topology.urysohns_lemma ⟷ Mathlib.Topology.UrysohnsLemma

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

@@ -331,7 +331,7 @@ theorem continuous_lim (c : CU X) : Continuous c.lim :=
     exact Real.dist_le_of_mem_Icc_01 (c.lim_mem_Icc _) (c.lim_mem_Icc _)
   · by_cases hxl : x ∈ c.left.U
     · filter_upwards [IsOpen.mem_nhds c.left.open_U hxl, ihn c.left] with _ hyl hyd
-      rw [pow_succ, c.lim_eq_midpoint, c.lim_eq_midpoint,
+      rw [pow_succ', c.lim_eq_midpoint, c.lim_eq_midpoint,
         c.right.lim_of_mem_C _ (c.left_U_subset_right_C hyl),
         c.right.lim_of_mem_C _ (c.left_U_subset_right_C hxl)]
       refine' (dist_midpoint_midpoint_le _ _ _ _).trans _
@@ -342,7 +342,7 @@ theorem continuous_lim (c : CU X) : Continuous c.lim :=
         ihn c.left.right, ihn c.right] with y hyl hydl hydr
       replace hxl : x ∉ c.left.left.U; exact compl_subset_compl.2 c.left.left_U_subset_right_C hxl
       replace hyl : y ∉ c.left.left.U; exact compl_subset_compl.2 c.left.left_U_subset_right_C hyl
-      simp only [pow_succ, c.lim_eq_midpoint, c.left.lim_eq_midpoint,
+      simp only [pow_succ', c.lim_eq_midpoint, c.left.lim_eq_midpoint,
         c.left.left.lim_of_nmem_U _ hxl, c.left.left.lim_of_nmem_U _ hyl]
       refine' (dist_midpoint_midpoint_le _ _ _ _).trans _
       refine'

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

@@ -346,12 +346,12 @@ theorem continuous_lim (c : CU X) : Continuous c.lim :=
         c.left.left.lim_of_nmem_U _ hxl, c.left.left.lim_of_nmem_U _ hyl]
       refine' (dist_midpoint_midpoint_le _ _ _ _).trans _
       refine'
-        (div_le_div_of_le_of_nonneg (add_le_add_right (dist_midpoint_midpoint_le _ _ _ _) _)
+        (div_le_div_of_nonneg_right (add_le_add_right (dist_midpoint_midpoint_le _ _ _ _) _)
               zero_le_two).trans
           _
       rw [dist_self, zero_add]
       refine'
-        (div_le_div_of_le_of_nonneg (add_le_add (div_le_div_of_le_of_nonneg hydl zero_le_two) hydr)
+        (div_le_div_of_nonneg_right (add_le_add (div_le_div_of_nonneg_right hydl zero_le_two) hydr)
               zero_le_two).trans_eq
           _
       generalize (3 / 4 : ℝ) ^ n = r

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

@@ -365,7 +365,7 @@ end Urysohns
 
 variable [NormalSpace X]
 
-#print exists_continuous_zero_one_of_closed /-
+#print exists_continuous_zero_one_of_isClosed /-
 /-- Urysohns lemma: if `s` and `t` are two disjoint closed sets in a normal topological space `X`,
 then there exists a continuous function `f : X → ℝ` such that
 
@@ -373,7 +373,7 @@ then there exists a continuous function `f : X → ℝ` such that
 * `f` equals one on `t`;
 * `0 ≤ f x ≤ 1` for all `x`.
 -/
-theorem exists_continuous_zero_one_of_closed {s t : Set X} (hs : IsClosed s) (ht : IsClosed t)
+theorem exists_continuous_zero_one_of_isClosed {s t : Set X} (hs : IsClosed s) (ht : IsClosed t)
     (hd : Disjoint s t) : ∃ f : C(X, ℝ), EqOn f 0 s ∧ EqOn f 1 t ∧ ∀ x, f x ∈ Icc (0 : ℝ) 1 :=
   by
   -- The actual proof is in the code above. Here we just repack it into the expected format.
@@ -381,6 +381,6 @@ theorem exists_continuous_zero_one_of_closed {s t : Set X} (hs : IsClosed s) (ht
   exact
     ⟨⟨c.lim, c.continuous_lim⟩, c.lim_of_mem_C, fun x hx => c.lim_of_nmem_U _ fun h => h hx,
       c.lim_mem_Icc⟩
-#align exists_continuous_zero_one_of_closed exists_continuous_zero_one_of_closed
+#align exists_continuous_zero_one_of_closed exists_continuous_zero_one_of_isClosed
 -/
 

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

@@ -3,9 +3,9 @@ Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
 -/
-import Mathbin.Analysis.NormedSpace.AddTorsor
-import Mathbin.LinearAlgebra.AffineSpace.Ordered
-import Mathbin.Topology.ContinuousFunction.Basic
+import Analysis.NormedSpace.AddTorsor
+import LinearAlgebra.AffineSpace.Ordered
+import Topology.ContinuousFunction.Basic
 
 #align_import topology.urysohns_lemma from "leanprover-community/mathlib"@"8eb9c42d4d34c77f6ee84ea766ae4070233a973c"
 

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

@@ -2,16 +2,13 @@
 Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
-
-! This file was ported from Lean 3 source module topology.urysohns_lemma
-! leanprover-community/mathlib commit 8eb9c42d4d34c77f6ee84ea766ae4070233a973c
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.NormedSpace.AddTorsor
 import Mathbin.LinearAlgebra.AffineSpace.Ordered
 import Mathbin.Topology.ContinuousFunction.Basic
 
+#align_import topology.urysohns_lemma from "leanprover-community/mathlib"@"8eb9c42d4d34c77f6ee84ea766ae4070233a973c"
+
 /-!
 # Urysohn's lemma
 

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

@@ -158,6 +158,7 @@ noncomputable def approx : ℕ → CU X → X → ℝ
 #align urysohns.CU.approx Urysohns.CU.approx
 -/
 
+#print Urysohns.CU.approx_of_mem_C /-
 theorem approx_of_mem_C (c : CU X) (n : ℕ) {x : X} (hx : x ∈ c.C) : c.approx n x = 0 :=
   by
   induction' n with n ihn generalizing c
@@ -166,7 +167,9 @@ theorem approx_of_mem_C (c : CU X) (n : ℕ) {x : X} (hx : x ∈ c.C) : c.approx
     rw [ihn, ihn, midpoint_self]
     exacts [c.subset_right_C hx, hx]
 #align urysohns.CU.approx_of_mem_C Urysohns.CU.approx_of_mem_C
+-/
 
+#print Urysohns.CU.approx_of_nmem_U /-
 theorem approx_of_nmem_U (c : CU X) (n : ℕ) {x : X} (hx : x ∉ c.U) : c.approx n x = 1 :=
   by
   induction' n with n ihn generalizing c
@@ -175,7 +178,9 @@ theorem approx_of_nmem_U (c : CU X) (n : ℕ) {x : X} (hx : x ∉ c.U) : c.appro
     rw [ihn, ihn, midpoint_self]
     exacts [hx, fun hU => hx <| c.left_U_subset hU]
 #align urysohns.CU.approx_of_nmem_U Urysohns.CU.approx_of_nmem_U
+-/
 
+#print Urysohns.CU.approx_nonneg /-
 theorem approx_nonneg (c : CU X) (n : ℕ) (x : X) : 0 ≤ c.approx n x :=
   by
   induction' n with n ihn generalizing c
@@ -183,7 +188,9 @@ theorem approx_nonneg (c : CU X) (n : ℕ) (x : X) : 0 ≤ c.approx n x :=
   · simp only [approx, midpoint_eq_smul_add, invOf_eq_inv]
     refine' mul_nonneg (inv_nonneg.2 zero_le_two) (add_nonneg _ _) <;> apply ihn
 #align urysohns.CU.approx_nonneg Urysohns.CU.approx_nonneg
+-/
 
+#print Urysohns.CU.approx_le_one /-
 theorem approx_le_one (c : CU X) (n : ℕ) (x : X) : c.approx n x ≤ 1 :=
   by
   induction' n with n ihn generalizing c
@@ -191,6 +198,7 @@ theorem approx_le_one (c : CU X) (n : ℕ) (x : X) : c.approx n x ≤ 1 :=
   · simp only [approx, midpoint_eq_smul_add, invOf_eq_inv, smul_eq_mul, ← div_eq_inv_mul]
     refine' Iff.mpr (div_le_one zero_lt_two) (add_le_add _ _) <;> apply ihn
 #align urysohns.CU.approx_le_one Urysohns.CU.approx_le_one
+-/
 
 #print Urysohns.CU.bddAbove_range_approx /-
 theorem bddAbove_range_approx (c : CU X) (x : X) : BddAbove (range fun n => c.approx n x) :=
@@ -198,6 +206,7 @@ theorem bddAbove_range_approx (c : CU X) (x : X) : BddAbove (range fun n => c.ap
 #align urysohns.CU.bdd_above_range_approx Urysohns.CU.bddAbove_range_approx
 -/
 
+#print Urysohns.CU.approx_le_approx_of_U_sub_C /-
 theorem approx_le_approx_of_U_sub_C {c₁ c₂ : CU X} (h : c₁.U ⊆ c₂.C) (n₁ n₂ : ℕ) (x : X) :
     c₂.approx n₂ x ≤ c₁.approx n₁ x :=
   by
@@ -211,6 +220,7 @@ theorem approx_le_approx_of_U_sub_C {c₁ c₂ : CU X} (h : c₁.U ⊆ c₂.C) (
       approx n₂ c₂ x ≤ 1 := approx_le_one _ _ _
       _ = approx n₁ c₁ x := (approx_of_nmem_U _ _ hx).symm
 #align urysohns.CU.approx_le_approx_of_U_sub_C Urysohns.CU.approx_le_approx_of_U_sub_C
+-/
 
 #print Urysohns.CU.approx_mem_Icc_right_left /-
 theorem approx_mem_Icc_right_left (c : CU X) (n : ℕ) (x : X) :
@@ -229,6 +239,7 @@ theorem approx_mem_Icc_right_left (c : CU X) (n : ℕ) (x : X) :
 #align urysohns.CU.approx_mem_Icc_right_left Urysohns.CU.approx_mem_Icc_right_left
 -/
 
+#print Urysohns.CU.approx_le_succ /-
 theorem approx_le_succ (c : CU X) (n : ℕ) (x : X) : c.approx n x ≤ c.approx (n + 1) x :=
   by
   induction' n with n ihn generalizing c
@@ -237,6 +248,7 @@ theorem approx_le_succ (c : CU X) (n : ℕ) (x : X) : c.approx n x ≤ c.approx
   · rw [approx, approx]
     exact midpoint_le_midpoint (ihn _) (ihn _)
 #align urysohns.CU.approx_le_succ Urysohns.CU.approx_le_succ
+-/
 
 #print Urysohns.CU.approx_mono /-
 theorem approx_mono (c : CU X) (x : X) : Monotone fun n => c.approx n x :=
@@ -262,36 +274,50 @@ theorem tendsto_approx_atTop (c : CU X) (x : X) :
 #align urysohns.CU.tendsto_approx_at_top Urysohns.CU.tendsto_approx_atTop
 -/
 
+#print Urysohns.CU.lim_of_mem_C /-
 theorem lim_of_mem_C (c : CU X) (x : X) (h : x ∈ c.C) : c.lim x = 0 := by
   simp only [CU.lim, approx_of_mem_C, h, ciSup_const]
 #align urysohns.CU.lim_of_mem_C Urysohns.CU.lim_of_mem_C
+-/
 
+#print Urysohns.CU.lim_of_nmem_U /-
 theorem lim_of_nmem_U (c : CU X) (x : X) (h : x ∉ c.U) : c.lim x = 1 := by
   simp only [CU.lim, approx_of_nmem_U c _ h, ciSup_const]
 #align urysohns.CU.lim_of_nmem_U Urysohns.CU.lim_of_nmem_U
+-/
 
+#print Urysohns.CU.lim_eq_midpoint /-
 theorem lim_eq_midpoint (c : CU X) (x : X) : c.lim x = midpoint ℝ (c.left.lim x) (c.right.lim x) :=
   by
   refine' tendsto_nhds_unique (c.tendsto_approx_at_top x) ((tendsto_add_at_top_iff_nat 1).1 _)
   simp only [approx]
   exact (c.left.tendsto_approx_at_top x).midpoint (c.right.tendsto_approx_at_top x)
 #align urysohns.CU.lim_eq_midpoint Urysohns.CU.lim_eq_midpoint
+-/
 
+#print Urysohns.CU.approx_le_lim /-
 theorem approx_le_lim (c : CU X) (x : X) (n : ℕ) : c.approx n x ≤ c.lim x :=
   le_ciSup (c.bddAbove_range_approx x) _
 #align urysohns.CU.approx_le_lim Urysohns.CU.approx_le_lim
+-/
 
+#print Urysohns.CU.lim_nonneg /-
 theorem lim_nonneg (c : CU X) (x : X) : 0 ≤ c.lim x :=
   (c.approx_nonneg 0 x).trans (c.approx_le_lim x 0)
 #align urysohns.CU.lim_nonneg Urysohns.CU.lim_nonneg
+-/
 
+#print Urysohns.CU.lim_le_one /-
 theorem lim_le_one (c : CU X) (x : X) : c.lim x ≤ 1 :=
   ciSup_le fun n => c.approx_le_one _ _
 #align urysohns.CU.lim_le_one Urysohns.CU.lim_le_one
+-/
 
+#print Urysohns.CU.lim_mem_Icc /-
 theorem lim_mem_Icc (c : CU X) (x : X) : c.lim x ∈ Icc (0 : ℝ) 1 :=
   ⟨c.lim_nonneg x, c.lim_le_one x⟩
 #align urysohns.CU.lim_mem_Icc Urysohns.CU.lim_mem_Icc
+-/
 
 #print Urysohns.CU.continuous_lim /-
 /-- Continuity of `urysohns.CU.lim`. See module docstring for a sketch of the proofs. -/
@@ -342,6 +368,7 @@ end Urysohns
 
 variable [NormalSpace X]
 
+#print exists_continuous_zero_one_of_closed /-
 /-- Urysohns lemma: if `s` and `t` are two disjoint closed sets in a normal topological space `X`,
 then there exists a continuous function `f : X → ℝ` such that
 
@@ -358,4 +385,5 @@ theorem exists_continuous_zero_one_of_closed {s t : Set X} (hs : IsClosed s) (ht
     ⟨⟨c.lim, c.continuous_lim⟩, c.lim_of_mem_C, fun x hx => c.lim_of_nmem_U _ fun h => h hx,
       c.lim_mem_Icc⟩
 #align exists_continuous_zero_one_of_closed exists_continuous_zero_one_of_closed
+-/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

@@ -206,12 +206,10 @@ theorem approx_le_approx_of_U_sub_C {c₁ c₂ : CU X} (h : c₁.U ⊆ c₂.C) (
     calc
       approx n₂ c₂ x = 0 := approx_of_mem_C _ _ (h hx)
       _ ≤ approx n₁ c₁ x := approx_nonneg _ _ _
-      
   ·
     calc
       approx n₂ c₂ x ≤ 1 := approx_le_one _ _ _
       _ = approx n₁ c₁ x := (approx_of_nmem_U _ _ hx).symm
-      
 #align urysohns.CU.approx_le_approx_of_U_sub_C Urysohns.CU.approx_le_approx_of_U_sub_C
 
 #print Urysohns.CU.approx_mem_Icc_right_left /-

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

@@ -309,7 +309,7 @@ theorem continuous_lim (c : CU X) : Continuous c.lim :=
     rw [pow_zero]
     exact Real.dist_le_of_mem_Icc_01 (c.lim_mem_Icc _) (c.lim_mem_Icc _)
   · by_cases hxl : x ∈ c.left.U
-    · filter_upwards [IsOpen.mem_nhds c.left.open_U hxl, ihn c.left]with _ hyl hyd
+    · filter_upwards [IsOpen.mem_nhds c.left.open_U hxl, ihn c.left] with _ hyl hyd
       rw [pow_succ, c.lim_eq_midpoint, c.lim_eq_midpoint,
         c.right.lim_of_mem_C _ (c.left_U_subset_right_C hyl),
         c.right.lim_of_mem_C _ (c.left_U_subset_right_C hxl)]
@@ -318,7 +318,7 @@ theorem continuous_lim (c : CU X) : Continuous c.lim :=
       exact mul_le_mul h1234.le hyd dist_nonneg (h0.trans h1234).le
     · replace hxl : x ∈ c.left.right.Cᶜ; exact compl_subset_compl.2 c.left.right.subset hxl
       filter_upwards [IsOpen.mem_nhds (isOpen_compl_iff.2 c.left.right.closed_C) hxl,
-        ihn c.left.right, ihn c.right]with y hyl hydl hydr
+        ihn c.left.right, ihn c.right] with y hyl hydl hydr
       replace hxl : x ∉ c.left.left.U; exact compl_subset_compl.2 c.left.left_U_subset_right_C hxl
       replace hyl : y ∉ c.left.left.U; exact compl_subset_compl.2 c.left.left_U_subset_right_C hyl
       simp only [pow_succ, c.lim_eq_midpoint, c.left.lim_eq_midpoint,

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

@@ -164,7 +164,7 @@ theorem approx_of_mem_C (c : CU X) (n : ℕ) {x : X} (hx : x ∈ c.C) : c.approx
   · exact indicator_of_not_mem (fun hU => hU <| c.subset hx) _
   · simp only [approx]
     rw [ihn, ihn, midpoint_self]
-    exacts[c.subset_right_C hx, hx]
+    exacts [c.subset_right_C hx, hx]
 #align urysohns.CU.approx_of_mem_C Urysohns.CU.approx_of_mem_C
 
 theorem approx_of_nmem_U (c : CU X) (n : ℕ) {x : X} (hx : x ∉ c.U) : c.approx n x = 1 :=
@@ -173,7 +173,7 @@ theorem approx_of_nmem_U (c : CU X) (n : ℕ) {x : X} (hx : x ∉ c.U) : c.appro
   · exact indicator_of_mem hx _
   · simp only [approx]
     rw [ihn, ihn, midpoint_self]
-    exacts[hx, fun hU => hx <| c.left_U_subset hU]
+    exacts [hx, fun hU => hx <| c.left_U_subset hU]
 #align urysohns.CU.approx_of_nmem_U Urysohns.CU.approx_of_nmem_U
 
 theorem approx_nonneg (c : CU X) (n : ℕ) (x : X) : 0 ≤ c.approx n x :=
@@ -227,7 +227,7 @@ theorem approx_mem_Icc_right_left (c : CU X) (n : ℕ) (x : X) :
   · simp only [approx, mem_Icc]
     refine' ⟨midpoint_le_midpoint _ (ihn _).1, midpoint_le_midpoint (ihn _).2 _⟩ <;>
       apply approx_le_approx_of_U_sub_C
-    exacts[subset_closure, subset_closure]
+    exacts [subset_closure, subset_closure]
 #align urysohns.CU.approx_mem_Icc_right_left Urysohns.CU.approx_mem_Icc_right_left
 -/
 
@@ -334,7 +334,7 @@ theorem continuous_lim (c : CU X) : Continuous c.lim :=
               zero_le_two).trans_eq
           _
       generalize (3 / 4 : ℝ) ^ n = r
-      field_simp [two_ne_zero' ℝ] ; ring
+      field_simp [two_ne_zero' ℝ]; ring
 #align urysohns.CU.continuous_lim Urysohns.CU.continuous_lim
 -/
 

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

@@ -81,7 +81,7 @@ variable {X : Type _} [TopologicalSpace X]
 
 open Set Filter TopologicalSpace
 
-open Topology Filter
+open scoped Topology Filter
 
 namespace Urysohns
 

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

@@ -158,12 +158,6 @@ noncomputable def approx : ℕ → CU X → X → ℝ
 #align urysohns.CU.approx Urysohns.CU.approx
 -/
 
-/- warning: urysohns.CU.approx_of_mem_C -> Urysohns.CU.approx_of_mem_C is a dubious translation:
-lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] (c : Urysohns.CU.{u1} X _inst_1) (n : Nat) {x : X}, (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) x (Urysohns.CU.c.{u1} X _inst_1 c)) -> (Eq.{1} Real (Urysohns.CU.approx.{u1} X _inst_1 _inst_2 n c x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
-but is expected to have type
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] (c : Urysohns.CU.{u1} X _inst_1) (n : Nat) {x : X}, (Membership.mem.{u1, u1} X (Set.{u1} X) (Set.instMembershipSet.{u1} X) x (Urysohns.CU.C.{u1} X _inst_1 c)) -> (Eq.{1} Real (Urysohns.CU.approx.{u1} X _inst_1 _inst_2 n c x) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
-Case conversion may be inaccurate. Consider using '#align urysohns.CU.approx_of_mem_C Urysohns.CU.approx_of_mem_Cₓ'. -/
 theorem approx_of_mem_C (c : CU X) (n : ℕ) {x : X} (hx : x ∈ c.C) : c.approx n x = 0 :=
   by
   induction' n with n ihn generalizing c
@@ -173,12 +167,6 @@ theorem approx_of_mem_C (c : CU X) (n : ℕ) {x : X} (hx : x ∈ c.C) : c.approx
     exacts[c.subset_right_C hx, hx]
 #align urysohns.CU.approx_of_mem_C Urysohns.CU.approx_of_mem_C
 
-/- warning: urysohns.CU.approx_of_nmem_U -> Urysohns.CU.approx_of_nmem_U is a dubious translation:
-lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] (c : Urysohns.CU.{u1} X _inst_1) (n : Nat) {x : X}, (Not (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) x (Urysohns.CU.u.{u1} X _inst_1 c))) -> (Eq.{1} Real (Urysohns.CU.approx.{u1} X _inst_1 _inst_2 n c x) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align urysohns.CU.approx_of_nmem_U Urysohns.CU.approx_of_nmem_Uₓ'. -/
 theorem approx_of_nmem_U (c : CU X) (n : ℕ) {x : X} (hx : x ∉ c.U) : c.approx n x = 1 :=
   by
   induction' n with n ihn generalizing c
@@ -188,12 +176,6 @@ theorem approx_of_nmem_U (c : CU X) (n : ℕ) {x : X} (hx : x ∉ c.U) : c.appro
     exacts[hx, fun hU => hx <| c.left_U_subset hU]
 #align urysohns.CU.approx_of_nmem_U Urysohns.CU.approx_of_nmem_U
 
-/- warning: urysohns.CU.approx_nonneg -> Urysohns.CU.approx_nonneg 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 urysohns.CU.approx_nonneg Urysohns.CU.approx_nonnegₓ'. -/
 theorem approx_nonneg (c : CU X) (n : ℕ) (x : X) : 0 ≤ c.approx n x :=
   by
   induction' n with n ihn generalizing c
@@ -202,12 +184,6 @@ theorem approx_nonneg (c : CU X) (n : ℕ) (x : X) : 0 ≤ c.approx n x :=
     refine' mul_nonneg (inv_nonneg.2 zero_le_two) (add_nonneg _ _) <;> apply ihn
 #align urysohns.CU.approx_nonneg Urysohns.CU.approx_nonneg
 
-/- warning: urysohns.CU.approx_le_one -> Urysohns.CU.approx_le_one is a dubious translation:
-lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] (c : Urysohns.CU.{u1} X _inst_1) (n : Nat) (x : X), LE.le.{0} Real Real.hasLe (Urysohns.CU.approx.{u1} X _inst_1 _inst_2 n c x) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align urysohns.CU.approx_le_one Urysohns.CU.approx_le_oneₓ'. -/
 theorem approx_le_one (c : CU X) (n : ℕ) (x : X) : c.approx n x ≤ 1 :=
   by
   induction' n with n ihn generalizing c
@@ -222,12 +198,6 @@ theorem bddAbove_range_approx (c : CU X) (x : X) : BddAbove (range fun n => c.ap
 #align urysohns.CU.bdd_above_range_approx Urysohns.CU.bddAbove_range_approx
 -/
 
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-lean 3 declaration is
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-but is expected to have type
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] {c₁ : Urysohns.CU.{u1} X _inst_1} {c₂ : Urysohns.CU.{u1} X _inst_1}, (HasSubset.Subset.{u1} (Set.{u1} X) (Set.instHasSubsetSet.{u1} X) (Urysohns.CU.U.{u1} X _inst_1 c₁) (Urysohns.CU.C.{u1} X _inst_1 c₂)) -> (forall (n₁ : Nat) (n₂ : Nat) (x : X), LE.le.{0} Real Real.instLEReal (Urysohns.CU.approx.{u1} X _inst_1 _inst_2 n₂ c₂ x) (Urysohns.CU.approx.{u1} X _inst_1 _inst_2 n₁ c₁ x))
-Case conversion may be inaccurate. Consider using '#align urysohns.CU.approx_le_approx_of_U_sub_C Urysohns.CU.approx_le_approx_of_U_sub_Cₓ'. -/
 theorem approx_le_approx_of_U_sub_C {c₁ c₂ : CU X} (h : c₁.U ⊆ c₂.C) (n₁ n₂ : ℕ) (x : X) :
     c₂.approx n₂ x ≤ c₁.approx n₁ x :=
   by
@@ -261,12 +231,6 @@ theorem approx_mem_Icc_right_left (c : CU X) (n : ℕ) (x : X) :
 #align urysohns.CU.approx_mem_Icc_right_left Urysohns.CU.approx_mem_Icc_right_left
 -/
 
-/- warning: urysohns.CU.approx_le_succ -> Urysohns.CU.approx_le_succ 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 urysohns.CU.approx_le_succ Urysohns.CU.approx_le_succₓ'. -/
 theorem approx_le_succ (c : CU X) (n : ℕ) (x : X) : c.approx n x ≤ c.approx (n + 1) x :=
   by
   induction' n with n ihn generalizing c
@@ -300,32 +264,14 @@ theorem tendsto_approx_atTop (c : CU X) (x : X) :
 #align urysohns.CU.tendsto_approx_at_top Urysohns.CU.tendsto_approx_atTop
 -/
 
-/- warning: urysohns.CU.lim_of_mem_C -> Urysohns.CU.lim_of_mem_C 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] [_inst_2 : NormalSpace.{u1} X _inst_1] (c : Urysohns.CU.{u1} X _inst_1) (x : X), (Membership.mem.{u1, u1} X (Set.{u1} X) (Set.instMembershipSet.{u1} X) x (Urysohns.CU.C.{u1} X _inst_1 c)) -> (Eq.{1} Real (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 c x) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
-Case conversion may be inaccurate. Consider using '#align urysohns.CU.lim_of_mem_C Urysohns.CU.lim_of_mem_Cₓ'. -/
 theorem lim_of_mem_C (c : CU X) (x : X) (h : x ∈ c.C) : c.lim x = 0 := by
   simp only [CU.lim, approx_of_mem_C, h, ciSup_const]
 #align urysohns.CU.lim_of_mem_C Urysohns.CU.lim_of_mem_C
 
-/- warning: urysohns.CU.lim_of_nmem_U -> Urysohns.CU.lim_of_nmem_U is a dubious translation:
-lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] (c : Urysohns.CU.{u1} X _inst_1) (x : X), (Not (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) x (Urysohns.CU.u.{u1} X _inst_1 c))) -> (Eq.{1} Real (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 c x) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))
-but is expected to have type
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] (c : Urysohns.CU.{u1} X _inst_1) (x : X), (Not (Membership.mem.{u1, u1} X (Set.{u1} X) (Set.instMembershipSet.{u1} X) x (Urysohns.CU.U.{u1} X _inst_1 c))) -> (Eq.{1} Real (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 c x) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))
-Case conversion may be inaccurate. Consider using '#align urysohns.CU.lim_of_nmem_U Urysohns.CU.lim_of_nmem_Uₓ'. -/
 theorem lim_of_nmem_U (c : CU X) (x : X) (h : x ∉ c.U) : c.lim x = 1 := by
   simp only [CU.lim, approx_of_nmem_U c _ h, ciSup_const]
 #align urysohns.CU.lim_of_nmem_U Urysohns.CU.lim_of_nmem_U
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align urysohns.CU.lim_eq_midpoint Urysohns.CU.lim_eq_midpointₓ'. -/
 theorem lim_eq_midpoint (c : CU X) (x : X) : c.lim x = midpoint ℝ (c.left.lim x) (c.right.lim x) :=
   by
   refine' tendsto_nhds_unique (c.tendsto_approx_at_top x) ((tendsto_add_at_top_iff_nat 1).1 _)
@@ -333,42 +279,18 @@ theorem lim_eq_midpoint (c : CU X) (x : X) : c.lim x = midpoint ℝ (c.left.lim
   exact (c.left.tendsto_approx_at_top x).midpoint (c.right.tendsto_approx_at_top x)
 #align urysohns.CU.lim_eq_midpoint Urysohns.CU.lim_eq_midpoint
 
-/- warning: urysohns.CU.approx_le_lim -> Urysohns.CU.approx_le_lim 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 urysohns.CU.approx_le_lim Urysohns.CU.approx_le_limₓ'. -/
 theorem approx_le_lim (c : CU X) (x : X) (n : ℕ) : c.approx n x ≤ c.lim x :=
   le_ciSup (c.bddAbove_range_approx x) _
 #align urysohns.CU.approx_le_lim Urysohns.CU.approx_le_lim
 
-/- warning: urysohns.CU.lim_nonneg -> Urysohns.CU.lim_nonneg 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 urysohns.CU.lim_nonneg Urysohns.CU.lim_nonnegₓ'. -/
 theorem lim_nonneg (c : CU X) (x : X) : 0 ≤ c.lim x :=
   (c.approx_nonneg 0 x).trans (c.approx_le_lim x 0)
 #align urysohns.CU.lim_nonneg Urysohns.CU.lim_nonneg
 
-/- warning: urysohns.CU.lim_le_one -> Urysohns.CU.lim_le_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 urysohns.CU.lim_le_one Urysohns.CU.lim_le_oneₓ'. -/
 theorem lim_le_one (c : CU X) (x : X) : c.lim x ≤ 1 :=
   ciSup_le fun n => c.approx_le_one _ _
 #align urysohns.CU.lim_le_one Urysohns.CU.lim_le_one
 
-/- warning: urysohns.CU.lim_mem_Icc -> Urysohns.CU.lim_mem_Icc 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 urysohns.CU.lim_mem_Icc Urysohns.CU.lim_mem_Iccₓ'. -/
 theorem lim_mem_Icc (c : CU X) (x : X) : c.lim x ∈ Icc (0 : ℝ) 1 :=
   ⟨c.lim_nonneg x, c.lim_le_one x⟩
 #align urysohns.CU.lim_mem_Icc Urysohns.CU.lim_mem_Icc
@@ -422,12 +344,6 @@ end Urysohns
 
 variable [NormalSpace X]
 
-/- warning: exists_continuous_zero_one_of_closed -> exists_continuous_zero_one_of_closed is a dubious translation:
-lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] {s : Set.{u1} X} {t : Set.{u1} X}, (IsClosed.{u1} X _inst_1 s) -> (IsClosed.{u1} X _inst_1 t) -> (Disjoint.{u1} (Set.{u1} X) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} X) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} X) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} X) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} X) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} X) (Set.completeBooleanAlgebra.{u1} X)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} X) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} X) (Set.booleanAlgebra.{u1} X))) s t) -> (Exists.{succ u1} (ContinuousMap.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (fun (f : ContinuousMap.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) => And (Set.EqOn.{u1, 0} X Real (coeFn.{succ u1, succ u1} (ContinuousMap.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (fun (_x : ContinuousMap.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) => X -> Real) (ContinuousMap.hasCoeToFun.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) f) (OfNat.ofNat.{u1} (X -> Real) 0 (OfNat.mk.{u1} (X -> Real) 0 (Zero.zero.{u1} (X -> Real) (Pi.instZero.{u1, 0} X (fun (ᾰ : X) => Real) (fun (i : X) => Real.hasZero))))) s) (And (Set.EqOn.{u1, 0} X Real (coeFn.{succ u1, succ u1} (ContinuousMap.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (fun (_x : ContinuousMap.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) => X -> Real) (ContinuousMap.hasCoeToFun.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) f) (OfNat.ofNat.{u1} (X -> Real) 1 (OfNat.mk.{u1} (X -> Real) 1 (One.one.{u1} (X -> Real) (Pi.instOne.{u1, 0} X (fun (ᾰ : X) => Real) (fun (i : X) => Real.hasOne))))) t) (forall (x : X), Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) (coeFn.{succ u1, succ u1} (ContinuousMap.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (fun (_x : ContinuousMap.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) => X -> Real) (ContinuousMap.hasCoeToFun.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) f 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))))))))
-but is expected to have type
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] {s : Set.{u1} X} {t : Set.{u1} X}, (IsClosed.{u1} X _inst_1 s) -> (IsClosed.{u1} X _inst_1 t) -> (Disjoint.{u1} (Set.{u1} X) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} X) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} X) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} X) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} X) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} X) (Set.instCompleteBooleanAlgebraSet.{u1} X)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} X) (Preorder.toLE.{u1} (Set.{u1} X) (PartialOrder.toPreorder.{u1} (Set.{u1} X) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} X) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} X) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} X) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} X) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} X) (Set.instCompleteBooleanAlgebraSet.{u1} X)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} X) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} X) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} X) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} X) (Set.instCompleteBooleanAlgebraSet.{u1} X)))))) s t) -> (Exists.{succ u1} (ContinuousMap.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (fun (f : ContinuousMap.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) => And (Set.EqOn.{u1, 0} X Real (FunLike.coe.{succ u1, succ u1, 1} (ContinuousMap.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) X (fun (_x : X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : X) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousMap.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousMap.instContinuousMapClassContinuousMap.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)))) f) (OfNat.ofNat.{u1} (X -> Real) 0 (Zero.toOfNat0.{u1} (X -> Real) (Pi.instZero.{u1, 0} X (fun (a._@.Mathlib.Data.Set.Function._hyg.1349 : X) => Real) (fun (i : X) => Real.instZeroReal)))) s) (And (Set.EqOn.{u1, 0} X Real (FunLike.coe.{succ u1, succ u1, 1} (ContinuousMap.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) X (fun (_x : X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : X) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousMap.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousMap.instContinuousMapClassContinuousMap.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)))) f) (OfNat.ofNat.{u1} (X -> Real) 1 (One.toOfNat1.{u1} (X -> Real) (Pi.instOne.{u1, 0} X (fun (a._@.Mathlib.Data.Set.Function._hyg.1349 : X) => Real) (fun (i : X) => Real.instOneReal)))) t) (forall (x : X), Membership.mem.{0, 0} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : X) => Real) x) (Set.{0} Real) (Set.instMembershipSet.{0} Real) (FunLike.coe.{succ u1, succ u1, 1} (ContinuousMap.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) X (fun (_x : X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : X) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousMap.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousMap.instContinuousMapClassContinuousMap.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)))) f 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)))))))
-Case conversion may be inaccurate. Consider using '#align exists_continuous_zero_one_of_closed exists_continuous_zero_one_of_closedₓ'. -/
 /-- Urysohns lemma: if `s` and `t` are two disjoint closed sets in a normal topological space `X`,
 then there exists a continuous function `f : X → ℝ` such that
 

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

@@ -394,14 +394,11 @@ theorem continuous_lim (c : CU X) : Continuous c.lim :=
       refine' (dist_midpoint_midpoint_le _ _ _ _).trans _
       rw [dist_self, add_zero, div_eq_inv_mul]
       exact mul_le_mul h1234.le hyd dist_nonneg (h0.trans h1234).le
-    · replace hxl : x ∈ c.left.right.Cᶜ
-      exact compl_subset_compl.2 c.left.right.subset hxl
+    · replace hxl : x ∈ c.left.right.Cᶜ; exact compl_subset_compl.2 c.left.right.subset hxl
       filter_upwards [IsOpen.mem_nhds (isOpen_compl_iff.2 c.left.right.closed_C) hxl,
         ihn c.left.right, ihn c.right]with y hyl hydl hydr
-      replace hxl : x ∉ c.left.left.U
-      exact compl_subset_compl.2 c.left.left_U_subset_right_C hxl
-      replace hyl : y ∉ c.left.left.U
-      exact compl_subset_compl.2 c.left.left_U_subset_right_C hyl
+      replace hxl : x ∉ c.left.left.U; exact compl_subset_compl.2 c.left.left_U_subset_right_C hxl
+      replace hyl : y ∉ c.left.left.U; exact compl_subset_compl.2 c.left.left_U_subset_right_C hyl
       simp only [pow_succ, c.lim_eq_midpoint, c.left.lim_eq_midpoint,
         c.left.left.lim_of_nmem_U _ hxl, c.left.left.lim_of_nmem_U _ hyl]
       refine' (dist_midpoint_midpoint_le _ _ _ _).trans _
@@ -415,8 +412,7 @@ theorem continuous_lim (c : CU X) : Continuous c.lim :=
               zero_le_two).trans_eq
           _
       generalize (3 / 4 : ℝ) ^ n = r
-      field_simp [two_ne_zero' ℝ]
-      ring
+      field_simp [two_ne_zero' ℝ] ; ring
 #align urysohns.CU.continuous_lim Urysohns.CU.continuous_lim
 -/
 

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

@@ -324,7 +324,7 @@ theorem lim_of_nmem_U (c : CU X) (x : X) (h : x ∉ c.U) : c.lim x = 1 := by
 lean 3 declaration is
   forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] (c : Urysohns.CU.{u1} X _inst_1) (x : X), Eq.{1} Real (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 c x) (midpoint.{0, 0, 0} Real Real Real Real.ring (invertibleTwo.{0} Real Real.divisionRing (StrictOrderedSemiring.to_charZero.{0} Real Real.strictOrderedSemiring)) Real.addCommGroup Real.module (addGroupIsAddTorsor.{0} Real Real.addGroup) (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 (Urysohns.CU.left.{u1} X _inst_1 _inst_2 c) x) (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 (Urysohns.CU.right.{u1} X _inst_1 _inst_2 c) x))
 but is expected to have type
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] (c : Urysohns.CU.{u1} X _inst_1) (x : X), Eq.{1} Real (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 c x) (midpoint.{0, 0, 0} Real Real Real Real.instRingReal (invertibleTwo.{0} Real Real.instDivisionRingReal (StrictOrderedSemiring.to_charZero.{0} Real Real.strictOrderedSemiring)) Real.instAddCommGroupReal (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{0} Real Real.instRingReal) (NormedAddTorsor.toAddTorsor.{0, 0} Real Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) Real.pseudoMetricSpace (SeminormedAddCommGroup.toNormedAddTorsor.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))))) (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 (Urysohns.CU.left.{u1} X _inst_1 _inst_2 c) x) (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 (Urysohns.CU.right.{u1} X _inst_1 _inst_2 c) x))
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] (c : Urysohns.CU.{u1} X _inst_1) (x : X), Eq.{1} Real (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 c x) (midpoint.{0, 0, 0} Real Real Real Real.instRingReal (invertibleTwo.{0} Real Real.instDivisionRingReal (StrictOrderedSemiring.to_charZero.{0} Real Real.strictOrderedSemiring)) Real.instAddCommGroupReal (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (NormedAddTorsor.toAddTorsor.{0, 0} Real Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) Real.pseudoMetricSpace (SeminormedAddCommGroup.toNormedAddTorsor.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))))) (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 (Urysohns.CU.left.{u1} X _inst_1 _inst_2 c) x) (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 (Urysohns.CU.right.{u1} X _inst_1 _inst_2 c) x))
 Case conversion may be inaccurate. Consider using '#align urysohns.CU.lim_eq_midpoint Urysohns.CU.lim_eq_midpointₓ'. -/
 theorem lim_eq_midpoint (c : CU X) (x : X) : c.lim x = midpoint ℝ (c.left.lim x) (c.right.lim x) :=
   by

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

@@ -296,7 +296,7 @@ protected noncomputable def lim (c : CU X) (x : X) : ℝ :=
 #print Urysohns.CU.tendsto_approx_atTop /-
 theorem tendsto_approx_atTop (c : CU X) (x : X) :
     Tendsto (fun n => c.approx n x) atTop (𝓝 <| c.lim x) :=
-  tendsto_atTop_csupᵢ (c.approx_mono x) ⟨1, fun x ⟨n, hn⟩ => hn ▸ c.approx_le_one _ _⟩
+  tendsto_atTop_ciSup (c.approx_mono x) ⟨1, fun x ⟨n, hn⟩ => hn ▸ c.approx_le_one _ _⟩
 #align urysohns.CU.tendsto_approx_at_top Urysohns.CU.tendsto_approx_atTop
 -/
 
@@ -307,7 +307,7 @@ but is expected to have type
   forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] (c : Urysohns.CU.{u1} X _inst_1) (x : X), (Membership.mem.{u1, u1} X (Set.{u1} X) (Set.instMembershipSet.{u1} X) x (Urysohns.CU.C.{u1} X _inst_1 c)) -> (Eq.{1} Real (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 c x) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
 Case conversion may be inaccurate. Consider using '#align urysohns.CU.lim_of_mem_C Urysohns.CU.lim_of_mem_Cₓ'. -/
 theorem lim_of_mem_C (c : CU X) (x : X) (h : x ∈ c.C) : c.lim x = 0 := by
-  simp only [CU.lim, approx_of_mem_C, h, csupᵢ_const]
+  simp only [CU.lim, approx_of_mem_C, h, ciSup_const]
 #align urysohns.CU.lim_of_mem_C Urysohns.CU.lim_of_mem_C
 
 /- warning: urysohns.CU.lim_of_nmem_U -> Urysohns.CU.lim_of_nmem_U is a dubious translation:
@@ -317,7 +317,7 @@ but is expected to have type
   forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] (c : Urysohns.CU.{u1} X _inst_1) (x : X), (Not (Membership.mem.{u1, u1} X (Set.{u1} X) (Set.instMembershipSet.{u1} X) x (Urysohns.CU.U.{u1} X _inst_1 c))) -> (Eq.{1} Real (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 c x) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))
 Case conversion may be inaccurate. Consider using '#align urysohns.CU.lim_of_nmem_U Urysohns.CU.lim_of_nmem_Uₓ'. -/
 theorem lim_of_nmem_U (c : CU X) (x : X) (h : x ∉ c.U) : c.lim x = 1 := by
-  simp only [CU.lim, approx_of_nmem_U c _ h, csupᵢ_const]
+  simp only [CU.lim, approx_of_nmem_U c _ h, ciSup_const]
 #align urysohns.CU.lim_of_nmem_U Urysohns.CU.lim_of_nmem_U
 
 /- warning: urysohns.CU.lim_eq_midpoint -> Urysohns.CU.lim_eq_midpoint is a dubious translation:
@@ -340,7 +340,7 @@ but is expected to have type
   forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] (c : Urysohns.CU.{u1} X _inst_1) (x : X) (n : Nat), LE.le.{0} Real Real.instLEReal (Urysohns.CU.approx.{u1} X _inst_1 _inst_2 n c x) (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 c x)
 Case conversion may be inaccurate. Consider using '#align urysohns.CU.approx_le_lim Urysohns.CU.approx_le_limₓ'. -/
 theorem approx_le_lim (c : CU X) (x : X) (n : ℕ) : c.approx n x ≤ c.lim x :=
-  le_csupᵢ (c.bddAbove_range_approx x) _
+  le_ciSup (c.bddAbove_range_approx x) _
 #align urysohns.CU.approx_le_lim Urysohns.CU.approx_le_lim
 
 /- warning: urysohns.CU.lim_nonneg -> Urysohns.CU.lim_nonneg is a dubious translation:
@@ -360,7 +360,7 @@ but is expected to have type
   forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] (c : Urysohns.CU.{u1} X _inst_1) (x : X), LE.le.{0} Real Real.instLEReal (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 c x) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))
 Case conversion may be inaccurate. Consider using '#align urysohns.CU.lim_le_one Urysohns.CU.lim_le_oneₓ'. -/
 theorem lim_le_one (c : CU X) (x : X) : c.lim x ≤ 1 :=
-  csupᵢ_le fun n => c.approx_le_one _ _
+  ciSup_le fun n => c.approx_le_one _ _
 #align urysohns.CU.lim_le_one Urysohns.CU.lim_le_one
 
 /- warning: urysohns.CU.lim_mem_Icc -> Urysohns.CU.lim_mem_Icc is a dubious translation:

mathlib commit https://github.com/leanprover-community/mathlib/commit/9b2b58d6b14b895b2f375108e765cb47de71aebd

@@ -324,7 +324,7 @@ theorem lim_of_nmem_U (c : CU X) (x : X) (h : x ∉ c.U) : c.lim x = 1 := by
 lean 3 declaration is
   forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] (c : Urysohns.CU.{u1} X _inst_1) (x : X), Eq.{1} Real (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 c x) (midpoint.{0, 0, 0} Real Real Real Real.ring (invertibleTwo.{0} Real Real.divisionRing (StrictOrderedSemiring.to_charZero.{0} Real Real.strictOrderedSemiring)) Real.addCommGroup Real.module (addGroupIsAddTorsor.{0} Real Real.addGroup) (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 (Urysohns.CU.left.{u1} X _inst_1 _inst_2 c) x) (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 (Urysohns.CU.right.{u1} X _inst_1 _inst_2 c) x))
 but is expected to have type
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] (c : Urysohns.CU.{u1} X _inst_1) (x : X), Eq.{1} Real (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 c x) (midpoint.{0, 0, 0} Real Real Real Real.instRingReal (invertibleTwo.{0} Real Real.instDivisionRingReal (StrictOrderedSemiring.to_charZero.{0} Real Real.strictOrderedSemiring)) Real.instAddCommGroupReal instModuleRealSemiringInstAddCommMonoidReal (NormedAddTorsor.toAddTorsor.{0, 0} Real Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) Real.pseudoMetricSpace (SeminormedAddCommGroup.toNormedAddTorsor.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))))) (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 (Urysohns.CU.left.{u1} X _inst_1 _inst_2 c) x) (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 (Urysohns.CU.right.{u1} X _inst_1 _inst_2 c) x))
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] (c : Urysohns.CU.{u1} X _inst_1) (x : X), Eq.{1} Real (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 c x) (midpoint.{0, 0, 0} Real Real Real Real.instRingReal (invertibleTwo.{0} Real Real.instDivisionRingReal (StrictOrderedSemiring.to_charZero.{0} Real Real.strictOrderedSemiring)) Real.instAddCommGroupReal (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{0} Real Real.instRingReal) (NormedAddTorsor.toAddTorsor.{0, 0} Real Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) Real.pseudoMetricSpace (SeminormedAddCommGroup.toNormedAddTorsor.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))))) (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 (Urysohns.CU.left.{u1} X _inst_1 _inst_2 c) x) (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 (Urysohns.CU.right.{u1} X _inst_1 _inst_2 c) x))
 Case conversion may be inaccurate. Consider using '#align urysohns.CU.lim_eq_midpoint Urysohns.CU.lim_eq_midpointₓ'. -/
 theorem lim_eq_midpoint (c : CU X) (x : X) : c.lim x = midpoint ℝ (c.left.lim x) (c.right.lim x) :=
   by

mathlib commit https://github.com/leanprover-community/mathlib/commit/730c6d4cab72b9d84fcfb9e95e8796e9cd8f40ba

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
 
 ! This file was ported from Lean 3 source module topology.urysohns_lemma
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 8eb9c42d4d34c77f6ee84ea766ae4070233a973c
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Topology.ContinuousFunction.Basic
 /-!
 # Urysohn's lemma
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we prove Urysohn's lemma `exists_continuous_zero_one_of_closed`: for any two disjoint
 closed sets `s` and `t` in a normal topological space `X` there exists a continuous function
 `f : X → ℝ` such that

mathlib commit https://github.com/leanprover-community/mathlib/commit/49b7f94aab3a3bdca1f9f34c5d818afb253b3993

@@ -82,6 +82,7 @@ open Topology Filter
 
 namespace Urysohns
 
+#print Urysohns.CU /-
 /-- An auxiliary type for the proof of Urysohn's lemma: a pair of a closed set `C` and its
 open neighborhood `U`. -/
 @[protect_proj]
@@ -91,6 +92,7 @@ structure CU (X : Type _) [TopologicalSpace X] where
   open_u : IsOpen U
   Subset : C ⊆ U
 #align urysohns.CU Urysohns.CU
+-/
 
 instance : Inhabited (CU X) :=
   ⟨⟨∅, univ, isClosed_empty, isOpen_univ, empty_subset _⟩⟩
@@ -99,6 +101,7 @@ variable [NormalSpace X]
 
 namespace CU
 
+#print Urysohns.CU.left /-
 /-- Due to `normal_exists_closure_subset`, for each `c : CU X` there exists an open set `u`
 such chat `c.C ⊆ u` and `closure u ⊆ c.U`. `c.left` is the pair `(c.C, u)`. -/
 @[simps C]
@@ -109,7 +112,9 @@ def left (c : CU X) : CU X where
   open_u := (normal_exists_closure_subset c.closed_c c.open_u c.Subset).choose_spec.1
   Subset := (normal_exists_closure_subset c.closed_c c.open_u c.Subset).choose_spec.2.1
 #align urysohns.CU.left Urysohns.CU.left
+-/
 
+#print Urysohns.CU.right /-
 /-- Due to `normal_exists_closure_subset`, for each `c : CU X` there exists an open set `u`
 such chat `c.C ⊆ u` and `closure u ⊆ c.U`. `c.right` is the pair `(closure u, c.U)`. -/
 @[simps U]
@@ -121,44 +126,71 @@ def right (c : CU X) : CU X
   open_u := c.open_u
   Subset := (normal_exists_closure_subset c.closed_c c.open_u c.Subset).choose_spec.2.2
 #align urysohns.CU.right Urysohns.CU.right
+-/
 
-theorem left_u_subset_right_c (c : CU X) : c.left.U ⊆ c.right.C :=
+#print Urysohns.CU.left_U_subset_right_C /-
+theorem left_U_subset_right_C (c : CU X) : c.left.U ⊆ c.right.C :=
   subset_closure
-#align urysohns.CU.left_U_subset_right_C Urysohns.CU.left_u_subset_right_c
+#align urysohns.CU.left_U_subset_right_C Urysohns.CU.left_U_subset_right_C
+-/
 
-theorem left_u_subset (c : CU X) : c.left.U ⊆ c.U :=
-  Subset.trans c.left_u_subset_right_c c.right.Subset
-#align urysohns.CU.left_U_subset Urysohns.CU.left_u_subset
+#print Urysohns.CU.left_U_subset /-
+theorem left_U_subset (c : CU X) : c.left.U ⊆ c.U :=
+  Subset.trans c.left_U_subset_right_C c.right.Subset
+#align urysohns.CU.left_U_subset Urysohns.CU.left_U_subset
+-/
 
-theorem subset_right_c (c : CU X) : c.C ⊆ c.right.C :=
-  Subset.trans c.left.Subset c.left_u_subset_right_c
-#align urysohns.CU.subset_right_C Urysohns.CU.subset_right_c
+#print Urysohns.CU.subset_right_C /-
+theorem subset_right_C (c : CU X) : c.C ⊆ c.right.C :=
+  Subset.trans c.left.Subset c.left_U_subset_right_C
+#align urysohns.CU.subset_right_C Urysohns.CU.subset_right_C
+-/
 
+#print Urysohns.CU.approx /-
 /-- `n`-th approximation to a continuous function `f : X → ℝ` such that `f = 0` on `c.C` and `f = 1`
 outside of `c.U`. -/
 noncomputable def approx : ℕ → CU X → X → ℝ
   | 0, c, x => indicator (c.Uᶜ) 1 x
   | n + 1, c, x => midpoint ℝ (approx n c.left x) (approx n c.right x)
 #align urysohns.CU.approx Urysohns.CU.approx
+-/
 
-theorem approx_of_mem_c (c : CU X) (n : ℕ) {x : X} (hx : x ∈ c.C) : c.approx n x = 0 :=
+/- warning: urysohns.CU.approx_of_mem_C -> Urysohns.CU.approx_of_mem_C is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] (c : Urysohns.CU.{u1} X _inst_1) (n : Nat) {x : X}, (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) x (Urysohns.CU.c.{u1} X _inst_1 c)) -> (Eq.{1} Real (Urysohns.CU.approx.{u1} X _inst_1 _inst_2 n c x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] (c : Urysohns.CU.{u1} X _inst_1) (n : Nat) {x : X}, (Membership.mem.{u1, u1} X (Set.{u1} X) (Set.instMembershipSet.{u1} X) x (Urysohns.CU.C.{u1} X _inst_1 c)) -> (Eq.{1} Real (Urysohns.CU.approx.{u1} X _inst_1 _inst_2 n c x) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+Case conversion may be inaccurate. Consider using '#align urysohns.CU.approx_of_mem_C Urysohns.CU.approx_of_mem_Cₓ'. -/
+theorem approx_of_mem_C (c : CU X) (n : ℕ) {x : X} (hx : x ∈ c.C) : c.approx n x = 0 :=
   by
   induction' n with n ihn generalizing c
   · exact indicator_of_not_mem (fun hU => hU <| c.subset hx) _
   · simp only [approx]
     rw [ihn, ihn, midpoint_self]
     exacts[c.subset_right_C hx, hx]
-#align urysohns.CU.approx_of_mem_C Urysohns.CU.approx_of_mem_c
-
-theorem approx_of_nmem_u (c : CU X) (n : ℕ) {x : X} (hx : x ∉ c.U) : c.approx n x = 1 :=
+#align urysohns.CU.approx_of_mem_C Urysohns.CU.approx_of_mem_C
+
+/- warning: urysohns.CU.approx_of_nmem_U -> Urysohns.CU.approx_of_nmem_U is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] (c : Urysohns.CU.{u1} X _inst_1) (n : Nat) {x : X}, (Not (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) x (Urysohns.CU.u.{u1} X _inst_1 c))) -> (Eq.{1} Real (Urysohns.CU.approx.{u1} X _inst_1 _inst_2 n c x) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] (c : Urysohns.CU.{u1} X _inst_1) (n : Nat) {x : X}, (Not (Membership.mem.{u1, u1} X (Set.{u1} X) (Set.instMembershipSet.{u1} X) x (Urysohns.CU.U.{u1} X _inst_1 c))) -> (Eq.{1} Real (Urysohns.CU.approx.{u1} X _inst_1 _inst_2 n c x) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))
+Case conversion may be inaccurate. Consider using '#align urysohns.CU.approx_of_nmem_U Urysohns.CU.approx_of_nmem_Uₓ'. -/
+theorem approx_of_nmem_U (c : CU X) (n : ℕ) {x : X} (hx : x ∉ c.U) : c.approx n x = 1 :=
   by
   induction' n with n ihn generalizing c
   · exact indicator_of_mem hx _
   · simp only [approx]
     rw [ihn, ihn, midpoint_self]
     exacts[hx, fun hU => hx <| c.left_U_subset hU]
-#align urysohns.CU.approx_of_nmem_U Urysohns.CU.approx_of_nmem_u
-
+#align urysohns.CU.approx_of_nmem_U Urysohns.CU.approx_of_nmem_U
+
+/- warning: urysohns.CU.approx_nonneg -> Urysohns.CU.approx_nonneg is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] (c : Urysohns.CU.{u1} X _inst_1) (n : Nat) (x : X), LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Urysohns.CU.approx.{u1} X _inst_1 _inst_2 n c x)
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] (c : Urysohns.CU.{u1} X _inst_1) (n : Nat) (x : X), LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Urysohns.CU.approx.{u1} X _inst_1 _inst_2 n c x)
+Case conversion may be inaccurate. Consider using '#align urysohns.CU.approx_nonneg Urysohns.CU.approx_nonnegₓ'. -/
 theorem approx_nonneg (c : CU X) (n : ℕ) (x : X) : 0 ≤ c.approx n x :=
   by
   induction' n with n ihn generalizing c
@@ -167,6 +199,12 @@ theorem approx_nonneg (c : CU X) (n : ℕ) (x : X) : 0 ≤ c.approx n x :=
     refine' mul_nonneg (inv_nonneg.2 zero_le_two) (add_nonneg _ _) <;> apply ihn
 #align urysohns.CU.approx_nonneg Urysohns.CU.approx_nonneg
 
+/- warning: urysohns.CU.approx_le_one -> Urysohns.CU.approx_le_one is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] (c : Urysohns.CU.{u1} X _inst_1) (n : Nat) (x : X), LE.le.{0} Real Real.hasLe (Urysohns.CU.approx.{u1} X _inst_1 _inst_2 n c x) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] (c : Urysohns.CU.{u1} X _inst_1) (n : Nat) (x : X), LE.le.{0} Real Real.instLEReal (Urysohns.CU.approx.{u1} X _inst_1 _inst_2 n c x) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))
+Case conversion may be inaccurate. Consider using '#align urysohns.CU.approx_le_one Urysohns.CU.approx_le_oneₓ'. -/
 theorem approx_le_one (c : CU X) (n : ℕ) (x : X) : c.approx n x ≤ 1 :=
   by
   induction' n with n ihn generalizing c
@@ -175,11 +213,19 @@ theorem approx_le_one (c : CU X) (n : ℕ) (x : X) : c.approx n x ≤ 1 :=
     refine' Iff.mpr (div_le_one zero_lt_two) (add_le_add _ _) <;> apply ihn
 #align urysohns.CU.approx_le_one Urysohns.CU.approx_le_one
 
+#print Urysohns.CU.bddAbove_range_approx /-
 theorem bddAbove_range_approx (c : CU X) (x : X) : BddAbove (range fun n => c.approx n x) :=
   ⟨1, fun y ⟨n, hn⟩ => hn ▸ c.approx_le_one n x⟩
 #align urysohns.CU.bdd_above_range_approx Urysohns.CU.bddAbove_range_approx
+-/
 
-theorem approx_le_approx_of_u_sub_c {c₁ c₂ : CU X} (h : c₁.U ⊆ c₂.C) (n₁ n₂ : ℕ) (x : X) :
+/- warning: urysohns.CU.approx_le_approx_of_U_sub_C -> Urysohns.CU.approx_le_approx_of_U_sub_C is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] {c₁ : Urysohns.CU.{u1} X _inst_1} {c₂ : Urysohns.CU.{u1} X _inst_1}, (HasSubset.Subset.{u1} (Set.{u1} X) (Set.hasSubset.{u1} X) (Urysohns.CU.u.{u1} X _inst_1 c₁) (Urysohns.CU.c.{u1} X _inst_1 c₂)) -> (forall (n₁ : Nat) (n₂ : Nat) (x : X), LE.le.{0} Real Real.hasLe (Urysohns.CU.approx.{u1} X _inst_1 _inst_2 n₂ c₂ x) (Urysohns.CU.approx.{u1} X _inst_1 _inst_2 n₁ c₁ x))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] {c₁ : Urysohns.CU.{u1} X _inst_1} {c₂ : Urysohns.CU.{u1} X _inst_1}, (HasSubset.Subset.{u1} (Set.{u1} X) (Set.instHasSubsetSet.{u1} X) (Urysohns.CU.U.{u1} X _inst_1 c₁) (Urysohns.CU.C.{u1} X _inst_1 c₂)) -> (forall (n₁ : Nat) (n₂ : Nat) (x : X), LE.le.{0} Real Real.instLEReal (Urysohns.CU.approx.{u1} X _inst_1 _inst_2 n₂ c₂ x) (Urysohns.CU.approx.{u1} X _inst_1 _inst_2 n₁ c₁ x))
+Case conversion may be inaccurate. Consider using '#align urysohns.CU.approx_le_approx_of_U_sub_C Urysohns.CU.approx_le_approx_of_U_sub_Cₓ'. -/
+theorem approx_le_approx_of_U_sub_C {c₁ c₂ : CU X} (h : c₁.U ⊆ c₂.C) (n₁ n₂ : ℕ) (x : X) :
     c₂.approx n₂ x ≤ c₁.approx n₁ x :=
   by
   by_cases hx : x ∈ c₁.U
@@ -193,8 +239,9 @@ theorem approx_le_approx_of_u_sub_c {c₁ c₂ : CU X} (h : c₁.U ⊆ c₂.C) (
       approx n₂ c₂ x ≤ 1 := approx_le_one _ _ _
       _ = approx n₁ c₁ x := (approx_of_nmem_U _ _ hx).symm
       
-#align urysohns.CU.approx_le_approx_of_U_sub_C Urysohns.CU.approx_le_approx_of_u_sub_c
+#align urysohns.CU.approx_le_approx_of_U_sub_C Urysohns.CU.approx_le_approx_of_U_sub_C
 
+#print Urysohns.CU.approx_mem_Icc_right_left /-
 theorem approx_mem_Icc_right_left (c : CU X) (n : ℕ) (x : X) :
     c.approx n x ∈ Icc (c.right.approx n x) (c.left.approx n x) :=
   by
@@ -209,7 +256,14 @@ theorem approx_mem_Icc_right_left (c : CU X) (n : ℕ) (x : X) :
       apply approx_le_approx_of_U_sub_C
     exacts[subset_closure, subset_closure]
 #align urysohns.CU.approx_mem_Icc_right_left Urysohns.CU.approx_mem_Icc_right_left
+-/
 
+/- warning: urysohns.CU.approx_le_succ -> Urysohns.CU.approx_le_succ is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] (c : Urysohns.CU.{u1} X _inst_1) (n : Nat) (x : X), LE.le.{0} Real Real.hasLe (Urysohns.CU.approx.{u1} X _inst_1 _inst_2 n c x) (Urysohns.CU.approx.{u1} X _inst_1 _inst_2 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) c x)
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] (c : Urysohns.CU.{u1} X _inst_1) (n : Nat) (x : X), LE.le.{0} Real Real.instLEReal (Urysohns.CU.approx.{u1} X _inst_1 _inst_2 n c x) (Urysohns.CU.approx.{u1} X _inst_1 _inst_2 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) c x)
+Case conversion may be inaccurate. Consider using '#align urysohns.CU.approx_le_succ Urysohns.CU.approx_le_succₓ'. -/
 theorem approx_le_succ (c : CU X) (n : ℕ) (x : X) : c.approx n x ≤ c.approx (n + 1) x :=
   by
   induction' n with n ihn generalizing c
@@ -219,10 +273,13 @@ theorem approx_le_succ (c : CU X) (n : ℕ) (x : X) : c.approx n x ≤ c.approx
     exact midpoint_le_midpoint (ihn _) (ihn _)
 #align urysohns.CU.approx_le_succ Urysohns.CU.approx_le_succ
 
+#print Urysohns.CU.approx_mono /-
 theorem approx_mono (c : CU X) (x : X) : Monotone fun n => c.approx n x :=
   monotone_nat_of_le_succ fun n => c.approx_le_succ n x
 #align urysohns.CU.approx_mono Urysohns.CU.approx_mono
+-/
 
+#print Urysohns.CU.lim /-
 /-- A continuous function `f : X → ℝ` such that
 
 * `0 ≤ f x ≤ 1` for all `x`;
@@ -231,20 +288,41 @@ theorem approx_mono (c : CU X) (x : X) : Monotone fun n => c.approx n x :=
 protected noncomputable def lim (c : CU X) (x : X) : ℝ :=
   ⨆ n, c.approx n x
 #align urysohns.CU.lim Urysohns.CU.lim
+-/
 
+#print Urysohns.CU.tendsto_approx_atTop /-
 theorem tendsto_approx_atTop (c : CU X) (x : X) :
     Tendsto (fun n => c.approx n x) atTop (𝓝 <| c.lim x) :=
   tendsto_atTop_csupᵢ (c.approx_mono x) ⟨1, fun x ⟨n, hn⟩ => hn ▸ c.approx_le_one _ _⟩
 #align urysohns.CU.tendsto_approx_at_top Urysohns.CU.tendsto_approx_atTop
+-/
 
-theorem lim_of_mem_c (c : CU X) (x : X) (h : x ∈ c.C) : c.lim x = 0 := by
+/- warning: urysohns.CU.lim_of_mem_C -> Urysohns.CU.lim_of_mem_C is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] (c : Urysohns.CU.{u1} X _inst_1) (x : X), (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) x (Urysohns.CU.c.{u1} X _inst_1 c)) -> (Eq.{1} Real (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 c x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] (c : Urysohns.CU.{u1} X _inst_1) (x : X), (Membership.mem.{u1, u1} X (Set.{u1} X) (Set.instMembershipSet.{u1} X) x (Urysohns.CU.C.{u1} X _inst_1 c)) -> (Eq.{1} Real (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 c x) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+Case conversion may be inaccurate. Consider using '#align urysohns.CU.lim_of_mem_C Urysohns.CU.lim_of_mem_Cₓ'. -/
+theorem lim_of_mem_C (c : CU X) (x : X) (h : x ∈ c.C) : c.lim x = 0 := by
   simp only [CU.lim, approx_of_mem_C, h, csupᵢ_const]
-#align urysohns.CU.lim_of_mem_C Urysohns.CU.lim_of_mem_c
-
-theorem lim_of_nmem_u (c : CU X) (x : X) (h : x ∉ c.U) : c.lim x = 1 := by
+#align urysohns.CU.lim_of_mem_C Urysohns.CU.lim_of_mem_C
+
+/- warning: urysohns.CU.lim_of_nmem_U -> Urysohns.CU.lim_of_nmem_U is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] (c : Urysohns.CU.{u1} X _inst_1) (x : X), (Not (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) x (Urysohns.CU.u.{u1} X _inst_1 c))) -> (Eq.{1} Real (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 c x) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] (c : Urysohns.CU.{u1} X _inst_1) (x : X), (Not (Membership.mem.{u1, u1} X (Set.{u1} X) (Set.instMembershipSet.{u1} X) x (Urysohns.CU.U.{u1} X _inst_1 c))) -> (Eq.{1} Real (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 c x) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))
+Case conversion may be inaccurate. Consider using '#align urysohns.CU.lim_of_nmem_U Urysohns.CU.lim_of_nmem_Uₓ'. -/
+theorem lim_of_nmem_U (c : CU X) (x : X) (h : x ∉ c.U) : c.lim x = 1 := by
   simp only [CU.lim, approx_of_nmem_U c _ h, csupᵢ_const]
-#align urysohns.CU.lim_of_nmem_U Urysohns.CU.lim_of_nmem_u
-
+#align urysohns.CU.lim_of_nmem_U Urysohns.CU.lim_of_nmem_U
+
+/- warning: urysohns.CU.lim_eq_midpoint -> Urysohns.CU.lim_eq_midpoint is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] (c : Urysohns.CU.{u1} X _inst_1) (x : X), Eq.{1} Real (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 c x) (midpoint.{0, 0, 0} Real Real Real Real.ring (invertibleTwo.{0} Real Real.divisionRing (StrictOrderedSemiring.to_charZero.{0} Real Real.strictOrderedSemiring)) Real.addCommGroup Real.module (addGroupIsAddTorsor.{0} Real Real.addGroup) (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 (Urysohns.CU.left.{u1} X _inst_1 _inst_2 c) x) (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 (Urysohns.CU.right.{u1} X _inst_1 _inst_2 c) x))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] (c : Urysohns.CU.{u1} X _inst_1) (x : X), Eq.{1} Real (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 c x) (midpoint.{0, 0, 0} Real Real Real Real.instRingReal (invertibleTwo.{0} Real Real.instDivisionRingReal (StrictOrderedSemiring.to_charZero.{0} Real Real.strictOrderedSemiring)) Real.instAddCommGroupReal instModuleRealSemiringInstAddCommMonoidReal (NormedAddTorsor.toAddTorsor.{0, 0} Real Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) Real.pseudoMetricSpace (SeminormedAddCommGroup.toNormedAddTorsor.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))))) (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 (Urysohns.CU.left.{u1} X _inst_1 _inst_2 c) x) (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 (Urysohns.CU.right.{u1} X _inst_1 _inst_2 c) x))
+Case conversion may be inaccurate. Consider using '#align urysohns.CU.lim_eq_midpoint Urysohns.CU.lim_eq_midpointₓ'. -/
 theorem lim_eq_midpoint (c : CU X) (x : X) : c.lim x = midpoint ℝ (c.left.lim x) (c.right.lim x) :=
   by
   refine' tendsto_nhds_unique (c.tendsto_approx_at_top x) ((tendsto_add_at_top_iff_nat 1).1 _)
@@ -252,22 +330,47 @@ theorem lim_eq_midpoint (c : CU X) (x : X) : c.lim x = midpoint ℝ (c.left.lim
   exact (c.left.tendsto_approx_at_top x).midpoint (c.right.tendsto_approx_at_top x)
 #align urysohns.CU.lim_eq_midpoint Urysohns.CU.lim_eq_midpoint
 
+/- warning: urysohns.CU.approx_le_lim -> Urysohns.CU.approx_le_lim is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] (c : Urysohns.CU.{u1} X _inst_1) (x : X) (n : Nat), LE.le.{0} Real Real.hasLe (Urysohns.CU.approx.{u1} X _inst_1 _inst_2 n c x) (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 c x)
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] (c : Urysohns.CU.{u1} X _inst_1) (x : X) (n : Nat), LE.le.{0} Real Real.instLEReal (Urysohns.CU.approx.{u1} X _inst_1 _inst_2 n c x) (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 c x)
+Case conversion may be inaccurate. Consider using '#align urysohns.CU.approx_le_lim Urysohns.CU.approx_le_limₓ'. -/
 theorem approx_le_lim (c : CU X) (x : X) (n : ℕ) : c.approx n x ≤ c.lim x :=
   le_csupᵢ (c.bddAbove_range_approx x) _
 #align urysohns.CU.approx_le_lim Urysohns.CU.approx_le_lim
 
+/- warning: urysohns.CU.lim_nonneg -> Urysohns.CU.lim_nonneg is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] (c : Urysohns.CU.{u1} X _inst_1) (x : X), LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 c x)
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] (c : Urysohns.CU.{u1} X _inst_1) (x : X), LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 c x)
+Case conversion may be inaccurate. Consider using '#align urysohns.CU.lim_nonneg Urysohns.CU.lim_nonnegₓ'. -/
 theorem lim_nonneg (c : CU X) (x : X) : 0 ≤ c.lim x :=
   (c.approx_nonneg 0 x).trans (c.approx_le_lim x 0)
 #align urysohns.CU.lim_nonneg Urysohns.CU.lim_nonneg
 
+/- warning: urysohns.CU.lim_le_one -> Urysohns.CU.lim_le_one is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] (c : Urysohns.CU.{u1} X _inst_1) (x : X), LE.le.{0} Real Real.hasLe (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 c x) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] (c : Urysohns.CU.{u1} X _inst_1) (x : X), LE.le.{0} Real Real.instLEReal (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 c x) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))
+Case conversion may be inaccurate. Consider using '#align urysohns.CU.lim_le_one Urysohns.CU.lim_le_oneₓ'. -/
 theorem lim_le_one (c : CU X) (x : X) : c.lim x ≤ 1 :=
   csupᵢ_le fun n => c.approx_le_one _ _
 #align urysohns.CU.lim_le_one Urysohns.CU.lim_le_one
 
+/- warning: urysohns.CU.lim_mem_Icc -> Urysohns.CU.lim_mem_Icc is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] (c : Urysohns.CU.{u1} X _inst_1) (x : X), Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 c 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))))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] (c : Urysohns.CU.{u1} X _inst_1) (x : X), Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (Urysohns.CU.lim.{u1} X _inst_1 _inst_2 c 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)))
+Case conversion may be inaccurate. Consider using '#align urysohns.CU.lim_mem_Icc Urysohns.CU.lim_mem_Iccₓ'. -/
 theorem lim_mem_Icc (c : CU X) (x : X) : c.lim x ∈ Icc (0 : ℝ) 1 :=
   ⟨c.lim_nonneg x, c.lim_le_one x⟩
 #align urysohns.CU.lim_mem_Icc Urysohns.CU.lim_mem_Icc
 
+#print Urysohns.CU.continuous_lim /-
 /-- Continuity of `urysohns.CU.lim`. See module docstring for a sketch of the proofs. -/
 theorem continuous_lim (c : CU X) : Continuous c.lim :=
   by
@@ -312,6 +415,7 @@ theorem continuous_lim (c : CU X) : Continuous c.lim :=
       field_simp [two_ne_zero' ℝ]
       ring
 #align urysohns.CU.continuous_lim Urysohns.CU.continuous_lim
+-/
 
 end CU
 
@@ -319,6 +423,12 @@ end Urysohns
 
 variable [NormalSpace X]
 
+/- warning: exists_continuous_zero_one_of_closed -> exists_continuous_zero_one_of_closed is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] {s : Set.{u1} X} {t : Set.{u1} X}, (IsClosed.{u1} X _inst_1 s) -> (IsClosed.{u1} X _inst_1 t) -> (Disjoint.{u1} (Set.{u1} X) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} X) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} X) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} X) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} X) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} X) (Set.completeBooleanAlgebra.{u1} X)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} X) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} X) (Set.booleanAlgebra.{u1} X))) s t) -> (Exists.{succ u1} (ContinuousMap.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (fun (f : ContinuousMap.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) => And (Set.EqOn.{u1, 0} X Real (coeFn.{succ u1, succ u1} (ContinuousMap.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (fun (_x : ContinuousMap.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) => X -> Real) (ContinuousMap.hasCoeToFun.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) f) (OfNat.ofNat.{u1} (X -> Real) 0 (OfNat.mk.{u1} (X -> Real) 0 (Zero.zero.{u1} (X -> Real) (Pi.instZero.{u1, 0} X (fun (ᾰ : X) => Real) (fun (i : X) => Real.hasZero))))) s) (And (Set.EqOn.{u1, 0} X Real (coeFn.{succ u1, succ u1} (ContinuousMap.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (fun (_x : ContinuousMap.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) => X -> Real) (ContinuousMap.hasCoeToFun.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) f) (OfNat.ofNat.{u1} (X -> Real) 1 (OfNat.mk.{u1} (X -> Real) 1 (One.one.{u1} (X -> Real) (Pi.instOne.{u1, 0} X (fun (ᾰ : X) => Real) (fun (i : X) => Real.hasOne))))) t) (forall (x : X), Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) (coeFn.{succ u1, succ u1} (ContinuousMap.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (fun (_x : ContinuousMap.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) => X -> Real) (ContinuousMap.hasCoeToFun.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) f 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))))))))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] {s : Set.{u1} X} {t : Set.{u1} X}, (IsClosed.{u1} X _inst_1 s) -> (IsClosed.{u1} X _inst_1 t) -> (Disjoint.{u1} (Set.{u1} X) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} X) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} X) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} X) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} X) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} X) (Set.instCompleteBooleanAlgebraSet.{u1} X)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} X) (Preorder.toLE.{u1} (Set.{u1} X) (PartialOrder.toPreorder.{u1} (Set.{u1} X) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} X) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} X) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} X) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} X) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} X) (Set.instCompleteBooleanAlgebraSet.{u1} X)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} X) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} X) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} X) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} X) (Set.instCompleteBooleanAlgebraSet.{u1} X)))))) s t) -> (Exists.{succ u1} (ContinuousMap.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (fun (f : ContinuousMap.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) => And (Set.EqOn.{u1, 0} X Real (FunLike.coe.{succ u1, succ u1, 1} (ContinuousMap.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) X (fun (_x : X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : X) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousMap.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousMap.instContinuousMapClassContinuousMap.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)))) f) (OfNat.ofNat.{u1} (X -> Real) 0 (Zero.toOfNat0.{u1} (X -> Real) (Pi.instZero.{u1, 0} X (fun (a._@.Mathlib.Data.Set.Function._hyg.1349 : X) => Real) (fun (i : X) => Real.instZeroReal)))) s) (And (Set.EqOn.{u1, 0} X Real (FunLike.coe.{succ u1, succ u1, 1} (ContinuousMap.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) X (fun (_x : X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : X) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousMap.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousMap.instContinuousMapClassContinuousMap.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)))) f) (OfNat.ofNat.{u1} (X -> Real) 1 (One.toOfNat1.{u1} (X -> Real) (Pi.instOne.{u1, 0} X (fun (a._@.Mathlib.Data.Set.Function._hyg.1349 : X) => Real) (fun (i : X) => Real.instOneReal)))) t) (forall (x : X), Membership.mem.{0, 0} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : X) => Real) x) (Set.{0} Real) (Set.instMembershipSet.{0} Real) (FunLike.coe.{succ u1, succ u1, 1} (ContinuousMap.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) X (fun (_x : X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : X) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousMap.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousMap.instContinuousMapClassContinuousMap.{u1, 0} X Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)))) f 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)))))))
+Case conversion may be inaccurate. Consider using '#align exists_continuous_zero_one_of_closed exists_continuous_zero_one_of_closedₓ'. -/
 /-- Urysohns lemma: if `s` and `t` are two disjoint closed sets in a normal topological space `X`,
 then there exists a continuous function `f : X → ℝ` such that
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/ddec54a71a0dd025c05445d467f1a2b7d586a3ba

@@ -234,7 +234,7 @@ protected noncomputable def lim (c : CU X) (x : X) : ℝ :=
 
 theorem tendsto_approx_atTop (c : CU X) (x : X) :
     Tendsto (fun n => c.approx n x) atTop (𝓝 <| c.lim x) :=
-  tendsto_atTop_csupr (c.approx_mono x) ⟨1, fun x ⟨n, hn⟩ => hn ▸ c.approx_le_one _ _⟩
+  tendsto_atTop_csupᵢ (c.approx_mono x) ⟨1, fun x ⟨n, hn⟩ => hn ▸ c.approx_le_one _ _⟩
 #align urysohns.CU.tendsto_approx_at_top Urysohns.CU.tendsto_approx_atTop
 
 theorem lim_of_mem_c (c : CU X) (x : X) (h : x ∈ c.C) : c.lim x = 0 := by

mathlib commit https://github.com/leanprover-community/mathlib/commit/3b267e70a936eebb21ab546f49a8df34dd300b25

@@ -86,7 +86,7 @@ namespace Urysohns
 open neighborhood `U`. -/
 @[protect_proj]
 structure CU (X : Type _) [TopologicalSpace X] where
-  (c U : Set X)
+  (C U : Set X)
   closed_c : IsClosed C
   open_u : IsOpen U
   Subset : C ⊆ U
@@ -101,9 +101,9 @@ namespace CU
 
 /-- Due to `normal_exists_closure_subset`, for each `c : CU X` there exists an open set `u`
 such chat `c.C ⊆ u` and `closure u ⊆ c.U`. `c.left` is the pair `(c.C, u)`. -/
-@[simps c]
+@[simps C]
 def left (c : CU X) : CU X where
-  c := c.c
+  C := c.C
   U := (normal_exists_closure_subset c.closed_c c.open_u c.Subset).some
   closed_c := c.closed_c
   open_u := (normal_exists_closure_subset c.closed_c c.open_u c.Subset).choose_spec.1
@@ -115,14 +115,14 @@ such chat `c.C ⊆ u` and `closure u ⊆ c.U`. `c.right` is the pair `(closure u
 @[simps U]
 def right (c : CU X) : CU X
     where
-  c := closure (normal_exists_closure_subset c.closed_c c.open_u c.Subset).some
+  C := closure (normal_exists_closure_subset c.closed_c c.open_u c.Subset).some
   U := c.U
   closed_c := isClosed_closure
   open_u := c.open_u
   Subset := (normal_exists_closure_subset c.closed_c c.open_u c.Subset).choose_spec.2.2
 #align urysohns.CU.right Urysohns.CU.right
 
-theorem left_u_subset_right_c (c : CU X) : c.left.U ⊆ c.right.c :=
+theorem left_u_subset_right_c (c : CU X) : c.left.U ⊆ c.right.C :=
   subset_closure
 #align urysohns.CU.left_U_subset_right_C Urysohns.CU.left_u_subset_right_c
 
@@ -130,7 +130,7 @@ theorem left_u_subset (c : CU X) : c.left.U ⊆ c.U :=
   Subset.trans c.left_u_subset_right_c c.right.Subset
 #align urysohns.CU.left_U_subset Urysohns.CU.left_u_subset
 
-theorem subset_right_c (c : CU X) : c.c ⊆ c.right.c :=
+theorem subset_right_c (c : CU X) : c.C ⊆ c.right.C :=
   Subset.trans c.left.Subset c.left_u_subset_right_c
 #align urysohns.CU.subset_right_C Urysohns.CU.subset_right_c
 
@@ -141,7 +141,7 @@ noncomputable def approx : ℕ → CU X → X → ℝ
   | n + 1, c, x => midpoint ℝ (approx n c.left x) (approx n c.right x)
 #align urysohns.CU.approx Urysohns.CU.approx
 
-theorem approx_of_mem_c (c : CU X) (n : ℕ) {x : X} (hx : x ∈ c.c) : c.approx n x = 0 :=
+theorem approx_of_mem_c (c : CU X) (n : ℕ) {x : X} (hx : x ∈ c.C) : c.approx n x = 0 :=
   by
   induction' n with n ihn generalizing c
   · exact indicator_of_not_mem (fun hU => hU <| c.subset hx) _
@@ -179,7 +179,7 @@ theorem bddAbove_range_approx (c : CU X) (x : X) : BddAbove (range fun n => c.ap
   ⟨1, fun y ⟨n, hn⟩ => hn ▸ c.approx_le_one n x⟩
 #align urysohns.CU.bdd_above_range_approx Urysohns.CU.bddAbove_range_approx
 
-theorem approx_le_approx_of_u_sub_c {c₁ c₂ : CU X} (h : c₁.U ⊆ c₂.c) (n₁ n₂ : ℕ) (x : X) :
+theorem approx_le_approx_of_u_sub_c {c₁ c₂ : CU X} (h : c₁.U ⊆ c₂.C) (n₁ n₂ : ℕ) (x : X) :
     c₂.approx n₂ x ≤ c₁.approx n₁ x :=
   by
   by_cases hx : x ∈ c₁.U
@@ -237,7 +237,7 @@ theorem tendsto_approx_atTop (c : CU X) (x : X) :
   tendsto_atTop_csupr (c.approx_mono x) ⟨1, fun x ⟨n, hn⟩ => hn ▸ c.approx_le_one _ _⟩
 #align urysohns.CU.tendsto_approx_at_top Urysohns.CU.tendsto_approx_atTop
 
-theorem lim_of_mem_c (c : CU X) (x : X) (h : x ∈ c.c) : c.lim x = 0 := by
+theorem lim_of_mem_c (c : CU X) (x : X) (h : x ∈ c.C) : c.lim x = 0 := by
   simp only [CU.lim, approx_of_mem_C, h, csupᵢ_const]
 #align urysohns.CU.lim_of_mem_C Urysohns.CU.lim_of_mem_c
 

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

We change the following field in the definition of an additive commutative monoid:

 nsmul_succ : ∀ (n : ℕ) (x : G),
-  AddMonoid.nsmul (n + 1) x = x + AddMonoid.nsmul n x
+  AddMonoid.nsmul (n + 1) x = AddMonoid.nsmul n x + x

where the latter is more natural

We adjust the definitions of ^ in monoids, groups, etc. Originally there was a warning comment about why this natural order was preferred

use x * npowRec n x and not npowRec n x * x in the definition to make sure that definitional unfolding of npowRec is blocked, to avoid deep recursion issues.

but it seems to no longer apply.

Remarks on the PR :

• pow_succ and pow_succ' have switched their meanings.
• Most of the time, the proofs were adjusted by priming/unpriming one lemma, or exchanging left and right; a few proofs were more complicated to adjust.
• In particular, [Mathlib/NumberTheory/RamificationInertia.lean] used Ideal.IsPrime.mul_mem_pow which is defined in [Mathlib/RingTheory/DedekindDomain/Ideal.lean]. Changing the order of operation forced me to add the symmetric lemma Ideal.IsPrime.mem_pow_mul.
• the docstring for Cauchy condensation test in [Mathlib/Analysis/PSeries.lean] was mathematically incorrect, I added the mention that the function is antitone.

@@ -288,7 +288,7 @@ theorem continuous_lim (c : CU P) : Continuous c.lim := by
     exact Real.dist_le_of_mem_Icc_01 (c.lim_mem_Icc _) (c.lim_mem_Icc _)
   · by_cases hxl : x ∈ c.left.U
     · filter_upwards [IsOpen.mem_nhds c.left.open_U hxl, ihn c.left] with _ hyl hyd
-      rw [pow_succ, c.lim_eq_midpoint, c.lim_eq_midpoint,
+      rw [pow_succ', c.lim_eq_midpoint, c.lim_eq_midpoint,
         c.right.lim_of_mem_C _ (c.left_U_subset_right_C hyl),
         c.right.lim_of_mem_C _ (c.left_U_subset_right_C hxl)]
       refine' (dist_midpoint_midpoint_le _ _ _ _).trans _

This is presumably not exhaustive, but covers about a hundred instances.

Style opinions (e.g., why a particular change is great/not a good idea) are very welcome; I'm still forming my own.

@@ -283,7 +283,7 @@ theorem continuous_lim (c : CU P) : Continuous c.lim := by
       (Metric.nhds_basis_closedBall_pow (h0.trans h1234) h1).tendsto_right_iff.2 fun n _ => _
   simp only [Metric.mem_closedBall]
   induction' n with n ihn generalizing c
-  · refine' eventually_of_forall fun y => _
+  · filter_upwards with y
     rw [pow_zero]
     exact Real.dist_le_of_mem_Icc_01 (c.lim_mem_Icc _) (c.lim_mem_Icc _)
   · by_cases hxl : x ∈ c.left.U

The new names and argument orders match the corresponding * lemmas, which I already took care of in a previous PR.

From LeanAPAP

@@ -305,8 +305,8 @@ theorem continuous_lim (c : CU P) : Continuous c.lim := by
       simp only [pow_succ, c.lim_eq_midpoint, c.left.lim_eq_midpoint,
         c.left.left.lim_of_nmem_U _ hxl, c.left.left.lim_of_nmem_U _ hyl]
       refine' (dist_midpoint_midpoint_le _ _ _ _).trans _
-      refine' (div_le_div_of_le zero_le_two
-        (add_le_add_right (dist_midpoint_midpoint_le _ _ _ _) _)).trans _
+      refine' (div_le_div_of_nonneg_right (add_le_add_right (dist_midpoint_midpoint_le _ _ _ _) _)
+        zero_le_two).trans _
       rw [dist_self, zero_add]
       set r := (3 / 4 : ℝ) ^ n
       calc _ ≤ (r / 2 + r) / 2 := by gcongr

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>

@@ -187,6 +187,7 @@ theorem approx_le_one (c : CU P) (n : ℕ) (x : X) : c.approx n x ≤ 1 := by
   · exact indicator_apply_le' (fun _ => le_rfl) fun _ => zero_le_one
   · simp only [approx, midpoint_eq_smul_add, invOf_eq_inv, smul_eq_mul, ← div_eq_inv_mul]
     have := add_le_add (ihn (left c)) (ihn (right c))
+    set_option tactic.skipAssignedInstances false in
     norm_num at this
     exact Iff.mpr (div_le_one zero_lt_two) this
 #align urysohns.CU.approx_le_one Urysohns.CU.approx_le_one

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

@@ -434,14 +434,14 @@ theorem exists_continuous_one_zero_of_isCompact_of_isGδ [RegularSpace X] [Local
       have : mᶜ ⊆ (U n ∩ interior m)ᶜ := by
         simpa using (inter_subset_right _ _).trans interior_subset
       exact fm n (this hx)
-    simp [B]
+    simp [g, B]
   have I n x : u n * f n x ≤ u n := mul_le_of_le_one_right (u_pos n).le (f_range n x).2
   have S x : Summable (fun n ↦ u n * f n x) := Summable.of_nonneg_of_le
       (fun n ↦ mul_nonneg (u_pos n).le (f_range n x).1) (fun n ↦ I n x) u_sum
   refine ⟨⟨g, ?_⟩, ?_, hgmc.mono (subset_compl_comm.mp mt), ?_, fun x ↦ ⟨?_, ?_⟩⟩
   · apply continuous_tsum (fun n ↦ continuous_const.mul (f n).continuous) u_sum (fun n x ↦ ?_)
     simpa [abs_of_nonneg, (u_pos n).le, (f_range n x).1] using I n x
-  · apply Subset.antisymm (fun x hx ↦ by simp [fs _ hx, hu]) ?_
+  · apply Subset.antisymm (fun x hx ↦ by simp [g, fs _ hx, hu]) ?_
     apply compl_subset_compl.1
     intro x hx
     obtain ⟨n, hn⟩ : ∃ n, x ∉ U n := by simpa [hU] using hx

No changes to tactic file, it's just boring fixes throughout the library.

This follows on from #6964.

Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -293,14 +293,14 @@ theorem continuous_lim (c : CU P) : Continuous c.lim := by
       refine' (dist_midpoint_midpoint_le _ _ _ _).trans _
       rw [dist_self, add_zero, div_eq_inv_mul]
       gcongr
-    · replace hxl : x ∈ c.left.right.Cᶜ
-      exact compl_subset_compl.2 c.left.right.subset hxl
+    · replace hxl : x ∈ c.left.right.Cᶜ :=
+        compl_subset_compl.2 c.left.right.subset hxl
       filter_upwards [IsOpen.mem_nhds (isOpen_compl_iff.2 c.left.right.closed_C) hxl,
         ihn c.left.right, ihn c.right] with y hyl hydl hydr
-      replace hxl : x ∉ c.left.left.U
-      exact compl_subset_compl.2 c.left.left_U_subset_right_C hxl
-      replace hyl : y ∉ c.left.left.U
-      exact compl_subset_compl.2 c.left.left_U_subset_right_C hyl
+      replace hxl : x ∉ c.left.left.U :=
+        compl_subset_compl.2 c.left.left_U_subset_right_C hxl
+      replace hyl : y ∉ c.left.left.U :=
+        compl_subset_compl.2 c.left.left_U_subset_right_C hyl
       simp only [pow_succ, c.lim_eq_midpoint, c.left.lim_eq_midpoint,
         c.left.left.lim_of_nmem_U _ hxl, c.left.left.lim_of_nmem_U _ hyl]
       refine' (dist_midpoint_midpoint_le _ _ _ _).trans _

@@ -6,7 +6,9 @@ Authors: Yury G. Kudryashov
 import Mathlib.Analysis.NormedSpace.AddTorsor
 import Mathlib.LinearAlgebra.AffineSpace.Ordered
 import Mathlib.Topology.ContinuousFunction.Basic
-import Mathlib.Algebra.Order.Support
+import Mathlib.Topology.GDelta
+import Mathlib.Analysis.NormedSpace.FunctionSeries
+import Mathlib.Analysis.SpecificLimits.Basic
 
 #align_import topology.urysohns_lemma from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
 
@@ -398,3 +400,68 @@ theorem exists_continuous_one_zero_of_isCompact [RegularSpace X] [LocallyCompact
     exact interior_subset hx
   · have : 0 ≤ f x ∧ f x ≤ 1 := by simpa using h'f x
     simp [this]
+
+/-- Urysohn's lemma: if `s` and `t` are two disjoint sets in a regular locally compact topological
+space `X`, with `s` compact and `t` closed, then there exists a continuous compactly supported
+function `f : X → ℝ` such that
+
+* `f` equals one on `s`;
+* `f` equals zero on `t`;
+* `0 ≤ f x ≤ 1` for all `x`.
+
+Moreover, if `s` is Gδ, one can ensure that `f ⁻¹ {1}` is exactly `s`.
+-/
+theorem exists_continuous_one_zero_of_isCompact_of_isGδ [RegularSpace X] [LocallyCompactSpace X]
+    {s t : Set X} (hs : IsCompact s) (h's : IsGδ s) (ht : IsClosed t) (hd : Disjoint s t) :
+    ∃ f : C(X, ℝ), s = f ⁻¹' {1} ∧ EqOn f 0 t ∧ HasCompactSupport f
+      ∧ ∀ x, f x ∈ Icc (0 : ℝ) 1 := by
+  rcases h's.eq_iInter_nat with ⟨U, U_open, hU⟩
+  obtain ⟨m, m_comp, -, sm, mt⟩ : ∃ m, IsCompact m ∧ IsClosed m ∧ s ⊆ interior m ∧ m ⊆ tᶜ :=
+    exists_compact_closed_between hs ht.isOpen_compl hd.symm.subset_compl_left
+  have A n : ∃ f : C(X, ℝ), EqOn f 1 s ∧ EqOn f 0 (U n ∩ interior m)ᶜ ∧ HasCompactSupport f
+      ∧ ∀ x, f x ∈ Icc (0 : ℝ) 1 := by
+    apply exists_continuous_one_zero_of_isCompact hs
+      ((U_open n).inter isOpen_interior).isClosed_compl
+    rw [disjoint_compl_right_iff_subset]
+    exact subset_inter ((hU.subset.trans (iInter_subset U n))) sm
+  choose f fs fm _hf f_range using A
+  obtain ⟨u, u_pos, u_sum, hu⟩ : ∃ (u : ℕ → ℝ), (∀ i, 0 < u i) ∧ Summable u ∧ ∑' i, u i = 1 :=
+    ⟨fun n ↦ 1/2/2^n, fun n ↦ by positivity, summable_geometric_two' 1, tsum_geometric_two' 1⟩
+  let g : X → ℝ := fun x ↦ ∑' n, u n * f n x
+  have hgmc : EqOn g 0 mᶜ := by
+    intro x hx
+    have B n : f n x = 0 := by
+      have : mᶜ ⊆ (U n ∩ interior m)ᶜ := by
+        simpa using (inter_subset_right _ _).trans interior_subset
+      exact fm n (this hx)
+    simp [B]
+  have I n x : u n * f n x ≤ u n := mul_le_of_le_one_right (u_pos n).le (f_range n x).2
+  have S x : Summable (fun n ↦ u n * f n x) := Summable.of_nonneg_of_le
+      (fun n ↦ mul_nonneg (u_pos n).le (f_range n x).1) (fun n ↦ I n x) u_sum
+  refine ⟨⟨g, ?_⟩, ?_, hgmc.mono (subset_compl_comm.mp mt), ?_, fun x ↦ ⟨?_, ?_⟩⟩
+  · apply continuous_tsum (fun n ↦ continuous_const.mul (f n).continuous) u_sum (fun n x ↦ ?_)
+    simpa [abs_of_nonneg, (u_pos n).le, (f_range n x).1] using I n x
+  · apply Subset.antisymm (fun x hx ↦ by simp [fs _ hx, hu]) ?_
+    apply compl_subset_compl.1
+    intro x hx
+    obtain ⟨n, hn⟩ : ∃ n, x ∉ U n := by simpa [hU] using hx
+    have fnx : f n x = 0 := fm _ (by simp [hn])
+    have : g x < 1 := by
+      apply lt_of_lt_of_le ?_ hu.le
+      exact tsum_lt_tsum (i := n) (fun i ↦ I i x) (by simp [fnx, u_pos n]) (S x) u_sum
+    simpa using this.ne
+  · exact HasCompactSupport.of_support_subset_isCompact m_comp
+      (Function.support_subset_iff'.mpr hgmc)
+  · exact tsum_nonneg (fun n ↦ mul_nonneg (u_pos n).le (f_range n x).1)
+  · apply le_trans _ hu.le
+    exact tsum_le_tsum (fun n ↦ I n x) (S x) u_sum
+
+theorem exists_continuous_nonneg_pos [RegularSpace X] [LocallyCompactSpace X] (x : X) :
+    ∃ f : C(X, ℝ), HasCompactSupport f ∧ 0 ≤ (f : X → ℝ) ∧ f x ≠ 0 := by
+  rcases exists_compact_mem_nhds x with ⟨k, hk, k_mem⟩
+  rcases exists_continuous_one_zero_of_isCompact hk isClosed_empty (disjoint_empty k)
+    with ⟨f, fk, -, f_comp, hf⟩
+  refine ⟨f, f_comp, fun x ↦ (hf x).1, ?_⟩
+  have := fk (mem_of_mem_nhds k_mem)
+  simp only [ContinuousMap.coe_mk, Pi.one_apply] at this
+  simp [this]

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -6,6 +6,7 @@ Authors: Yury G. Kudryashov
 import Mathlib.Analysis.NormedSpace.AddTorsor
 import Mathlib.LinearAlgebra.AffineSpace.Ordered
 import Mathlib.Topology.ContinuousFunction.Basic
+import Mathlib.Algebra.Order.Support
 
 #align_import topology.urysohns_lemma from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
 

This was noticed in the discussion around #9393.

@@ -301,8 +301,8 @@ theorem continuous_lim (c : CU P) : Continuous c.lim := by
       simp only [pow_succ, c.lim_eq_midpoint, c.left.lim_eq_midpoint,
         c.left.left.lim_of_nmem_U _ hxl, c.left.left.lim_of_nmem_U _ hyl]
       refine' (dist_midpoint_midpoint_le _ _ _ _).trans _
-      refine' (div_le_div_of_le_of_nonneg (add_le_add_right (dist_midpoint_midpoint_le _ _ _ _) _)
-        zero_le_two).trans _
+      refine' (div_le_div_of_le zero_le_two
+        (add_le_add_right (dist_midpoint_midpoint_le _ _ _ _) _)).trans _
       rw [dist_self, zero_add]
       set r := (3 / 4 : ℝ) ^ n
       calc _ ≤ (r / 2 + r) / 2 := by gcongr

Three particular examples which caught my eye; not exhaustive.

@@ -12,7 +12,7 @@ import Mathlib.Topology.ContinuousFunction.Basic
 /-!
 # Urysohn's lemma
 
-In this file we prove Urysohn's lemma `exists_continuous_zero_one_of_closed`: for any two disjoint
+In this file we prove Urysohn's lemma `exists_continuous_zero_one_of_isClosed`: for any two disjoint
 closed sets `s` and `t` in a normal topological space `X` there exists a continuous function
 `f : X → ℝ` such that
 
@@ -320,7 +320,7 @@ then there exists a continuous function `f : X → ℝ` such that
 * `f` equals one on `t`;
 * `0 ≤ f x ≤ 1` for all `x`.
 -/
-theorem exists_continuous_zero_one_of_closed [NormalSpace X]
+theorem exists_continuous_zero_one_of_isClosed [NormalSpace X]
     {s t : Set X} (hs : IsClosed s) (ht : IsClosed t)
     (hd : Disjoint s t) : ∃ f : C(X, ℝ), EqOn f 0 s ∧ EqOn f 1 t ∧ ∀ x, f x ∈ Icc (0 : ℝ) 1 := by
   -- The actual proof is in the code above. Here we just repack it into the expected format.
@@ -338,7 +338,7 @@ theorem exists_continuous_zero_one_of_closed [NormalSpace X]
       exact ⟨v, v_open, cv, hv, trivial⟩ }
   exact ⟨⟨c.lim, c.continuous_lim⟩, c.lim_of_mem_C, fun x hx => c.lim_of_nmem_U _ fun h => h hx,
     c.lim_mem_Icc⟩
-#align exists_continuous_zero_one_of_closed exists_continuous_zero_one_of_closed
+#align exists_continuous_zero_one_of_closed exists_continuous_zero_one_of_isClosed
 
 /-- Urysohn's lemma: if `s` and `t` are two disjoint sets in a regular locally compact topological
 space `X`, with `s` compact and `t` closed, then there exists a continuous

Also change a few theorems to instances, as instance loops are not a problem any more.

@@ -20,6 +20,14 @@ closed sets `s` and `t` in a normal topological space `X` there exists a continu
 * `f` equals one on `t`;
 * `0 ≤ f x ≤ 1` for all `x`.
 
+We also give versions in a regular locally compact space where one assumes that `s` is compact
+and `t` is closed, in `exists_continuous_zero_one_of_isCompact`
+and `exists_continuous_one_zero_of_isCompact` (the latter providing additionally a function with
+compact support).
+
+We write a generic proof so that it applies both to normal spaces and to regular locally
+compact spaces.
+
 ## Implementation notes
 
 Most paper sources prove Urysohn's lemma using a family of open sets indexed by dyadic rational
@@ -28,10 +36,10 @@ needs to formalize the "dyadic induction", then prove that the resulting family
 monotone). So, we formalize a slightly different proof.
 
 Let `Urysohns.CU` be the type of pairs `(C, U)` of a closed set `C` and an open set `U` such that
-`C ⊆ U`. Since `X` is a normal topological space, for each `c : CU X` there exists an open set `u`
+`C ⊆ U`. Since `X` is a normal topological space, for each `c : CU` there exists an open set `u`
 such that `c.C ⊆ u ∧ closure u ⊆ c.U`. We define `c.left` and `c.right` to be `(c.C, u)` and
 `(closure u, c.U)`, respectively. Then we define a family of functions
-`Urysohns.CU.approx (c : Urysohns.CU X) (n : ℕ) : X → ℝ` by recursion on `n`:
+`Urysohns.CU.approx (c : Urysohns.CU) (n : ℕ) : X → ℝ` by recursion on `n`:
 
 * `c.approx 0` is the indicator of `c.Uᶜ`;
 * `c.approx (n + 1) x = (c.left.approx n x + c.right.approx n x) / 2`.
@@ -66,76 +74,88 @@ lemmas about `midpoint`.
 
 ## Tags
 
-Urysohn's lemma, normal topological space
+Urysohn's lemma, normal topological space, locally compact topological space
 -/
 
 
 variable {X : Type*} [TopologicalSpace X]
 
 open Set Filter TopologicalSpace Topology Filter
+open scoped Pointwise
 
 namespace Urysohns
 
 set_option linter.uppercaseLean3 false
 
 /-- An auxiliary type for the proof of Urysohn's lemma: a pair of a closed set `C` and its
-open neighborhood `U`. -/
-structure CU (X : Type*) [TopologicalSpace X] where
-  protected (C U : Set X)
+open neighborhood `U`, together with the assumption that `C` satisfies the property `P C`. The
+latter assumption will make it possible to prove simultaneously both versions of Urysohn's lemma,
+in normal spaces (with `P` always true) and in locally compact spaces (with `P = IsCompact`).
+We put also in the structure the assumption that, for any such pair, one may find an intermediate
+pair inbetween satisfying `P`, to avoid carrying it around in the argument. -/
+structure CU {X : Type*} [TopologicalSpace X] (P : Set X → Prop) where
+  /-- The inner set in the inductive construction towards Urysohn's lemma -/
+  protected C : Set X
+  /-- The outer set in the inductive construction towards Urysohn's lemma -/
+  protected U : Set X
+  protected P_C : P C
   protected closed_C : IsClosed C
   protected open_U : IsOpen U
   protected subset : C ⊆ U
+  protected hP : ∀ {c u : Set X}, IsClosed c → P c → IsOpen u → c ⊆ u →
+    ∃ v, IsOpen v ∧ c ⊆ v ∧ closure v ⊆ u ∧ P (closure v)
 #align urysohns.CU Urysohns.CU
 
-instance : Inhabited (CU X) :=
-  ⟨⟨∅, univ, isClosed_empty, isOpen_univ, empty_subset _⟩⟩
-
-variable [NormalSpace X]
-
 namespace CU
 
-/-- Due to `normal_exists_closure_subset`, for each `c : CU X` there exists an open set `u`
+variable {P : Set X → Prop}
+
+/-- By assumption, for each `c : CU P` there exists an open set `u`
 such that `c.C ⊆ u` and `closure u ⊆ c.U`. `c.left` is the pair `(c.C, u)`. -/
 @[simps C]
-def left (c : CU X) : CU X where
+def left (c : CU P) : CU P where
   C := c.C
-  U := (normal_exists_closure_subset c.closed_C c.open_U c.subset).choose
+  U := (c.hP c.closed_C c.P_C c.open_U c.subset).choose
   closed_C := c.closed_C
-  open_U := (normal_exists_closure_subset c.closed_C c.open_U c.subset).choose_spec.1
-  subset := (normal_exists_closure_subset c.closed_C c.open_U c.subset).choose_spec.2.1
+  P_C := c.P_C
+  open_U := (c.hP c.closed_C c.P_C c.open_U c.subset).choose_spec.1
+  subset := (c.hP c.closed_C c.P_C c.open_U c.subset).choose_spec.2.1
+  hP := c.hP
 #align urysohns.CU.left Urysohns.CU.left
 
-/-- Due to `normal_exists_closure_subset`, for each `c : CU X` there exists an open set `u`
+/-- By assumption, for each `c : CU P` there exists an open set `u`
 such that `c.C ⊆ u` and `closure u ⊆ c.U`. `c.right` is the pair `(closure u, c.U)`. -/
 @[simps U]
-def right (c : CU X) : CU X where
-  C := closure (normal_exists_closure_subset c.closed_C c.open_U c.subset).choose
+def right (c : CU P) : CU P where
+  C := closure (c.hP c.closed_C c.P_C c.open_U c.subset).choose
   U := c.U
   closed_C := isClosed_closure
+  P_C := (c.hP c.closed_C c.P_C c.open_U c.subset).choose_spec.2.2.2
   open_U := c.open_U
-  subset := (normal_exists_closure_subset c.closed_C c.open_U c.subset).choose_spec.2.2
+  subset := (c.hP c.closed_C c.P_C c.open_U c.subset).choose_spec.2.2.1
+  hP := c.hP
 #align urysohns.CU.right Urysohns.CU.right
 
-theorem left_U_subset_right_C (c : CU X) : c.left.U ⊆ c.right.C :=
+theorem left_U_subset_right_C (c : CU P) : c.left.U ⊆ c.right.C :=
   subset_closure
 #align urysohns.CU.left_U_subset_right_C Urysohns.CU.left_U_subset_right_C
 
-theorem left_U_subset (c : CU X) : c.left.U ⊆ c.U :=
+theorem left_U_subset (c : CU P) : c.left.U ⊆ c.U :=
   Subset.trans c.left_U_subset_right_C c.right.subset
 #align urysohns.CU.left_U_subset Urysohns.CU.left_U_subset
 
-theorem subset_right_C (c : CU X) : c.C ⊆ c.right.C :=
+theorem subset_right_C (c : CU P) : c.C ⊆ c.right.C :=
   Subset.trans c.left.subset c.left_U_subset_right_C
 #align urysohns.CU.subset_right_C Urysohns.CU.subset_right_C
 
 /-- `n`-th approximation to a continuous function `f : X → ℝ` such that `f = 0` on `c.C` and `f = 1`
 outside of `c.U`. -/
-noncomputable def approx : ℕ → CU X → X → ℝ
+noncomputable def approx : ℕ → CU P → X → ℝ
   | 0, c, x => indicator c.Uᶜ 1 x
   | n + 1, c, x => midpoint ℝ (approx n c.left x) (approx n c.right x)
 #align urysohns.CU.approx Urysohns.CU.approx
 
-theorem approx_of_mem_C (c : CU X) (n : ℕ) {x : X} (hx : x ∈ c.C) : c.approx n x = 0 := by
+theorem approx_of_mem_C (c : CU P) (n : ℕ) {x : X} (hx : x ∈ c.C) : c.approx n x = 0 := by
   induction' n with n ihn generalizing c
   · exact indicator_of_not_mem (fun (hU : x ∈ c.Uᶜ) => hU <| c.subset hx) _
   · simp only [approx]
@@ -143,7 +163,7 @@ theorem approx_of_mem_C (c : CU X) (n : ℕ) {x : X} (hx : x ∈ c.C) : c.approx
     exacts [c.subset_right_C hx, hx]
 #align urysohns.CU.approx_of_mem_C Urysohns.CU.approx_of_mem_C
 
-theorem approx_of_nmem_U (c : CU X) (n : ℕ) {x : X} (hx : x ∉ c.U) : c.approx n x = 1 := by
+theorem approx_of_nmem_U (c : CU P) (n : ℕ) {x : X} (hx : x ∉ c.U) : c.approx n x = 1 := by
   induction' n with n ihn generalizing c
   · rw [← mem_compl_iff] at hx
     exact indicator_of_mem hx _
@@ -152,14 +172,14 @@ theorem approx_of_nmem_U (c : CU X) (n : ℕ) {x : X} (hx : x ∉ c.U) : c.appro
     exacts [hx, fun hU => hx <| c.left_U_subset hU]
 #align urysohns.CU.approx_of_nmem_U Urysohns.CU.approx_of_nmem_U
 
-theorem approx_nonneg (c : CU X) (n : ℕ) (x : X) : 0 ≤ c.approx n x := by
+theorem approx_nonneg (c : CU P) (n : ℕ) (x : X) : 0 ≤ c.approx n x := by
   induction' n with n ihn generalizing c
   · exact indicator_nonneg (fun _ _ => zero_le_one) _
   · simp only [approx, midpoint_eq_smul_add, invOf_eq_inv]
     refine' mul_nonneg (inv_nonneg.2 zero_le_two) (add_nonneg _ _) <;> apply ihn
 #align urysohns.CU.approx_nonneg Urysohns.CU.approx_nonneg
 
-theorem approx_le_one (c : CU X) (n : ℕ) (x : X) : c.approx n x ≤ 1 := by
+theorem approx_le_one (c : CU P) (n : ℕ) (x : X) : c.approx n x ≤ 1 := by
   induction' n with n ihn generalizing c
   · exact indicator_apply_le' (fun _ => le_rfl) fun _ => zero_le_one
   · simp only [approx, midpoint_eq_smul_add, invOf_eq_inv, smul_eq_mul, ← div_eq_inv_mul]
@@ -168,11 +188,11 @@ theorem approx_le_one (c : CU X) (n : ℕ) (x : X) : c.approx n x ≤ 1 := by
     exact Iff.mpr (div_le_one zero_lt_two) this
 #align urysohns.CU.approx_le_one Urysohns.CU.approx_le_one
 
-theorem bddAbove_range_approx (c : CU X) (x : X) : BddAbove (range fun n => c.approx n x) :=
+theorem bddAbove_range_approx (c : CU P) (x : X) : BddAbove (range fun n => c.approx n x) :=
   ⟨1, fun _ ⟨n, hn⟩ => hn ▸ c.approx_le_one n x⟩
 #align urysohns.CU.bdd_above_range_approx Urysohns.CU.bddAbove_range_approx
 
-theorem approx_le_approx_of_U_sub_C {c₁ c₂ : CU X} (h : c₁.U ⊆ c₂.C) (n₁ n₂ : ℕ) (x : X) :
+theorem approx_le_approx_of_U_sub_C {c₁ c₂ : CU P} (h : c₁.U ⊆ c₂.C) (n₁ n₂ : ℕ) (x : X) :
     c₂.approx n₂ x ≤ c₁.approx n₁ x := by
   by_cases hx : x ∈ c₁.U
   · calc
@@ -183,7 +203,7 @@ theorem approx_le_approx_of_U_sub_C {c₁ c₂ : CU X} (h : c₁.U ⊆ c₂.C) (
       _ = approx n₁ c₁ x := (approx_of_nmem_U _ _ hx).symm
 #align urysohns.CU.approx_le_approx_of_U_sub_C Urysohns.CU.approx_le_approx_of_U_sub_C
 
-theorem approx_mem_Icc_right_left (c : CU X) (n : ℕ) (x : X) :
+theorem approx_mem_Icc_right_left (c : CU P) (n : ℕ) (x : X) :
     c.approx n x ∈ Icc (c.right.approx n x) (c.left.approx n x) := by
   induction' n with n ihn generalizing c
   · exact ⟨le_rfl, indicator_le_indicator_of_subset (compl_subset_compl.2 c.left_U_subset)
@@ -194,7 +214,7 @@ theorem approx_mem_Icc_right_left (c : CU X) (n : ℕ) (x : X) :
     exacts [subset_closure, subset_closure]
 #align urysohns.CU.approx_mem_Icc_right_left Urysohns.CU.approx_mem_Icc_right_left
 
-theorem approx_le_succ (c : CU X) (n : ℕ) (x : X) : c.approx n x ≤ c.approx (n + 1) x := by
+theorem approx_le_succ (c : CU P) (n : ℕ) (x : X) : c.approx n x ≤ c.approx (n + 1) x := by
   induction' n with n ihn generalizing c
   · simp only [approx, right_U, right_le_midpoint]
     exact (approx_mem_Icc_right_left c 0 x).2
@@ -202,7 +222,7 @@ theorem approx_le_succ (c : CU X) (n : ℕ) (x : X) : c.approx n x ≤ c.approx
     exact midpoint_le_midpoint (ihn _) (ihn _)
 #align urysohns.CU.approx_le_succ Urysohns.CU.approx_le_succ
 
-theorem approx_mono (c : CU X) (x : X) : Monotone fun n => c.approx n x :=
+theorem approx_mono (c : CU P) (x : X) : Monotone fun n => c.approx n x :=
   monotone_nat_of_le_succ fun n => c.approx_le_succ n x
 #align urysohns.CU.approx_mono Urysohns.CU.approx_mono
 
@@ -211,48 +231,48 @@ theorem approx_mono (c : CU X) (x : X) : Monotone fun n => c.approx n x :=
 * `0 ≤ f x ≤ 1` for all `x`;
 * `f` equals zero on `c.C` and equals one outside of `c.U`;
 -/
-protected noncomputable def lim (c : CU X) (x : X) : ℝ :=
+protected noncomputable def lim (c : CU P) (x : X) : ℝ :=
   ⨆ n, c.approx n x
 #align urysohns.CU.lim Urysohns.CU.lim
 
-theorem tendsto_approx_atTop (c : CU X) (x : X) :
+theorem tendsto_approx_atTop (c : CU P) (x : X) :
     Tendsto (fun n => c.approx n x) atTop (𝓝 <| c.lim x) :=
   tendsto_atTop_ciSup (c.approx_mono x) ⟨1, fun _ ⟨_, hn⟩ => hn ▸ c.approx_le_one _ _⟩
 #align urysohns.CU.tendsto_approx_at_top Urysohns.CU.tendsto_approx_atTop
 
-theorem lim_of_mem_C (c : CU X) (x : X) (h : x ∈ c.C) : c.lim x = 0 := by
+theorem lim_of_mem_C (c : CU P) (x : X) (h : x ∈ c.C) : c.lim x = 0 := by
   simp only [CU.lim, approx_of_mem_C, h, ciSup_const]
 #align urysohns.CU.lim_of_mem_C Urysohns.CU.lim_of_mem_C
 
-theorem lim_of_nmem_U (c : CU X) (x : X) (h : x ∉ c.U) : c.lim x = 1 := by
+theorem lim_of_nmem_U (c : CU P) (x : X) (h : x ∉ c.U) : c.lim x = 1 := by
   simp only [CU.lim, approx_of_nmem_U c _ h, ciSup_const]
 #align urysohns.CU.lim_of_nmem_U Urysohns.CU.lim_of_nmem_U
 
-theorem lim_eq_midpoint (c : CU X) (x : X) :
+theorem lim_eq_midpoint (c : CU P) (x : X) :
     c.lim x = midpoint ℝ (c.left.lim x) (c.right.lim x) := by
   refine' tendsto_nhds_unique (c.tendsto_approx_atTop x) ((tendsto_add_atTop_iff_nat 1).1 _)
   simp only [approx]
   exact (c.left.tendsto_approx_atTop x).midpoint (c.right.tendsto_approx_atTop x)
 #align urysohns.CU.lim_eq_midpoint Urysohns.CU.lim_eq_midpoint
 
-theorem approx_le_lim (c : CU X) (x : X) (n : ℕ) : c.approx n x ≤ c.lim x :=
+theorem approx_le_lim (c : CU P) (x : X) (n : ℕ) : c.approx n x ≤ c.lim x :=
   le_ciSup (c.bddAbove_range_approx x) _
 #align urysohns.CU.approx_le_lim Urysohns.CU.approx_le_lim
 
-theorem lim_nonneg (c : CU X) (x : X) : 0 ≤ c.lim x :=
+theorem lim_nonneg (c : CU P) (x : X) : 0 ≤ c.lim x :=
   (c.approx_nonneg 0 x).trans (c.approx_le_lim x 0)
 #align urysohns.CU.lim_nonneg Urysohns.CU.lim_nonneg
 
-theorem lim_le_one (c : CU X) (x : X) : c.lim x ≤ 1 :=
+theorem lim_le_one (c : CU P) (x : X) : c.lim x ≤ 1 :=
   ciSup_le fun _ => c.approx_le_one _ _
 #align urysohns.CU.lim_le_one Urysohns.CU.lim_le_one
 
-theorem lim_mem_Icc (c : CU X) (x : X) : c.lim x ∈ Icc (0 : ℝ) 1 :=
+theorem lim_mem_Icc (c : CU P) (x : X) : c.lim x ∈ Icc (0 : ℝ) 1 :=
   ⟨c.lim_nonneg x, c.lim_le_one x⟩
 #align urysohns.CU.lim_mem_Icc Urysohns.CU.lim_mem_Icc
 
 /-- Continuity of `Urysohns.CU.lim`. See module docstring for a sketch of the proofs. -/
-theorem continuous_lim (c : CU X) : Continuous c.lim := by
+theorem continuous_lim (c : CU P) : Continuous c.lim := by
   obtain ⟨h0, h1234, h1⟩ : 0 < (2⁻¹ : ℝ) ∧ (2⁻¹ : ℝ) < 3 / 4 ∧ (3 / 4 : ℝ) < 1 := by norm_num
   refine'
     continuous_iff_continuousAt.2 fun x =>
@@ -293,8 +313,6 @@ end CU
 
 end Urysohns
 
-variable [NormalSpace X]
-
 /-- Urysohn's lemma: if `s` and `t` are two disjoint closed sets in a normal topological space `X`,
 then there exists a continuous function `f : X → ℝ` such that
 
@@ -302,10 +320,80 @@ then there exists a continuous function `f : X → ℝ` such that
 * `f` equals one on `t`;
 * `0 ≤ f x ≤ 1` for all `x`.
 -/
-theorem exists_continuous_zero_one_of_closed {s t : Set X} (hs : IsClosed s) (ht : IsClosed t)
+theorem exists_continuous_zero_one_of_closed [NormalSpace X]
+    {s t : Set X} (hs : IsClosed s) (ht : IsClosed t)
     (hd : Disjoint s t) : ∃ f : C(X, ℝ), EqOn f 0 s ∧ EqOn f 1 t ∧ ∀ x, f x ∈ Icc (0 : ℝ) 1 := by
   -- The actual proof is in the code above. Here we just repack it into the expected format.
-  set c : Urysohns.CU X := ⟨s, tᶜ, hs, ht.isOpen_compl, disjoint_left.1 hd⟩
+  let P : Set X → Prop := fun _ ↦ True
+  set c : Urysohns.CU P :=
+  { C := s
+    U := tᶜ
+    P_C := trivial
+    closed_C := hs
+    open_U := ht.isOpen_compl
+    subset := disjoint_left.1 hd
+    hP := by
+      rintro c u c_closed - u_open cu
+      rcases normal_exists_closure_subset c_closed u_open cu with ⟨v, v_open, cv, hv⟩
+      exact ⟨v, v_open, cv, hv, trivial⟩ }
   exact ⟨⟨c.lim, c.continuous_lim⟩, c.lim_of_mem_C, fun x hx => c.lim_of_nmem_U _ fun h => h hx,
     c.lim_mem_Icc⟩
 #align exists_continuous_zero_one_of_closed exists_continuous_zero_one_of_closed
+
+/-- Urysohn's lemma: if `s` and `t` are two disjoint sets in a regular locally compact topological
+space `X`, with `s` compact and `t` closed, then there exists a continuous
+function `f : X → ℝ` such that
+
+* `f` equals zero on `s`;
+* `f` equals one on `t`;
+* `0 ≤ f x ≤ 1` for all `x`.
+-/
+theorem exists_continuous_zero_one_of_isCompact [RegularSpace X] [LocallyCompactSpace X]
+    {s t : Set X} (hs : IsCompact s) (ht : IsClosed t) (hd : Disjoint s t) :
+    ∃ f : C(X, ℝ), EqOn f 0 s ∧ EqOn f 1 t ∧ ∀ x, f x ∈ Icc (0 : ℝ) 1 := by
+  obtain ⟨k, k_comp, k_closed, sk, kt⟩ : ∃ k, IsCompact k ∧ IsClosed k ∧ s ⊆ interior k ∧ k ⊆ tᶜ :=
+    exists_compact_closed_between hs ht.isOpen_compl hd.symm.subset_compl_left
+  let P : Set X → Prop := IsCompact
+  set c : Urysohns.CU P :=
+  { C := k
+    U := tᶜ
+    P_C := k_comp
+    closed_C := k_closed
+    open_U := ht.isOpen_compl
+    subset := kt
+    hP := by
+      rintro c u - c_comp u_open cu
+      rcases exists_compact_closed_between c_comp u_open cu with ⟨k, k_comp, k_closed, ck, ku⟩
+      have A : closure (interior k) ⊆ k :=
+        (IsClosed.closure_subset_iff k_closed).2 interior_subset
+      refine ⟨interior k, isOpen_interior, ck, A.trans ku,
+        k_comp.of_isClosed_subset isClosed_closure A⟩ }
+  exact ⟨⟨c.lim, c.continuous_lim⟩, fun x hx ↦ c.lim_of_mem_C _ (sk.trans interior_subset hx),
+    fun x hx => c.lim_of_nmem_U _ fun h => h hx, c.lim_mem_Icc⟩
+
+/-- Urysohn's lemma: if `s` and `t` are two disjoint sets in a regular locally compact topological
+space `X`, with `s` compact and `t` closed, then there exists a continuous compactly supported
+function `f : X → ℝ` such that
+
+* `f` equals one on `s`;
+* `f` equals zero on `t`;
+* `0 ≤ f x ≤ 1` for all `x`.
+-/
+theorem exists_continuous_one_zero_of_isCompact [RegularSpace X] [LocallyCompactSpace X]
+    {s t : Set X} (hs : IsCompact s) (ht : IsClosed t) (hd : Disjoint s t) :
+    ∃ f : C(X, ℝ), EqOn f 1 s ∧ EqOn f 0 t ∧ HasCompactSupport f ∧ ∀ x, f x ∈ Icc (0 : ℝ) 1 := by
+  obtain ⟨k, k_comp, k_closed, sk, kt⟩ : ∃ k, IsCompact k ∧ IsClosed k ∧ s ⊆ interior k ∧ k ⊆ tᶜ :=
+    exists_compact_closed_between hs ht.isOpen_compl hd.symm.subset_compl_left
+  rcases exists_continuous_zero_one_of_isCompact hs isOpen_interior.isClosed_compl
+    (disjoint_compl_right_iff_subset.mpr sk) with ⟨⟨f, hf⟩, hfs, hft, h'f⟩
+  have A : t ⊆ (interior k)ᶜ := subset_compl_comm.mpr (interior_subset.trans kt)
+  refine ⟨⟨fun x ↦ 1 - f x, continuous_const.sub hf⟩, fun x hx ↦ by simpa using hfs hx,
+    fun x hx ↦ by simpa [sub_eq_zero] using (hft (A hx)).symm, ?_, fun x ↦ ?_⟩
+  · apply HasCompactSupport.intro' k_comp k_closed (fun x hx ↦ ?_)
+    simp only [ContinuousMap.coe_mk, sub_eq_zero]
+    apply (hft _).symm
+    contrapose! hx
+    simp only [mem_compl_iff, not_not] at hx
+    exact interior_subset hx
+  · have : 0 ≤ f x ∧ f x ≤ 1 := by simpa using h'f x
+    simp [this]

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

@@ -263,7 +263,7 @@ theorem continuous_lim (c : CU X) : Continuous c.lim := by
     rw [pow_zero]
     exact Real.dist_le_of_mem_Icc_01 (c.lim_mem_Icc _) (c.lim_mem_Icc _)
   · by_cases hxl : x ∈ c.left.U
-    · filter_upwards [IsOpen.mem_nhds c.left.open_U hxl, ihn c.left]with _ hyl hyd
+    · filter_upwards [IsOpen.mem_nhds c.left.open_U hxl, ihn c.left] with _ hyl hyd
       rw [pow_succ, c.lim_eq_midpoint, c.lim_eq_midpoint,
         c.right.lim_of_mem_C _ (c.left_U_subset_right_C hyl),
         c.right.lim_of_mem_C _ (c.left_U_subset_right_C hxl)]
@@ -273,7 +273,7 @@ theorem continuous_lim (c : CU X) : Continuous c.lim := by
     · replace hxl : x ∈ c.left.right.Cᶜ
       exact compl_subset_compl.2 c.left.right.subset hxl
       filter_upwards [IsOpen.mem_nhds (isOpen_compl_iff.2 c.left.right.closed_C) hxl,
-        ihn c.left.right, ihn c.right]with y hyl hydl hydr
+        ihn c.left.right, ihn c.right] with y hyl hydl hydr
       replace hxl : x ∉ c.left.left.U
       exact compl_subset_compl.2 c.left.left_U_subset_right_C hxl
       replace hyl : y ∉ c.left.left.U

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

This has nice performance benefits.

@@ -70,7 +70,7 @@ Urysohn's lemma, normal topological space
 -/
 
 
-variable {X : Type _} [TopologicalSpace X]
+variable {X : Type*} [TopologicalSpace X]
 
 open Set Filter TopologicalSpace Topology Filter
 
@@ -80,7 +80,7 @@ set_option linter.uppercaseLean3 false
 
 /-- An auxiliary type for the proof of Urysohn's lemma: a pair of a closed set `C` and its
 open neighborhood `U`. -/
-structure CU (X : Type _) [TopologicalSpace X] where
+structure CU (X : Type*) [TopologicalSpace X] where
   protected (C U : Set X)
   protected closed_C : IsClosed C
   protected open_U : IsOpen U

• depends on: #5966

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

@@ -2,16 +2,13 @@
 Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
-
-! This file was ported from Lean 3 source module topology.urysohns_lemma
-! 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.Analysis.NormedSpace.AddTorsor
 import Mathlib.LinearAlgebra.AffineSpace.Ordered
 import Mathlib.Topology.ContinuousFunction.Basic
 
+#align_import topology.urysohns_lemma from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
+
 /-!
 # Urysohn's lemma
 

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

@@ -134,7 +134,7 @@ theorem subset_right_C (c : CU X) : c.C ⊆ c.right.C :=
 /-- `n`-th approximation to a continuous function `f : X → ℝ` such that `f = 0` on `c.C` and `f = 1`
 outside of `c.U`. -/
 noncomputable def approx : ℕ → CU X → X → ℝ
-  | 0, c, x => indicator (c.Uᶜ) 1 x
+  | 0, c, x => indicator c.Uᶜ 1 x
   | n + 1, c, x => midpoint ℝ (approx n c.left x) (approx n c.right x)
 #align urysohns.CU.approx Urysohns.CU.approx
 

These are all doc fixes

@@ -98,7 +98,7 @@ variable [NormalSpace X]
 namespace CU
 
 /-- Due to `normal_exists_closure_subset`, for each `c : CU X` there exists an open set `u`
-such chat `c.C ⊆ u` and `closure u ⊆ c.U`. `c.left` is the pair `(c.C, u)`. -/
+such that `c.C ⊆ u` and `closure u ⊆ c.U`. `c.left` is the pair `(c.C, u)`. -/
 @[simps C]
 def left (c : CU X) : CU X where
   C := c.C
@@ -109,7 +109,7 @@ def left (c : CU X) : CU X where
 #align urysohns.CU.left Urysohns.CU.left
 
 /-- Due to `normal_exists_closure_subset`, for each `c : CU X` there exists an open set `u`
-such chat `c.C ⊆ u` and `closure u ⊆ c.U`. `c.right` is the pair `(closure u, c.U)`. -/
+such that `c.C ⊆ u` and `closure u ⊆ c.U`. `c.right` is the pair `(closure u, c.U)`. -/
 @[simps U]
 def right (c : CU X) : CU X where
   C := closure (normal_exists_closure_subset c.closed_C c.open_U c.subset).choose

100 sample uses of the new tactic gcongr, added in #3965.

@@ -272,7 +272,7 @@ theorem continuous_lim (c : CU X) : Continuous c.lim := by
         c.right.lim_of_mem_C _ (c.left_U_subset_right_C hxl)]
       refine' (dist_midpoint_midpoint_le _ _ _ _).trans _
       rw [dist_self, add_zero, div_eq_inv_mul]
-      exact mul_le_mul h1234.le hyd dist_nonneg (h0.trans h1234).le
+      gcongr
     · replace hxl : x ∈ c.left.right.Cᶜ
       exact compl_subset_compl.2 c.left.right.subset hxl
       filter_upwards [IsOpen.mem_nhds (isOpen_compl_iff.2 c.left.right.closed_C) hxl,
@@ -287,11 +287,9 @@ theorem continuous_lim (c : CU X) : Continuous c.lim := by
       refine' (div_le_div_of_le_of_nonneg (add_le_add_right (dist_midpoint_midpoint_le _ _ _ _) _)
         zero_le_two).trans _
       rw [dist_self, zero_add]
-      refine' (div_le_div_of_le_of_nonneg (add_le_add (div_le_div_of_le_of_nonneg hydl zero_le_two)
-        hydr) zero_le_two).trans_eq _
-      generalize (3 / 4 : ℝ) ^ n = r
-      field_simp [two_ne_zero' ℝ]
-      ring
+      set r := (3 / 4 : ℝ) ^ n
+      calc _ ≤ (r / 2 + r) / 2 := by gcongr
+        _ = _ := by field_simp; ring
 #align urysohns.CU.continuous_lim Urysohns.CU.continuous_lim
 
 end CU

As discussed on Zulip

Renames

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

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

@@ -220,15 +220,15 @@ protected noncomputable def lim (c : CU X) (x : X) : ℝ :=
 
 theorem tendsto_approx_atTop (c : CU X) (x : X) :
     Tendsto (fun n => c.approx n x) atTop (𝓝 <| c.lim x) :=
-  tendsto_atTop_csupᵢ (c.approx_mono x) ⟨1, fun _ ⟨_, hn⟩ => hn ▸ c.approx_le_one _ _⟩
+  tendsto_atTop_ciSup (c.approx_mono x) ⟨1, fun _ ⟨_, hn⟩ => hn ▸ c.approx_le_one _ _⟩
 #align urysohns.CU.tendsto_approx_at_top Urysohns.CU.tendsto_approx_atTop
 
 theorem lim_of_mem_C (c : CU X) (x : X) (h : x ∈ c.C) : c.lim x = 0 := by
-  simp only [CU.lim, approx_of_mem_C, h, csupᵢ_const]
+  simp only [CU.lim, approx_of_mem_C, h, ciSup_const]
 #align urysohns.CU.lim_of_mem_C Urysohns.CU.lim_of_mem_C
 
 theorem lim_of_nmem_U (c : CU X) (x : X) (h : x ∉ c.U) : c.lim x = 1 := by
-  simp only [CU.lim, approx_of_nmem_U c _ h, csupᵢ_const]
+  simp only [CU.lim, approx_of_nmem_U c _ h, ciSup_const]
 #align urysohns.CU.lim_of_nmem_U Urysohns.CU.lim_of_nmem_U
 
 theorem lim_eq_midpoint (c : CU X) (x : X) :
@@ -239,7 +239,7 @@ theorem lim_eq_midpoint (c : CU X) (x : X) :
 #align urysohns.CU.lim_eq_midpoint Urysohns.CU.lim_eq_midpoint
 
 theorem approx_le_lim (c : CU X) (x : X) (n : ℕ) : c.approx n x ≤ c.lim x :=
-  le_csupᵢ (c.bddAbove_range_approx x) _
+  le_ciSup (c.bddAbove_range_approx x) _
 #align urysohns.CU.approx_le_lim Urysohns.CU.approx_le_lim
 
 theorem lim_nonneg (c : CU X) (x : X) : 0 ≤ c.lim x :=
@@ -247,7 +247,7 @@ theorem lim_nonneg (c : CU X) (x : X) : 0 ≤ c.lim x :=
 #align urysohns.CU.lim_nonneg Urysohns.CU.lim_nonneg
 
 theorem lim_le_one (c : CU X) (x : X) : c.lim x ≤ 1 :=
-  csupᵢ_le fun _ => c.approx_le_one _ _
+  ciSup_le fun _ => c.approx_le_one _ _
 #align urysohns.CU.lim_le_one Urysohns.CU.lim_le_one
 
 theorem lim_mem_Icc (c : CU X) (x : X) : c.lim x ∈ Icc (0 : ℝ) 1 :=

@@ -75,9 +75,7 @@ Urysohn's lemma, normal topological space
 
 variable {X : Type _} [TopologicalSpace X]
 
-open Set Filter TopologicalSpace
-
-open Topology Filter
+open Set Filter TopologicalSpace Topology Filter
 
 namespace Urysohns
 
@@ -89,7 +87,7 @@ structure CU (X : Type _) [TopologicalSpace X] where
   protected (C U : Set X)
   protected closed_C : IsClosed C
   protected open_U : IsOpen U
-  protected Subset : C ⊆ U
+  protected subset : C ⊆ U
 #align urysohns.CU Urysohns.CU
 
 instance : Inhabited (CU X) :=
@@ -104,21 +102,21 @@ such chat `c.C ⊆ u` and `closure u ⊆ c.U`. `c.left` is the pair `(c.C, u)`.
 @[simps C]
 def left (c : CU X) : CU X where
   C := c.C
-  U := (normal_exists_closure_subset c.closed_C c.open_U c.Subset).choose
+  U := (normal_exists_closure_subset c.closed_C c.open_U c.subset).choose
   closed_C := c.closed_C
-  open_U := (normal_exists_closure_subset c.closed_C c.open_U c.Subset).choose_spec.1
-  Subset := (normal_exists_closure_subset c.closed_C c.open_U c.Subset).choose_spec.2.1
+  open_U := (normal_exists_closure_subset c.closed_C c.open_U c.subset).choose_spec.1
+  subset := (normal_exists_closure_subset c.closed_C c.open_U c.subset).choose_spec.2.1
 #align urysohns.CU.left Urysohns.CU.left
 
 /-- Due to `normal_exists_closure_subset`, for each `c : CU X` there exists an open set `u`
 such chat `c.C ⊆ u` and `closure u ⊆ c.U`. `c.right` is the pair `(closure u, c.U)`. -/
 @[simps U]
 def right (c : CU X) : CU X where
-  C := closure (normal_exists_closure_subset c.closed_C c.open_U c.Subset).choose
+  C := closure (normal_exists_closure_subset c.closed_C c.open_U c.subset).choose
   U := c.U
   closed_C := isClosed_closure
   open_U := c.open_U
-  Subset := (normal_exists_closure_subset c.closed_C c.open_U c.Subset).choose_spec.2.2
+  subset := (normal_exists_closure_subset c.closed_C c.open_U c.subset).choose_spec.2.2
 #align urysohns.CU.right Urysohns.CU.right
 
 theorem left_U_subset_right_C (c : CU X) : c.left.U ⊆ c.right.C :=
@@ -126,11 +124,11 @@ theorem left_U_subset_right_C (c : CU X) : c.left.U ⊆ c.right.C :=
 #align urysohns.CU.left_U_subset_right_C Urysohns.CU.left_U_subset_right_C
 
 theorem left_U_subset (c : CU X) : c.left.U ⊆ c.U :=
-  Subset.trans c.left_U_subset_right_C c.right.Subset
+  Subset.trans c.left_U_subset_right_C c.right.subset
 #align urysohns.CU.left_U_subset Urysohns.CU.left_U_subset
 
 theorem subset_right_C (c : CU X) : c.C ⊆ c.right.C :=
-  Subset.trans c.left.Subset c.left_U_subset_right_C
+  Subset.trans c.left.subset c.left_U_subset_right_C
 #align urysohns.CU.subset_right_C Urysohns.CU.subset_right_C
 
 /-- `n`-th approximation to a continuous function `f : X → ℝ` such that `f = 0` on `c.C` and `f = 1`
@@ -142,7 +140,7 @@ noncomputable def approx : ℕ → CU X → X → ℝ
 
 theorem approx_of_mem_C (c : CU X) (n : ℕ) {x : X} (hx : x ∈ c.C) : c.approx n x = 0 := by
   induction' n with n ihn generalizing c
-  · exact indicator_of_not_mem (fun (hU : x ∈ c.Uᶜ) => hU <| c.Subset hx) _
+  · exact indicator_of_not_mem (fun (hU : x ∈ c.Uᶜ) => hU <| c.subset hx) _
   · simp only [approx]
     rw [ihn, ihn, midpoint_self]
     exacts [c.subset_right_C hx, hx]
@@ -276,7 +274,7 @@ theorem continuous_lim (c : CU X) : Continuous c.lim := by
       rw [dist_self, add_zero, div_eq_inv_mul]
       exact mul_le_mul h1234.le hyd dist_nonneg (h0.trans h1234).le
     · replace hxl : x ∈ c.left.right.Cᶜ
-      exact compl_subset_compl.2 c.left.right.Subset hxl
+      exact compl_subset_compl.2 c.left.right.subset hxl
       filter_upwards [IsOpen.mem_nhds (isOpen_compl_iff.2 c.left.right.closed_C) hxl,
         ihn c.left.right, ihn c.right]with y hyl hydl hydr
       replace hxl : x ∉ c.left.left.U

Co-authored-by: Lucas V. R <lvr@s-viva.xyz> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com>