topology.shrinking_lemma ⟷ Mathlib.Topology.ShrinkingLemma

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

@@ -43,7 +43,7 @@ variable {ι X : Type _} [TopologicalSpace X] [NormalSpace X]
 namespace ShrinkingLemma
 
 #print ShrinkingLemma.PartialRefinement /-
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (i «expr ∉ » carrier) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (i «expr ∉ » carrier) -/
 -- the trivial refinement needs `u` to be a covering
 /-- Auxiliary definition for the proof of `shrinking_lemma`. A partial refinement of a covering
 `⋃ i, u i` of a set `s` is a map `v : ι → set X` and a set `carrier : set ι` such that
@@ -177,7 +177,7 @@ theorem find_apply_of_mem {c : Set (PartialRefinement u s)} (hc : IsChain (· 
 #align shrinking_lemma.partial_refinement.find_apply_of_mem ShrinkingLemma.PartialRefinement.find_apply_of_mem
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (i «expr ∉ » chain_Sup_carrier c) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (i «expr ∉ » chain_Sup_carrier c) -/
 #print ShrinkingLemma.PartialRefinement.chainSup /-
 /-- Least upper bound of a nonempty chain of partial refinements. -/
 def chainSup (c : Set (PartialRefinement u s)) (hc : IsChain (· ≤ ·) c) (ne : c.Nonempty)
@@ -212,9 +212,9 @@ theorem le_chainSup {c : Set (PartialRefinement u s)} (hc : IsChain (· ≤ ·)
 #align shrinking_lemma.partial_refinement.le_chain_Sup ShrinkingLemma.PartialRefinement.le_chainSup
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (j «expr ≠ » i) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (j «expr ≠ » i) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (j «expr ≠ » i) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (j «expr ≠ » i) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (j «expr ≠ » i) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (j «expr ≠ » i) -/
 #print ShrinkingLemma.PartialRefinement.exists_gt /-
 /-- If `s` is a closed set, `v` is a partial refinement, and `i` is an index such that
 `i ∉ v.carrier`, then there exists a partial refinement that is strictly greater than `v`. -/

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

@@ -190,7 +190,7 @@ def chainSup (c : Set (PartialRefinement u s)) (hc : IsChain (· ≤ ·) c) (ne
   rcases em (∃ (i : _) (_ : i ∉ chain_Sup_carrier c), x ∈ u i) with (⟨i, hi, hxi⟩ | hx)
   · use i
     rwa [(find c Ne i).apply_eq (mt (mem_find_carrier_iff _).1 hi)]
-  · simp_rw [not_exists, not_imp_not, chain_Sup_carrier, mem_Union₂] at hx 
+  · simp_rw [not_exists, not_imp_not, chain_Sup_carrier, mem_Union₂] at hx
     haveI : Nonempty (partial_refinement u s) := ⟨ne.some⟩
     choose! v hvc hiv using hx
     rcases(hfin x hxs).exists_maximal_wrt v _ (mem_Union.1 (hU hxs)) with
@@ -235,12 +235,12 @@ theorem exists_gt (v : PartialRefinement u s) (hs : IsClosed s) (i : ι) (hi : i
   · refine' fun x hx => mem_Union.2 _
     rcases em (∃ (j : _) (_ : j ≠ i), x ∈ v j) with (⟨j, hji, hj⟩ | h)
     · use j; rwa [update_noteq hji]
-    · push_neg at h ; use i; rw [update_same]; exact hvi ⟨hx, mem_bInter h⟩
+    · push_neg at h; use i; rw [update_same]; exact hvi ⟨hx, mem_bInter h⟩
   · rintro j (rfl | hj)
     · rwa [update_same, ← v.apply_eq hi]
     · rw [update_noteq (ne_of_mem_of_not_mem hj hi)]; exact v.closure_subset hj
   · intro j hj
-    rw [mem_insert_iff, not_or] at hj 
+    rw [mem_insert_iff, not_or] at hj
     rw [update_noteq hj.1, v.apply_eq hj.2]
   · refine' ⟨subset_insert _ _, fun j hj => _⟩
     exact (update_noteq (ne_of_mem_of_not_mem hj hi) _ _).symm

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

@@ -262,7 +262,21 @@ to a new open cover so that the closure of each new open set is contained in the
 original open set. -/
 theorem exists_subset_iUnion_closure_subset (hs : IsClosed s) (uo : ∀ i, IsOpen (u i))
     (uf : ∀ x ∈ s, {i | x ∈ u i}.Finite) (us : s ⊆ ⋃ i, u i) :
-    ∃ v : ι → Set X, s ⊆ iUnion v ∧ (∀ i, IsOpen (v i)) ∧ ∀ i, closure (v i) ⊆ u i := by classical
+    ∃ v : ι → Set X, s ⊆ iUnion v ∧ (∀ i, IsOpen (v i)) ∧ ∀ i, closure (v i) ⊆ u i := by
+  classical
+  haveI : Nonempty (partial_refinement u s) := ⟨⟨u, ∅, uo, us, fun _ => False.elim, fun _ _ => rfl⟩⟩
+  have :
+    ∀ c : Set (partial_refinement u s), IsChain (· ≤ ·) c → c.Nonempty → ∃ ub, ∀ v ∈ c, v ≤ ub :=
+    fun c hc ne =>
+    ⟨partial_refinement.chain_Sup c hc Ne uf us, fun v hv =>
+      partial_refinement.le_chain_Sup _ _ _ _ hv⟩
+  rcases zorn_nonempty_partialOrder this with ⟨v, hv⟩
+  suffices : ∀ i, i ∈ v.carrier
+  exact ⟨v, v.subset_Union, fun i => v.is_open _, fun i => v.closure_subset (this i)⟩
+  contrapose! hv
+  rcases hv with ⟨i, hi⟩
+  rcases v.exists_gt hs i hi with ⟨v', hlt⟩
+  exact ⟨v', hlt.le, hlt.ne'⟩
 #align exists_subset_Union_closure_subset exists_subset_iUnion_closure_subset
 -/
 

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

@@ -262,21 +262,7 @@ to a new open cover so that the closure of each new open set is contained in the
 original open set. -/
 theorem exists_subset_iUnion_closure_subset (hs : IsClosed s) (uo : ∀ i, IsOpen (u i))
     (uf : ∀ x ∈ s, {i | x ∈ u i}.Finite) (us : s ⊆ ⋃ i, u i) :
-    ∃ v : ι → Set X, s ⊆ iUnion v ∧ (∀ i, IsOpen (v i)) ∧ ∀ i, closure (v i) ⊆ u i := by
-  classical
-  haveI : Nonempty (partial_refinement u s) := ⟨⟨u, ∅, uo, us, fun _ => False.elim, fun _ _ => rfl⟩⟩
-  have :
-    ∀ c : Set (partial_refinement u s), IsChain (· ≤ ·) c → c.Nonempty → ∃ ub, ∀ v ∈ c, v ≤ ub :=
-    fun c hc ne =>
-    ⟨partial_refinement.chain_Sup c hc Ne uf us, fun v hv =>
-      partial_refinement.le_chain_Sup _ _ _ _ hv⟩
-  rcases zorn_nonempty_partialOrder this with ⟨v, hv⟩
-  suffices : ∀ i, i ∈ v.carrier
-  exact ⟨v, v.subset_Union, fun i => v.is_open _, fun i => v.closure_subset (this i)⟩
-  contrapose! hv
-  rcases hv with ⟨i, hi⟩
-  rcases v.exists_gt hs i hi with ⟨v', hlt⟩
-  exact ⟨v', hlt.le, hlt.ne'⟩
+    ∃ v : ι → Set X, s ⊆ iUnion v ∧ (∀ i, IsOpen (v i)) ∧ ∀ i, closure (v i) ⊆ u i := by classical
 #align exists_subset_Union_closure_subset exists_subset_iUnion_closure_subset
 -/
 

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

@@ -3,7 +3,7 @@ Copyright (c) 2021 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov, Reid Barton
 -/
-import Mathbin.Topology.Separation
+import Topology.Separation
 
 #align_import topology.shrinking_lemma from "leanprover-community/mathlib"@"0a0ec35061ed9960bf0e7ffb0335f44447b58977"
 
@@ -43,7 +43,7 @@ variable {ι X : Type _} [TopologicalSpace X] [NormalSpace X]
 namespace ShrinkingLemma
 
 #print ShrinkingLemma.PartialRefinement /-
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » carrier) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (i «expr ∉ » carrier) -/
 -- the trivial refinement needs `u` to be a covering
 /-- Auxiliary definition for the proof of `shrinking_lemma`. A partial refinement of a covering
 `⋃ i, u i` of a set `s` is a map `v : ι → set X` and a set `carrier : set ι` such that
@@ -177,7 +177,7 @@ theorem find_apply_of_mem {c : Set (PartialRefinement u s)} (hc : IsChain (· 
 #align shrinking_lemma.partial_refinement.find_apply_of_mem ShrinkingLemma.PartialRefinement.find_apply_of_mem
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » chain_Sup_carrier c) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (i «expr ∉ » chain_Sup_carrier c) -/
 #print ShrinkingLemma.PartialRefinement.chainSup /-
 /-- Least upper bound of a nonempty chain of partial refinements. -/
 def chainSup (c : Set (PartialRefinement u s)) (hc : IsChain (· ≤ ·) c) (ne : c.Nonempty)
@@ -212,9 +212,9 @@ theorem le_chainSup {c : Set (PartialRefinement u s)} (hc : IsChain (· ≤ ·)
 #align shrinking_lemma.partial_refinement.le_chain_Sup ShrinkingLemma.PartialRefinement.le_chainSup
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (j «expr ≠ » i) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (j «expr ≠ » i) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (j «expr ≠ » i) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (j «expr ≠ » i) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (j «expr ≠ » i) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (j «expr ≠ » i) -/
 #print ShrinkingLemma.PartialRefinement.exists_gt /-
 /-- If `s` is a closed set, `v` is a partial refinement, and `i` is an index such that
 `i ∉ v.carrier`, then there exists a partial refinement that is strictly greater than `v`. -/

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

@@ -2,14 +2,11 @@
 Copyright (c) 2021 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov, Reid Barton
-
-! This file was ported from Lean 3 source module topology.shrinking_lemma
-! leanprover-community/mathlib commit 0a0ec35061ed9960bf0e7ffb0335f44447b58977
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Topology.Separation
 
+#align_import topology.shrinking_lemma from "leanprover-community/mathlib"@"0a0ec35061ed9960bf0e7ffb0335f44447b58977"
+
 /-!
 # The shrinking lemma
 
@@ -46,7 +43,7 @@ variable {ι X : Type _} [TopologicalSpace X] [NormalSpace X]
 namespace ShrinkingLemma
 
 #print ShrinkingLemma.PartialRefinement /-
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (i «expr ∉ » carrier) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » carrier) -/
 -- the trivial refinement needs `u` to be a covering
 /-- Auxiliary definition for the proof of `shrinking_lemma`. A partial refinement of a covering
 `⋃ i, u i` of a set `s` is a map `v : ι → set X` and a set `carrier : set ι` such that
@@ -180,7 +177,7 @@ theorem find_apply_of_mem {c : Set (PartialRefinement u s)} (hc : IsChain (· 
 #align shrinking_lemma.partial_refinement.find_apply_of_mem ShrinkingLemma.PartialRefinement.find_apply_of_mem
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (i «expr ∉ » chain_Sup_carrier c) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » chain_Sup_carrier c) -/
 #print ShrinkingLemma.PartialRefinement.chainSup /-
 /-- Least upper bound of a nonempty chain of partial refinements. -/
 def chainSup (c : Set (PartialRefinement u s)) (hc : IsChain (· ≤ ·) c) (ne : c.Nonempty)
@@ -215,9 +212,9 @@ theorem le_chainSup {c : Set (PartialRefinement u s)} (hc : IsChain (· ≤ ·)
 #align shrinking_lemma.partial_refinement.le_chain_Sup ShrinkingLemma.PartialRefinement.le_chainSup
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (j «expr ≠ » i) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (j «expr ≠ » i) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (j «expr ≠ » i) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (j «expr ≠ » i) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (j «expr ≠ » i) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (j «expr ≠ » i) -/
 #print ShrinkingLemma.PartialRefinement.exists_gt /-
 /-- If `s` is a closed set, `v` is a partial refinement, and `i` is an index such that
 `i ∉ v.carrier`, then there exists a partial refinement that is strictly greater than `v`. -/

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

@@ -45,6 +45,7 @@ variable {ι X : Type _} [TopologicalSpace X] [NormalSpace X]
 
 namespace ShrinkingLemma
 
+#print ShrinkingLemma.PartialRefinement /-
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (i «expr ∉ » carrier) -/
 -- the trivial refinement needs `u` to be a covering
 /-- Auxiliary definition for the proof of `shrinking_lemma`. A partial refinement of a covering
@@ -67,6 +68,7 @@ structure PartialRefinement (u : ι → Set X) (s : Set X) where
   closure_subset' : ∀ i ∈ carrier, closure (to_fun i) ⊆ u i
   apply_eq' : ∀ (i) (_ : i ∉ carrier), to_fun i = u i
 #align shrinking_lemma.partial_refinement ShrinkingLemma.PartialRefinement
+-/
 
 namespace PartialRefinement
 
@@ -75,26 +77,36 @@ variable {u : ι → Set X} {s : Set X}
 instance : CoeFun (PartialRefinement u s) fun _ => ι → Set X :=
   ⟨toFun⟩
 
+#print ShrinkingLemma.PartialRefinement.subset_iUnion /-
 theorem subset_iUnion (v : PartialRefinement u s) : s ⊆ ⋃ i, v i :=
   v.subset_Union'
 #align shrinking_lemma.partial_refinement.subset_Union ShrinkingLemma.PartialRefinement.subset_iUnion
+-/
 
+#print ShrinkingLemma.PartialRefinement.closure_subset /-
 theorem closure_subset (v : PartialRefinement u s) {i : ι} (hi : i ∈ v.carrier) :
     closure (v i) ⊆ u i :=
   v.closure_subset' i hi
 #align shrinking_lemma.partial_refinement.closure_subset ShrinkingLemma.PartialRefinement.closure_subset
+-/
 
+#print ShrinkingLemma.PartialRefinement.apply_eq /-
 theorem apply_eq (v : PartialRefinement u s) {i : ι} (hi : i ∉ v.carrier) : v i = u i :=
   v.apply_eq' i hi
 #align shrinking_lemma.partial_refinement.apply_eq ShrinkingLemma.PartialRefinement.apply_eq
+-/
 
+#print ShrinkingLemma.PartialRefinement.isOpen /-
 protected theorem isOpen (v : PartialRefinement u s) (i : ι) : IsOpen (v i) :=
   v.is_open' i
 #align shrinking_lemma.partial_refinement.is_open ShrinkingLemma.PartialRefinement.isOpen
+-/
 
+#print ShrinkingLemma.PartialRefinement.subset /-
 protected theorem subset (v : PartialRefinement u s) (i : ι) : v i ⊆ u i :=
   if h : i ∈ v.carrier then Subset.trans subset_closure (v.closure_subset h) else (v.apply_eq h).le
 #align shrinking_lemma.partial_refinement.subset ShrinkingLemma.PartialRefinement.subset
+-/
 
 attribute [ext] partial_refinement
 
@@ -112,6 +124,7 @@ instance : PartialOrder (PartialRefinement u s)
         else (v₁.apply_eq hx).trans (Eq.symm <| v₂.apply_eq <| hc ▸ hx))
       hc
 
+#print ShrinkingLemma.PartialRefinement.apply_eq_of_chain /-
 /-- If two partial refinements `v₁`, `v₂` belong to a chain (hence, they are comparable)
 and `i` belongs to the carriers of both partial refinements, then `v₁ i = v₂ i`. -/
 theorem apply_eq_of_chain {c : Set (PartialRefinement u s)} (hc : IsChain (· ≤ ·) c) {v₁ v₂}
@@ -121,23 +134,31 @@ theorem apply_eq_of_chain {c : Set (PartialRefinement u s)} (hc : IsChain (· 
   · cases hc.total h₁ h₂ <;> [skip; symm] <;> apply_assumption <;> assumption'
   exact hle.2 _ hi₁
 #align shrinking_lemma.partial_refinement.apply_eq_of_chain ShrinkingLemma.PartialRefinement.apply_eq_of_chain
+-/
 
+#print ShrinkingLemma.PartialRefinement.chainSupCarrier /-
 /-- The carrier of the least upper bound of a non-empty chain of partial refinements
 is the union of their carriers. -/
 def chainSupCarrier (c : Set (PartialRefinement u s)) : Set ι :=
   ⋃ v ∈ c, carrier v
 #align shrinking_lemma.partial_refinement.chain_Sup_carrier ShrinkingLemma.PartialRefinement.chainSupCarrier
+-/
 
+#print ShrinkingLemma.PartialRefinement.find /-
 /-- Choice of an element of a nonempty chain of partial refinements. If `i` belongs to one of
 `carrier v`, `v ∈ c`, then `find c ne i` is one of these partial refinements. -/
 def find (c : Set (PartialRefinement u s)) (ne : c.Nonempty) (i : ι) : PartialRefinement u s :=
   if hi : ∃ v ∈ c, i ∈ carrier v then hi.some else Ne.some
 #align shrinking_lemma.partial_refinement.find ShrinkingLemma.PartialRefinement.find
+-/
 
+#print ShrinkingLemma.PartialRefinement.find_mem /-
 theorem find_mem {c : Set (PartialRefinement u s)} (i : ι) (ne : c.Nonempty) : find c Ne i ∈ c := by
   rw [find]; split_ifs; exacts [h.some_spec.fst, ne.some_spec]
 #align shrinking_lemma.partial_refinement.find_mem ShrinkingLemma.PartialRefinement.find_mem
+-/
 
+#print ShrinkingLemma.PartialRefinement.mem_find_carrier_iff /-
 theorem mem_find_carrier_iff {c : Set (PartialRefinement u s)} {i : ι} (ne : c.Nonempty) :
     i ∈ (find c Ne i).carrier ↔ i ∈ chainSupCarrier c :=
   by
@@ -149,14 +170,18 @@ theorem mem_find_carrier_iff {c : Set (PartialRefinement u s)} {i : ι} (ne : c.
       ⟨fun hi => h ⟨_, ne.some_spec, hi⟩, mt mem_Union₂.1 h⟩
     simp only [this]
 #align shrinking_lemma.partial_refinement.mem_find_carrier_iff ShrinkingLemma.PartialRefinement.mem_find_carrier_iff
+-/
 
+#print ShrinkingLemma.PartialRefinement.find_apply_of_mem /-
 theorem find_apply_of_mem {c : Set (PartialRefinement u s)} (hc : IsChain (· ≤ ·) c)
     (ne : c.Nonempty) {i v} (hv : v ∈ c) (hi : i ∈ carrier v) : find c Ne i i = v i :=
   apply_eq_of_chain hc (find_mem _ _) hv ((mem_find_carrier_iff _).2 <| mem_iUnion₂.2 ⟨v, hv, hi⟩)
     hi
 #align shrinking_lemma.partial_refinement.find_apply_of_mem ShrinkingLemma.PartialRefinement.find_apply_of_mem
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (i «expr ∉ » chain_Sup_carrier c) -/
+#print ShrinkingLemma.PartialRefinement.chainSup /-
 /-- Least upper bound of a nonempty chain of partial refinements. -/
 def chainSup (c : Set (PartialRefinement u s)) (hc : IsChain (· ≤ ·) c) (ne : c.Nonempty)
     (hfin : ∀ x ∈ s, {i | x ∈ u i}.Finite) (hU : s ⊆ ⋃ i, u i) : PartialRefinement u s :=
@@ -179,17 +204,21 @@ def chainSup (c : Set (PartialRefinement u s)) (hc : IsChain (· ≤ ·) c) (ne
     have : v j ≤ v i := (hc.total (hvc _ hxi) (hvc _ hj')).elim (fun h => (hmax j hj' h).ge) id
     rwa [find_apply_of_mem hc Ne (hvc _ hxi) (this.1 <| hiv _ hj')]
 #align shrinking_lemma.partial_refinement.chain_Sup ShrinkingLemma.PartialRefinement.chainSup
+-/
 
+#print ShrinkingLemma.PartialRefinement.le_chainSup /-
 /-- `chain_Sup hu c hc ne hfin hU` is an upper bound of the chain `c`. -/
 theorem le_chainSup {c : Set (PartialRefinement u s)} (hc : IsChain (· ≤ ·) c) (ne : c.Nonempty)
     (hfin : ∀ x ∈ s, {i | x ∈ u i}.Finite) (hU : s ⊆ ⋃ i, u i) {v} (hv : v ∈ c) :
     v ≤ chainSup c hc Ne hfin hU :=
   ⟨fun i hi => mem_biUnion hv hi, fun i hi => (find_apply_of_mem hc _ hv hi).symm⟩
 #align shrinking_lemma.partial_refinement.le_chain_Sup ShrinkingLemma.PartialRefinement.le_chainSup
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (j «expr ≠ » i) -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (j «expr ≠ » i) -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (j «expr ≠ » i) -/
+#print ShrinkingLemma.PartialRefinement.exists_gt /-
 /-- If `s` is a closed set, `v` is a partial refinement, and `i` is an index such that
 `i ∉ v.carrier`, then there exists a partial refinement that is strictly greater than `v`. -/
 theorem exists_gt (v : PartialRefinement u s) (hs : IsClosed s) (i : ι) (hi : i ∉ v.carrier) :
@@ -220,6 +249,7 @@ theorem exists_gt (v : PartialRefinement u s) (hs : IsClosed s) (i : ι) (hi : i
     exact (update_noteq (ne_of_mem_of_not_mem hj hi) _ _).symm
   · exact fun hle => hi (hle.1 <| mem_insert _ _)
 #align shrinking_lemma.partial_refinement.exists_gt ShrinkingLemma.PartialRefinement.exists_gt
+-/
 
 end PartialRefinement
 

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

@@ -45,7 +45,7 @@ variable {ι X : Type _} [TopologicalSpace X] [NormalSpace X]
 
 namespace ShrinkingLemma
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » carrier) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (i «expr ∉ » carrier) -/
 -- the trivial refinement needs `u` to be a covering
 /-- Auxiliary definition for the proof of `shrinking_lemma`. A partial refinement of a covering
 `⋃ i, u i` of a set `s` is a map `v : ι → set X` and a set `carrier : set ι` such that
@@ -156,7 +156,7 @@ theorem find_apply_of_mem {c : Set (PartialRefinement u s)} (hc : IsChain (· 
     hi
 #align shrinking_lemma.partial_refinement.find_apply_of_mem ShrinkingLemma.PartialRefinement.find_apply_of_mem
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » chain_Sup_carrier c) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (i «expr ∉ » chain_Sup_carrier c) -/
 /-- Least upper bound of a nonempty chain of partial refinements. -/
 def chainSup (c : Set (PartialRefinement u s)) (hc : IsChain (· ≤ ·) c) (ne : c.Nonempty)
     (hfin : ∀ x ∈ s, {i | x ∈ u i}.Finite) (hU : s ⊆ ⋃ i, u i) : PartialRefinement u s :=
@@ -187,9 +187,9 @@ theorem le_chainSup {c : Set (PartialRefinement u s)} (hc : IsChain (· ≤ ·)
   ⟨fun i hi => mem_biUnion hv hi, fun i hi => (find_apply_of_mem hc _ hv hi).symm⟩
 #align shrinking_lemma.partial_refinement.le_chain_Sup ShrinkingLemma.PartialRefinement.le_chainSup
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (j «expr ≠ » i) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (j «expr ≠ » i) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (j «expr ≠ » i) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (j «expr ≠ » i) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (j «expr ≠ » i) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (j «expr ≠ » i) -/
 /-- If `s` is a closed set, `v` is a partial refinement, and `i` is an index such that
 `i ∉ v.carrier`, then there exists a partial refinement that is strictly greater than `v`. -/
 theorem exists_gt (v : PartialRefinement u s) (hs : IsClosed s) (i : ι) (hi : i ∉ v.carrier) :

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

@@ -159,7 +159,7 @@ theorem find_apply_of_mem {c : Set (PartialRefinement u s)} (hc : IsChain (· 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » chain_Sup_carrier c) -/
 /-- Least upper bound of a nonempty chain of partial refinements. -/
 def chainSup (c : Set (PartialRefinement u s)) (hc : IsChain (· ≤ ·) c) (ne : c.Nonempty)
-    (hfin : ∀ x ∈ s, { i | x ∈ u i }.Finite) (hU : s ⊆ ⋃ i, u i) : PartialRefinement u s :=
+    (hfin : ∀ x ∈ s, {i | x ∈ u i}.Finite) (hU : s ⊆ ⋃ i, u i) : PartialRefinement u s :=
   by
   refine'
     ⟨fun i => find c Ne i i, chain_Sup_carrier c, fun i => (find _ _ _).IsOpen i, fun x hxs =>
@@ -182,7 +182,7 @@ def chainSup (c : Set (PartialRefinement u s)) (hc : IsChain (· ≤ ·) c) (ne
 
 /-- `chain_Sup hu c hc ne hfin hU` is an upper bound of the chain `c`. -/
 theorem le_chainSup {c : Set (PartialRefinement u s)} (hc : IsChain (· ≤ ·) c) (ne : c.Nonempty)
-    (hfin : ∀ x ∈ s, { i | x ∈ u i }.Finite) (hU : s ⊆ ⋃ i, u i) {v} (hv : v ∈ c) :
+    (hfin : ∀ x ∈ s, {i | x ∈ u i}.Finite) (hU : s ⊆ ⋃ i, u i) {v} (hv : v ∈ c) :
     v ≤ chainSup c hc Ne hfin hU :=
   ⟨fun i hi => mem_biUnion hv hi, fun i hi => (find_apply_of_mem hc _ hv hi).symm⟩
 #align shrinking_lemma.partial_refinement.le_chain_Sup ShrinkingLemma.PartialRefinement.le_chainSup
@@ -209,7 +209,7 @@ theorem exists_gt (v : PartialRefinement u s) (hs : IsClosed s) (i : ι) (hi : i
   · refine' fun x hx => mem_Union.2 _
     rcases em (∃ (j : _) (_ : j ≠ i), x ∈ v j) with (⟨j, hji, hj⟩ | h)
     · use j; rwa [update_noteq hji]
-    · push_neg  at h ; use i; rw [update_same]; exact hvi ⟨hx, mem_bInter h⟩
+    · push_neg at h ; use i; rw [update_same]; exact hvi ⟨hx, mem_bInter h⟩
   · rintro j (rfl | hj)
     · rwa [update_same, ← v.apply_eq hi]
     · rw [update_noteq (ne_of_mem_of_not_mem hj hi)]; exact v.closure_subset hj
@@ -234,23 +234,22 @@ variable {u : ι → Set X} {s : Set X}
 to a new open cover so that the closure of each new open set is contained in the corresponding
 original open set. -/
 theorem exists_subset_iUnion_closure_subset (hs : IsClosed s) (uo : ∀ i, IsOpen (u i))
-    (uf : ∀ x ∈ s, { i | x ∈ u i }.Finite) (us : s ⊆ ⋃ i, u i) :
+    (uf : ∀ x ∈ s, {i | x ∈ u i}.Finite) (us : s ⊆ ⋃ i, u i) :
     ∃ v : ι → Set X, s ⊆ iUnion v ∧ (∀ i, IsOpen (v i)) ∧ ∀ i, closure (v i) ⊆ u i := by
   classical
-    haveI : Nonempty (partial_refinement u s) :=
-      ⟨⟨u, ∅, uo, us, fun _ => False.elim, fun _ _ => rfl⟩⟩
-    have :
-      ∀ c : Set (partial_refinement u s), IsChain (· ≤ ·) c → c.Nonempty → ∃ ub, ∀ v ∈ c, v ≤ ub :=
-      fun c hc ne =>
-      ⟨partial_refinement.chain_Sup c hc Ne uf us, fun v hv =>
-        partial_refinement.le_chain_Sup _ _ _ _ hv⟩
-    rcases zorn_nonempty_partialOrder this with ⟨v, hv⟩
-    suffices : ∀ i, i ∈ v.carrier
-    exact ⟨v, v.subset_Union, fun i => v.is_open _, fun i => v.closure_subset (this i)⟩
-    contrapose! hv
-    rcases hv with ⟨i, hi⟩
-    rcases v.exists_gt hs i hi with ⟨v', hlt⟩
-    exact ⟨v', hlt.le, hlt.ne'⟩
+  haveI : Nonempty (partial_refinement u s) := ⟨⟨u, ∅, uo, us, fun _ => False.elim, fun _ _ => rfl⟩⟩
+  have :
+    ∀ c : Set (partial_refinement u s), IsChain (· ≤ ·) c → c.Nonempty → ∃ ub, ∀ v ∈ c, v ≤ ub :=
+    fun c hc ne =>
+    ⟨partial_refinement.chain_Sup c hc Ne uf us, fun v hv =>
+      partial_refinement.le_chain_Sup _ _ _ _ hv⟩
+  rcases zorn_nonempty_partialOrder this with ⟨v, hv⟩
+  suffices : ∀ i, i ∈ v.carrier
+  exact ⟨v, v.subset_Union, fun i => v.is_open _, fun i => v.closure_subset (this i)⟩
+  contrapose! hv
+  rcases hv with ⟨i, hi⟩
+  rcases v.exists_gt hs i hi with ⟨v', hlt⟩
+  exact ⟨v', hlt.le, hlt.ne'⟩
 #align exists_subset_Union_closure_subset exists_subset_iUnion_closure_subset
 -/
 
@@ -259,7 +258,7 @@ theorem exists_subset_iUnion_closure_subset (hs : IsClosed s) (uo : ∀ i, IsOpe
 to a new closed cover so that each new closed set is contained in the corresponding original open
 set. See also `exists_subset_Union_closure_subset` for a stronger statement. -/
 theorem exists_subset_iUnion_closed_subset (hs : IsClosed s) (uo : ∀ i, IsOpen (u i))
-    (uf : ∀ x ∈ s, { i | x ∈ u i }.Finite) (us : s ⊆ ⋃ i, u i) :
+    (uf : ∀ x ∈ s, {i | x ∈ u i}.Finite) (us : s ⊆ ⋃ i, u i) :
     ∃ v : ι → Set X, s ⊆ iUnion v ∧ (∀ i, IsClosed (v i)) ∧ ∀ i, v i ⊆ u i :=
   let ⟨v, hsv, hvo, hv⟩ := exists_subset_iUnion_closure_subset hs uo uf us
   ⟨fun i => closure (v i), Subset.trans hsv (iUnion_mono fun i => subset_closure), fun i =>
@@ -271,7 +270,7 @@ theorem exists_subset_iUnion_closed_subset (hs : IsClosed s) (uo : ∀ i, IsOpen
 /-- Shrinking lemma. A point-finite open cover of a closed subset of a normal space can be "shrunk"
 to a new open cover so that the closure of each new open set is contained in the corresponding
 original open set. -/
-theorem exists_iUnion_eq_closure_subset (uo : ∀ i, IsOpen (u i)) (uf : ∀ x, { i | x ∈ u i }.Finite)
+theorem exists_iUnion_eq_closure_subset (uo : ∀ i, IsOpen (u i)) (uf : ∀ x, {i | x ∈ u i}.Finite)
     (uU : (⋃ i, u i) = univ) :
     ∃ v : ι → Set X, iUnion v = univ ∧ (∀ i, IsOpen (v i)) ∧ ∀ i, closure (v i) ⊆ u i :=
   let ⟨v, vU, hv⟩ := exists_subset_iUnion_closure_subset isClosed_univ uo (fun x _ => uf x) uU.ge
@@ -283,7 +282,7 @@ theorem exists_iUnion_eq_closure_subset (uo : ∀ i, IsOpen (u i)) (uf : ∀ x,
 /-- Shrinking lemma. A point-finite open cover of a closed subset of a normal space can be "shrunk"
 to a new closed cover so that each of the new closed sets is contained in the corresponding
 original open set. See also `exists_Union_eq_closure_subset` for a stronger statement. -/
-theorem exists_iUnion_eq_closed_subset (uo : ∀ i, IsOpen (u i)) (uf : ∀ x, { i | x ∈ u i }.Finite)
+theorem exists_iUnion_eq_closed_subset (uo : ∀ i, IsOpen (u i)) (uf : ∀ x, {i | x ∈ u i}.Finite)
     (uU : (⋃ i, u i) = univ) :
     ∃ v : ι → Set X, iUnion v = univ ∧ (∀ i, IsClosed (v i)) ∧ ∀ i, v i ⊆ u i :=
   let ⟨v, vU, hv⟩ := exists_subset_iUnion_closed_subset isClosed_univ uo (fun x _ => uf x) uU.ge

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

@@ -118,7 +118,7 @@ theorem apply_eq_of_chain {c : Set (PartialRefinement u s)} (hc : IsChain (· 
     (h₁ : v₁ ∈ c) (h₂ : v₂ ∈ c) {i} (hi₁ : i ∈ v₁.carrier) (hi₂ : i ∈ v₂.carrier) : v₁ i = v₂ i :=
   by
   wlog hle : v₁ ≤ v₂
-  · cases hc.total h₁ h₂ <;> [skip;symm] <;> apply_assumption <;> assumption'
+  · cases hc.total h₁ h₂ <;> [skip; symm] <;> apply_assumption <;> assumption'
   exact hle.2 _ hi₁
 #align shrinking_lemma.partial_refinement.apply_eq_of_chain ShrinkingLemma.PartialRefinement.apply_eq_of_chain
 
@@ -135,7 +135,7 @@ def find (c : Set (PartialRefinement u s)) (ne : c.Nonempty) (i : ι) : PartialR
 #align shrinking_lemma.partial_refinement.find ShrinkingLemma.PartialRefinement.find
 
 theorem find_mem {c : Set (PartialRefinement u s)} (i : ι) (ne : c.Nonempty) : find c Ne i ∈ c := by
-  rw [find]; split_ifs; exacts[h.some_spec.fst, ne.some_spec]
+  rw [find]; split_ifs; exacts [h.some_spec.fst, ne.some_spec]
 #align shrinking_lemma.partial_refinement.find_mem ShrinkingLemma.PartialRefinement.find_mem
 
 theorem mem_find_carrier_iff {c : Set (PartialRefinement u s)} {i : ι} (ne : c.Nonempty) :
@@ -165,10 +165,10 @@ def chainSup (c : Set (PartialRefinement u s)) (hc : IsChain (· ≤ ·) c) (ne
     ⟨fun i => find c Ne i i, chain_Sup_carrier c, fun i => (find _ _ _).IsOpen i, fun x hxs =>
       mem_Union.2 _, fun i hi => (find c Ne i).closure_subset ((mem_find_carrier_iff _).2 hi),
       fun i hi => (find c Ne i).apply_eq (mt (mem_find_carrier_iff _).1 hi)⟩
-  rcases em (∃ (i : _)(_ : i ∉ chain_Sup_carrier c), x ∈ u i) with (⟨i, hi, hxi⟩ | hx)
+  rcases em (∃ (i : _) (_ : i ∉ chain_Sup_carrier c), x ∈ u i) with (⟨i, hi, hxi⟩ | hx)
   · use i
     rwa [(find c Ne i).apply_eq (mt (mem_find_carrier_iff _).1 hi)]
-  · simp_rw [not_exists, not_imp_not, chain_Sup_carrier, mem_Union₂] at hx
+  · simp_rw [not_exists, not_imp_not, chain_Sup_carrier, mem_Union₂] at hx 
     haveI : Nonempty (partial_refinement u s) := ⟨ne.some⟩
     choose! v hvc hiv using hx
     rcases(hfin x hxs).exists_maximal_wrt v _ (mem_Union.1 (hU hxs)) with
@@ -207,14 +207,14 @@ theorem exists_gt (v : PartialRefinement u s) (hs : IsClosed s) (i : ι) (hi : i
   refine' ⟨⟨update v i vi, insert i v.carrier, _, _, _, _⟩, _, _⟩
   · intro j; by_cases h : j = i <;> simp [h, ovi, v.is_open]
   · refine' fun x hx => mem_Union.2 _
-    rcases em (∃ (j : _)(_ : j ≠ i), x ∈ v j) with (⟨j, hji, hj⟩ | h)
+    rcases em (∃ (j : _) (_ : j ≠ i), x ∈ v j) with (⟨j, hji, hj⟩ | h)
     · use j; rwa [update_noteq hji]
-    · push_neg  at h; use i; rw [update_same]; exact hvi ⟨hx, mem_bInter h⟩
+    · push_neg  at h ; use i; rw [update_same]; exact hvi ⟨hx, mem_bInter h⟩
   · rintro j (rfl | hj)
     · rwa [update_same, ← v.apply_eq hi]
     · rw [update_noteq (ne_of_mem_of_not_mem hj hi)]; exact v.closure_subset hj
   · intro j hj
-    rw [mem_insert_iff, not_or] at hj
+    rw [mem_insert_iff, not_or] at hj 
     rw [update_noteq hj.1, v.apply_eq hj.2]
   · refine' ⟨subset_insert _ _, fun j hj => _⟩
     exact (update_noteq (ne_of_mem_of_not_mem hj hi) _ _).symm

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

@@ -37,7 +37,7 @@ normal space, shrinking lemma
 
 open Set Function
 
-open Classical
+open scoped Classical
 
 noncomputable section
 

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

@@ -45,12 +45,6 @@ variable {ι X : Type _} [TopologicalSpace X] [NormalSpace X]
 
 namespace ShrinkingLemma
 
-/- warning: shrinking_lemma.partial_refinement -> ShrinkingLemma.PartialRefinement is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : NormalSpace.{u2} X _inst_1], (ι -> (Set.{u2} X)) -> (Set.{u2} X) -> Sort.{max (succ u1) (succ u2)}
-but is expected to have type
-  forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X], (ι -> (Set.{u2} X)) -> (Set.{u2} X) -> Sort.{max (succ u1) (succ u2)}
-Case conversion may be inaccurate. Consider using '#align shrinking_lemma.partial_refinement ShrinkingLemma.PartialRefinementₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » carrier) -/
 -- the trivial refinement needs `u` to be a covering
 /-- Auxiliary definition for the proof of `shrinking_lemma`. A partial refinement of a covering
@@ -81,53 +75,23 @@ variable {u : ι → Set X} {s : Set X}
 instance : CoeFun (PartialRefinement u s) fun _ => ι → Set X :=
   ⟨toFun⟩
 
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-Case conversion may be inaccurate. Consider using '#align shrinking_lemma.partial_refinement.subset_Union ShrinkingLemma.PartialRefinement.subset_iUnionₓ'. -/
 theorem subset_iUnion (v : PartialRefinement u s) : s ⊆ ⋃ i, v i :=
   v.subset_Union'
 #align shrinking_lemma.partial_refinement.subset_Union ShrinkingLemma.PartialRefinement.subset_iUnion
 
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-Case conversion may be inaccurate. Consider using '#align shrinking_lemma.partial_refinement.closure_subset ShrinkingLemma.PartialRefinement.closure_subsetₓ'. -/
 theorem closure_subset (v : PartialRefinement u s) {i : ι} (hi : i ∈ v.carrier) :
     closure (v i) ⊆ u i :=
   v.closure_subset' i hi
 #align shrinking_lemma.partial_refinement.closure_subset ShrinkingLemma.PartialRefinement.closure_subset
 
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 theorem apply_eq (v : PartialRefinement u s) {i : ι} (hi : i ∉ v.carrier) : v i = u i :=
   v.apply_eq' i hi
 #align shrinking_lemma.partial_refinement.apply_eq ShrinkingLemma.PartialRefinement.apply_eq
 
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 protected theorem isOpen (v : PartialRefinement u s) (i : ι) : IsOpen (v i) :=
   v.is_open' i
 #align shrinking_lemma.partial_refinement.is_open ShrinkingLemma.PartialRefinement.isOpen
 
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 protected theorem subset (v : PartialRefinement u s) (i : ι) : v i ⊆ u i :=
   if h : i ∈ v.carrier then Subset.trans subset_closure (v.closure_subset h) else (v.apply_eq h).le
 #align shrinking_lemma.partial_refinement.subset ShrinkingLemma.PartialRefinement.subset
@@ -148,12 +112,6 @@ instance : PartialOrder (PartialRefinement u s)
         else (v₁.apply_eq hx).trans (Eq.symm <| v₂.apply_eq <| hc ▸ hx))
       hc
 
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 /-- If two partial refinements `v₁`, `v₂` belong to a chain (hence, they are comparable)
 and `i` belongs to the carriers of both partial refinements, then `v₁ i = v₂ i`. -/
 theorem apply_eq_of_chain {c : Set (PartialRefinement u s)} (hc : IsChain (· ≤ ·) c) {v₁ v₂}
@@ -164,46 +122,22 @@ theorem apply_eq_of_chain {c : Set (PartialRefinement u s)} (hc : IsChain (· 
   exact hle.2 _ hi₁
 #align shrinking_lemma.partial_refinement.apply_eq_of_chain ShrinkingLemma.PartialRefinement.apply_eq_of_chain
 
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 /-- The carrier of the least upper bound of a non-empty chain of partial refinements
 is the union of their carriers. -/
 def chainSupCarrier (c : Set (PartialRefinement u s)) : Set ι :=
   ⋃ v ∈ c, carrier v
 #align shrinking_lemma.partial_refinement.chain_Sup_carrier ShrinkingLemma.PartialRefinement.chainSupCarrier
 
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 /-- Choice of an element of a nonempty chain of partial refinements. If `i` belongs to one of
 `carrier v`, `v ∈ c`, then `find c ne i` is one of these partial refinements. -/
 def find (c : Set (PartialRefinement u s)) (ne : c.Nonempty) (i : ι) : PartialRefinement u s :=
   if hi : ∃ v ∈ c, i ∈ carrier v then hi.some else Ne.some
 #align shrinking_lemma.partial_refinement.find ShrinkingLemma.PartialRefinement.find
 
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 theorem find_mem {c : Set (PartialRefinement u s)} (i : ι) (ne : c.Nonempty) : find c Ne i ∈ c := by
   rw [find]; split_ifs; exacts[h.some_spec.fst, ne.some_spec]
 #align shrinking_lemma.partial_refinement.find_mem ShrinkingLemma.PartialRefinement.find_mem
 
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 theorem mem_find_carrier_iff {c : Set (PartialRefinement u s)} {i : ι} (ne : c.Nonempty) :
     i ∈ (find c Ne i).carrier ↔ i ∈ chainSupCarrier c :=
   by
@@ -216,24 +150,12 @@ theorem mem_find_carrier_iff {c : Set (PartialRefinement u s)} {i : ι} (ne : c.
     simp only [this]
 #align shrinking_lemma.partial_refinement.mem_find_carrier_iff ShrinkingLemma.PartialRefinement.mem_find_carrier_iff
 
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-Case conversion may be inaccurate. Consider using '#align shrinking_lemma.partial_refinement.find_apply_of_mem ShrinkingLemma.PartialRefinement.find_apply_of_memₓ'. -/
 theorem find_apply_of_mem {c : Set (PartialRefinement u s)} (hc : IsChain (· ≤ ·) c)
     (ne : c.Nonempty) {i v} (hv : v ∈ c) (hi : i ∈ carrier v) : find c Ne i i = v i :=
   apply_eq_of_chain hc (find_mem _ _) hv ((mem_find_carrier_iff _).2 <| mem_iUnion₂.2 ⟨v, hv, hi⟩)
     hi
 #align shrinking_lemma.partial_refinement.find_apply_of_mem ShrinkingLemma.PartialRefinement.find_apply_of_mem
 
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-Case conversion may be inaccurate. Consider using '#align shrinking_lemma.partial_refinement.chain_Sup ShrinkingLemma.PartialRefinement.chainSupₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » chain_Sup_carrier c) -/
 /-- Least upper bound of a nonempty chain of partial refinements. -/
 def chainSup (c : Set (PartialRefinement u s)) (hc : IsChain (· ≤ ·) c) (ne : c.Nonempty)
@@ -258,12 +180,6 @@ def chainSup (c : Set (PartialRefinement u s)) (hc : IsChain (· ≤ ·) c) (ne
     rwa [find_apply_of_mem hc Ne (hvc _ hxi) (this.1 <| hiv _ hj')]
 #align shrinking_lemma.partial_refinement.chain_Sup ShrinkingLemma.PartialRefinement.chainSup
 
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-Case conversion may be inaccurate. Consider using '#align shrinking_lemma.partial_refinement.le_chain_Sup ShrinkingLemma.PartialRefinement.le_chainSupₓ'. -/
 /-- `chain_Sup hu c hc ne hfin hU` is an upper bound of the chain `c`. -/
 theorem le_chainSup {c : Set (PartialRefinement u s)} (hc : IsChain (· ≤ ·) c) (ne : c.Nonempty)
     (hfin : ∀ x ∈ s, { i | x ∈ u i }.Finite) (hU : s ⊆ ⋃ i, u i) {v} (hv : v ∈ c) :
@@ -271,12 +187,6 @@ theorem le_chainSup {c : Set (PartialRefinement u s)} (hc : IsChain (· ≤ ·)
   ⟨fun i hi => mem_biUnion hv hi, fun i hi => (find_apply_of_mem hc _ hv hi).symm⟩
 #align shrinking_lemma.partial_refinement.le_chain_Sup ShrinkingLemma.PartialRefinement.le_chainSup
 
-/- warning: shrinking_lemma.partial_refinement.exists_gt -> ShrinkingLemma.PartialRefinement.exists_gt is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align shrinking_lemma.partial_refinement.exists_gt ShrinkingLemma.PartialRefinement.exists_gtₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (j «expr ≠ » i) -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (j «expr ≠ » i) -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (j «expr ≠ » i) -/

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

@@ -194,11 +194,8 @@ lean 3 declaration is
 but is expected to have type
   forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] {_inst_2 : ι -> (Set.{u2} X)} {u : Set.{u2} X} {s : Set.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)} (c : ι) (i : Set.Nonempty.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) s), Membership.mem.{max u2 u1, max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Set.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)) (Set.instMembershipSet.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)) (ShrinkingLemma.PartialRefinement.find.{u1, u2} ι X _inst_1 _inst_2 u s i c) s
 Case conversion may be inaccurate. Consider using '#align shrinking_lemma.partial_refinement.find_mem ShrinkingLemma.PartialRefinement.find_memₓ'. -/
-theorem find_mem {c : Set (PartialRefinement u s)} (i : ι) (ne : c.Nonempty) : find c Ne i ∈ c :=
-  by
-  rw [find]
-  split_ifs
-  exacts[h.some_spec.fst, ne.some_spec]
+theorem find_mem {c : Set (PartialRefinement u s)} (i : ι) (ne : c.Nonempty) : find c Ne i ∈ c := by
+  rw [find]; split_ifs; exacts[h.some_spec.fst, ne.some_spec]
 #align shrinking_lemma.partial_refinement.find_mem ShrinkingLemma.PartialRefinement.find_mem
 
 /- warning: shrinking_lemma.partial_refinement.mem_find_carrier_iff -> ShrinkingLemma.PartialRefinement.mem_find_carrier_iff is a dubious translation:
@@ -298,20 +295,14 @@ theorem exists_gt (v : PartialRefinement u s) (hs : IsClosed s) (i : ι) (hi : i
     IsClosed.inter hs (isClosed_biInter fun _ _ => isClosed_compl_iff.2 <| v.is_open _)
   rcases normal_exists_closure_subset C (v.is_open i) I with ⟨vi, ovi, hvi, cvi⟩
   refine' ⟨⟨update v i vi, insert i v.carrier, _, _, _, _⟩, _, _⟩
-  · intro j
-    by_cases h : j = i <;> simp [h, ovi, v.is_open]
+  · intro j; by_cases h : j = i <;> simp [h, ovi, v.is_open]
   · refine' fun x hx => mem_Union.2 _
     rcases em (∃ (j : _)(_ : j ≠ i), x ∈ v j) with (⟨j, hji, hj⟩ | h)
-    · use j
-      rwa [update_noteq hji]
-    · push_neg  at h
-      use i
-      rw [update_same]
-      exact hvi ⟨hx, mem_bInter h⟩
+    · use j; rwa [update_noteq hji]
+    · push_neg  at h; use i; rw [update_same]; exact hvi ⟨hx, mem_bInter h⟩
   · rintro j (rfl | hj)
     · rwa [update_same, ← v.apply_eq hi]
-    · rw [update_noteq (ne_of_mem_of_not_mem hj hi)]
-      exact v.closure_subset hj
+    · rw [update_noteq (ne_of_mem_of_not_mem hj hi)]; exact v.closure_subset hj
   · intro j hj
     rw [mem_insert_iff, not_or] at hj
     rw [update_noteq hj.1, v.apply_eq hj.2]

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

@@ -160,7 +160,7 @@ theorem apply_eq_of_chain {c : Set (PartialRefinement u s)} (hc : IsChain (· 
     (h₁ : v₁ ∈ c) (h₂ : v₂ ∈ c) {i} (hi₁ : i ∈ v₁.carrier) (hi₂ : i ∈ v₂.carrier) : v₁ i = v₂ i :=
   by
   wlog hle : v₁ ≤ v₂
-  · cases hc.total h₁ h₂ <;> [skip, symm] <;> apply_assumption <;> assumption'
+  · cases hc.total h₁ h₂ <;> [skip;symm] <;> apply_assumption <;> assumption'
   exact hle.2 _ hi₁
 #align shrinking_lemma.partial_refinement.apply_eq_of_chain ShrinkingLemma.PartialRefinement.apply_eq_of_chain
 

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

@@ -150,7 +150,7 @@ instance : PartialOrder (PartialRefinement u s)
 
 /- warning: shrinking_lemma.partial_refinement.apply_eq_of_chain -> ShrinkingLemma.PartialRefinement.apply_eq_of_chain is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : NormalSpace.{u2} X _inst_1] {u : ι -> (Set.{u2} X)} {s : Set.{u2} X} {c : Set.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)}, (IsChain.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (ShrinkingLemma.PartialRefinement.partialOrder.{u1, u2} ι X _inst_1 _inst_2 u s)))) c) -> (forall {v₁ : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s} {v₂ : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s}, (Membership.Mem.{max u1 u2, max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (Set.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)) (Set.hasMem.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)) v₁ c) -> (Membership.Mem.{max u1 u2, max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (Set.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)) (Set.hasMem.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)) v₂ c) -> (forall {i : ι}, (Membership.Mem.{u1, u1} ι (Set.{u1} ι) (Set.hasMem.{u1} ι) i (ShrinkingLemma.PartialRefinement.carrier.{u1, u2} ι X _inst_1 _inst_2 u s v₁)) -> (Membership.Mem.{u1, u1} ι (Set.{u1} ι) (Set.hasMem.{u1} ι) i (ShrinkingLemma.PartialRefinement.carrier.{u1, u2} ι X _inst_1 _inst_2 u s v₂)) -> (Eq.{succ u2} (Set.{u2} X) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (fun (_x : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) => ι -> (Set.{u2} X)) (ShrinkingLemma.PartialRefinement.hasCoeToFun.{u1, u2} ι X _inst_1 _inst_2 u s) v₁ i) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (fun (_x : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) => ι -> (Set.{u2} X)) (ShrinkingLemma.PartialRefinement.hasCoeToFun.{u1, u2} ι X _inst_1 _inst_2 u s) v₂ i))))
+  forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : NormalSpace.{u2} X _inst_1] {u : ι -> (Set.{u2} X)} {s : Set.{u2} X} {c : Set.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)}, (IsChain.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (Preorder.toHasLe.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (ShrinkingLemma.PartialRefinement.partialOrder.{u1, u2} ι X _inst_1 _inst_2 u s)))) c) -> (forall {v₁ : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s} {v₂ : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s}, (Membership.Mem.{max u1 u2, max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (Set.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)) (Set.hasMem.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)) v₁ c) -> (Membership.Mem.{max u1 u2, max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (Set.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)) (Set.hasMem.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)) v₂ c) -> (forall {i : ι}, (Membership.Mem.{u1, u1} ι (Set.{u1} ι) (Set.hasMem.{u1} ι) i (ShrinkingLemma.PartialRefinement.carrier.{u1, u2} ι X _inst_1 _inst_2 u s v₁)) -> (Membership.Mem.{u1, u1} ι (Set.{u1} ι) (Set.hasMem.{u1} ι) i (ShrinkingLemma.PartialRefinement.carrier.{u1, u2} ι X _inst_1 _inst_2 u s v₂)) -> (Eq.{succ u2} (Set.{u2} X) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (fun (_x : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) => ι -> (Set.{u2} X)) (ShrinkingLemma.PartialRefinement.hasCoeToFun.{u1, u2} ι X _inst_1 _inst_2 u s) v₁ i) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (fun (_x : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) => ι -> (Set.{u2} X)) (ShrinkingLemma.PartialRefinement.hasCoeToFun.{u1, u2} ι X _inst_1 _inst_2 u s) v₂ i))))
 but is expected to have type
   forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] {_inst_2 : ι -> (Set.{u2} X)} {u : Set.{u2} X} {s : Set.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)}, (IsChain.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (fun (x._@.Mathlib.Topology.ShrinkingLemma._hyg.471 : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (x._@.Mathlib.Topology.ShrinkingLemma._hyg.473 : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) => LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (ShrinkingLemma.PartialRefinement.instPartialOrderPartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u))) x._@.Mathlib.Topology.ShrinkingLemma._hyg.471 x._@.Mathlib.Topology.ShrinkingLemma._hyg.473) s) -> (forall {hc : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u} {v₁ : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u}, (Membership.mem.{max u1 u2, max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Set.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)) (Set.instMembershipSet.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)) hc s) -> (Membership.mem.{max u1 u2, max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Set.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)) (Set.instMembershipSet.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)) v₁ s) -> (forall {h₂ : ι}, (Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) h₂ (ShrinkingLemma.PartialRefinement.carrier.{u1, u2} ι X _inst_1 _inst_2 u hc)) -> (Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) h₂ (ShrinkingLemma.PartialRefinement.carrier.{u1, u2} ι X _inst_1 _inst_2 u v₁)) -> (Eq.{succ u2} (Set.{u2} X) (ShrinkingLemma.PartialRefinement.toFun.{u1, u2} ι X _inst_1 _inst_2 u hc h₂) (ShrinkingLemma.PartialRefinement.toFun.{u1, u2} ι X _inst_1 _inst_2 u v₁ h₂))))
 Case conversion may be inaccurate. Consider using '#align shrinking_lemma.partial_refinement.apply_eq_of_chain ShrinkingLemma.PartialRefinement.apply_eq_of_chainₓ'. -/
@@ -221,7 +221,7 @@ theorem mem_find_carrier_iff {c : Set (PartialRefinement u s)} {i : ι} (ne : c.
 
 /- warning: shrinking_lemma.partial_refinement.find_apply_of_mem -> ShrinkingLemma.PartialRefinement.find_apply_of_mem is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : NormalSpace.{u2} X _inst_1] {u : ι -> (Set.{u2} X)} {s : Set.{u2} X} {c : Set.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)}, (IsChain.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (ShrinkingLemma.PartialRefinement.partialOrder.{u1, u2} ι X _inst_1 _inst_2 u s)))) c) -> (forall (ne : Set.Nonempty.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) c) {i : ι} {v : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s}, (Membership.Mem.{max u1 u2, max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (Set.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)) (Set.hasMem.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)) v c) -> (Membership.Mem.{u1, u1} ι (Set.{u1} ι) (Set.hasMem.{u1} ι) i (ShrinkingLemma.PartialRefinement.carrier.{u1, u2} ι X _inst_1 _inst_2 u s v)) -> (Eq.{succ u2} (Set.{u2} X) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (fun (_x : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) => ι -> (Set.{u2} X)) (ShrinkingLemma.PartialRefinement.hasCoeToFun.{u1, u2} ι X _inst_1 _inst_2 u s) (ShrinkingLemma.PartialRefinement.find.{u1, u2} ι X _inst_1 _inst_2 u s c ne i) i) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (fun (_x : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) => ι -> (Set.{u2} X)) (ShrinkingLemma.PartialRefinement.hasCoeToFun.{u1, u2} ι X _inst_1 _inst_2 u s) v i)))
+  forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : NormalSpace.{u2} X _inst_1] {u : ι -> (Set.{u2} X)} {s : Set.{u2} X} {c : Set.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)}, (IsChain.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (Preorder.toHasLe.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (ShrinkingLemma.PartialRefinement.partialOrder.{u1, u2} ι X _inst_1 _inst_2 u s)))) c) -> (forall (ne : Set.Nonempty.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) c) {i : ι} {v : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s}, (Membership.Mem.{max u1 u2, max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (Set.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)) (Set.hasMem.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)) v c) -> (Membership.Mem.{u1, u1} ι (Set.{u1} ι) (Set.hasMem.{u1} ι) i (ShrinkingLemma.PartialRefinement.carrier.{u1, u2} ι X _inst_1 _inst_2 u s v)) -> (Eq.{succ u2} (Set.{u2} X) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (fun (_x : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) => ι -> (Set.{u2} X)) (ShrinkingLemma.PartialRefinement.hasCoeToFun.{u1, u2} ι X _inst_1 _inst_2 u s) (ShrinkingLemma.PartialRefinement.find.{u1, u2} ι X _inst_1 _inst_2 u s c ne i) i) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (fun (_x : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) => ι -> (Set.{u2} X)) (ShrinkingLemma.PartialRefinement.hasCoeToFun.{u1, u2} ι X _inst_1 _inst_2 u s) v i)))
 but is expected to have type
   forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] {_inst_2 : ι -> (Set.{u2} X)} {u : Set.{u2} X} {s : Set.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)}, (IsChain.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (fun (x._@.Mathlib.Topology.ShrinkingLemma._hyg.895 : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (x._@.Mathlib.Topology.ShrinkingLemma._hyg.897 : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) => LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (ShrinkingLemma.PartialRefinement.instPartialOrderPartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u))) x._@.Mathlib.Topology.ShrinkingLemma._hyg.895 x._@.Mathlib.Topology.ShrinkingLemma._hyg.897) s) -> (forall (hc : Set.Nonempty.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) s) {ne : ι} {i : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u}, (Membership.mem.{max u1 u2, max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Set.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)) (Set.instMembershipSet.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)) i s) -> (Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) ne (ShrinkingLemma.PartialRefinement.carrier.{u1, u2} ι X _inst_1 _inst_2 u i)) -> (Eq.{succ u2} (Set.{u2} X) (ShrinkingLemma.PartialRefinement.toFun.{u1, u2} ι X _inst_1 _inst_2 u (ShrinkingLemma.PartialRefinement.find.{u1, u2} ι X _inst_1 _inst_2 u s hc ne) ne) (ShrinkingLemma.PartialRefinement.toFun.{u1, u2} ι X _inst_1 _inst_2 u i ne)))
 Case conversion may be inaccurate. Consider using '#align shrinking_lemma.partial_refinement.find_apply_of_mem ShrinkingLemma.PartialRefinement.find_apply_of_memₓ'. -/
@@ -233,7 +233,7 @@ theorem find_apply_of_mem {c : Set (PartialRefinement u s)} (hc : IsChain (· 
 
 /- warning: shrinking_lemma.partial_refinement.chain_Sup -> ShrinkingLemma.PartialRefinement.chainSup is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : NormalSpace.{u2} X _inst_1] {u : ι -> (Set.{u2} X)} {s : Set.{u2} X} (c : Set.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)), (IsChain.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (ShrinkingLemma.PartialRefinement.partialOrder.{u1, u2} ι X _inst_1 _inst_2 u s)))) c) -> (Set.Nonempty.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) c) -> (forall (x : X), (Membership.Mem.{u2, u2} X (Set.{u2} X) (Set.hasMem.{u2} X) x s) -> (Set.Finite.{u1} ι (setOf.{u1} ι (fun (i : ι) => Membership.Mem.{u2, u2} X (Set.{u2} X) (Set.hasMem.{u2} X) x (u i))))) -> (HasSubset.Subset.{u2} (Set.{u2} X) (Set.hasSubset.{u2} X) s (Set.iUnion.{u2, succ u1} X ι (fun (i : ι) => u i))) -> (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)
+  forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : NormalSpace.{u2} X _inst_1] {u : ι -> (Set.{u2} X)} {s : Set.{u2} X} (c : Set.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)), (IsChain.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (Preorder.toHasLe.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (ShrinkingLemma.PartialRefinement.partialOrder.{u1, u2} ι X _inst_1 _inst_2 u s)))) c) -> (Set.Nonempty.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) c) -> (forall (x : X), (Membership.Mem.{u2, u2} X (Set.{u2} X) (Set.hasMem.{u2} X) x s) -> (Set.Finite.{u1} ι (setOf.{u1} ι (fun (i : ι) => Membership.Mem.{u2, u2} X (Set.{u2} X) (Set.hasMem.{u2} X) x (u i))))) -> (HasSubset.Subset.{u2} (Set.{u2} X) (Set.hasSubset.{u2} X) s (Set.iUnion.{u2, succ u1} X ι (fun (i : ι) => u i))) -> (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)
 but is expected to have type
   forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] {_inst_2 : ι -> (Set.{u2} X)} {u : Set.{u2} X} (s : Set.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)), (IsChain.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (fun (x._@.Mathlib.Topology.ShrinkingLemma._hyg.986 : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (x._@.Mathlib.Topology.ShrinkingLemma._hyg.988 : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) => LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (ShrinkingLemma.PartialRefinement.instPartialOrderPartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u))) x._@.Mathlib.Topology.ShrinkingLemma._hyg.986 x._@.Mathlib.Topology.ShrinkingLemma._hyg.988) s) -> (Set.Nonempty.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) s) -> (forall (x : X), (Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) x u) -> (Set.Finite.{u1} ι (setOf.{u1} ι (fun (i : ι) => Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) x (_inst_2 i))))) -> (HasSubset.Subset.{u2} (Set.{u2} X) (Set.instHasSubsetSet.{u2} X) u (Set.iUnion.{u2, succ u1} X ι (fun (i : ι) => _inst_2 i))) -> (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)
 Case conversion may be inaccurate. Consider using '#align shrinking_lemma.partial_refinement.chain_Sup ShrinkingLemma.PartialRefinement.chainSupₓ'. -/
@@ -263,7 +263,7 @@ def chainSup (c : Set (PartialRefinement u s)) (hc : IsChain (· ≤ ·) c) (ne
 
 /- warning: shrinking_lemma.partial_refinement.le_chain_Sup -> ShrinkingLemma.PartialRefinement.le_chainSup is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : NormalSpace.{u2} X _inst_1] {u : ι -> (Set.{u2} X)} {s : Set.{u2} X} {c : Set.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)} (hc : IsChain.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (ShrinkingLemma.PartialRefinement.partialOrder.{u1, u2} ι X _inst_1 _inst_2 u s)))) c) (ne : Set.Nonempty.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) c) (hfin : forall (x : X), (Membership.Mem.{u2, u2} X (Set.{u2} X) (Set.hasMem.{u2} X) x s) -> (Set.Finite.{u1} ι (setOf.{u1} ι (fun (i : ι) => Membership.Mem.{u2, u2} X (Set.{u2} X) (Set.hasMem.{u2} X) x (u i))))) (hU : HasSubset.Subset.{u2} (Set.{u2} X) (Set.hasSubset.{u2} X) s (Set.iUnion.{u2, succ u1} X ι (fun (i : ι) => u i))) {v : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s}, (Membership.Mem.{max u1 u2, max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (Set.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)) (Set.hasMem.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)) v c) -> (LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (ShrinkingLemma.PartialRefinement.partialOrder.{u1, u2} ι X _inst_1 _inst_2 u s))) v (ShrinkingLemma.PartialRefinement.chainSup.{u1, u2} ι X _inst_1 _inst_2 u s c hc ne hfin hU))
+  forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : NormalSpace.{u2} X _inst_1] {u : ι -> (Set.{u2} X)} {s : Set.{u2} X} {c : Set.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)} (hc : IsChain.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (Preorder.toHasLe.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (ShrinkingLemma.PartialRefinement.partialOrder.{u1, u2} ι X _inst_1 _inst_2 u s)))) c) (ne : Set.Nonempty.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) c) (hfin : forall (x : X), (Membership.Mem.{u2, u2} X (Set.{u2} X) (Set.hasMem.{u2} X) x s) -> (Set.Finite.{u1} ι (setOf.{u1} ι (fun (i : ι) => Membership.Mem.{u2, u2} X (Set.{u2} X) (Set.hasMem.{u2} X) x (u i))))) (hU : HasSubset.Subset.{u2} (Set.{u2} X) (Set.hasSubset.{u2} X) s (Set.iUnion.{u2, succ u1} X ι (fun (i : ι) => u i))) {v : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s}, (Membership.Mem.{max u1 u2, max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (Set.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)) (Set.hasMem.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)) v c) -> (LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (Preorder.toHasLe.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (ShrinkingLemma.PartialRefinement.partialOrder.{u1, u2} ι X _inst_1 _inst_2 u s))) v (ShrinkingLemma.PartialRefinement.chainSup.{u1, u2} ι X _inst_1 _inst_2 u s c hc ne hfin hU))
 but is expected to have type
   forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] {_inst_2 : ι -> (Set.{u2} X)} {u : Set.{u2} X} {s : Set.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)} (c : IsChain.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (fun (x._@.Mathlib.Topology.ShrinkingLemma._hyg.1456 : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (x._@.Mathlib.Topology.ShrinkingLemma._hyg.1458 : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) => LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (ShrinkingLemma.PartialRefinement.instPartialOrderPartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u))) x._@.Mathlib.Topology.ShrinkingLemma._hyg.1456 x._@.Mathlib.Topology.ShrinkingLemma._hyg.1458) s) (hc : Set.Nonempty.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) s) (ne : forall (x : X), (Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) x u) -> (Set.Finite.{u1} ι (setOf.{u1} ι (fun (i : ι) => Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) x (_inst_2 i))))) (hfin : HasSubset.Subset.{u2} (Set.{u2} X) (Set.instHasSubsetSet.{u2} X) u (Set.iUnion.{u2, succ u1} X ι (fun (i : ι) => _inst_2 i))) {hU : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u}, (Membership.mem.{max u1 u2, max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Set.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)) (Set.instMembershipSet.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)) hU s) -> (LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (ShrinkingLemma.PartialRefinement.instPartialOrderPartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u))) hU (ShrinkingLemma.PartialRefinement.chainSup.{u1, u2} ι X _inst_1 _inst_2 u s c hc ne hfin))
 Case conversion may be inaccurate. Consider using '#align shrinking_lemma.partial_refinement.le_chain_Sup ShrinkingLemma.PartialRefinement.le_chainSupₓ'. -/
@@ -276,7 +276,7 @@ theorem le_chainSup {c : Set (PartialRefinement u s)} (hc : IsChain (· ≤ ·)
 
 /- warning: shrinking_lemma.partial_refinement.exists_gt -> ShrinkingLemma.PartialRefinement.exists_gt is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : NormalSpace.{u2} X _inst_1] {u : ι -> (Set.{u2} X)} {s : Set.{u2} X} (v : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s), (IsClosed.{u2} X _inst_1 s) -> (forall (i : ι), (Not (Membership.Mem.{u1, u1} ι (Set.{u1} ι) (Set.hasMem.{u1} ι) i (ShrinkingLemma.PartialRefinement.carrier.{u1, u2} ι X _inst_1 _inst_2 u s v))) -> (Exists.{max (succ u1) (succ u2)} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (fun (v' : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) => LT.lt.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (Preorder.toLT.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (ShrinkingLemma.PartialRefinement.partialOrder.{u1, u2} ι X _inst_1 _inst_2 u s))) v v')))
+  forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : NormalSpace.{u2} X _inst_1] {u : ι -> (Set.{u2} X)} {s : Set.{u2} X} (v : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s), (IsClosed.{u2} X _inst_1 s) -> (forall (i : ι), (Not (Membership.Mem.{u1, u1} ι (Set.{u1} ι) (Set.hasMem.{u1} ι) i (ShrinkingLemma.PartialRefinement.carrier.{u1, u2} ι X _inst_1 _inst_2 u s v))) -> (Exists.{max (succ u1) (succ u2)} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (fun (v' : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) => LT.lt.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (Preorder.toHasLt.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (ShrinkingLemma.PartialRefinement.partialOrder.{u1, u2} ι X _inst_1 _inst_2 u s))) v v')))
 but is expected to have type
   forall {ι : Type.{u2}} {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] {u : ι -> (Set.{u1} X)} {s : Set.{u1} X} (v : ShrinkingLemma.PartialRefinement.{u2, u1} ι X _inst_1 u s), (IsClosed.{u1} X _inst_1 s) -> (forall (i : ι), (Not (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i (ShrinkingLemma.PartialRefinement.carrier.{u2, u1} ι X _inst_1 u s v))) -> (Exists.{max (succ u2) (succ u1)} (ShrinkingLemma.PartialRefinement.{u2, u1} ι X _inst_1 u s) (fun (v' : ShrinkingLemma.PartialRefinement.{u2, u1} ι X _inst_1 u s) => LT.lt.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u2, u1} ι X _inst_1 u s) (Preorder.toLT.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u2, u1} ι X _inst_1 u s) (PartialOrder.toPreorder.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u2, u1} ι X _inst_1 u s) (ShrinkingLemma.PartialRefinement.instPartialOrderPartialRefinement.{u2, u1} ι X _inst_1 u s))) v v')))
 Case conversion may be inaccurate. Consider using '#align shrinking_lemma.partial_refinement.exists_gt ShrinkingLemma.PartialRefinement.exists_gtₓ'. -/

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

@@ -81,15 +81,15 @@ variable {u : ι → Set X} {s : Set X}
 instance : CoeFun (PartialRefinement u s) fun _ => ι → Set X :=
   ⟨toFun⟩
 
-/- warning: shrinking_lemma.partial_refinement.subset_Union -> ShrinkingLemma.PartialRefinement.subset_unionᵢ is a dubious translation:
+/- warning: shrinking_lemma.partial_refinement.subset_Union -> ShrinkingLemma.PartialRefinement.subset_iUnion is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : NormalSpace.{u2} X _inst_1] {u : ι -> (Set.{u2} X)} {s : Set.{u2} X} (v : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s), HasSubset.Subset.{u2} (Set.{u2} X) (Set.hasSubset.{u2} X) s (Set.unionᵢ.{u2, succ u1} X ι (fun (i : ι) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (fun (_x : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) => ι -> (Set.{u2} X)) (ShrinkingLemma.PartialRefinement.hasCoeToFun.{u1, u2} ι X _inst_1 _inst_2 u s) v i))
+  forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : NormalSpace.{u2} X _inst_1] {u : ι -> (Set.{u2} X)} {s : Set.{u2} X} (v : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s), HasSubset.Subset.{u2} (Set.{u2} X) (Set.hasSubset.{u2} X) s (Set.iUnion.{u2, succ u1} X ι (fun (i : ι) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (fun (_x : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) => ι -> (Set.{u2} X)) (ShrinkingLemma.PartialRefinement.hasCoeToFun.{u1, u2} ι X _inst_1 _inst_2 u s) v i))
 but is expected to have type
-  forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] {_inst_2 : ι -> (Set.{u2} X)} {u : Set.{u2} X} (s : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u), HasSubset.Subset.{u2} (Set.{u2} X) (Set.instHasSubsetSet.{u2} X) u (Set.unionᵢ.{u2, succ u1} X ι (fun (i : ι) => ShrinkingLemma.PartialRefinement.toFun.{u1, u2} ι X _inst_1 _inst_2 u s i))
-Case conversion may be inaccurate. Consider using '#align shrinking_lemma.partial_refinement.subset_Union ShrinkingLemma.PartialRefinement.subset_unionᵢₓ'. -/
-theorem subset_unionᵢ (v : PartialRefinement u s) : s ⊆ ⋃ i, v i :=
+  forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] {_inst_2 : ι -> (Set.{u2} X)} {u : Set.{u2} X} (s : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u), HasSubset.Subset.{u2} (Set.{u2} X) (Set.instHasSubsetSet.{u2} X) u (Set.iUnion.{u2, succ u1} X ι (fun (i : ι) => ShrinkingLemma.PartialRefinement.toFun.{u1, u2} ι X _inst_1 _inst_2 u s i))
+Case conversion may be inaccurate. Consider using '#align shrinking_lemma.partial_refinement.subset_Union ShrinkingLemma.PartialRefinement.subset_iUnionₓ'. -/
+theorem subset_iUnion (v : PartialRefinement u s) : s ⊆ ⋃ i, v i :=
   v.subset_Union'
-#align shrinking_lemma.partial_refinement.subset_Union ShrinkingLemma.PartialRefinement.subset_unionᵢ
+#align shrinking_lemma.partial_refinement.subset_Union ShrinkingLemma.PartialRefinement.subset_iUnion
 
 /- warning: shrinking_lemma.partial_refinement.closure_subset -> ShrinkingLemma.PartialRefinement.closure_subset is a dubious translation:
 lean 3 declaration is
@@ -227,15 +227,15 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align shrinking_lemma.partial_refinement.find_apply_of_mem ShrinkingLemma.PartialRefinement.find_apply_of_memₓ'. -/
 theorem find_apply_of_mem {c : Set (PartialRefinement u s)} (hc : IsChain (· ≤ ·) c)
     (ne : c.Nonempty) {i v} (hv : v ∈ c) (hi : i ∈ carrier v) : find c Ne i i = v i :=
-  apply_eq_of_chain hc (find_mem _ _) hv ((mem_find_carrier_iff _).2 <| mem_unionᵢ₂.2 ⟨v, hv, hi⟩)
+  apply_eq_of_chain hc (find_mem _ _) hv ((mem_find_carrier_iff _).2 <| mem_iUnion₂.2 ⟨v, hv, hi⟩)
     hi
 #align shrinking_lemma.partial_refinement.find_apply_of_mem ShrinkingLemma.PartialRefinement.find_apply_of_mem
 
 /- warning: shrinking_lemma.partial_refinement.chain_Sup -> ShrinkingLemma.PartialRefinement.chainSup is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : NormalSpace.{u2} X _inst_1] {u : ι -> (Set.{u2} X)} {s : Set.{u2} X} (c : Set.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)), (IsChain.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (ShrinkingLemma.PartialRefinement.partialOrder.{u1, u2} ι X _inst_1 _inst_2 u s)))) c) -> (Set.Nonempty.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) c) -> (forall (x : X), (Membership.Mem.{u2, u2} X (Set.{u2} X) (Set.hasMem.{u2} X) x s) -> (Set.Finite.{u1} ι (setOf.{u1} ι (fun (i : ι) => Membership.Mem.{u2, u2} X (Set.{u2} X) (Set.hasMem.{u2} X) x (u i))))) -> (HasSubset.Subset.{u2} (Set.{u2} X) (Set.hasSubset.{u2} X) s (Set.unionᵢ.{u2, succ u1} X ι (fun (i : ι) => u i))) -> (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)
+  forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : NormalSpace.{u2} X _inst_1] {u : ι -> (Set.{u2} X)} {s : Set.{u2} X} (c : Set.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)), (IsChain.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (ShrinkingLemma.PartialRefinement.partialOrder.{u1, u2} ι X _inst_1 _inst_2 u s)))) c) -> (Set.Nonempty.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) c) -> (forall (x : X), (Membership.Mem.{u2, u2} X (Set.{u2} X) (Set.hasMem.{u2} X) x s) -> (Set.Finite.{u1} ι (setOf.{u1} ι (fun (i : ι) => Membership.Mem.{u2, u2} X (Set.{u2} X) (Set.hasMem.{u2} X) x (u i))))) -> (HasSubset.Subset.{u2} (Set.{u2} X) (Set.hasSubset.{u2} X) s (Set.iUnion.{u2, succ u1} X ι (fun (i : ι) => u i))) -> (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)
 but is expected to have type
-  forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] {_inst_2 : ι -> (Set.{u2} X)} {u : Set.{u2} X} (s : Set.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)), (IsChain.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (fun (x._@.Mathlib.Topology.ShrinkingLemma._hyg.986 : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (x._@.Mathlib.Topology.ShrinkingLemma._hyg.988 : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) => LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (ShrinkingLemma.PartialRefinement.instPartialOrderPartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u))) x._@.Mathlib.Topology.ShrinkingLemma._hyg.986 x._@.Mathlib.Topology.ShrinkingLemma._hyg.988) s) -> (Set.Nonempty.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) s) -> (forall (x : X), (Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) x u) -> (Set.Finite.{u1} ι (setOf.{u1} ι (fun (i : ι) => Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) x (_inst_2 i))))) -> (HasSubset.Subset.{u2} (Set.{u2} X) (Set.instHasSubsetSet.{u2} X) u (Set.unionᵢ.{u2, succ u1} X ι (fun (i : ι) => _inst_2 i))) -> (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)
+  forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] {_inst_2 : ι -> (Set.{u2} X)} {u : Set.{u2} X} (s : Set.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)), (IsChain.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (fun (x._@.Mathlib.Topology.ShrinkingLemma._hyg.986 : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (x._@.Mathlib.Topology.ShrinkingLemma._hyg.988 : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) => LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (ShrinkingLemma.PartialRefinement.instPartialOrderPartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u))) x._@.Mathlib.Topology.ShrinkingLemma._hyg.986 x._@.Mathlib.Topology.ShrinkingLemma._hyg.988) s) -> (Set.Nonempty.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) s) -> (forall (x : X), (Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) x u) -> (Set.Finite.{u1} ι (setOf.{u1} ι (fun (i : ι) => Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) x (_inst_2 i))))) -> (HasSubset.Subset.{u2} (Set.{u2} X) (Set.instHasSubsetSet.{u2} X) u (Set.iUnion.{u2, succ u1} X ι (fun (i : ι) => _inst_2 i))) -> (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)
 Case conversion may be inaccurate. Consider using '#align shrinking_lemma.partial_refinement.chain_Sup ShrinkingLemma.PartialRefinement.chainSupₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » chain_Sup_carrier c) -/
 /-- Least upper bound of a nonempty chain of partial refinements. -/
@@ -254,7 +254,7 @@ def chainSup (c : Set (PartialRefinement u s)) (hc : IsChain (· ≤ ·) c) (ne
     choose! v hvc hiv using hx
     rcases(hfin x hxs).exists_maximal_wrt v _ (mem_Union.1 (hU hxs)) with
       ⟨i, hxi : x ∈ u i, hmax : ∀ j, x ∈ u j → v i ≤ v j → v i = v j⟩
-    rcases mem_Union.1 ((v i).subset_unionᵢ hxs) with ⟨j, hj⟩
+    rcases mem_Union.1 ((v i).subset_iUnion hxs) with ⟨j, hj⟩
     use j
     have hj' : x ∈ u j := (v i).Subset _ hj
     have : v j ≤ v i := (hc.total (hvc _ hxi) (hvc _ hj')).elim (fun h => (hmax j hj' h).ge) id
@@ -263,15 +263,15 @@ def chainSup (c : Set (PartialRefinement u s)) (hc : IsChain (· ≤ ·) c) (ne
 
 /- warning: shrinking_lemma.partial_refinement.le_chain_Sup -> ShrinkingLemma.PartialRefinement.le_chainSup is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : NormalSpace.{u2} X _inst_1] {u : ι -> (Set.{u2} X)} {s : Set.{u2} X} {c : Set.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)} (hc : IsChain.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (ShrinkingLemma.PartialRefinement.partialOrder.{u1, u2} ι X _inst_1 _inst_2 u s)))) c) (ne : Set.Nonempty.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) c) (hfin : forall (x : X), (Membership.Mem.{u2, u2} X (Set.{u2} X) (Set.hasMem.{u2} X) x s) -> (Set.Finite.{u1} ι (setOf.{u1} ι (fun (i : ι) => Membership.Mem.{u2, u2} X (Set.{u2} X) (Set.hasMem.{u2} X) x (u i))))) (hU : HasSubset.Subset.{u2} (Set.{u2} X) (Set.hasSubset.{u2} X) s (Set.unionᵢ.{u2, succ u1} X ι (fun (i : ι) => u i))) {v : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s}, (Membership.Mem.{max u1 u2, max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (Set.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)) (Set.hasMem.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)) v c) -> (LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (ShrinkingLemma.PartialRefinement.partialOrder.{u1, u2} ι X _inst_1 _inst_2 u s))) v (ShrinkingLemma.PartialRefinement.chainSup.{u1, u2} ι X _inst_1 _inst_2 u s c hc ne hfin hU))
+  forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : NormalSpace.{u2} X _inst_1] {u : ι -> (Set.{u2} X)} {s : Set.{u2} X} {c : Set.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)} (hc : IsChain.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (ShrinkingLemma.PartialRefinement.partialOrder.{u1, u2} ι X _inst_1 _inst_2 u s)))) c) (ne : Set.Nonempty.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) c) (hfin : forall (x : X), (Membership.Mem.{u2, u2} X (Set.{u2} X) (Set.hasMem.{u2} X) x s) -> (Set.Finite.{u1} ι (setOf.{u1} ι (fun (i : ι) => Membership.Mem.{u2, u2} X (Set.{u2} X) (Set.hasMem.{u2} X) x (u i))))) (hU : HasSubset.Subset.{u2} (Set.{u2} X) (Set.hasSubset.{u2} X) s (Set.iUnion.{u2, succ u1} X ι (fun (i : ι) => u i))) {v : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s}, (Membership.Mem.{max u1 u2, max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (Set.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)) (Set.hasMem.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)) v c) -> (LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (ShrinkingLemma.PartialRefinement.partialOrder.{u1, u2} ι X _inst_1 _inst_2 u s))) v (ShrinkingLemma.PartialRefinement.chainSup.{u1, u2} ι X _inst_1 _inst_2 u s c hc ne hfin hU))
 but is expected to have type
-  forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] {_inst_2 : ι -> (Set.{u2} X)} {u : Set.{u2} X} {s : Set.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)} (c : IsChain.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (fun (x._@.Mathlib.Topology.ShrinkingLemma._hyg.1456 : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (x._@.Mathlib.Topology.ShrinkingLemma._hyg.1458 : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) => LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (ShrinkingLemma.PartialRefinement.instPartialOrderPartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u))) x._@.Mathlib.Topology.ShrinkingLemma._hyg.1456 x._@.Mathlib.Topology.ShrinkingLemma._hyg.1458) s) (hc : Set.Nonempty.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) s) (ne : forall (x : X), (Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) x u) -> (Set.Finite.{u1} ι (setOf.{u1} ι (fun (i : ι) => Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) x (_inst_2 i))))) (hfin : HasSubset.Subset.{u2} (Set.{u2} X) (Set.instHasSubsetSet.{u2} X) u (Set.unionᵢ.{u2, succ u1} X ι (fun (i : ι) => _inst_2 i))) {hU : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u}, (Membership.mem.{max u1 u2, max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Set.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)) (Set.instMembershipSet.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)) hU s) -> (LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (ShrinkingLemma.PartialRefinement.instPartialOrderPartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u))) hU (ShrinkingLemma.PartialRefinement.chainSup.{u1, u2} ι X _inst_1 _inst_2 u s c hc ne hfin))
+  forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] {_inst_2 : ι -> (Set.{u2} X)} {u : Set.{u2} X} {s : Set.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)} (c : IsChain.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (fun (x._@.Mathlib.Topology.ShrinkingLemma._hyg.1456 : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (x._@.Mathlib.Topology.ShrinkingLemma._hyg.1458 : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) => LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (ShrinkingLemma.PartialRefinement.instPartialOrderPartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u))) x._@.Mathlib.Topology.ShrinkingLemma._hyg.1456 x._@.Mathlib.Topology.ShrinkingLemma._hyg.1458) s) (hc : Set.Nonempty.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) s) (ne : forall (x : X), (Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) x u) -> (Set.Finite.{u1} ι (setOf.{u1} ι (fun (i : ι) => Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) x (_inst_2 i))))) (hfin : HasSubset.Subset.{u2} (Set.{u2} X) (Set.instHasSubsetSet.{u2} X) u (Set.iUnion.{u2, succ u1} X ι (fun (i : ι) => _inst_2 i))) {hU : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u}, (Membership.mem.{max u1 u2, max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Set.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)) (Set.instMembershipSet.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)) hU s) -> (LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (ShrinkingLemma.PartialRefinement.instPartialOrderPartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u))) hU (ShrinkingLemma.PartialRefinement.chainSup.{u1, u2} ι X _inst_1 _inst_2 u s c hc ne hfin))
 Case conversion may be inaccurate. Consider using '#align shrinking_lemma.partial_refinement.le_chain_Sup ShrinkingLemma.PartialRefinement.le_chainSupₓ'. -/
 /-- `chain_Sup hu c hc ne hfin hU` is an upper bound of the chain `c`. -/
 theorem le_chainSup {c : Set (PartialRefinement u s)} (hc : IsChain (· ≤ ·) c) (ne : c.Nonempty)
     (hfin : ∀ x ∈ s, { i | x ∈ u i }.Finite) (hU : s ⊆ ⋃ i, u i) {v} (hv : v ∈ c) :
     v ≤ chainSup c hc Ne hfin hU :=
-  ⟨fun i hi => mem_bunionᵢ hv hi, fun i hi => (find_apply_of_mem hc _ hv hi).symm⟩
+  ⟨fun i hi => mem_biUnion hv hi, fun i hi => (find_apply_of_mem hc _ hv hi).symm⟩
 #align shrinking_lemma.partial_refinement.le_chain_Sup ShrinkingLemma.PartialRefinement.le_chainSup
 
 /- warning: shrinking_lemma.partial_refinement.exists_gt -> ShrinkingLemma.PartialRefinement.exists_gt is a dubious translation:
@@ -295,7 +295,7 @@ theorem exists_gt (v : PartialRefinement u s) (hs : IsClosed s) (i : ι) (hi : i
     rcases mem_Union.1 (v.subset_Union hxs) with ⟨j, hj⟩
     exact (em (j = i)).elim (fun h => h ▸ hj) fun h => (H j h hj).elim
   have C : IsClosed (s ∩ ⋂ (j) (_ : j ≠ i), v jᶜ) :=
-    IsClosed.inter hs (isClosed_binterᵢ fun _ _ => isClosed_compl_iff.2 <| v.is_open _)
+    IsClosed.inter hs (isClosed_biInter fun _ _ => isClosed_compl_iff.2 <| v.is_open _)
   rcases normal_exists_closure_subset C (v.is_open i) I with ⟨vi, ovi, hvi, cvi⟩
   refine' ⟨⟨update v i vi, insert i v.carrier, _, _, _, _⟩, _, _⟩
   · intro j
@@ -328,13 +328,13 @@ open ShrinkingLemma
 
 variable {u : ι → Set X} {s : Set X}
 
-#print exists_subset_unionᵢ_closure_subset /-
+#print exists_subset_iUnion_closure_subset /-
 /-- Shrinking lemma. A point-finite open cover of a closed subset of a normal space can be "shrunk"
 to a new open cover so that the closure of each new open set is contained in the corresponding
 original open set. -/
-theorem exists_subset_unionᵢ_closure_subset (hs : IsClosed s) (uo : ∀ i, IsOpen (u i))
+theorem exists_subset_iUnion_closure_subset (hs : IsClosed s) (uo : ∀ i, IsOpen (u i))
     (uf : ∀ x ∈ s, { i | x ∈ u i }.Finite) (us : s ⊆ ⋃ i, u i) :
-    ∃ v : ι → Set X, s ⊆ unionᵢ v ∧ (∀ i, IsOpen (v i)) ∧ ∀ i, closure (v i) ⊆ u i := by
+    ∃ v : ι → Set X, s ⊆ iUnion v ∧ (∀ i, IsOpen (v i)) ∧ ∀ i, closure (v i) ⊆ u i := by
   classical
     haveI : Nonempty (partial_refinement u s) :=
       ⟨⟨u, ∅, uo, us, fun _ => False.elim, fun _ _ => rfl⟩⟩
@@ -350,43 +350,43 @@ theorem exists_subset_unionᵢ_closure_subset (hs : IsClosed s) (uo : ∀ i, IsO
     rcases hv with ⟨i, hi⟩
     rcases v.exists_gt hs i hi with ⟨v', hlt⟩
     exact ⟨v', hlt.le, hlt.ne'⟩
-#align exists_subset_Union_closure_subset exists_subset_unionᵢ_closure_subset
+#align exists_subset_Union_closure_subset exists_subset_iUnion_closure_subset
 -/
 
-#print exists_subset_unionᵢ_closed_subset /-
+#print exists_subset_iUnion_closed_subset /-
 /-- Shrinking lemma. A point-finite open cover of a closed subset of a normal space can be "shrunk"
 to a new closed cover so that each new closed set is contained in the corresponding original open
 set. See also `exists_subset_Union_closure_subset` for a stronger statement. -/
-theorem exists_subset_unionᵢ_closed_subset (hs : IsClosed s) (uo : ∀ i, IsOpen (u i))
+theorem exists_subset_iUnion_closed_subset (hs : IsClosed s) (uo : ∀ i, IsOpen (u i))
     (uf : ∀ x ∈ s, { i | x ∈ u i }.Finite) (us : s ⊆ ⋃ i, u i) :
-    ∃ v : ι → Set X, s ⊆ unionᵢ v ∧ (∀ i, IsClosed (v i)) ∧ ∀ i, v i ⊆ u i :=
-  let ⟨v, hsv, hvo, hv⟩ := exists_subset_unionᵢ_closure_subset hs uo uf us
-  ⟨fun i => closure (v i), Subset.trans hsv (unionᵢ_mono fun i => subset_closure), fun i =>
+    ∃ v : ι → Set X, s ⊆ iUnion v ∧ (∀ i, IsClosed (v i)) ∧ ∀ i, v i ⊆ u i :=
+  let ⟨v, hsv, hvo, hv⟩ := exists_subset_iUnion_closure_subset hs uo uf us
+  ⟨fun i => closure (v i), Subset.trans hsv (iUnion_mono fun i => subset_closure), fun i =>
     isClosed_closure, hv⟩
-#align exists_subset_Union_closed_subset exists_subset_unionᵢ_closed_subset
+#align exists_subset_Union_closed_subset exists_subset_iUnion_closed_subset
 -/
 
-#print exists_unionᵢ_eq_closure_subset /-
+#print exists_iUnion_eq_closure_subset /-
 /-- Shrinking lemma. A point-finite open cover of a closed subset of a normal space can be "shrunk"
 to a new open cover so that the closure of each new open set is contained in the corresponding
 original open set. -/
-theorem exists_unionᵢ_eq_closure_subset (uo : ∀ i, IsOpen (u i)) (uf : ∀ x, { i | x ∈ u i }.Finite)
+theorem exists_iUnion_eq_closure_subset (uo : ∀ i, IsOpen (u i)) (uf : ∀ x, { i | x ∈ u i }.Finite)
     (uU : (⋃ i, u i) = univ) :
-    ∃ v : ι → Set X, unionᵢ v = univ ∧ (∀ i, IsOpen (v i)) ∧ ∀ i, closure (v i) ⊆ u i :=
-  let ⟨v, vU, hv⟩ := exists_subset_unionᵢ_closure_subset isClosed_univ uo (fun x _ => uf x) uU.ge
+    ∃ v : ι → Set X, iUnion v = univ ∧ (∀ i, IsOpen (v i)) ∧ ∀ i, closure (v i) ⊆ u i :=
+  let ⟨v, vU, hv⟩ := exists_subset_iUnion_closure_subset isClosed_univ uo (fun x _ => uf x) uU.ge
   ⟨v, univ_subset_iff.1 vU, hv⟩
-#align exists_Union_eq_closure_subset exists_unionᵢ_eq_closure_subset
+#align exists_Union_eq_closure_subset exists_iUnion_eq_closure_subset
 -/
 
-#print exists_unionᵢ_eq_closed_subset /-
+#print exists_iUnion_eq_closed_subset /-
 /-- Shrinking lemma. A point-finite open cover of a closed subset of a normal space can be "shrunk"
 to a new closed cover so that each of the new closed sets is contained in the corresponding
 original open set. See also `exists_Union_eq_closure_subset` for a stronger statement. -/
-theorem exists_unionᵢ_eq_closed_subset (uo : ∀ i, IsOpen (u i)) (uf : ∀ x, { i | x ∈ u i }.Finite)
+theorem exists_iUnion_eq_closed_subset (uo : ∀ i, IsOpen (u i)) (uf : ∀ x, { i | x ∈ u i }.Finite)
     (uU : (⋃ i, u i) = univ) :
-    ∃ v : ι → Set X, unionᵢ v = univ ∧ (∀ i, IsClosed (v i)) ∧ ∀ i, v i ⊆ u i :=
-  let ⟨v, vU, hv⟩ := exists_subset_unionᵢ_closed_subset isClosed_univ uo (fun x _ => uf x) uU.ge
+    ∃ v : ι → Set X, iUnion v = univ ∧ (∀ i, IsClosed (v i)) ∧ ∀ i, v i ⊆ u i :=
+  let ⟨v, vU, hv⟩ := exists_subset_iUnion_closed_subset isClosed_univ uo (fun x _ => uf x) uU.ge
   ⟨v, univ_subset_iff.1 vU, hv⟩
-#align exists_Union_eq_closed_subset exists_unionᵢ_eq_closed_subset
+#align exists_Union_eq_closed_subset exists_iUnion_eq_closed_subset
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/36b8aa61ea7c05727161f96a0532897bd72aedab

@@ -265,7 +265,7 @@ def chainSup (c : Set (PartialRefinement u s)) (hc : IsChain (· ≤ ·) c) (ne
 lean 3 declaration is
   forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : NormalSpace.{u2} X _inst_1] {u : ι -> (Set.{u2} X)} {s : Set.{u2} X} {c : Set.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)} (hc : IsChain.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (ShrinkingLemma.PartialRefinement.partialOrder.{u1, u2} ι X _inst_1 _inst_2 u s)))) c) (ne : Set.Nonempty.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) c) (hfin : forall (x : X), (Membership.Mem.{u2, u2} X (Set.{u2} X) (Set.hasMem.{u2} X) x s) -> (Set.Finite.{u1} ι (setOf.{u1} ι (fun (i : ι) => Membership.Mem.{u2, u2} X (Set.{u2} X) (Set.hasMem.{u2} X) x (u i))))) (hU : HasSubset.Subset.{u2} (Set.{u2} X) (Set.hasSubset.{u2} X) s (Set.unionᵢ.{u2, succ u1} X ι (fun (i : ι) => u i))) {v : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s}, (Membership.Mem.{max u1 u2, max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (Set.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)) (Set.hasMem.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)) v c) -> (LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (ShrinkingLemma.PartialRefinement.partialOrder.{u1, u2} ι X _inst_1 _inst_2 u s))) v (ShrinkingLemma.PartialRefinement.chainSup.{u1, u2} ι X _inst_1 _inst_2 u s c hc ne hfin hU))
 but is expected to have type
-  forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] {_inst_2 : ι -> (Set.{u2} X)} {u : Set.{u2} X} {s : Set.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)} (c : IsChain.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (fun (x._@.Mathlib.Topology.ShrinkingLemma._hyg.1458 : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (x._@.Mathlib.Topology.ShrinkingLemma._hyg.1460 : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) => LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (ShrinkingLemma.PartialRefinement.instPartialOrderPartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u))) x._@.Mathlib.Topology.ShrinkingLemma._hyg.1458 x._@.Mathlib.Topology.ShrinkingLemma._hyg.1460) s) (hc : Set.Nonempty.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) s) (ne : forall (x : X), (Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) x u) -> (Set.Finite.{u1} ι (setOf.{u1} ι (fun (i : ι) => Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) x (_inst_2 i))))) (hfin : HasSubset.Subset.{u2} (Set.{u2} X) (Set.instHasSubsetSet.{u2} X) u (Set.unionᵢ.{u2, succ u1} X ι (fun (i : ι) => _inst_2 i))) {hU : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u}, (Membership.mem.{max u1 u2, max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Set.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)) (Set.instMembershipSet.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)) hU s) -> (LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (ShrinkingLemma.PartialRefinement.instPartialOrderPartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u))) hU (ShrinkingLemma.PartialRefinement.chainSup.{u1, u2} ι X _inst_1 _inst_2 u s c hc ne hfin))
+  forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] {_inst_2 : ι -> (Set.{u2} X)} {u : Set.{u2} X} {s : Set.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)} (c : IsChain.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (fun (x._@.Mathlib.Topology.ShrinkingLemma._hyg.1456 : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (x._@.Mathlib.Topology.ShrinkingLemma._hyg.1458 : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) => LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (ShrinkingLemma.PartialRefinement.instPartialOrderPartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u))) x._@.Mathlib.Topology.ShrinkingLemma._hyg.1456 x._@.Mathlib.Topology.ShrinkingLemma._hyg.1458) s) (hc : Set.Nonempty.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) s) (ne : forall (x : X), (Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) x u) -> (Set.Finite.{u1} ι (setOf.{u1} ι (fun (i : ι) => Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) x (_inst_2 i))))) (hfin : HasSubset.Subset.{u2} (Set.{u2} X) (Set.instHasSubsetSet.{u2} X) u (Set.unionᵢ.{u2, succ u1} X ι (fun (i : ι) => _inst_2 i))) {hU : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u}, (Membership.mem.{max u1 u2, max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Set.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)) (Set.instMembershipSet.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)) hU s) -> (LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (ShrinkingLemma.PartialRefinement.instPartialOrderPartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u))) hU (ShrinkingLemma.PartialRefinement.chainSup.{u1, u2} ι X _inst_1 _inst_2 u s c hc ne hfin))
 Case conversion may be inaccurate. Consider using '#align shrinking_lemma.partial_refinement.le_chain_Sup ShrinkingLemma.PartialRefinement.le_chainSupₓ'. -/
 /-- `chain_Sup hu c hc ne hfin hU` is an upper bound of the chain `c`. -/
 theorem le_chainSup {c : Set (PartialRefinement u s)} (hc : IsChain (· ≤ ·) c) (ne : c.Nonempty)

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

@@ -152,7 +152,7 @@ instance : PartialOrder (PartialRefinement u s)
 lean 3 declaration is
   forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : NormalSpace.{u2} X _inst_1] {u : ι -> (Set.{u2} X)} {s : Set.{u2} X} {c : Set.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)}, (IsChain.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (ShrinkingLemma.PartialRefinement.partialOrder.{u1, u2} ι X _inst_1 _inst_2 u s)))) c) -> (forall {v₁ : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s} {v₂ : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s}, (Membership.Mem.{max u1 u2, max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (Set.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)) (Set.hasMem.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)) v₁ c) -> (Membership.Mem.{max u1 u2, max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (Set.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)) (Set.hasMem.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)) v₂ c) -> (forall {i : ι}, (Membership.Mem.{u1, u1} ι (Set.{u1} ι) (Set.hasMem.{u1} ι) i (ShrinkingLemma.PartialRefinement.carrier.{u1, u2} ι X _inst_1 _inst_2 u s v₁)) -> (Membership.Mem.{u1, u1} ι (Set.{u1} ι) (Set.hasMem.{u1} ι) i (ShrinkingLemma.PartialRefinement.carrier.{u1, u2} ι X _inst_1 _inst_2 u s v₂)) -> (Eq.{succ u2} (Set.{u2} X) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (fun (_x : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) => ι -> (Set.{u2} X)) (ShrinkingLemma.PartialRefinement.hasCoeToFun.{u1, u2} ι X _inst_1 _inst_2 u s) v₁ i) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (fun (_x : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) => ι -> (Set.{u2} X)) (ShrinkingLemma.PartialRefinement.hasCoeToFun.{u1, u2} ι X _inst_1 _inst_2 u s) v₂ i))))
 but is expected to have type
-  forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] {_inst_2 : ι -> (Set.{u2} X)} {u : Set.{u2} X} {s : Set.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)}, (IsChain.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (fun (x._@.Mathlib.Topology.ShrinkingLemma._hyg.468 : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (x._@.Mathlib.Topology.ShrinkingLemma._hyg.470 : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) => LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (ShrinkingLemma.PartialRefinement.instPartialOrderPartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u))) x._@.Mathlib.Topology.ShrinkingLemma._hyg.468 x._@.Mathlib.Topology.ShrinkingLemma._hyg.470) s) -> (forall {hc : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u} {v₁ : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u}, (Membership.mem.{max u1 u2, max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Set.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)) (Set.instMembershipSet.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)) hc s) -> (Membership.mem.{max u1 u2, max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Set.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)) (Set.instMembershipSet.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)) v₁ s) -> (forall {h₂ : ι}, (Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) h₂ (ShrinkingLemma.PartialRefinement.carrier.{u1, u2} ι X _inst_1 _inst_2 u hc)) -> (Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) h₂ (ShrinkingLemma.PartialRefinement.carrier.{u1, u2} ι X _inst_1 _inst_2 u v₁)) -> (Eq.{succ u2} (Set.{u2} X) (ShrinkingLemma.PartialRefinement.toFun.{u1, u2} ι X _inst_1 _inst_2 u hc h₂) (ShrinkingLemma.PartialRefinement.toFun.{u1, u2} ι X _inst_1 _inst_2 u v₁ h₂))))
+  forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] {_inst_2 : ι -> (Set.{u2} X)} {u : Set.{u2} X} {s : Set.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)}, (IsChain.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (fun (x._@.Mathlib.Topology.ShrinkingLemma._hyg.471 : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (x._@.Mathlib.Topology.ShrinkingLemma._hyg.473 : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) => LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (ShrinkingLemma.PartialRefinement.instPartialOrderPartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u))) x._@.Mathlib.Topology.ShrinkingLemma._hyg.471 x._@.Mathlib.Topology.ShrinkingLemma._hyg.473) s) -> (forall {hc : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u} {v₁ : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u}, (Membership.mem.{max u1 u2, max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Set.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)) (Set.instMembershipSet.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)) hc s) -> (Membership.mem.{max u1 u2, max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Set.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)) (Set.instMembershipSet.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)) v₁ s) -> (forall {h₂ : ι}, (Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) h₂ (ShrinkingLemma.PartialRefinement.carrier.{u1, u2} ι X _inst_1 _inst_2 u hc)) -> (Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) h₂ (ShrinkingLemma.PartialRefinement.carrier.{u1, u2} ι X _inst_1 _inst_2 u v₁)) -> (Eq.{succ u2} (Set.{u2} X) (ShrinkingLemma.PartialRefinement.toFun.{u1, u2} ι X _inst_1 _inst_2 u hc h₂) (ShrinkingLemma.PartialRefinement.toFun.{u1, u2} ι X _inst_1 _inst_2 u v₁ h₂))))
 Case conversion may be inaccurate. Consider using '#align shrinking_lemma.partial_refinement.apply_eq_of_chain ShrinkingLemma.PartialRefinement.apply_eq_of_chainₓ'. -/
 /-- If two partial refinements `v₁`, `v₂` belong to a chain (hence, they are comparable)
 and `i` belongs to the carriers of both partial refinements, then `v₁ i = v₂ i`. -/
@@ -223,7 +223,7 @@ theorem mem_find_carrier_iff {c : Set (PartialRefinement u s)} {i : ι} (ne : c.
 lean 3 declaration is
   forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : NormalSpace.{u2} X _inst_1] {u : ι -> (Set.{u2} X)} {s : Set.{u2} X} {c : Set.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)}, (IsChain.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (ShrinkingLemma.PartialRefinement.partialOrder.{u1, u2} ι X _inst_1 _inst_2 u s)))) c) -> (forall (ne : Set.Nonempty.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) c) {i : ι} {v : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s}, (Membership.Mem.{max u1 u2, max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (Set.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)) (Set.hasMem.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)) v c) -> (Membership.Mem.{u1, u1} ι (Set.{u1} ι) (Set.hasMem.{u1} ι) i (ShrinkingLemma.PartialRefinement.carrier.{u1, u2} ι X _inst_1 _inst_2 u s v)) -> (Eq.{succ u2} (Set.{u2} X) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (fun (_x : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) => ι -> (Set.{u2} X)) (ShrinkingLemma.PartialRefinement.hasCoeToFun.{u1, u2} ι X _inst_1 _inst_2 u s) (ShrinkingLemma.PartialRefinement.find.{u1, u2} ι X _inst_1 _inst_2 u s c ne i) i) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (fun (_x : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) => ι -> (Set.{u2} X)) (ShrinkingLemma.PartialRefinement.hasCoeToFun.{u1, u2} ι X _inst_1 _inst_2 u s) v i)))
 but is expected to have type
-  forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] {_inst_2 : ι -> (Set.{u2} X)} {u : Set.{u2} X} {s : Set.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)}, (IsChain.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (fun (x._@.Mathlib.Topology.ShrinkingLemma._hyg.890 : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (x._@.Mathlib.Topology.ShrinkingLemma._hyg.892 : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) => LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (ShrinkingLemma.PartialRefinement.instPartialOrderPartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u))) x._@.Mathlib.Topology.ShrinkingLemma._hyg.890 x._@.Mathlib.Topology.ShrinkingLemma._hyg.892) s) -> (forall (hc : Set.Nonempty.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) s) {ne : ι} {i : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u}, (Membership.mem.{max u1 u2, max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Set.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)) (Set.instMembershipSet.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)) i s) -> (Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) ne (ShrinkingLemma.PartialRefinement.carrier.{u1, u2} ι X _inst_1 _inst_2 u i)) -> (Eq.{succ u2} (Set.{u2} X) (ShrinkingLemma.PartialRefinement.toFun.{u1, u2} ι X _inst_1 _inst_2 u (ShrinkingLemma.PartialRefinement.find.{u1, u2} ι X _inst_1 _inst_2 u s hc ne) ne) (ShrinkingLemma.PartialRefinement.toFun.{u1, u2} ι X _inst_1 _inst_2 u i ne)))
+  forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] {_inst_2 : ι -> (Set.{u2} X)} {u : Set.{u2} X} {s : Set.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)}, (IsChain.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (fun (x._@.Mathlib.Topology.ShrinkingLemma._hyg.895 : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (x._@.Mathlib.Topology.ShrinkingLemma._hyg.897 : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) => LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (ShrinkingLemma.PartialRefinement.instPartialOrderPartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u))) x._@.Mathlib.Topology.ShrinkingLemma._hyg.895 x._@.Mathlib.Topology.ShrinkingLemma._hyg.897) s) -> (forall (hc : Set.Nonempty.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) s) {ne : ι} {i : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u}, (Membership.mem.{max u1 u2, max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Set.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)) (Set.instMembershipSet.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)) i s) -> (Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) ne (ShrinkingLemma.PartialRefinement.carrier.{u1, u2} ι X _inst_1 _inst_2 u i)) -> (Eq.{succ u2} (Set.{u2} X) (ShrinkingLemma.PartialRefinement.toFun.{u1, u2} ι X _inst_1 _inst_2 u (ShrinkingLemma.PartialRefinement.find.{u1, u2} ι X _inst_1 _inst_2 u s hc ne) ne) (ShrinkingLemma.PartialRefinement.toFun.{u1, u2} ι X _inst_1 _inst_2 u i ne)))
 Case conversion may be inaccurate. Consider using '#align shrinking_lemma.partial_refinement.find_apply_of_mem ShrinkingLemma.PartialRefinement.find_apply_of_memₓ'. -/
 theorem find_apply_of_mem {c : Set (PartialRefinement u s)} (hc : IsChain (· ≤ ·) c)
     (ne : c.Nonempty) {i v} (hv : v ∈ c) (hi : i ∈ carrier v) : find c Ne i i = v i :=
@@ -235,7 +235,7 @@ theorem find_apply_of_mem {c : Set (PartialRefinement u s)} (hc : IsChain (· 
 lean 3 declaration is
   forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : NormalSpace.{u2} X _inst_1] {u : ι -> (Set.{u2} X)} {s : Set.{u2} X} (c : Set.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)), (IsChain.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (ShrinkingLemma.PartialRefinement.partialOrder.{u1, u2} ι X _inst_1 _inst_2 u s)))) c) -> (Set.Nonempty.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) c) -> (forall (x : X), (Membership.Mem.{u2, u2} X (Set.{u2} X) (Set.hasMem.{u2} X) x s) -> (Set.Finite.{u1} ι (setOf.{u1} ι (fun (i : ι) => Membership.Mem.{u2, u2} X (Set.{u2} X) (Set.hasMem.{u2} X) x (u i))))) -> (HasSubset.Subset.{u2} (Set.{u2} X) (Set.hasSubset.{u2} X) s (Set.unionᵢ.{u2, succ u1} X ι (fun (i : ι) => u i))) -> (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)
 but is expected to have type
-  forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] {_inst_2 : ι -> (Set.{u2} X)} {u : Set.{u2} X} (s : Set.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)), (IsChain.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (fun (x._@.Mathlib.Topology.ShrinkingLemma._hyg.979 : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (x._@.Mathlib.Topology.ShrinkingLemma._hyg.981 : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) => LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (ShrinkingLemma.PartialRefinement.instPartialOrderPartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u))) x._@.Mathlib.Topology.ShrinkingLemma._hyg.979 x._@.Mathlib.Topology.ShrinkingLemma._hyg.981) s) -> (Set.Nonempty.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) s) -> (forall (x : X), (Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) x u) -> (Set.Finite.{u1} ι (setOf.{u1} ι (fun (i : ι) => Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) x (_inst_2 i))))) -> (HasSubset.Subset.{u2} (Set.{u2} X) (Set.instHasSubsetSet.{u2} X) u (Set.unionᵢ.{u2, succ u1} X ι (fun (i : ι) => _inst_2 i))) -> (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)
+  forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] {_inst_2 : ι -> (Set.{u2} X)} {u : Set.{u2} X} (s : Set.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)), (IsChain.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (fun (x._@.Mathlib.Topology.ShrinkingLemma._hyg.986 : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (x._@.Mathlib.Topology.ShrinkingLemma._hyg.988 : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) => LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (ShrinkingLemma.PartialRefinement.instPartialOrderPartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u))) x._@.Mathlib.Topology.ShrinkingLemma._hyg.986 x._@.Mathlib.Topology.ShrinkingLemma._hyg.988) s) -> (Set.Nonempty.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) s) -> (forall (x : X), (Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) x u) -> (Set.Finite.{u1} ι (setOf.{u1} ι (fun (i : ι) => Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) x (_inst_2 i))))) -> (HasSubset.Subset.{u2} (Set.{u2} X) (Set.instHasSubsetSet.{u2} X) u (Set.unionᵢ.{u2, succ u1} X ι (fun (i : ι) => _inst_2 i))) -> (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)
 Case conversion may be inaccurate. Consider using '#align shrinking_lemma.partial_refinement.chain_Sup ShrinkingLemma.PartialRefinement.chainSupₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » chain_Sup_carrier c) -/
 /-- Least upper bound of a nonempty chain of partial refinements. -/
@@ -265,7 +265,7 @@ def chainSup (c : Set (PartialRefinement u s)) (hc : IsChain (· ≤ ·) c) (ne
 lean 3 declaration is
   forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : NormalSpace.{u2} X _inst_1] {u : ι -> (Set.{u2} X)} {s : Set.{u2} X} {c : Set.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)} (hc : IsChain.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (ShrinkingLemma.PartialRefinement.partialOrder.{u1, u2} ι X _inst_1 _inst_2 u s)))) c) (ne : Set.Nonempty.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) c) (hfin : forall (x : X), (Membership.Mem.{u2, u2} X (Set.{u2} X) (Set.hasMem.{u2} X) x s) -> (Set.Finite.{u1} ι (setOf.{u1} ι (fun (i : ι) => Membership.Mem.{u2, u2} X (Set.{u2} X) (Set.hasMem.{u2} X) x (u i))))) (hU : HasSubset.Subset.{u2} (Set.{u2} X) (Set.hasSubset.{u2} X) s (Set.unionᵢ.{u2, succ u1} X ι (fun (i : ι) => u i))) {v : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s}, (Membership.Mem.{max u1 u2, max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (Set.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)) (Set.hasMem.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s)) v c) -> (LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u s) (ShrinkingLemma.PartialRefinement.partialOrder.{u1, u2} ι X _inst_1 _inst_2 u s))) v (ShrinkingLemma.PartialRefinement.chainSup.{u1, u2} ι X _inst_1 _inst_2 u s c hc ne hfin hU))
 but is expected to have type
-  forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] {_inst_2 : ι -> (Set.{u2} X)} {u : Set.{u2} X} {s : Set.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)} (c : IsChain.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (fun (x._@.Mathlib.Topology.ShrinkingLemma._hyg.1450 : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (x._@.Mathlib.Topology.ShrinkingLemma._hyg.1452 : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) => LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (ShrinkingLemma.PartialRefinement.instPartialOrderPartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u))) x._@.Mathlib.Topology.ShrinkingLemma._hyg.1450 x._@.Mathlib.Topology.ShrinkingLemma._hyg.1452) s) (hc : Set.Nonempty.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) s) (ne : forall (x : X), (Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) x u) -> (Set.Finite.{u1} ι (setOf.{u1} ι (fun (i : ι) => Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) x (_inst_2 i))))) (hfin : HasSubset.Subset.{u2} (Set.{u2} X) (Set.instHasSubsetSet.{u2} X) u (Set.unionᵢ.{u2, succ u1} X ι (fun (i : ι) => _inst_2 i))) {hU : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u}, (Membership.mem.{max u1 u2, max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Set.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)) (Set.instMembershipSet.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)) hU s) -> (LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (ShrinkingLemma.PartialRefinement.instPartialOrderPartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u))) hU (ShrinkingLemma.PartialRefinement.chainSup.{u1, u2} ι X _inst_1 _inst_2 u s c hc ne hfin))
+  forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] {_inst_2 : ι -> (Set.{u2} X)} {u : Set.{u2} X} {s : Set.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)} (c : IsChain.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (fun (x._@.Mathlib.Topology.ShrinkingLemma._hyg.1458 : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (x._@.Mathlib.Topology.ShrinkingLemma._hyg.1460 : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) => LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (ShrinkingLemma.PartialRefinement.instPartialOrderPartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u))) x._@.Mathlib.Topology.ShrinkingLemma._hyg.1458 x._@.Mathlib.Topology.ShrinkingLemma._hyg.1460) s) (hc : Set.Nonempty.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) s) (ne : forall (x : X), (Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) x u) -> (Set.Finite.{u1} ι (setOf.{u1} ι (fun (i : ι) => Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) x (_inst_2 i))))) (hfin : HasSubset.Subset.{u2} (Set.{u2} X) (Set.instHasSubsetSet.{u2} X) u (Set.unionᵢ.{u2, succ u1} X ι (fun (i : ι) => _inst_2 i))) {hU : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u}, (Membership.mem.{max u1 u2, max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Set.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)) (Set.instMembershipSet.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)) hU s) -> (LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (ShrinkingLemma.PartialRefinement.instPartialOrderPartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u))) hU (ShrinkingLemma.PartialRefinement.chainSup.{u1, u2} ι X _inst_1 _inst_2 u s c hc ne hfin))
 Case conversion may be inaccurate. Consider using '#align shrinking_lemma.partial_refinement.le_chain_Sup ShrinkingLemma.PartialRefinement.le_chainSupₓ'. -/
 /-- `chain_Sup hu c hc ne hfin hU` is an upper bound of the chain `c`. -/
 theorem le_chainSup {c : Set (PartialRefinement u s)} (hc : IsChain (· ≤ ·) c) (ne : c.Nonempty)

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

@@ -51,7 +51,7 @@ lean 3 declaration is
 but is expected to have type
   forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X], (ι -> (Set.{u2} X)) -> (Set.{u2} X) -> Sort.{max (succ u1) (succ u2)}
 Case conversion may be inaccurate. Consider using '#align shrinking_lemma.partial_refinement ShrinkingLemma.PartialRefinementₓ'. -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (i «expr ∉ » carrier) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » carrier) -/
 -- the trivial refinement needs `u` to be a covering
 /-- Auxiliary definition for the proof of `shrinking_lemma`. A partial refinement of a covering
 `⋃ i, u i` of a set `s` is a map `v : ι → set X` and a set `carrier : set ι` such that
@@ -237,7 +237,7 @@ lean 3 declaration is
 but is expected to have type
   forall {ι : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] {_inst_2 : ι -> (Set.{u2} X)} {u : Set.{u2} X} (s : Set.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)), (IsChain.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (fun (x._@.Mathlib.Topology.ShrinkingLemma._hyg.979 : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (x._@.Mathlib.Topology.ShrinkingLemma._hyg.981 : ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) => LE.le.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (Preorder.toLE.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (PartialOrder.toPreorder.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) (ShrinkingLemma.PartialRefinement.instPartialOrderPartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u))) x._@.Mathlib.Topology.ShrinkingLemma._hyg.979 x._@.Mathlib.Topology.ShrinkingLemma._hyg.981) s) -> (Set.Nonempty.{max u1 u2} (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u) s) -> (forall (x : X), (Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) x u) -> (Set.Finite.{u1} ι (setOf.{u1} ι (fun (i : ι) => Membership.mem.{u2, u2} X (Set.{u2} X) (Set.instMembershipSet.{u2} X) x (_inst_2 i))))) -> (HasSubset.Subset.{u2} (Set.{u2} X) (Set.instHasSubsetSet.{u2} X) u (Set.unionᵢ.{u2, succ u1} X ι (fun (i : ι) => _inst_2 i))) -> (ShrinkingLemma.PartialRefinement.{u1, u2} ι X _inst_1 _inst_2 u)
 Case conversion may be inaccurate. Consider using '#align shrinking_lemma.partial_refinement.chain_Sup ShrinkingLemma.PartialRefinement.chainSupₓ'. -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (i «expr ∉ » chain_Sup_carrier c) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » chain_Sup_carrier c) -/
 /-- Least upper bound of a nonempty chain of partial refinements. -/
 def chainSup (c : Set (PartialRefinement u s)) (hc : IsChain (· ≤ ·) c) (ne : c.Nonempty)
     (hfin : ∀ x ∈ s, { i | x ∈ u i }.Finite) (hU : s ⊆ ⋃ i, u i) : PartialRefinement u s :=
@@ -280,9 +280,9 @@ lean 3 declaration is
 but is expected to have type
   forall {ι : Type.{u2}} {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : NormalSpace.{u1} X _inst_1] {u : ι -> (Set.{u1} X)} {s : Set.{u1} X} (v : ShrinkingLemma.PartialRefinement.{u2, u1} ι X _inst_1 u s), (IsClosed.{u1} X _inst_1 s) -> (forall (i : ι), (Not (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i (ShrinkingLemma.PartialRefinement.carrier.{u2, u1} ι X _inst_1 u s v))) -> (Exists.{max (succ u2) (succ u1)} (ShrinkingLemma.PartialRefinement.{u2, u1} ι X _inst_1 u s) (fun (v' : ShrinkingLemma.PartialRefinement.{u2, u1} ι X _inst_1 u s) => LT.lt.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u2, u1} ι X _inst_1 u s) (Preorder.toLT.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u2, u1} ι X _inst_1 u s) (PartialOrder.toPreorder.{max u2 u1} (ShrinkingLemma.PartialRefinement.{u2, u1} ι X _inst_1 u s) (ShrinkingLemma.PartialRefinement.instPartialOrderPartialRefinement.{u2, u1} ι X _inst_1 u s))) v v')))
 Case conversion may be inaccurate. Consider using '#align shrinking_lemma.partial_refinement.exists_gt ShrinkingLemma.PartialRefinement.exists_gtₓ'. -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (j «expr ≠ » i) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (j «expr ≠ » i) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (j «expr ≠ » i) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (j «expr ≠ » i) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (j «expr ≠ » i) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (j «expr ≠ » i) -/
 /-- If `s` is a closed set, `v` is a partial refinement, and `i` is an index such that
 `i ∉ v.carrier`, then there exists a partial refinement that is strictly greater than `v`. -/
 theorem exists_gt (v : PartialRefinement u s) (hs : IsClosed s) (i : ι) (hi : i ∉ v.carrier) :

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

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

@@ -51,7 +51,7 @@ namespace ShrinkingLemma
 This type is equipped with the following partial order: `v ≤ v'` if `v.carrier ⊆ v'.carrier`
 and `v i = v' i` for `i ∈ v.carrier`. We will use Zorn's lemma to prove that this type has
 a maximal element, then show that the maximal element must have `carrier = univ`. -/
--- Porting note: @[nolint has_nonempty_instance] is not here yet
+-- Porting note(#5171): this linter isn't ported yet. @[nolint has_nonempty_instance]
 @[ext] structure PartialRefinement (u : ι → Set X) (s : Set X) where
   /-- A family of sets that form a partial refinement of `u`. -/
   toFun : ι → Set X

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

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

@@ -51,7 +51,7 @@ namespace ShrinkingLemma
 This type is equipped with the following partial order: `v ≤ v'` if `v.carrier ⊆ v'.carrier`
 and `v i = v' i` for `i ∈ v.carrier`. We will use Zorn's lemma to prove that this type has
 a maximal element, then show that the maximal element must have `carrier = univ`. -/
--- porting note: @[nolint has_nonempty_instance] is not here yet
+-- Porting note: @[nolint has_nonempty_instance] is not here yet
 @[ext] structure PartialRefinement (u : ι → Set X) (s : Set X) where
   /-- A family of sets that form a partial refinement of `u`. -/
   toFun : ι → Set X

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>

@@ -223,8 +223,8 @@ theorem exists_subset_iUnion_closure_subset (hs : IsClosed s) (uo : ∀ i, IsOpe
       IsChain (· ≤ ·) c → c.Nonempty → ∃ ub, ∀ v ∈ c, v ≤ ub :=
     fun c hc ne => ⟨.chainSup c hc ne uf us, fun v hv => PartialRefinement.le_chainSup _ _ _ _ hv⟩
   rcases zorn_nonempty_partialOrder this with ⟨v, hv⟩
-  suffices : ∀ i, i ∈ v.carrier
-  exact ⟨v, v.subset_iUnion, fun i => v.isOpen _, fun i => v.closure_subset (this i)⟩
+  suffices ∀ i, i ∈ v.carrier from
+    ⟨v, v.subset_iUnion, fun i => v.isOpen _, fun i => v.closure_subset (this i)⟩
   contrapose! hv
   rcases hv with ⟨i, hi⟩
   rcases v.exists_gt hs i hi with ⟨v', hlt⟩

Changes in this PR shouldn't change the public API. The only changes about ∃ x ∈ s, _ is inside a proof.

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

@@ -185,7 +185,7 @@ theorem exists_gt (v : PartialRefinement u s) (hs : IsClosed s) (i : ι) (hi : i
   · intro j
     rcases eq_or_ne j i with (rfl| hne) <;> simp [*, v.isOpen]
   · refine' fun x hx => mem_iUnion.2 _
-    rcases em (∃ (j : _) (_ : j ≠ i), x ∈ v j) with (⟨j, hji, hj⟩ | h)
+    rcases em (∃ j ≠ i, x ∈ v j) with (⟨j, hji, hj⟩ | h)
     · use j
       rwa [update_noteq hji]
     · push_neg at h

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

@@ -151,7 +151,7 @@ def chainSup (c : Set (PartialRefinement u s)) (hc : IsChain (· ≤ ·) c) (ne
     · simp_rw [not_exists, not_and, not_imp_not, chainSupCarrier, mem_iUnion₂] at hx
       haveI : Nonempty (PartialRefinement u s) := ⟨ne.some⟩
       choose! v hvc hiv using hx
-      rcases(hfin x hxs).exists_maximal_wrt v _ (mem_iUnion.1 (hU hxs)) with
+      rcases (hfin x hxs).exists_maximal_wrt v _ (mem_iUnion.1 (hU hxs)) with
         ⟨i, hxi : x ∈ u i, hmax : ∀ j, x ∈ u j → v i ≤ v j → v i = v j⟩
       rcases mem_iUnion.1 ((v i).subset_iUnion hxs) with ⟨j, hj⟩
       use j

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

This has nice performance benefits.

@@ -35,7 +35,7 @@ open scoped Classical
 
 noncomputable section
 
-variable {ι X : Type _} [TopologicalSpace X] [NormalSpace X]
+variable {ι X : Type*} [TopologicalSpace X] [NormalSpace X]
 
 namespace ShrinkingLemma
 

• depends on: #5966

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

@@ -2,14 +2,11 @@
 Copyright (c) 2021 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov, Reid Barton
-
-! This file was ported from Lean 3 source module topology.shrinking_lemma
-! leanprover-community/mathlib commit 4c19a16e4b705bf135cf9a80ac18fcc99c438514
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Topology.Separation
 
+#align_import topology.shrinking_lemma from "leanprover-community/mathlib"@"4c19a16e4b705bf135cf9a80ac18fcc99c438514"
+
 /-!
 # The shrinking lemma
 

@@ -249,7 +249,7 @@ theorem exists_subset_iUnion_closed_subset (hs : IsClosed s) (uo : ∀ i, IsOpen
 to a new open cover so that the closure of each new open set is contained in the corresponding
 original open set. -/
 theorem exists_iUnion_eq_closure_subset (uo : ∀ i, IsOpen (u i)) (uf : ∀ x, { i | x ∈ u i }.Finite)
-    (uU : (⋃ i, u i) = univ) :
+    (uU : ⋃ i, u i = univ) :
     ∃ v : ι → Set X, iUnion v = univ ∧ (∀ i, IsOpen (v i)) ∧ ∀ i, closure (v i) ⊆ u i :=
   let ⟨v, vU, hv⟩ := exists_subset_iUnion_closure_subset isClosed_univ uo (fun x _ => uf x) uU.ge
   ⟨v, univ_subset_iff.1 vU, hv⟩
@@ -259,7 +259,7 @@ theorem exists_iUnion_eq_closure_subset (uo : ∀ i, IsOpen (u i)) (uf : ∀ x,
 to a new closed cover so that each of the new closed sets is contained in the corresponding
 original open set. See also `exists_iUnion_eq_closure_subset` for a stronger statement. -/
 theorem exists_iUnion_eq_closed_subset (uo : ∀ i, IsOpen (u i)) (uf : ∀ x, { i | x ∈ u i }.Finite)
-    (uU : (⋃ i, u i) = univ) :
+    (uU : ⋃ i, u i = univ) :
     ∃ v : ι → Set X, iUnion v = univ ∧ (∀ i, IsClosed (v i)) ∧ ∀ i, v i ⊆ u i :=
   let ⟨v, vU, hv⟩ := exists_subset_iUnion_closed_subset isClosed_univ uo (fun x _ => uf x) uU.ge
   ⟨v, univ_subset_iff.1 vU, hv⟩

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

@@ -176,12 +176,12 @@ theorem le_chainSup {c : Set (PartialRefinement u s)} (hc : IsChain (· ≤ ·)
 `i ∉ v.carrier`, then there exists a partial refinement that is strictly greater than `v`. -/
 theorem exists_gt (v : PartialRefinement u s) (hs : IsClosed s) (i : ι) (hi : i ∉ v.carrier) :
     ∃ v' : PartialRefinement u s, v < v' := by
-  have I : (s ∩ ⋂ (j) (_ : j ≠ i), v jᶜ) ⊆ v i := by
+  have I : (s ∩ ⋂ (j) (_ : j ≠ i), (v j)ᶜ) ⊆ v i := by
     simp only [subset_def, mem_inter_iff, mem_iInter, and_imp]
     intro x hxs H
     rcases mem_iUnion.1 (v.subset_iUnion hxs) with ⟨j, hj⟩
     exact (em (j = i)).elim (fun h => h ▸ hj) fun h => (H j h hj).elim
-  have C : IsClosed (s ∩ ⋂ (j) (_ : j ≠ i), v jᶜ) :=
+  have C : IsClosed (s ∩ ⋂ (j) (_ : j ≠ i), (v j)ᶜ) :=
     IsClosed.inter hs (isClosed_biInter fun _ _ => isClosed_compl_iff.2 <| v.isOpen _)
   rcases normal_exists_closure_subset C (v.isOpen i) I with ⟨vi, ovi, hvi, cvi⟩
   refine' ⟨⟨update v i vi, insert i v.carrier, _, _, _, _⟩, _, _⟩

Changes are of the form

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

@@ -191,7 +191,7 @@ theorem exists_gt (v : PartialRefinement u s) (hs : IsClosed s) (i : ι) (hi : i
     rcases em (∃ (j : _) (_ : j ≠ i), x ∈ v j) with (⟨j, hji, hj⟩ | h)
     · use j
       rwa [update_noteq hji]
-    · push_neg  at h
+    · push_neg at h
       use i
       rw [update_same]
       exact hvi ⟨hx, mem_biInter h⟩

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

@@ -188,7 +188,7 @@ theorem exists_gt (v : PartialRefinement u s) (hs : IsClosed s) (i : ι) (hi : i
   · intro j
     rcases eq_or_ne j i with (rfl| hne) <;> simp [*, v.isOpen]
   · refine' fun x hx => mem_iUnion.2 _
-    rcases em (∃ (j : _)(_ : j ≠ i), x ∈ v j) with (⟨j, hji, hj⟩ | h)
+    rcases em (∃ (j : _) (_ : j ≠ i), x ∈ v j) with (⟨j, hji, hj⟩ | h)
     · use j
       rwa [update_noteq hji]
     · push_neg  at h

@@ -176,12 +176,12 @@ theorem le_chainSup {c : Set (PartialRefinement u s)} (hc : IsChain (· ≤ ·)
 `i ∉ v.carrier`, then there exists a partial refinement that is strictly greater than `v`. -/
 theorem exists_gt (v : PartialRefinement u s) (hs : IsClosed s) (i : ι) (hi : i ∉ v.carrier) :
     ∃ v' : PartialRefinement u s, v < v' := by
-  have I : (s ∩ ⋂ (j) (_hj : j ≠ i), v jᶜ) ⊆ v i := by
+  have I : (s ∩ ⋂ (j) (_ : j ≠ i), v jᶜ) ⊆ v i := by
     simp only [subset_def, mem_inter_iff, mem_iInter, and_imp]
     intro x hxs H
     rcases mem_iUnion.1 (v.subset_iUnion hxs) with ⟨j, hj⟩
     exact (em (j = i)).elim (fun h => h ▸ hj) fun h => (H j h hj).elim
-  have C : IsClosed (s ∩ ⋂ (j) (_hj : j ≠ i), v jᶜ) :=
+  have C : IsClosed (s ∩ ⋂ (j) (_ : j ≠ i), v jᶜ) :=
     IsClosed.inter hs (isClosed_biInter fun _ _ => isClosed_compl_iff.2 <| v.isOpen _)
   rcases normal_exists_closure_subset C (v.isOpen i) I with ⟨vi, ovi, hvi, cvi⟩
   refine' ⟨⟨update v i vi, insert i v.carrier, _, _, _, _⟩, _, _⟩

Run codespell Mathlib and keep some suggestions.

@@ -51,7 +51,7 @@ namespace ShrinkingLemma
 * if `i ∈ carrier v`, then `closure (v i) ⊆ u i`;
 * if `i ∉ carrier`, then `v i = u i`.
 
-This type is equipped with the folowing partial order: `v ≤ v'` if `v.carrier ⊆ v'.carrier`
+This type is equipped with the following partial order: `v ≤ v'` if `v.carrier ⊆ v'.carrier`
 and `v i = v' i` for `i ∈ v.carrier`. We will use Zorn's lemma to prove that this type has
 a maximal element, then show that the maximal element must have `carrier = univ`. -/
 -- porting note: @[nolint has_nonempty_instance] is not here yet

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>

@@ -23,8 +23,8 @@ general result that works for any covering but needs the axiom of choice.
 
 We prove two versions of the lemma:
 
-* `exists_subset_unionᵢ_closure_subset` deals with a covering of a closed set in a normal space;
-* `exists_unionᵢ_eq_closure_subset` deals with a covering of the whole space.
+* `exists_subset_iUnion_closure_subset` deals with a covering of a closed set in a normal space;
+* `exists_iUnion_eq_closure_subset` deals with a covering of the whole space.
 
 ## Tags
 
@@ -63,7 +63,7 @@ a maximal element, then show that the maximal element must have `carrier = univ`
   /-- Each set from the partially refined family is open. -/
   protected isOpen : ∀ i, IsOpen (toFun i)
   /-- The partially refined family still covers the set. -/
-  subset_unionᵢ : s ⊆ ⋃ i, toFun i
+  subset_iUnion : s ⊆ ⋃ i, toFun i
   /-- For each `i ∈ carrier`, the original set includes the closure of the refined set. -/
   closure_subset : ∀ {i}, i ∈ carrier → closure (toFun i) ⊆ u i
   /-- Sets that correspond to `i ∉ carrier` are not modified. -/
@@ -76,7 +76,7 @@ variable {u : ι → Set X} {s : Set X}
 
 instance : CoeFun (PartialRefinement u s) fun _ => ι → Set X := ⟨toFun⟩
 
-#align shrinking_lemma.partial_refinement.subset_Union ShrinkingLemma.PartialRefinement.subset_unionᵢ
+#align shrinking_lemma.partial_refinement.subset_Union ShrinkingLemma.PartialRefinement.subset_iUnion
 #align shrinking_lemma.partial_refinement.closure_subset ShrinkingLemma.PartialRefinement.closure_subset
 #align shrinking_lemma.partial_refinement.apply_eq ShrinkingLemma.PartialRefinement.apply_eq
 #align shrinking_lemma.partial_refinement.is_open ShrinkingLemma.PartialRefinement.isOpen
@@ -129,15 +129,15 @@ theorem mem_find_carrier_iff {c : Set (PartialRefinement u s)} {i : ι} (ne : c.
   rw [find]
   split_ifs with h
   · have := h.choose_spec
-    exact iff_of_true this.2 (mem_unionᵢ₂.2 ⟨_, this.1, this.2⟩)
+    exact iff_of_true this.2 (mem_iUnion₂.2 ⟨_, this.1, this.2⟩)
   · push_neg at h
     refine iff_of_false (h _ ne.some_mem) ?_
-    simpa only [chainSupCarrier, mem_unionᵢ₂, not_exists]
+    simpa only [chainSupCarrier, mem_iUnion₂, not_exists]
 #align shrinking_lemma.partial_refinement.mem_find_carrier_iff ShrinkingLemma.PartialRefinement.mem_find_carrier_iff
 
 theorem find_apply_of_mem {c : Set (PartialRefinement u s)} (hc : IsChain (· ≤ ·) c)
     (ne : c.Nonempty) {i v} (hv : v ∈ c) (hi : i ∈ carrier v) : find c ne i i = v i :=
-  apply_eq_of_chain hc (find_mem _ _) hv ((mem_find_carrier_iff _).2 <| mem_unionᵢ₂.2 ⟨v, hv, hi⟩)
+  apply_eq_of_chain hc (find_mem _ _) hv ((mem_find_carrier_iff _).2 <| mem_iUnion₂.2 ⟨v, hv, hi⟩)
     hi
 #align shrinking_lemma.partial_refinement.find_apply_of_mem ShrinkingLemma.PartialRefinement.find_apply_of_mem
 
@@ -147,16 +147,16 @@ def chainSup (c : Set (PartialRefinement u s)) (hc : IsChain (· ≤ ·) c) (ne
   toFun i := find c ne i i
   carrier := chainSupCarrier c
   isOpen i := (find _ _ _).isOpen i
-  subset_unionᵢ x hxs := mem_unionᵢ.2 <| by
+  subset_iUnion x hxs := mem_iUnion.2 <| by
     rcases em (∃ i, i ∉ chainSupCarrier c ∧ x ∈ u i) with (⟨i, hi, hxi⟩ | hx)
     · use i
       simpa only [(find c ne i).apply_eq (mt (mem_find_carrier_iff _).1 hi)]
-    · simp_rw [not_exists, not_and, not_imp_not, chainSupCarrier, mem_unionᵢ₂] at hx
+    · simp_rw [not_exists, not_and, not_imp_not, chainSupCarrier, mem_iUnion₂] at hx
       haveI : Nonempty (PartialRefinement u s) := ⟨ne.some⟩
       choose! v hvc hiv using hx
-      rcases(hfin x hxs).exists_maximal_wrt v _ (mem_unionᵢ.1 (hU hxs)) with
+      rcases(hfin x hxs).exists_maximal_wrt v _ (mem_iUnion.1 (hU hxs)) with
         ⟨i, hxi : x ∈ u i, hmax : ∀ j, x ∈ u j → v i ≤ v j → v i = v j⟩
-      rcases mem_unionᵢ.1 ((v i).subset_unionᵢ hxs) with ⟨j, hj⟩
+      rcases mem_iUnion.1 ((v i).subset_iUnion hxs) with ⟨j, hj⟩
       use j
       have hj' : x ∈ u j := (v i).subset _ hj
       have : v j ≤ v i := (hc.total (hvc _ hxi) (hvc _ hj')).elim (fun h => (hmax j hj' h).ge) id
@@ -169,7 +169,7 @@ def chainSup (c : Set (PartialRefinement u s)) (hc : IsChain (· ≤ ·) c) (ne
 theorem le_chainSup {c : Set (PartialRefinement u s)} (hc : IsChain (· ≤ ·) c) (ne : c.Nonempty)
     (hfin : ∀ x ∈ s, { i | x ∈ u i }.Finite) (hU : s ⊆ ⋃ i, u i) {v} (hv : v ∈ c) :
     v ≤ chainSup c hc ne hfin hU :=
-  ⟨fun _ hi => mem_bunionᵢ hv hi, fun _ hi => (find_apply_of_mem hc _ hv hi).symm⟩
+  ⟨fun _ hi => mem_biUnion hv hi, fun _ hi => (find_apply_of_mem hc _ hv hi).symm⟩
 #align shrinking_lemma.partial_refinement.le_chain_Sup ShrinkingLemma.PartialRefinement.le_chainSup
 
 /-- If `s` is a closed set, `v` is a partial refinement, and `i` is an index such that
@@ -177,24 +177,24 @@ theorem le_chainSup {c : Set (PartialRefinement u s)} (hc : IsChain (· ≤ ·)
 theorem exists_gt (v : PartialRefinement u s) (hs : IsClosed s) (i : ι) (hi : i ∉ v.carrier) :
     ∃ v' : PartialRefinement u s, v < v' := by
   have I : (s ∩ ⋂ (j) (_hj : j ≠ i), v jᶜ) ⊆ v i := by
-    simp only [subset_def, mem_inter_iff, mem_interᵢ, and_imp]
+    simp only [subset_def, mem_inter_iff, mem_iInter, and_imp]
     intro x hxs H
-    rcases mem_unionᵢ.1 (v.subset_unionᵢ hxs) with ⟨j, hj⟩
+    rcases mem_iUnion.1 (v.subset_iUnion hxs) with ⟨j, hj⟩
     exact (em (j = i)).elim (fun h => h ▸ hj) fun h => (H j h hj).elim
   have C : IsClosed (s ∩ ⋂ (j) (_hj : j ≠ i), v jᶜ) :=
-    IsClosed.inter hs (isClosed_binterᵢ fun _ _ => isClosed_compl_iff.2 <| v.isOpen _)
+    IsClosed.inter hs (isClosed_biInter fun _ _ => isClosed_compl_iff.2 <| v.isOpen _)
   rcases normal_exists_closure_subset C (v.isOpen i) I with ⟨vi, ovi, hvi, cvi⟩
   refine' ⟨⟨update v i vi, insert i v.carrier, _, _, _, _⟩, _, _⟩
   · intro j
     rcases eq_or_ne j i with (rfl| hne) <;> simp [*, v.isOpen]
-  · refine' fun x hx => mem_unionᵢ.2 _
+  · refine' fun x hx => mem_iUnion.2 _
     rcases em (∃ (j : _)(_ : j ≠ i), x ∈ v j) with (⟨j, hji, hj⟩ | h)
     · use j
       rwa [update_noteq hji]
     · push_neg  at h
       use i
       rw [update_same]
-      exact hvi ⟨hx, mem_binterᵢ h⟩
+      exact hvi ⟨hx, mem_biInter h⟩
   · rintro j (rfl | hj)
     · rwa [update_same, ← v.apply_eq hi]
     · rw [update_noteq (ne_of_mem_of_not_mem hj hi)]
@@ -218,49 +218,49 @@ variable {u : ι → Set X} {s : Set X}
 /-- **Shrinking lemma**. A point-finite open cover of a closed subset of a normal space can be
 "shrunk" to a new open cover so that the closure of each new open set is contained in the
 corresponding original open set. -/
-theorem exists_subset_unionᵢ_closure_subset (hs : IsClosed s) (uo : ∀ i, IsOpen (u i))
+theorem exists_subset_iUnion_closure_subset (hs : IsClosed s) (uo : ∀ i, IsOpen (u i))
     (uf : ∀ x ∈ s, { i | x ∈ u i }.Finite) (us : s ⊆ ⋃ i, u i) :
-    ∃ v : ι → Set X, s ⊆ unionᵢ v ∧ (∀ i, IsOpen (v i)) ∧ ∀ i, closure (v i) ⊆ u i := by
+    ∃ v : ι → Set X, s ⊆ iUnion v ∧ (∀ i, IsOpen (v i)) ∧ ∀ i, closure (v i) ⊆ u i := by
   haveI : Nonempty (PartialRefinement u s) := ⟨⟨u, ∅, uo, us, False.elim, fun _ => rfl⟩⟩
   have : ∀ c : Set (PartialRefinement u s),
       IsChain (· ≤ ·) c → c.Nonempty → ∃ ub, ∀ v ∈ c, v ≤ ub :=
     fun c hc ne => ⟨.chainSup c hc ne uf us, fun v hv => PartialRefinement.le_chainSup _ _ _ _ hv⟩
   rcases zorn_nonempty_partialOrder this with ⟨v, hv⟩
   suffices : ∀ i, i ∈ v.carrier
-  exact ⟨v, v.subset_unionᵢ, fun i => v.isOpen _, fun i => v.closure_subset (this i)⟩
+  exact ⟨v, v.subset_iUnion, fun i => v.isOpen _, fun i => v.closure_subset (this i)⟩
   contrapose! hv
   rcases hv with ⟨i, hi⟩
   rcases v.exists_gt hs i hi with ⟨v', hlt⟩
   exact ⟨v', hlt.le, hlt.ne'⟩
-#align exists_subset_Union_closure_subset exists_subset_unionᵢ_closure_subset
+#align exists_subset_Union_closure_subset exists_subset_iUnion_closure_subset
 
 /-- **Shrinking lemma**. A point-finite open cover of a closed subset of a normal space can be
 "shrunk" to a new closed cover so that each new closed set is contained in the corresponding
-original open set. See also `exists_subset_unionᵢ_closure_subset` for a stronger statement. -/
-theorem exists_subset_unionᵢ_closed_subset (hs : IsClosed s) (uo : ∀ i, IsOpen (u i))
+original open set. See also `exists_subset_iUnion_closure_subset` for a stronger statement. -/
+theorem exists_subset_iUnion_closed_subset (hs : IsClosed s) (uo : ∀ i, IsOpen (u i))
     (uf : ∀ x ∈ s, { i | x ∈ u i }.Finite) (us : s ⊆ ⋃ i, u i) :
-    ∃ v : ι → Set X, s ⊆ unionᵢ v ∧ (∀ i, IsClosed (v i)) ∧ ∀ i, v i ⊆ u i :=
-  let ⟨v, hsv, _, hv⟩ := exists_subset_unionᵢ_closure_subset hs uo uf us
-  ⟨fun i => closure (v i), Subset.trans hsv (unionᵢ_mono fun _ => subset_closure),
+    ∃ v : ι → Set X, s ⊆ iUnion v ∧ (∀ i, IsClosed (v i)) ∧ ∀ i, v i ⊆ u i :=
+  let ⟨v, hsv, _, hv⟩ := exists_subset_iUnion_closure_subset hs uo uf us
+  ⟨fun i => closure (v i), Subset.trans hsv (iUnion_mono fun _ => subset_closure),
     fun _ => isClosed_closure, hv⟩
-#align exists_subset_Union_closed_subset exists_subset_unionᵢ_closed_subset
+#align exists_subset_Union_closed_subset exists_subset_iUnion_closed_subset
 
 /-- Shrinking lemma. A point-finite open cover of a closed subset of a normal space can be "shrunk"
 to a new open cover so that the closure of each new open set is contained in the corresponding
 original open set. -/
-theorem exists_unionᵢ_eq_closure_subset (uo : ∀ i, IsOpen (u i)) (uf : ∀ x, { i | x ∈ u i }.Finite)
+theorem exists_iUnion_eq_closure_subset (uo : ∀ i, IsOpen (u i)) (uf : ∀ x, { i | x ∈ u i }.Finite)
     (uU : (⋃ i, u i) = univ) :
-    ∃ v : ι → Set X, unionᵢ v = univ ∧ (∀ i, IsOpen (v i)) ∧ ∀ i, closure (v i) ⊆ u i :=
-  let ⟨v, vU, hv⟩ := exists_subset_unionᵢ_closure_subset isClosed_univ uo (fun x _ => uf x) uU.ge
+    ∃ v : ι → Set X, iUnion v = univ ∧ (∀ i, IsOpen (v i)) ∧ ∀ i, closure (v i) ⊆ u i :=
+  let ⟨v, vU, hv⟩ := exists_subset_iUnion_closure_subset isClosed_univ uo (fun x _ => uf x) uU.ge
   ⟨v, univ_subset_iff.1 vU, hv⟩
-#align exists_Union_eq_closure_subset exists_unionᵢ_eq_closure_subset
+#align exists_Union_eq_closure_subset exists_iUnion_eq_closure_subset
 
 /-- Shrinking lemma. A point-finite open cover of a closed subset of a normal space can be "shrunk"
 to a new closed cover so that each of the new closed sets is contained in the corresponding
-original open set. See also `exists_unionᵢ_eq_closure_subset` for a stronger statement. -/
-theorem exists_unionᵢ_eq_closed_subset (uo : ∀ i, IsOpen (u i)) (uf : ∀ x, { i | x ∈ u i }.Finite)
+original open set. See also `exists_iUnion_eq_closure_subset` for a stronger statement. -/
+theorem exists_iUnion_eq_closed_subset (uo : ∀ i, IsOpen (u i)) (uf : ∀ x, { i | x ∈ u i }.Finite)
     (uU : (⋃ i, u i) = univ) :
-    ∃ v : ι → Set X, unionᵢ v = univ ∧ (∀ i, IsClosed (v i)) ∧ ∀ i, v i ⊆ u i :=
-  let ⟨v, vU, hv⟩ := exists_subset_unionᵢ_closed_subset isClosed_univ uo (fun x _ => uf x) uU.ge
+    ∃ v : ι → Set X, iUnion v = univ ∧ (∀ i, IsClosed (v i)) ∧ ∀ i, v i ⊆ u i :=
+  let ⟨v, vU, hv⟩ := exists_subset_iUnion_closed_subset isClosed_univ uo (fun x _ => uf x) uU.ge
   ⟨v, univ_subset_iff.1 vU, hv⟩
-#align exists_Union_eq_closed_subset exists_unionᵢ_eq_closed_subset
+#align exists_Union_eq_closed_subset exists_iUnion_eq_closed_subset