -110,7 +110,7 @@ theorem coe_mk_mk (f : I → X) (h₁) (h₂ : f 0 = x) (h₃ : f 1 = y) :
     ⇑(mk ⟨f, h₁⟩ h₂ h₃ : Path x y) = f :=
   rfl
 #align path.coe_mk Path.coe_mk_mk
--- porting note: the name `Path.coe_mk` better refes to a new lemma below
+-- porting note: the name `Path.coe_mk` better refers to a new lemma below
 
 variable (γ : Path x y)
 

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

@@ -277,7 +277,7 @@ theorem extend_one : γ.extend 1 = y := by simp
 @[simp]
 theorem extend_extends' {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b)
     (t : (Icc 0 1 : Set ℝ)) : γ.extend t = γ t :=
-  Icc_extend_coe _ γ t
+  IccExtend_val _ γ t
 #align path.extend_extends' Path.extend_extends'
 
 @[simp]

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

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

@@ -251,8 +251,8 @@ theorem continuous_extend : Continuous γ.extend :=
 
 theorem _root_.Filter.Tendsto.path_extend {X Y : Type _} [TopologicalSpace X] [TopologicalSpace Y]
     {l r : Y → X} {y : Y} {l₁ : Filter ℝ} {l₂ : Filter X} {γ : ∀ y, Path (l y) (r y)}
-    (hγ : Tendsto (↿γ) (𝓝 y ×ᶠ l₁.map (projIcc 0 1 zero_le_one)) l₂) :
-    Tendsto (↿fun x => (γ x).extend) (𝓝 y ×ᶠ l₁) l₂ :=
+    (hγ : Tendsto (↿γ) (𝓝 y ×ˢ l₁.map (projIcc 0 1 zero_le_one)) l₂) :
+    Tendsto (↿fun x => (γ x).extend) (𝓝 y ×ˢ l₁) l₂ :=
   Filter.Tendsto.IccExtend _ hγ
 #align filter.tendsto.path_extend Filter.Tendsto.path_extend
 

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

@@ -67,9 +67,7 @@ on `(-∞, 0]` and to `y` on `[1, +∞)`.
 
 noncomputable section
 
-open Classical Topology Filter unitInterval
-
-open Filter Set Function unitInterval
+open Classical Topology Filter unitInterval Set Function
 
 variable {X Y : Type _} [TopologicalSpace X] [TopologicalSpace Y] {x y z : X} {ι : Type _}
 
@@ -326,11 +324,7 @@ def trans (γ : Path x y) (γ' : Path y z) : Path x z where
     refine'
       (Continuous.if_le _ _ continuous_id continuous_const (by norm_num)).comp
         continuous_subtype_val <;>
-    -- TODO: the following are provable by `continuity` but it is too slow
-    -- porting note: the new `continuity` succeeds and it isn't too slow!
     continuity
-    --exacts[γ.continuous_extend.comp (continuous_const.mul continuous_id),
-     -- γ'.continuous_extend.comp ((continuous_const.mul continuous_id).sub continuous_const)]
   source' := by norm_num
   target' := by norm_num
 #align path.trans Path.trans
@@ -684,7 +678,6 @@ theorem truncate_continuous_family {X : Type _} [TopologicalSpace X] {a b : X} (
 theorem truncate_const_continuous_family {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b)
     (t : ℝ) : Continuous ↿(γ.truncate t) := by
   have key : Continuous (fun x => (t, x) : ℝ × I → ℝ × ℝ × I) := by continuity
-    --continuous_const.prod_mk continuous_id
   exact γ.truncate_continuous_family.comp key
 #align path.truncate_const_continuous_family Path.truncate_const_continuous_family
 

Enable the cancelDenoms preprocessor in linarith. Closes #2714.

• depends on: #3797

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

@@ -354,6 +354,8 @@ theorem trans_symm (γ : Path x y) (γ' : Path y z) : (γ.trans γ').symm = γ'.
       exact h
     -- porting note: was `linarith [unitInterval.nonneg t, unitInterval.le_one t]` but `linarith`
     -- doesn't know about `ℚ` yet. https://github.com/leanprover-community/mathlib4/issues/2714
+    -- porting note: although `linarith` now knows about `ℚ`, it still fails here as it doesn't
+    -- find `LinearOrder X`.
     simp_rw [unitInterval.symm, ht]
     norm_num
   · refine' congr_arg _ (Subtype.ext _)
@@ -362,12 +364,14 @@ theorem trans_symm (γ : Path x y) (γ' : Path y z) : (γ.trans γ').symm = γ'.
   · refine' congr_arg _ (Subtype.ext _)
     norm_num [mul_sub, h]
     ring
-  · exfalso
+  · -- porting note: was `linarith [unitInterval.nonneg t, unitInterval.le_one t]` but `linarith`
+    -- doesn't know about `ℚ` yet. https://github.com/leanprover-community/mathlib4/issues/2714
+    -- porting note: although `linarith` now knows about `ℚ`, it still fails here as it doesn't
+    -- find `LinearOrder X`.
+    exfalso
     rw [sub_le_comm] at h
     norm_num at h h₂
     exact (h.trans h₂).ne rfl
-    -- porting note: was `linarith [unitInterval.nonneg t, unitInterval.le_one t]` but `linarith`
-    -- doesn't know about `ℚ` yet. https://github.com/leanprover-community/mathlib4/issues/2714
 #align path.trans_symm Path.trans_symm
 
 @[simp]
@@ -385,48 +389,31 @@ theorem trans_range {X : Type _} [TopologicalSpace X] {a b c : X} (γ₁ : Path
   · rintro x ⟨⟨t, ht0, ht1⟩, hxt⟩
     by_cases h : t ≤ 1 / 2
     · left
-      refine' ⟨⟨2 * t, ⟨by positivity, (le_div_iff' <| by norm_num).mp h⟩⟩, _⟩
-      -- porting note: was `use 2 * t, ⟨by linarith, by linarith⟩`
-      -- https://github.com/leanprover-community/mathlib4/issues/2714
+      use ⟨2 * t, ⟨by linarith, by linarith⟩⟩
       rw [← γ₁.extend_extends]
       rwa [coe_mk_mk, Function.comp_apply, if_pos h] at hxt
     · right
-      refine' ⟨⟨2 * t - 1, ⟨_, by norm_num; exact ht1⟩⟩, _⟩
-      -- porting note: was `use 2 * t - 1, ⟨by linarith, by linarith⟩`
-      -- https://github.com/leanprover-community/mathlib4/issues/2714
-      · rw [not_le, div_lt_iff (zero_lt_two : (0 : ℝ) < 2)] at h
-        norm_num
-        exact mul_comm t 2 ▸ h.le
+      use ⟨2 * t - 1, ⟨by linarith, by linarith⟩⟩
       rw [← γ₂.extend_extends]
       rwa [coe_mk_mk, Function.comp_apply, if_neg h] at hxt
   · rintro x (⟨⟨t, ht0, ht1⟩, hxt⟩ | ⟨⟨t, ht0, ht1⟩, hxt⟩)
-    · refine' ⟨⟨t / 2, ⟨by positivity,
-        (div_le_iff <| by norm_num).mpr <| ht1.trans (by norm_num)⟩⟩, _⟩
-      -- porting note: was `use ⟨t / 2, ⟨by linarith, by linarith⟩⟩`
-      -- https://github.com/leanprover-community/mathlib4/issues/2714
+    · use ⟨t / 2, ⟨by linarith, by linarith⟩⟩
       have : t / 2 ≤ 1 / 2 := (div_le_div_right (zero_lt_two : (0 : ℝ) < 2)).mpr ht1
       rw [coe_mk_mk, Function.comp_apply, if_pos this, Subtype.coe_mk]
       ring_nf
       rwa [γ₁.extend_extends]
     · by_cases h : t = 0
-      · refine' ⟨⟨1 / 2, ⟨by positivity, by norm_num⟩⟩, _⟩
-        -- porting note: was `use ⟨1 / 2, ⟨by linarith, by linarith⟩⟩`
-        -- https://github.com/leanprover-community/mathlib4/issues/2714
+      · use ⟨1 / 2, ⟨by linarith, by linarith⟩⟩
         rw [coe_mk_mk, Function.comp_apply, if_pos le_rfl, Subtype.coe_mk,
           mul_one_div_cancel (two_ne_zero' ℝ)]
         rw [γ₁.extend_one]
         rwa [← γ₂.extend_extends, h, γ₂.extend_zero] at hxt
-      · refine' ⟨⟨(t + 1) / 2, ⟨by positivity, _⟩⟩, _⟩
-        -- porting note: was `use ⟨(t + 1) / 2, ⟨by linarith, by linarith⟩⟩`
-        -- https://github.com/leanprover-community/mathlib4/issues/2714
-        · exact (div_le_iff <| by norm_num).mpr <| (add_le_add_right ht1 1).trans (by norm_num)
+      · use ⟨(t + 1) / 2, ⟨by linarith, by linarith⟩⟩
         replace h : t ≠ 0 := h
         have ht0 := lt_of_le_of_ne ht0 h.symm
         have : ¬(t + 1) / 2 ≤ 1 / 2 := by
           rw [not_le]
-          exact (div_lt_div_right (zero_lt_two : (0 : ℝ) < 2)).mpr (by norm_num; exact ht0)
-          -- porting note: was `linarith`
-          -- https://github.com/leanprover-community/mathlib4/issues/2714
+          linarith
         rw [coe_mk_mk, Function.comp_apply, Subtype.coe_mk, if_neg this]
         ring_nf
         rwa [γ₂.extend_extends]

This PR fixes two things:

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

@@ -520,7 +520,6 @@ theorem continuous_uncurry_extend_of_continuous_family {X ι : Type _} [Topologi
     Continuous ↿fun t => (γ t).extend := by
   refine' h.comp (continuous_id.prod_map continuous_projIcc)
   exact zero_le_one
-
 #align path.continuous_uncurry_extend_of_continuous_family Path.continuous_uncurry_extend_of_continuous_family
 
 @[continuity]

@@ -694,22 +694,12 @@ theorem truncate_continuous_family {X : Type _} [TopologicalSpace X] {a b : X} (
       (continuous_fst.comp continuous_snd))
 #align path.truncate_continuous_family Path.truncate_continuous_family
 
-/-
-  porting note: I'm not sure this would work with the new continuity because it doesn't leave side
-  goals.
-
-  TODO : When `continuity` gets quicker, change the proof back to :
-    `begin`
-      `simp only [CoeFun.coe, coe_fn, Path.truncate],`
-      `continuity,`
-      `exact continuous_subtype_val`
-    `end` -/
 @[continuity]
 theorem truncate_const_continuous_family {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b)
     (t : ℝ) : Continuous ↿(γ.truncate t) := by
-  have key : Continuous (fun x => (t, x) : ℝ × I → ℝ × ℝ × I) :=
-    continuous_const.prod_mk continuous_id
-  convert γ.truncate_continuous_family.comp key
+  have key : Continuous (fun x => (t, x) : ℝ × I → ℝ × ℝ × I) := by continuity
+    --continuous_const.prod_mk continuous_id
+  exact γ.truncate_continuous_family.comp key
 #align path.truncate_const_continuous_family Path.truncate_const_continuous_family
 
 @[simp]

@@ -57,7 +57,7 @@ For locally path connected spaces, we have
 
 By default, all paths have `I` as their source and `X` as their target, but there is an
 operation `Set.IccExtend` that will extend any continuous map `γ : I → X` into a continuous map
-`Icc_extend zero_le_one γ : ℝ → X` that is constant before `0` and after `1`.
+`IccExtend zero_le_one γ : ℝ → X` that is constant before `0` and after `1`.
 
 This is used to define `Path.extend` that turns `γ : Path x y` into a continuous map
 `γ.extend : ℝ → X` whose restriction to `I` is the original `γ`, and is equal to `x`
@@ -304,8 +304,7 @@ theorem refl_extend {X : Type _} [TopologicalSpace X] {a : X} : (Path.refl a).ex
 #align path.refl_extend Path.refl_extend
 
 /-- The path obtained from a map defined on `ℝ` by restriction to the unit interval. -/
-def ofLine {f : ℝ → X} (hf : ContinuousOn f I) (h₀ : f 0 = x) (h₁ : f 1 = y) : Path x y
-    where
+def ofLine {f : ℝ → X} (hf : ContinuousOn f I) (h₀ : f 0 = x) (h₁ : f 1 = y) : Path x y where
   toFun := f ∘ ((↑) : unitInterval → ℝ)
   continuous_toFun := hf.comp_continuous continuous_subtype_val Subtype.prop
   source' := h₀
@@ -321,8 +320,7 @@ attribute [local simp] Iic_def
 /-- Concatenation of two paths from `x` to `y` and from `y` to `z`, putting the first
 path on `[0, 1/2]` and the second one on `[1/2, 1]`. -/
 @[trans]
-def trans (γ : Path x y) (γ' : Path y z) : Path x z
-    where
+def trans (γ : Path x y) (γ' : Path y z) : Path x z where
   toFun := (fun t : ℝ => if t ≤ 1 / 2 then γ.extend (2 * t) else γ'.extend (2 * t - 1)) ∘ (↑)
   continuous_toFun := by
     refine'
@@ -479,8 +477,7 @@ theorem map_map (γ : Path x y) {Y : Type _} [TopologicalSpace Y] {Z : Type _} [
 #align path.map_map Path.map_map
 
 /-- Casting a path from `x` to `y` to a path from `x'` to `y'` when `x' = x` and `y' = y` -/
-def cast (γ : Path x y) {x' y'} (hx : x' = x) (hy : y' = y) : Path x' y'
-    where
+def cast (γ : Path x y) {x' y'} (hx : x' = x) (hy : y' = y) : Path x' y' where
   toFun := γ
   continuous_toFun := γ.continuous
   source' := by simp [hx]
@@ -570,8 +567,7 @@ variable {a₁ a₂ a₃ : X} {b₁ b₂ b₃ : Y}
 
 /-- Given a path in `X` and a path in `Y`, we can take their pointwise product to get a path in
 `X × Y`. -/
-protected def prod (γ₁ : Path a₁ a₂) (γ₂ : Path b₁ b₂) : Path (a₁, b₁) (a₂, b₂)
-    where
+protected def prod (γ₁ : Path a₁ a₂) (γ₂ : Path b₁ b₂) : Path (a₁, b₁) (a₂, b₂) where
   toContinuousMap := ContinuousMap.prodMk γ₁.toContinuousMap γ₂.toContinuousMap
   source' := by simp
   target' := by simp
@@ -601,8 +597,7 @@ variable {χ : ι → Type _} [∀ i, TopologicalSpace (χ i)] {as bs cs : ∀ i
 
 /-- Given a family of paths, one in each Xᵢ, we take their pointwise product to get a path in
 Π i, Xᵢ. -/
-protected def pi (γ : ∀ i, Path (as i) (bs i)) : Path as bs
-    where
+protected def pi (γ : ∀ i, Path (as i) (bs i)) : Path as bs where
   toContinuousMap := ContinuousMap.pi fun i => (γ i).toContinuousMap
   source' := by simp
   target' := by simp
@@ -649,8 +644,7 @@ protected theorem mul_apply [Mul X] [ContinuousMul X] {a₁ b₁ a₂ b₂ : X}
 /-- `γ.truncate t₀ t₁` is the path which follows the path `γ` on the
   time interval `[t₀, t₁]` and stays still otherwise. -/
 def truncate {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) (t₀ t₁ : ℝ) :
-    Path (γ.extend <| min t₀ t₁) (γ.extend t₁)
-    where
+    Path (γ.extend <| min t₀ t₁) (γ.extend t₁) where
   toFun s := γ.extend (min (max s t₀) t₁)
   continuous_toFun :=
     γ.continuous_extend.comp ((continuous_subtype_val.max continuous_const).min continuous_const)
@@ -675,12 +669,12 @@ def truncate {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) (t₀ t
     · rfl
 #align path.truncate Path.truncate
 
-/-- `γ.truncateOfLe t₀ t₁ h`, where `h : t₀ ≤ t₁` is `γ.truncate t₀ t₁`
+/-- `γ.truncateOfLE t₀ t₁ h`, where `h : t₀ ≤ t₁` is `γ.truncate t₀ t₁`
   casted as a path from `γ.extend t₀` to `γ.extend t₁`. -/
-def truncateOfLe {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) {t₀ t₁ : ℝ}
+def truncateOfLE {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) {t₀ t₁ : ℝ}
     (h : t₀ ≤ t₁) : Path (γ.extend t₀) (γ.extend t₁) :=
   (γ.truncate t₀ t₁).cast (by rw [min_eq_left h]) rfl
-#align path.truncate_of_le Path.truncateOfLe
+#align path.truncate_of_le Path.truncateOfLE
 
 theorem truncate_range {X : Type _} [TopologicalSpace X] {a b : X} (γ : Path a b) {t₀ t₁ : ℝ} :
     range (γ.truncate t₀ t₁) ⊆ range γ := by
@@ -783,13 +777,10 @@ theorem range_reparam (γ : Path x y) {f : I → I} (hfcont : Continuous f) (hf
     intro t
     have h₁ : Continuous (Set.IccExtend (zero_le_one' ℝ) f) := by continuity
     have := intermediate_value_Icc (zero_le_one' ℝ) h₁.continuousOn
-    · rw [IccExtend_left, IccExtend_right] at this
-      change Icc (f 0) (f 1) ⊆ _ at this
-      rw [hf₀, hf₁] at this
+    · rw [IccExtend_left, IccExtend_right, Icc.mk_zero, Icc.mk_one, hf₀, hf₁] at this
       rcases this t.2 with ⟨w, hw₁, hw₂⟩
       rw [IccExtend_of_mem _ _ hw₁] at hw₂
-      use ⟨w, hw₁⟩
-      exact hw₂
+      exact ⟨_, hw₂⟩
   rw [range_comp, this, image_univ]
 #align path.range_reparam Path.range_reparam
 
@@ -1057,8 +1048,7 @@ theorem IsPathConnected.exists_path_through_family {X : Type _} [TopologicalSpac
     {s : Set X} (h : IsPathConnected s) (p : Fin (n + 1) → X) (hp : ∀ i, p i ∈ s) :
     ∃ γ : Path (p 0) (p n), range γ ⊆ s ∧ ∀ i, p i ∈ range γ := by
   let p' : ℕ → X := fun k => if h : k < n + 1 then p ⟨k, h⟩ else p ⟨0, n.zero_lt_succ⟩
-  obtain ⟨γ, hγ⟩ : ∃ γ : Path (p' 0) (p' n), (∀ i ≤ n, p' i ∈ range γ) ∧ range γ ⊆ s :=
-    by
+  obtain ⟨γ, hγ⟩ : ∃ γ : Path (p' 0) (p' n), (∀ i ≤ n, p' i ∈ range γ) ∧ range γ ⊆ s := by
     have hp' : ∀ i ≤ n, p' i ∈ s := by
       intro i hi
       simp [Nat.lt_succ_of_le hi, hp]

The major thing to note is that I have replaced the CoeFun instance (which was p ↦ p.toContinuousMap.toFun) with FunLike.coe, but previously Path did not have a FunLike instance, so I have added a ContinuousMapClass instance. These are defeq.

This also meant there would have been two coercions from Path x y to C(I, X), namely, the one which was originally declared in this file (:= p ↦ p.toContinuousMap) and the one inherited from ContinuousMapClass. As a result I have opted for the deleting the former in favor of the latter. These are not definitionally equal, but with the rewrite lemmas in place, there seem to be no real issues.

Note: the biggest reason for switching to FunLike was that the previous coercions were causing absolute hell early in the file with timeouts. If you want to see what I mean, checkout an early commit and attempt to start fixing.

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