data.set.pairwise.lattice | Mathlib porting status

(last sync)

feat(order/sup_indep): More lemmas (#11932)

A few more lemmas about finset.sup_indep and set.pairwise_disjoint.

Diff

@@ -15,16 +15,16 @@ import data.set.pairwise.basic
 In this file we prove many facts about `pairwise` and the set lattice.
 -/
 
-open set function
+open function set order
 
-variables {α β γ ι ι' : Type*} {r p q : α → α → Prop}
+variables {α β γ ι ι' : Type*} {κ : Sort*} {r p q : α → α → Prop}
 
 section pairwise
 variables {f g : ι → α} {s t u : set α} {a b : α}
 
 namespace set
 
-lemma pairwise_Union {f : ι → set α} (h : directed (⊆) f) :
+lemma pairwise_Union {f : κ → set α} (h : directed (⊆) f) :
   (⋃ n, f n).pairwise r ↔ ∀ n, (f n).pairwise r :=
 begin
   split,
@@ -60,7 +60,7 @@ pairwise_sUnion h
 end partial_order_bot
 
 section complete_lattice
-variables [complete_lattice α]
+variables [complete_lattice α] {s : set ι} {t : set ι'}
 
 /-- Bind operation for `set.pairwise_disjoint`. If you want to only consider finsets of indices, you
 can use `set.pairwise_disjoint.bUnion_finset`. -/
@@ -78,8 +78,41 @@ begin
   { exact (hs hc hd $ ne_of_apply_ne _ hcd).mono (le_supr₂ a ha) (le_supr₂ b hb) }
 end
 
+/-- If the suprema of columns are pairwise disjoint and suprema of rows as well, then everything is
+pairwise disjoint. Not to be confused with `set.pairwise_disjoint.prod`. -/
+lemma pairwise_disjoint.prod_left {f : ι × ι' → α}
+  (hs : s.pairwise_disjoint $ λ i, ⨆ i' ∈ t, f (i, i'))
+  (ht : t.pairwise_disjoint $ λ i', ⨆ i ∈ s, f (i, i')) :
+  (s ×ˢ t : set (ι × ι')).pairwise_disjoint f :=
+begin
+  rintro ⟨i, i'⟩ hi ⟨j, j'⟩ hj h,
+  rw mem_prod at hi hj,
+  obtain rfl | hij := eq_or_ne i j,
+  { refine (ht hi.2 hj.2 $ (prod.mk.inj_left _).ne_iff.1 h).mono _ _,
+    { convert le_supr₂ i hi.1, refl },
+    { convert le_supr₂ i hj.1, refl } },
+  { refine (hs hi.1 hj.1 hij).mono _ _,
+    { convert le_supr₂ i' hi.2, refl },
+    { convert le_supr₂ j' hj.2, refl } }
+end
+
 end complete_lattice
 
+section frame
+variables [frame α]
+
+lemma pairwise_disjoint_prod_left {s : set ι} {t : set ι'} {f : ι × ι' → α} :
+  (s ×ˢ t : set (ι × ι')).pairwise_disjoint f ↔ s.pairwise_disjoint (λ i, ⨆ i' ∈ t, f (i, i')) ∧
+    t.pairwise_disjoint (λ i', ⨆ i ∈ s, f (i, i')) :=
+begin
+  refine (⟨λ h, ⟨λ i hi j hj hij, _, λ i hi j hj hij, _⟩, λ h, h.1.prod_left h.2⟩);
+    simp_rw [function.on_fun, supr_disjoint_iff, disjoint_supr_iff]; intros i' hi' j' hj',
+  { exact h (mk_mem_prod hi hi') (mk_mem_prod hj hj') (ne_of_apply_ne prod.fst hij) },
+  { exact h (mk_mem_prod hi' hi) (mk_mem_prod hj' hj) (ne_of_apply_ne prod.snd hij) }
+end
+
+end frame
+
 lemma bUnion_diff_bUnion_eq {s t : set ι} {f : ι → set α} (h : (s ∪ t).pairwise_disjoint f) :
   (⋃ i ∈ s, f i) \ (⋃ i ∈ t, f i) = (⋃ i ∈ s \ t, f i) :=
 begin

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -88,7 +88,7 @@ theorem PairwiseDisjoint.biUnion {s : Set ι'} {g : ι' → Set ι} {f : ι →
     (hg : ∀ i ∈ s, (g i).PairwiseDisjoint f) : (⋃ i ∈ s, g i).PairwiseDisjoint f :=
   by
   rintro a ha b hb hab
-  simp_rw [Set.mem_iUnion] at ha hb 
+  simp_rw [Set.mem_iUnion] at ha hb
   obtain ⟨c, hc, ha⟩ := ha
   obtain ⟨d, hd, hb⟩ := hb
   obtain hcd | hcd := eq_or_ne (g c) (g d)
@@ -107,7 +107,7 @@ theorem PairwiseDisjoint.prod_left {f : ι × ι' → α}
     (s ×ˢ t : Set (ι × ι')).PairwiseDisjoint f :=
   by
   rintro ⟨i, i'⟩ hi ⟨j, j'⟩ hj h
-  rw [mem_prod] at hi hj 
+  rw [mem_prod] at hi hj
   obtain rfl | hij := eq_or_ne i j
   · refine' (ht hi.2 hj.2 <| (Prod.mk.inj_left _).ne_iff.1 h).mono _ _
     · convert le_iSup₂ i hi.1; rfl

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
 -/
-import Mathbin.Data.Set.Lattice
-import Mathbin.Data.Set.Pairwise.Basic
+import Data.Set.Lattice
+import Data.Set.Pairwise.Basic
 
 #align_import data.set.pairwise.lattice from "leanprover-community/mathlib"@"c4c2ed622f43768eff32608d4a0f8a6cec1c047d"

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
-
-! This file was ported from Lean 3 source module data.set.pairwise.lattice
-! leanprover-community/mathlib commit c4c2ed622f43768eff32608d4a0f8a6cec1c047d
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Set.Lattice
 import Mathbin.Data.Set.Pairwise.Basic
 
+#align_import data.set.pairwise.lattice from "leanprover-community/mathlib"@"c4c2ed622f43768eff32608d4a0f8a6cec1c047d"
+
 /-!
 # Relations holding pairwise

bump to nightly-2023-06-20-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/0723536a0522d24fc2f159a096fb3304bef77472

1fb3229c

Diff

@@ -101,6 +101,7 @@ theorem PairwiseDisjoint.biUnion {s : Set ι'} {g : ι' → Set ι} {f : ι →
 -/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print Set.PairwiseDisjoint.prod_left /-
 /-- If the suprema of columns are pairwise disjoint and suprema of rows as well, then everything is
 pairwise disjoint. Not to be confused with `set.pairwise_disjoint.prod`. -/
 theorem PairwiseDisjoint.prod_left {f : ι × ι' → α}
@@ -118,6 +119,7 @@ theorem PairwiseDisjoint.prod_left {f : ι × ι' → α}
     · convert le_iSup₂ i' hi.2; rfl
     · convert le_iSup₂ j' hj.2; rfl
 #align set.pairwise_disjoint.prod_left Set.PairwiseDisjoint.prod_left
+-/
 
 end CompleteLattice
 
@@ -126,6 +128,7 @@ section Frame
 variable [Frame α]
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print Set.pairwiseDisjoint_prod_left /-
 theorem pairwiseDisjoint_prod_left {s : Set ι} {t : Set ι'} {f : ι × ι' → α} :
     (s ×ˢ t : Set (ι × ι')).PairwiseDisjoint f ↔
       (s.PairwiseDisjoint fun i => ⨆ i' ∈ t, f (i, i')) ∧
@@ -138,6 +141,7 @@ theorem pairwiseDisjoint_prod_left {s : Set ι} {t : Set ι'} {f : ι × ι' →
   · exact h (mk_mem_prod hi hi') (mk_mem_prod hj hj') (ne_of_apply_ne Prod.fst hij)
   · exact h (mk_mem_prod hi' hi) (mk_mem_prod hj' hj) (ne_of_apply_ne Prod.snd hij)
 #align set.pairwise_disjoint_prod_left Set.pairwiseDisjoint_prod_left
+-/
 
 end Frame

bump to nightly-2023-06-17-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/893964fc28cefbcffc7cb784ed00a2895b4e65cf

253178d1

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
 
 ! This file was ported from Lean 3 source module data.set.pairwise.lattice
-! leanprover-community/mathlib commit 31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0
+! leanprover-community/mathlib commit c4c2ed622f43768eff32608d4a0f8a6cec1c047d
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -21,9 +21,9 @@ In this file we prove many facts about `pairwise` and the set lattice.
 -/
 
 
-open Set Function
+open Function Set Order
 
-variable {α β γ ι ι' : Type _} {r p q : α → α → Prop}
+variable {α β γ ι ι' : Type _} {κ : Sort _} {r p q : α → α → Prop}
 
 section Pairwise
 
@@ -32,7 +32,7 @@ variable {f g : ι → α} {s t u : Set α} {a b : α}
 namespace Set
 
 #print Set.pairwise_iUnion /-
-theorem pairwise_iUnion {f : ι → Set α} (h : Directed (· ⊆ ·) f) :
+theorem pairwise_iUnion {f : κ → Set α} (h : Directed (· ⊆ ·) f) :
     (⋃ n, f n).Pairwise r ↔ ∀ n, (f n).Pairwise r :=
   by
   constructor
@@ -81,7 +81,7 @@ end PartialOrderBot
 
 section CompleteLattice
 
-variable [CompleteLattice α]
+variable [CompleteLattice α] {s : Set ι} {t : Set ι'}
 
 #print Set.PairwiseDisjoint.biUnion /-
 /-- Bind operation for `set.pairwise_disjoint`. If you want to only consider finsets of indices, you
@@ -100,8 +100,47 @@ theorem PairwiseDisjoint.biUnion {s : Set ι'} {g : ι' → Set ι} {f : ι →
 #align set.pairwise_disjoint.bUnion Set.PairwiseDisjoint.biUnion
 -/
 
+/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+/-- If the suprema of columns are pairwise disjoint and suprema of rows as well, then everything is
+pairwise disjoint. Not to be confused with `set.pairwise_disjoint.prod`. -/
+theorem PairwiseDisjoint.prod_left {f : ι × ι' → α}
+    (hs : s.PairwiseDisjoint fun i => ⨆ i' ∈ t, f (i, i'))
+    (ht : t.PairwiseDisjoint fun i' => ⨆ i ∈ s, f (i, i')) :
+    (s ×ˢ t : Set (ι × ι')).PairwiseDisjoint f :=
+  by
+  rintro ⟨i, i'⟩ hi ⟨j, j'⟩ hj h
+  rw [mem_prod] at hi hj 
+  obtain rfl | hij := eq_or_ne i j
+  · refine' (ht hi.2 hj.2 <| (Prod.mk.inj_left _).ne_iff.1 h).mono _ _
+    · convert le_iSup₂ i hi.1; rfl
+    · convert le_iSup₂ i hj.1; rfl
+  · refine' (hs hi.1 hj.1 hij).mono _ _
+    · convert le_iSup₂ i' hi.2; rfl
+    · convert le_iSup₂ j' hj.2; rfl
+#align set.pairwise_disjoint.prod_left Set.PairwiseDisjoint.prod_left
+
 end CompleteLattice
 
+section Frame
+
+variable [Frame α]
+
+/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+theorem pairwiseDisjoint_prod_left {s : Set ι} {t : Set ι'} {f : ι × ι' → α} :
+    (s ×ˢ t : Set (ι × ι')).PairwiseDisjoint f ↔
+      (s.PairwiseDisjoint fun i => ⨆ i' ∈ t, f (i, i')) ∧
+        t.PairwiseDisjoint fun i' => ⨆ i ∈ s, f (i, i') :=
+  by
+  refine'
+        ⟨fun h => ⟨fun i hi j hj hij => _, fun i hi j hj hij => _⟩, fun h => h.1.prod_left h.2⟩ <;>
+      simp_rw [Function.onFun, iSup_disjoint_iff, disjoint_iSup_iff] <;>
+    intro i' hi' j' hj'
+  · exact h (mk_mem_prod hi hi') (mk_mem_prod hj hj') (ne_of_apply_ne Prod.fst hij)
+  · exact h (mk_mem_prod hi' hi) (mk_mem_prod hj' hj) (ne_of_apply_ne Prod.snd hij)
+#align set.pairwise_disjoint_prod_left Set.pairwiseDisjoint_prod_left
+
+end Frame
+
 #print Set.biUnion_diff_biUnion_eq /-
 theorem biUnion_diff_biUnion_eq {s t : Set ι} {f : ι → Set α} (h : (s ∪ t).PairwiseDisjoint f) :
     ((⋃ i ∈ s, f i) \ ⋃ i ∈ t, f i) = ⋃ i ∈ s \ t, f i :=

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -31,6 +31,7 @@ variable {f g : ι → α} {s t u : Set α} {a b : α}
 
 namespace Set
 
+#print Set.pairwise_iUnion /-
 theorem pairwise_iUnion {f : ι → Set α} (h : Directed (· ⊆ ·) f) :
     (⋃ n, f n).Pairwise r ↔ ∀ n, (f n).Pairwise r :=
   by
@@ -43,6 +44,7 @@ theorem pairwise_iUnion {f : ι → Set α} (h : Directed (· ⊆ ·) f) :
     rcases h m n with ⟨p, mp, np⟩
     exact H p (mp hm) (np hn) hij
 #align set.pairwise_Union Set.pairwise_iUnion
+-/
 
 #print Set.pairwise_sUnion /-
 theorem pairwise_sUnion {r : α → α → Prop} {s : Set (Set α)} (h : DirectedOn (· ⊆ ·) s) :
@@ -61,10 +63,12 @@ section PartialOrderBot
 
 variable [PartialOrder α] [OrderBot α] {s t : Set ι} {f g : ι → α}
 
+#print Set.pairwiseDisjoint_iUnion /-
 theorem pairwiseDisjoint_iUnion {g : ι' → Set ι} (h : Directed (· ⊆ ·) g) :
     (⋃ n, g n).PairwiseDisjoint f ↔ ∀ ⦃n⦄, (g n).PairwiseDisjoint f :=
   pairwise_iUnion h
 #align set.pairwise_disjoint_Union Set.pairwiseDisjoint_iUnion
+-/
 
 #print Set.pairwiseDisjoint_sUnion /-
 theorem pairwiseDisjoint_sUnion {s : Set (Set ι)} (h : DirectedOn (· ⊆ ·) s) :
@@ -79,6 +83,7 @@ section CompleteLattice
 
 variable [CompleteLattice α]
 
+#print Set.PairwiseDisjoint.biUnion /-
 /-- Bind operation for `set.pairwise_disjoint`. If you want to only consider finsets of indices, you
 can use `set.pairwise_disjoint.bUnion_finset`. -/
 theorem PairwiseDisjoint.biUnion {s : Set ι'} {g : ι' → Set ι} {f : ι → α}
@@ -93,9 +98,11 @@ theorem PairwiseDisjoint.biUnion {s : Set ι'} {g : ι' → Set ι} {f : ι →
   · exact hg d hd (hcd.subst ha) hb hab
   · exact (hs hc hd <| ne_of_apply_ne _ hcd).mono (le_iSup₂ a ha) (le_iSup₂ b hb)
 #align set.pairwise_disjoint.bUnion Set.PairwiseDisjoint.biUnion
+-/
 
 end CompleteLattice
 
+#print Set.biUnion_diff_biUnion_eq /-
 theorem biUnion_diff_biUnion_eq {s t : Set ι} {f : ι → Set α} (h : (s ∪ t).PairwiseDisjoint f) :
     ((⋃ i ∈ s, f i) \ ⋃ i ∈ t, f i) = ⋃ i ∈ s \ t, f i :=
   by
@@ -105,13 +112,16 @@ theorem biUnion_diff_biUnion_eq {s t : Set ι} {f : ι → Set α} (h : (s ∪ t
   rw [mem_Union₂]; rintro ⟨j, hj, haj⟩
   exact (h (Or.inl hi.1) (Or.inr hj) (ne_of_mem_of_not_mem hj hi.2).symm).le_bot ⟨ha, haj⟩
 #align set.bUnion_diff_bUnion_eq Set.biUnion_diff_biUnion_eq
+-/
 
+#print Set.biUnionEqSigmaOfDisjoint /-
 /-- Equivalence between a disjoint bounded union and a dependent sum. -/
 noncomputable def biUnionEqSigmaOfDisjoint {s : Set ι} {f : ι → Set α} (h : s.PairwiseDisjoint f) :
     (⋃ i ∈ s, f i) ≃ Σ i : s, f i :=
   (Equiv.setCongr (biUnion_eq_iUnion _ _)).trans <|
     unionEqSigmaOfDisjoint fun ⟨i, hi⟩ ⟨j, hj⟩ ne => h hi hj fun eq => Ne <| Subtype.eq Eq
 #align set.bUnion_eq_sigma_of_disjoint Set.biUnionEqSigmaOfDisjoint
+-/
 
 end Set
 
@@ -119,6 +129,7 @@ section
 
 variable {f : ι → Set α} {s t : Set ι}
 
+#print Set.PairwiseDisjoint.subset_of_biUnion_subset_biUnion /-
 theorem Set.PairwiseDisjoint.subset_of_biUnion_subset_biUnion (h₀ : (s ∪ t).PairwiseDisjoint f)
     (h₁ : ∀ i ∈ s, (f i).Nonempty) (h : (⋃ i ∈ s, f i) ⊆ ⋃ i ∈ t, f i) : s ⊆ t :=
   by
@@ -128,17 +139,22 @@ theorem Set.PairwiseDisjoint.subset_of_biUnion_subset_biUnion (h₀ : (s ∪ t).
   rwa [h₀.eq (subset_union_left _ _ hi) (subset_union_right _ _ hj)
       (not_disjoint_iff.2 ⟨a, hai, haj⟩)]
 #align set.pairwise_disjoint.subset_of_bUnion_subset_bUnion Set.PairwiseDisjoint.subset_of_biUnion_subset_biUnion
+-/
 
+#print Pairwise.subset_of_biUnion_subset_biUnion /-
 theorem Pairwise.subset_of_biUnion_subset_biUnion (h₀ : Pairwise (Disjoint on f))
     (h₁ : ∀ i ∈ s, (f i).Nonempty) (h : (⋃ i ∈ s, f i) ⊆ ⋃ i ∈ t, f i) : s ⊆ t :=
   Set.PairwiseDisjoint.subset_of_biUnion_subset_biUnion (h₀.set_pairwise _) h₁ h
 #align pairwise.subset_of_bUnion_subset_bUnion Pairwise.subset_of_biUnion_subset_biUnion
+-/
 
+#print Pairwise.biUnion_injective /-
 theorem Pairwise.biUnion_injective (h₀ : Pairwise (Disjoint on f)) (h₁ : ∀ i, (f i).Nonempty) :
     Injective fun s : Set ι => ⋃ i ∈ s, f i := fun s t h =>
   ((h₀.subset_of_biUnion_subset_biUnion fun _ _ => h₁ _) <| h.Subset).antisymm <|
     (h₀.subset_of_biUnion_subset_biUnion fun _ _ => h₁ _) <| h.Superset
 #align pairwise.bUnion_injective Pairwise.biUnion_injective
+-/
 
 end

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -86,7 +86,7 @@ theorem PairwiseDisjoint.biUnion {s : Set ι'} {g : ι' → Set ι} {f : ι →
     (hg : ∀ i ∈ s, (g i).PairwiseDisjoint f) : (⋃ i ∈ s, g i).PairwiseDisjoint f :=
   by
   rintro a ha b hb hab
-  simp_rw [Set.mem_iUnion] at ha hb
+  simp_rw [Set.mem_iUnion] at ha hb 
   obtain ⟨c, hc, ha⟩ := ha
   obtain ⟨d, hd, hb⟩ := hb
   obtain hcd | hcd := eq_or_ne (g c) (g d)
@@ -108,7 +108,7 @@ theorem biUnion_diff_biUnion_eq {s t : Set ι} {f : ι → Set α} (h : (s ∪ t
 
 /-- Equivalence between a disjoint bounded union and a dependent sum. -/
 noncomputable def biUnionEqSigmaOfDisjoint {s : Set ι} {f : ι → Set α} (h : s.PairwiseDisjoint f) :
-    (⋃ i ∈ s, f i) ≃ Σi : s, f i :=
+    (⋃ i ∈ s, f i) ≃ Σ i : s, f i :=
   (Equiv.setCongr (biUnion_eq_iUnion _ _)).trans <|
     unionEqSigmaOfDisjoint fun ⟨i, hi⟩ ⟨j, hj⟩ ne => h hi hj fun eq => Ne <| Subtype.eq Eq
 #align set.bUnion_eq_sigma_of_disjoint Set.biUnionEqSigmaOfDisjoint

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -66,10 +66,12 @@ theorem pairwiseDisjoint_iUnion {g : ι' → Set ι} (h : Directed (· ⊆ ·) g
   pairwise_iUnion h
 #align set.pairwise_disjoint_Union Set.pairwiseDisjoint_iUnion
 
+#print Set.pairwiseDisjoint_sUnion /-
 theorem pairwiseDisjoint_sUnion {s : Set (Set ι)} (h : DirectedOn (· ⊆ ·) s) :
     (⋃₀ s).PairwiseDisjoint f ↔ ∀ ⦃a⦄, a ∈ s → Set.PairwiseDisjoint a f :=
   pairwise_sUnion h
 #align set.pairwise_disjoint_sUnion Set.pairwiseDisjoint_sUnion
+-/
 
 end PartialOrderBot

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -31,12 +31,6 @@ variable {f g : ι → α} {s t u : Set α} {a b : α}
 
 namespace Set
 
-/- warning: set.pairwise_Union -> Set.pairwise_iUnion is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Type.{u2}} {r : α -> α -> Prop} {f : ι -> (Set.{u1} α)}, (Directed.{u1, succ u2} (Set.{u1} α) ι (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α)) f) -> (Iff (Set.Pairwise.{u1} α (Set.iUnion.{u1, succ u2} α ι (fun (n : ι) => f n)) r) (forall (n : ι), Set.Pairwise.{u1} α (f n) r))
-but is expected to have type
-  forall {α : Type.{u2}} {ι : Type.{u1}} {r : α -> α -> Prop} {f : ι -> (Set.{u2} α)}, (Directed.{u2, succ u1} (Set.{u2} α) ι (fun (x._@.Mathlib.Data.Set.Pairwise.Lattice._hyg.120 : Set.{u2} α) (x._@.Mathlib.Data.Set.Pairwise.Lattice._hyg.122 : Set.{u2} α) => HasSubset.Subset.{u2} (Set.{u2} α) (Set.instHasSubsetSet.{u2} α) x._@.Mathlib.Data.Set.Pairwise.Lattice._hyg.120 x._@.Mathlib.Data.Set.Pairwise.Lattice._hyg.122) f) -> (Iff (Set.Pairwise.{u2} α (Set.iUnion.{u2, succ u1} α ι (fun (n : ι) => f n)) r) (forall (n : ι), Set.Pairwise.{u2} α (f n) r))
-Case conversion may be inaccurate. Consider using '#align set.pairwise_Union Set.pairwise_iUnionₓ'. -/
 theorem pairwise_iUnion {f : ι → Set α} (h : Directed (· ⊆ ·) f) :
     (⋃ n, f n).Pairwise r ↔ ∀ n, (f n).Pairwise r :=
   by
@@ -67,23 +61,11 @@ section PartialOrderBot
 
 variable [PartialOrder α] [OrderBot α] {s t : Set ι} {f g : ι → α}
 
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-Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Union Set.pairwiseDisjoint_iUnionₓ'. -/
 theorem pairwiseDisjoint_iUnion {g : ι' → Set ι} (h : Directed (· ⊆ ·) g) :
     (⋃ n, g n).PairwiseDisjoint f ↔ ∀ ⦃n⦄, (g n).PairwiseDisjoint f :=
   pairwise_iUnion h
 #align set.pairwise_disjoint_Union Set.pairwiseDisjoint_iUnion
 
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-Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_sUnion Set.pairwiseDisjoint_sUnionₓ'. -/
 theorem pairwiseDisjoint_sUnion {s : Set (Set ι)} (h : DirectedOn (· ⊆ ·) s) :
     (⋃₀ s).PairwiseDisjoint f ↔ ∀ ⦃a⦄, a ∈ s → Set.PairwiseDisjoint a f :=
   pairwise_sUnion h
@@ -95,12 +77,6 @@ section CompleteLattice
 
 variable [CompleteLattice α]
 
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-Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint.bUnion Set.PairwiseDisjoint.biUnionₓ'. -/
 /-- Bind operation for `set.pairwise_disjoint`. If you want to only consider finsets of indices, you
 can use `set.pairwise_disjoint.bUnion_finset`. -/
 theorem PairwiseDisjoint.biUnion {s : Set ι'} {g : ι' → Set ι} {f : ι → α}
@@ -118,12 +94,6 @@ theorem PairwiseDisjoint.biUnion {s : Set ι'} {g : ι' → Set ι} {f : ι →
 
 end CompleteLattice
 
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-Case conversion may be inaccurate. Consider using '#align set.bUnion_diff_bUnion_eq Set.biUnion_diff_biUnion_eqₓ'. -/
 theorem biUnion_diff_biUnion_eq {s t : Set ι} {f : ι → Set α} (h : (s ∪ t).PairwiseDisjoint f) :
     ((⋃ i ∈ s, f i) \ ⋃ i ∈ t, f i) = ⋃ i ∈ s \ t, f i :=
   by
@@ -134,12 +104,6 @@ theorem biUnion_diff_biUnion_eq {s t : Set ι} {f : ι → Set α} (h : (s ∪ t
   exact (h (Or.inl hi.1) (Or.inr hj) (ne_of_mem_of_not_mem hj hi.2).symm).le_bot ⟨ha, haj⟩
 #align set.bUnion_diff_bUnion_eq Set.biUnion_diff_biUnion_eq
 
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-Case conversion may be inaccurate. Consider using '#align set.bUnion_eq_sigma_of_disjoint Set.biUnionEqSigmaOfDisjointₓ'. -/
 /-- Equivalence between a disjoint bounded union and a dependent sum. -/
 noncomputable def biUnionEqSigmaOfDisjoint {s : Set ι} {f : ι → Set α} (h : s.PairwiseDisjoint f) :
     (⋃ i ∈ s, f i) ≃ Σi : s, f i :=
@@ -153,12 +117,6 @@ section
 
 variable {f : ι → Set α} {s t : Set ι}
 
-/- warning: set.pairwise_disjoint.subset_of_bUnion_subset_bUnion -> Set.PairwiseDisjoint.subset_of_biUnion_subset_biUnion is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint.subset_of_bUnion_subset_bUnion Set.PairwiseDisjoint.subset_of_biUnion_subset_biUnionₓ'. -/
 theorem Set.PairwiseDisjoint.subset_of_biUnion_subset_biUnion (h₀ : (s ∪ t).PairwiseDisjoint f)
     (h₁ : ∀ i ∈ s, (f i).Nonempty) (h : (⋃ i ∈ s, f i) ⊆ ⋃ i ∈ t, f i) : s ⊆ t :=
   by
@@ -169,23 +127,11 @@ theorem Set.PairwiseDisjoint.subset_of_biUnion_subset_biUnion (h₀ : (s ∪ t).
       (not_disjoint_iff.2 ⟨a, hai, haj⟩)]
 #align set.pairwise_disjoint.subset_of_bUnion_subset_bUnion Set.PairwiseDisjoint.subset_of_biUnion_subset_biUnion
 
-/- warning: pairwise.subset_of_bUnion_subset_bUnion -> Pairwise.subset_of_biUnion_subset_biUnion is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align pairwise.subset_of_bUnion_subset_bUnion Pairwise.subset_of_biUnion_subset_biUnionₓ'. -/
 theorem Pairwise.subset_of_biUnion_subset_biUnion (h₀ : Pairwise (Disjoint on f))
     (h₁ : ∀ i ∈ s, (f i).Nonempty) (h : (⋃ i ∈ s, f i) ⊆ ⋃ i ∈ t, f i) : s ⊆ t :=
   Set.PairwiseDisjoint.subset_of_biUnion_subset_biUnion (h₀.set_pairwise _) h₁ h
 #align pairwise.subset_of_bUnion_subset_bUnion Pairwise.subset_of_biUnion_subset_biUnion
 
-/- warning: pairwise.bUnion_injective -> Pairwise.biUnion_injective is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align pairwise.bUnion_injective Pairwise.biUnion_injectiveₓ'. -/
 theorem Pairwise.biUnion_injective (h₀ : Pairwise (Disjoint on f)) (h₁ : ∀ i, (f i).Nonempty) :
     Injective fun s : Set ι => ⋃ i ∈ s, f i := fun s t h =>
   ((h₀.subset_of_biUnion_subset_biUnion fun _ _ => h₁ _) <| h.Subset).antisymm <|

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -52,10 +52,8 @@ theorem pairwise_iUnion {f : ι → Set α} (h : Directed (· ⊆ ·) f) :
 
 #print Set.pairwise_sUnion /-
 theorem pairwise_sUnion {r : α → α → Prop} {s : Set (Set α)} (h : DirectedOn (· ⊆ ·) s) :
-    (⋃₀ s).Pairwise r ↔ ∀ a ∈ s, Set.Pairwise a r :=
-  by
-  rw [sUnion_eq_Union, pairwise_Union h.directed_coe, SetCoe.forall]
-  rfl
+    (⋃₀ s).Pairwise r ↔ ∀ a ∈ s, Set.Pairwise a r := by
+  rw [sUnion_eq_Union, pairwise_Union h.directed_coe, SetCoe.forall]; rfl
 #align set.pairwise_sUnion Set.pairwise_sUnion
 -/

bump to nightly-2023-05-16-16

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

9cb92e8c

Diff

@@ -71,7 +71,7 @@ variable [PartialOrder α] [OrderBot α] {s t : Set ι} {f g : ι → α}
 
 /- warning: set.pairwise_disjoint_Union -> Set.pairwiseDisjoint_iUnion is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Type.{u2}} {ι' : Type.{u3}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {f : ι -> α} {g : ι' -> (Set.{u2} ι)}, (Directed.{u2, succ u3} (Set.{u2} ι) ι' (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.hasSubset.{u2} ι)) g) -> (Iff (Set.PairwiseDisjoint.{u1, u2} α ι _inst_1 _inst_2 (Set.iUnion.{u2, succ u3} ι ι' (fun (n : ι') => g n)) f) (forall {{n : ι'}}, Set.PairwiseDisjoint.{u1, u2} α ι _inst_1 _inst_2 (g n) f))
+  forall {α : Type.{u1}} {ι : Type.{u2}} {ι' : Type.{u3}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {f : ι -> α} {g : ι' -> (Set.{u2} ι)}, (Directed.{u2, succ u3} (Set.{u2} ι) ι' (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.hasSubset.{u2} ι)) g) -> (Iff (Set.PairwiseDisjoint.{u1, u2} α ι _inst_1 _inst_2 (Set.iUnion.{u2, succ u3} ι ι' (fun (n : ι') => g n)) f) (forall {{n : ι'}}, Set.PairwiseDisjoint.{u1, u2} α ι _inst_1 _inst_2 (g n) f))
 but is expected to have type
   forall {α : Type.{u1}} {ι : Type.{u3}} {ι' : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {f : ι -> α} {g : ι' -> (Set.{u3} ι)}, (Directed.{u3, succ u2} (Set.{u3} ι) ι' (fun (x._@.Mathlib.Data.Set.Pairwise.Lattice._hyg.443 : Set.{u3} ι) (x._@.Mathlib.Data.Set.Pairwise.Lattice._hyg.445 : Set.{u3} ι) => HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) x._@.Mathlib.Data.Set.Pairwise.Lattice._hyg.443 x._@.Mathlib.Data.Set.Pairwise.Lattice._hyg.445) g) -> (Iff (Set.PairwiseDisjoint.{u1, u3} α ι _inst_1 _inst_2 (Set.iUnion.{u3, succ u2} ι ι' (fun (n : ι') => g n)) f) (forall {{n : ι'}}, Set.PairwiseDisjoint.{u1, u3} α ι _inst_1 _inst_2 (g n) f))
 Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Union Set.pairwiseDisjoint_iUnionₓ'. -/
@@ -80,12 +80,16 @@ theorem pairwiseDisjoint_iUnion {g : ι' → Set ι} (h : Directed (· ⊆ ·) g
   pairwise_iUnion h
 #align set.pairwise_disjoint_Union Set.pairwiseDisjoint_iUnion
 
-#print Set.pairwiseDisjoint_sUnion /-
+/- warning: set.pairwise_disjoint_sUnion -> Set.pairwiseDisjoint_sUnion is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {f : ι -> α} {s : Set.{u2} (Set.{u2} ι)}, (DirectedOn.{u2} (Set.{u2} ι) (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.hasSubset.{u2} ι)) s) -> (Iff (Set.PairwiseDisjoint.{u1, u2} α ι _inst_1 _inst_2 (Set.sUnion.{u2} ι s) f) (forall {{a : Set.{u2} ι}}, (Membership.Mem.{u2, u2} (Set.{u2} ι) (Set.{u2} (Set.{u2} ι)) (Set.hasMem.{u2} (Set.{u2} ι)) a s) -> (Set.PairwiseDisjoint.{u1, u2} α ι _inst_1 _inst_2 a f)))
+but is expected to have type
+  forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {f : ι -> α} {s : Set.{u2} (Set.{u2} ι)}, (DirectedOn.{u2} (Set.{u2} ι) (fun (x._@.Mathlib.Data.Set.Pairwise.Lattice._hyg.539 : Set.{u2} ι) (x._@.Mathlib.Data.Set.Pairwise.Lattice._hyg.541 : Set.{u2} ι) => HasSubset.Subset.{u2} (Set.{u2} ι) (Set.instHasSubsetSet.{u2} ι) x._@.Mathlib.Data.Set.Pairwise.Lattice._hyg.539 x._@.Mathlib.Data.Set.Pairwise.Lattice._hyg.541) s) -> (Iff (Set.PairwiseDisjoint.{u1, u2} α ι _inst_1 _inst_2 (Set.sUnion.{u2} ι s) f) (forall {{a : Set.{u2} ι}}, (Membership.mem.{u2, u2} (Set.{u2} ι) (Set.{u2} (Set.{u2} ι)) (Set.instMembershipSet.{u2} (Set.{u2} ι)) a s) -> (Set.PairwiseDisjoint.{u1, u2} α ι _inst_1 _inst_2 a f)))
+Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_sUnion Set.pairwiseDisjoint_sUnionₓ'. -/
 theorem pairwiseDisjoint_sUnion {s : Set (Set ι)} (h : DirectedOn (· ⊆ ·) s) :
     (⋃₀ s).PairwiseDisjoint f ↔ ∀ ⦃a⦄, a ∈ s → Set.PairwiseDisjoint a f :=
   pairwise_sUnion h
 #align set.pairwise_disjoint_sUnion Set.pairwiseDisjoint_sUnion
--/
 
 end PartialOrderBot
 
@@ -95,7 +99,7 @@ variable [CompleteLattice α]
 
 /- warning: set.pairwise_disjoint.bUnion -> Set.PairwiseDisjoint.biUnion is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Type.{u2}} {ι' : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u3} ι'} {g : ι' -> (Set.{u2} ι)} {f : ι -> α}, (Set.PairwiseDisjoint.{u1, u3} α ι' (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) s (fun (i' : ι') => iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i (g i')) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i (g i')) => f i)))) -> (forall (i : ι'), (Membership.Mem.{u3, u3} ι' (Set.{u3} ι') (Set.hasMem.{u3} ι') i s) -> (Set.PairwiseDisjoint.{u1, u2} α ι (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) (g i) f)) -> (Set.PairwiseDisjoint.{u1, u2} α ι (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) (Set.iUnion.{u2, succ u3} ι ι' (fun (i : ι') => Set.iUnion.{u2, 0} ι (Membership.Mem.{u3, u3} ι' (Set.{u3} ι') (Set.hasMem.{u3} ι') i s) (fun (H : Membership.Mem.{u3, u3} ι' (Set.{u3} ι') (Set.hasMem.{u3} ι') i s) => g i))) f)
+  forall {α : Type.{u1}} {ι : Type.{u2}} {ι' : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u3} ι'} {g : ι' -> (Set.{u2} ι)} {f : ι -> α}, (Set.PairwiseDisjoint.{u1, u3} α ι' (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) s (fun (i' : ι') => iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i (g i')) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i (g i')) => f i)))) -> (forall (i : ι'), (Membership.Mem.{u3, u3} ι' (Set.{u3} ι') (Set.hasMem.{u3} ι') i s) -> (Set.PairwiseDisjoint.{u1, u2} α ι (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) (g i) f)) -> (Set.PairwiseDisjoint.{u1, u2} α ι (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) (Set.iUnion.{u2, succ u3} ι ι' (fun (i : ι') => Set.iUnion.{u2, 0} ι (Membership.Mem.{u3, u3} ι' (Set.{u3} ι') (Set.hasMem.{u3} ι') i s) (fun (H : Membership.Mem.{u3, u3} ι' (Set.{u3} ι') (Set.hasMem.{u3} ι') i s) => g i))) f)
 but is expected to have type
   forall {α : Type.{u1}} {ι : Type.{u2}} {ι' : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u3} ι'} {g : ι' -> (Set.{u2} ι)} {f : ι -> α}, (Set.PairwiseDisjoint.{u1, u3} α ι' (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) s (fun (i' : ι') => iSup.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (i : ι) => iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i (g i')) (fun (H : Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i (g i')) => f i)))) -> (forall (i : ι'), (Membership.mem.{u3, u3} ι' (Set.{u3} ι') (Set.instMembershipSet.{u3} ι') i s) -> (Set.PairwiseDisjoint.{u1, u2} α ι (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) (g i) f)) -> (Set.PairwiseDisjoint.{u1, u2} α ι (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) (Set.iUnion.{u2, succ u3} ι ι' (fun (i : ι') => Set.iUnion.{u2, 0} ι (Membership.mem.{u3, u3} ι' (Set.{u3} ι') (Set.instMembershipSet.{u3} ι') i s) (fun (H : Membership.mem.{u3, u3} ι' (Set.{u3} ι') (Set.instMembershipSet.{u3} ι') i s) => g i))) f)
 Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint.bUnion Set.PairwiseDisjoint.biUnionₓ'. -/

bump to nightly-2023-05-14-08

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

d31da313

Diff

@@ -31,13 +31,13 @@ variable {f g : ι → α} {s t u : Set α} {a b : α}
 
 namespace Set
 
-/- warning: set.pairwise_Union -> Set.pairwise_unionᵢ is a dubious translation:
+/- warning: set.pairwise_Union -> Set.pairwise_iUnion is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Type.{u2}} {r : α -> α -> Prop} {f : ι -> (Set.{u1} α)}, (Directed.{u1, succ u2} (Set.{u1} α) ι (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α)) f) -> (Iff (Set.Pairwise.{u1} α (Set.unionᵢ.{u1, succ u2} α ι (fun (n : ι) => f n)) r) (forall (n : ι), Set.Pairwise.{u1} α (f n) r))
+  forall {α : Type.{u1}} {ι : Type.{u2}} {r : α -> α -> Prop} {f : ι -> (Set.{u1} α)}, (Directed.{u1, succ u2} (Set.{u1} α) ι (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α)) f) -> (Iff (Set.Pairwise.{u1} α (Set.iUnion.{u1, succ u2} α ι (fun (n : ι) => f n)) r) (forall (n : ι), Set.Pairwise.{u1} α (f n) r))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Type.{u1}} {r : α -> α -> Prop} {f : ι -> (Set.{u2} α)}, (Directed.{u2, succ u1} (Set.{u2} α) ι (fun (x._@.Mathlib.Data.Set.Pairwise.Lattice._hyg.120 : Set.{u2} α) (x._@.Mathlib.Data.Set.Pairwise.Lattice._hyg.122 : Set.{u2} α) => HasSubset.Subset.{u2} (Set.{u2} α) (Set.instHasSubsetSet.{u2} α) x._@.Mathlib.Data.Set.Pairwise.Lattice._hyg.120 x._@.Mathlib.Data.Set.Pairwise.Lattice._hyg.122) f) -> (Iff (Set.Pairwise.{u2} α (Set.unionᵢ.{u2, succ u1} α ι (fun (n : ι) => f n)) r) (forall (n : ι), Set.Pairwise.{u2} α (f n) r))
-Case conversion may be inaccurate. Consider using '#align set.pairwise_Union Set.pairwise_unionᵢₓ'. -/
-theorem pairwise_unionᵢ {f : ι → Set α} (h : Directed (· ⊆ ·) f) :
+  forall {α : Type.{u2}} {ι : Type.{u1}} {r : α -> α -> Prop} {f : ι -> (Set.{u2} α)}, (Directed.{u2, succ u1} (Set.{u2} α) ι (fun (x._@.Mathlib.Data.Set.Pairwise.Lattice._hyg.120 : Set.{u2} α) (x._@.Mathlib.Data.Set.Pairwise.Lattice._hyg.122 : Set.{u2} α) => HasSubset.Subset.{u2} (Set.{u2} α) (Set.instHasSubsetSet.{u2} α) x._@.Mathlib.Data.Set.Pairwise.Lattice._hyg.120 x._@.Mathlib.Data.Set.Pairwise.Lattice._hyg.122) f) -> (Iff (Set.Pairwise.{u2} α (Set.iUnion.{u2, succ u1} α ι (fun (n : ι) => f n)) r) (forall (n : ι), Set.Pairwise.{u2} α (f n) r))
+Case conversion may be inaccurate. Consider using '#align set.pairwise_Union Set.pairwise_iUnionₓ'. -/
+theorem pairwise_iUnion {f : ι → Set α} (h : Directed (· ⊆ ·) f) :
     (⋃ n, f n).Pairwise r ↔ ∀ n, (f n).Pairwise r :=
   by
   constructor
@@ -48,15 +48,15 @@ theorem pairwise_unionᵢ {f : ι → Set α} (h : Directed (· ⊆ ·) f) :
     rcases mem_Union.1 hj with ⟨n, hn⟩
     rcases h m n with ⟨p, mp, np⟩
     exact H p (mp hm) (np hn) hij
-#align set.pairwise_Union Set.pairwise_unionᵢ
+#align set.pairwise_Union Set.pairwise_iUnion
 
-#print Set.pairwise_unionₛ /-
-theorem pairwise_unionₛ {r : α → α → Prop} {s : Set (Set α)} (h : DirectedOn (· ⊆ ·) s) :
+#print Set.pairwise_sUnion /-
+theorem pairwise_sUnion {r : α → α → Prop} {s : Set (Set α)} (h : DirectedOn (· ⊆ ·) s) :
     (⋃₀ s).Pairwise r ↔ ∀ a ∈ s, Set.Pairwise a r :=
   by
   rw [sUnion_eq_Union, pairwise_Union h.directed_coe, SetCoe.forall]
   rfl
-#align set.pairwise_sUnion Set.pairwise_unionₛ
+#align set.pairwise_sUnion Set.pairwise_sUnion
 -/
 
 end Set
@@ -69,22 +69,22 @@ section PartialOrderBot
 
 variable [PartialOrder α] [OrderBot α] {s t : Set ι} {f g : ι → α}
 
-/- warning: set.pairwise_disjoint_Union -> Set.pairwiseDisjoint_unionᵢ is a dubious translation:
+/- warning: set.pairwise_disjoint_Union -> Set.pairwiseDisjoint_iUnion is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Type.{u2}} {ι' : Type.{u3}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {f : ι -> α} {g : ι' -> (Set.{u2} ι)}, (Directed.{u2, succ u3} (Set.{u2} ι) ι' (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.hasSubset.{u2} ι)) g) -> (Iff (Set.PairwiseDisjoint.{u1, u2} α ι _inst_1 _inst_2 (Set.unionᵢ.{u2, succ u3} ι ι' (fun (n : ι') => g n)) f) (forall {{n : ι'}}, Set.PairwiseDisjoint.{u1, u2} α ι _inst_1 _inst_2 (g n) f))
+  forall {α : Type.{u1}} {ι : Type.{u2}} {ι' : Type.{u3}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {f : ι -> α} {g : ι' -> (Set.{u2} ι)}, (Directed.{u2, succ u3} (Set.{u2} ι) ι' (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.hasSubset.{u2} ι)) g) -> (Iff (Set.PairwiseDisjoint.{u1, u2} α ι _inst_1 _inst_2 (Set.iUnion.{u2, succ u3} ι ι' (fun (n : ι') => g n)) f) (forall {{n : ι'}}, Set.PairwiseDisjoint.{u1, u2} α ι _inst_1 _inst_2 (g n) f))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Type.{u3}} {ι' : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {f : ι -> α} {g : ι' -> (Set.{u3} ι)}, (Directed.{u3, succ u2} (Set.{u3} ι) ι' (fun (x._@.Mathlib.Data.Set.Pairwise.Lattice._hyg.443 : Set.{u3} ι) (x._@.Mathlib.Data.Set.Pairwise.Lattice._hyg.445 : Set.{u3} ι) => HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) x._@.Mathlib.Data.Set.Pairwise.Lattice._hyg.443 x._@.Mathlib.Data.Set.Pairwise.Lattice._hyg.445) g) -> (Iff (Set.PairwiseDisjoint.{u1, u3} α ι _inst_1 _inst_2 (Set.unionᵢ.{u3, succ u2} ι ι' (fun (n : ι') => g n)) f) (forall {{n : ι'}}, Set.PairwiseDisjoint.{u1, u3} α ι _inst_1 _inst_2 (g n) f))
-Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Union Set.pairwiseDisjoint_unionᵢₓ'. -/
-theorem pairwiseDisjoint_unionᵢ {g : ι' → Set ι} (h : Directed (· ⊆ ·) g) :
+  forall {α : Type.{u1}} {ι : Type.{u3}} {ι' : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {f : ι -> α} {g : ι' -> (Set.{u3} ι)}, (Directed.{u3, succ u2} (Set.{u3} ι) ι' (fun (x._@.Mathlib.Data.Set.Pairwise.Lattice._hyg.443 : Set.{u3} ι) (x._@.Mathlib.Data.Set.Pairwise.Lattice._hyg.445 : Set.{u3} ι) => HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) x._@.Mathlib.Data.Set.Pairwise.Lattice._hyg.443 x._@.Mathlib.Data.Set.Pairwise.Lattice._hyg.445) g) -> (Iff (Set.PairwiseDisjoint.{u1, u3} α ι _inst_1 _inst_2 (Set.iUnion.{u3, succ u2} ι ι' (fun (n : ι') => g n)) f) (forall {{n : ι'}}, Set.PairwiseDisjoint.{u1, u3} α ι _inst_1 _inst_2 (g n) f))
+Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Union Set.pairwiseDisjoint_iUnionₓ'. -/
+theorem pairwiseDisjoint_iUnion {g : ι' → Set ι} (h : Directed (· ⊆ ·) g) :
     (⋃ n, g n).PairwiseDisjoint f ↔ ∀ ⦃n⦄, (g n).PairwiseDisjoint f :=
-  pairwise_unionᵢ h
-#align set.pairwise_disjoint_Union Set.pairwiseDisjoint_unionᵢ
+  pairwise_iUnion h
+#align set.pairwise_disjoint_Union Set.pairwiseDisjoint_iUnion
 
-#print Set.pairwiseDisjoint_unionₛ /-
-theorem pairwiseDisjoint_unionₛ {s : Set (Set ι)} (h : DirectedOn (· ⊆ ·) s) :
+#print Set.pairwiseDisjoint_sUnion /-
+theorem pairwiseDisjoint_sUnion {s : Set (Set ι)} (h : DirectedOn (· ⊆ ·) s) :
     (⋃₀ s).PairwiseDisjoint f ↔ ∀ ⦃a⦄, a ∈ s → Set.PairwiseDisjoint a f :=
-  pairwise_unionₛ h
-#align set.pairwise_disjoint_sUnion Set.pairwiseDisjoint_unionₛ
+  pairwise_sUnion h
+#align set.pairwise_disjoint_sUnion Set.pairwiseDisjoint_sUnion
 -/
 
 end PartialOrderBot
@@ -93,36 +93,36 @@ section CompleteLattice
 
 variable [CompleteLattice α]
 
-/- warning: set.pairwise_disjoint.bUnion -> Set.PairwiseDisjoint.bunionᵢ is a dubious translation:
+/- warning: set.pairwise_disjoint.bUnion -> Set.PairwiseDisjoint.biUnion is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Type.{u2}} {ι' : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u3} ι'} {g : ι' -> (Set.{u2} ι)} {f : ι -> α}, (Set.PairwiseDisjoint.{u1, u3} α ι' (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) s (fun (i' : ι') => supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i (g i')) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i (g i')) => f i)))) -> (forall (i : ι'), (Membership.Mem.{u3, u3} ι' (Set.{u3} ι') (Set.hasMem.{u3} ι') i s) -> (Set.PairwiseDisjoint.{u1, u2} α ι (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) (g i) f)) -> (Set.PairwiseDisjoint.{u1, u2} α ι (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) (Set.unionᵢ.{u2, succ u3} ι ι' (fun (i : ι') => Set.unionᵢ.{u2, 0} ι (Membership.Mem.{u3, u3} ι' (Set.{u3} ι') (Set.hasMem.{u3} ι') i s) (fun (H : Membership.Mem.{u3, u3} ι' (Set.{u3} ι') (Set.hasMem.{u3} ι') i s) => g i))) f)
+  forall {α : Type.{u1}} {ι : Type.{u2}} {ι' : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u3} ι'} {g : ι' -> (Set.{u2} ι)} {f : ι -> α}, (Set.PairwiseDisjoint.{u1, u3} α ι' (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) s (fun (i' : ι') => iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i (g i')) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i (g i')) => f i)))) -> (forall (i : ι'), (Membership.Mem.{u3, u3} ι' (Set.{u3} ι') (Set.hasMem.{u3} ι') i s) -> (Set.PairwiseDisjoint.{u1, u2} α ι (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) (g i) f)) -> (Set.PairwiseDisjoint.{u1, u2} α ι (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) (Set.iUnion.{u2, succ u3} ι ι' (fun (i : ι') => Set.iUnion.{u2, 0} ι (Membership.Mem.{u3, u3} ι' (Set.{u3} ι') (Set.hasMem.{u3} ι') i s) (fun (H : Membership.Mem.{u3, u3} ι' (Set.{u3} ι') (Set.hasMem.{u3} ι') i s) => g i))) f)
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Type.{u2}} {ι' : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u3} ι'} {g : ι' -> (Set.{u2} ι)} {f : ι -> α}, (Set.PairwiseDisjoint.{u1, u3} α ι' (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) s (fun (i' : ι') => supᵢ.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i (g i')) (fun (H : Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i (g i')) => f i)))) -> (forall (i : ι'), (Membership.mem.{u3, u3} ι' (Set.{u3} ι') (Set.instMembershipSet.{u3} ι') i s) -> (Set.PairwiseDisjoint.{u1, u2} α ι (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) (g i) f)) -> (Set.PairwiseDisjoint.{u1, u2} α ι (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) (Set.unionᵢ.{u2, succ u3} ι ι' (fun (i : ι') => Set.unionᵢ.{u2, 0} ι (Membership.mem.{u3, u3} ι' (Set.{u3} ι') (Set.instMembershipSet.{u3} ι') i s) (fun (H : Membership.mem.{u3, u3} ι' (Set.{u3} ι') (Set.instMembershipSet.{u3} ι') i s) => g i))) f)
-Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint.bUnion Set.PairwiseDisjoint.bunionᵢₓ'. -/
+  forall {α : Type.{u1}} {ι : Type.{u2}} {ι' : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u3} ι'} {g : ι' -> (Set.{u2} ι)} {f : ι -> α}, (Set.PairwiseDisjoint.{u1, u3} α ι' (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) s (fun (i' : ι') => iSup.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (i : ι) => iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i (g i')) (fun (H : Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i (g i')) => f i)))) -> (forall (i : ι'), (Membership.mem.{u3, u3} ι' (Set.{u3} ι') (Set.instMembershipSet.{u3} ι') i s) -> (Set.PairwiseDisjoint.{u1, u2} α ι (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) (g i) f)) -> (Set.PairwiseDisjoint.{u1, u2} α ι (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) (Set.iUnion.{u2, succ u3} ι ι' (fun (i : ι') => Set.iUnion.{u2, 0} ι (Membership.mem.{u3, u3} ι' (Set.{u3} ι') (Set.instMembershipSet.{u3} ι') i s) (fun (H : Membership.mem.{u3, u3} ι' (Set.{u3} ι') (Set.instMembershipSet.{u3} ι') i s) => g i))) f)
+Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint.bUnion Set.PairwiseDisjoint.biUnionₓ'. -/
 /-- Bind operation for `set.pairwise_disjoint`. If you want to only consider finsets of indices, you
 can use `set.pairwise_disjoint.bUnion_finset`. -/
-theorem PairwiseDisjoint.bunionᵢ {s : Set ι'} {g : ι' → Set ι} {f : ι → α}
+theorem PairwiseDisjoint.biUnion {s : Set ι'} {g : ι' → Set ι} {f : ι → α}
     (hs : s.PairwiseDisjoint fun i' : ι' => ⨆ i ∈ g i', f i)
     (hg : ∀ i ∈ s, (g i).PairwiseDisjoint f) : (⋃ i ∈ s, g i).PairwiseDisjoint f :=
   by
   rintro a ha b hb hab
-  simp_rw [Set.mem_unionᵢ] at ha hb
+  simp_rw [Set.mem_iUnion] at ha hb
   obtain ⟨c, hc, ha⟩ := ha
   obtain ⟨d, hd, hb⟩ := hb
   obtain hcd | hcd := eq_or_ne (g c) (g d)
   · exact hg d hd (hcd.subst ha) hb hab
-  · exact (hs hc hd <| ne_of_apply_ne _ hcd).mono (le_supᵢ₂ a ha) (le_supᵢ₂ b hb)
-#align set.pairwise_disjoint.bUnion Set.PairwiseDisjoint.bunionᵢ
+  · exact (hs hc hd <| ne_of_apply_ne _ hcd).mono (le_iSup₂ a ha) (le_iSup₂ b hb)
+#align set.pairwise_disjoint.bUnion Set.PairwiseDisjoint.biUnion
 
 end CompleteLattice
 
-/- warning: set.bUnion_diff_bUnion_eq -> Set.bunionᵢ_diff_bunionᵢ_eq is a dubious translation:
+/- warning: set.bUnion_diff_bUnion_eq -> Set.biUnion_diff_biUnion_eq is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Type.{u2}} {s : Set.{u2} ι} {t : Set.{u2} ι} {f : ι -> (Set.{u1} α)}, (Set.PairwiseDisjoint.{u1, u2} (Set.{u1} α) ι (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))) (Union.union.{u2} (Set.{u2} ι) (Set.hasUnion.{u2} ι) s t) f) -> (Eq.{succ u1} (Set.{u1} α) (SDiff.sdiff.{u1} (Set.{u1} α) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) (Set.unionᵢ.{u1, succ u2} α ι (fun (i : ι) => Set.unionᵢ.{u1, 0} α (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i s) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i s) => f i))) (Set.unionᵢ.{u1, succ u2} α ι (fun (i : ι) => Set.unionᵢ.{u1, 0} α (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i t) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i t) => f i)))) (Set.unionᵢ.{u1, succ u2} α ι (fun (i : ι) => Set.unionᵢ.{u1, 0} α (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i (SDiff.sdiff.{u2} (Set.{u2} ι) (BooleanAlgebra.toHasSdiff.{u2} (Set.{u2} ι) (Set.booleanAlgebra.{u2} ι)) s t)) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i (SDiff.sdiff.{u2} (Set.{u2} ι) (BooleanAlgebra.toHasSdiff.{u2} (Set.{u2} ι) (Set.booleanAlgebra.{u2} ι)) s t)) => f i))))
+  forall {α : Type.{u1}} {ι : Type.{u2}} {s : Set.{u2} ι} {t : Set.{u2} ι} {f : ι -> (Set.{u1} α)}, (Set.PairwiseDisjoint.{u1, u2} (Set.{u1} α) ι (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))) (Union.union.{u2} (Set.{u2} ι) (Set.hasUnion.{u2} ι) s t) f) -> (Eq.{succ u1} (Set.{u1} α) (SDiff.sdiff.{u1} (Set.{u1} α) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) (Set.iUnion.{u1, succ u2} α ι (fun (i : ι) => Set.iUnion.{u1, 0} α (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i s) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i s) => f i))) (Set.iUnion.{u1, succ u2} α ι (fun (i : ι) => Set.iUnion.{u1, 0} α (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i t) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i t) => f i)))) (Set.iUnion.{u1, succ u2} α ι (fun (i : ι) => Set.iUnion.{u1, 0} α (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i (SDiff.sdiff.{u2} (Set.{u2} ι) (BooleanAlgebra.toHasSdiff.{u2} (Set.{u2} ι) (Set.booleanAlgebra.{u2} ι)) s t)) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i (SDiff.sdiff.{u2} (Set.{u2} ι) (BooleanAlgebra.toHasSdiff.{u2} (Set.{u2} ι) (Set.booleanAlgebra.{u2} ι)) s t)) => f i))))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Type.{u2}} {s : Set.{u2} ι} {t : Set.{u2} ι} {f : ι -> (Set.{u1} α)}, (Set.PairwiseDisjoint.{u1, u2} (Set.{u1} α) ι (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (Union.union.{u2} (Set.{u2} ι) (Set.instUnionSet.{u2} ι) s t) f) -> (Eq.{succ u1} (Set.{u1} α) (SDiff.sdiff.{u1} (Set.{u1} α) (Set.instSDiffSet.{u1} α) (Set.unionᵢ.{u1, succ u2} α ι (fun (i : ι) => Set.unionᵢ.{u1, 0} α (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i s) (fun (H : Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i s) => f i))) (Set.unionᵢ.{u1, succ u2} α ι (fun (i : ι) => Set.unionᵢ.{u1, 0} α (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i t) (fun (H : Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i t) => f i)))) (Set.unionᵢ.{u1, succ u2} α ι (fun (i : ι) => Set.unionᵢ.{u1, 0} α (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i (SDiff.sdiff.{u2} (Set.{u2} ι) (Set.instSDiffSet.{u2} ι) s t)) (fun (H : Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i (SDiff.sdiff.{u2} (Set.{u2} ι) (Set.instSDiffSet.{u2} ι) s t)) => f i))))
-Case conversion may be inaccurate. Consider using '#align set.bUnion_diff_bUnion_eq Set.bunionᵢ_diff_bunionᵢ_eqₓ'. -/
-theorem bunionᵢ_diff_bunionᵢ_eq {s t : Set ι} {f : ι → Set α} (h : (s ∪ t).PairwiseDisjoint f) :
+  forall {α : Type.{u1}} {ι : Type.{u2}} {s : Set.{u2} ι} {t : Set.{u2} ι} {f : ι -> (Set.{u1} α)}, (Set.PairwiseDisjoint.{u1, u2} (Set.{u1} α) ι (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (Union.union.{u2} (Set.{u2} ι) (Set.instUnionSet.{u2} ι) s t) f) -> (Eq.{succ u1} (Set.{u1} α) (SDiff.sdiff.{u1} (Set.{u1} α) (Set.instSDiffSet.{u1} α) (Set.iUnion.{u1, succ u2} α ι (fun (i : ι) => Set.iUnion.{u1, 0} α (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i s) (fun (H : Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i s) => f i))) (Set.iUnion.{u1, succ u2} α ι (fun (i : ι) => Set.iUnion.{u1, 0} α (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i t) (fun (H : Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i t) => f i)))) (Set.iUnion.{u1, succ u2} α ι (fun (i : ι) => Set.iUnion.{u1, 0} α (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i (SDiff.sdiff.{u2} (Set.{u2} ι) (Set.instSDiffSet.{u2} ι) s t)) (fun (H : Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i (SDiff.sdiff.{u2} (Set.{u2} ι) (Set.instSDiffSet.{u2} ι) s t)) => f i))))
+Case conversion may be inaccurate. Consider using '#align set.bUnion_diff_bUnion_eq Set.biUnion_diff_biUnion_eqₓ'. -/
+theorem biUnion_diff_biUnion_eq {s t : Set ι} {f : ι → Set α} (h : (s ∪ t).PairwiseDisjoint f) :
     ((⋃ i ∈ s, f i) \ ⋃ i ∈ t, f i) = ⋃ i ∈ s \ t, f i :=
   by
   refine'
@@ -130,20 +130,20 @@ theorem bunionᵢ_diff_bunionᵢ_eq {s t : Set ι} {f : ι → Set α} (h : (s 
       (Union₂_subset fun i hi a ha => (mem_diff _).2 ⟨mem_bUnion hi.1 ha, _⟩)
   rw [mem_Union₂]; rintro ⟨j, hj, haj⟩
   exact (h (Or.inl hi.1) (Or.inr hj) (ne_of_mem_of_not_mem hj hi.2).symm).le_bot ⟨ha, haj⟩
-#align set.bUnion_diff_bUnion_eq Set.bunionᵢ_diff_bunionᵢ_eq
+#align set.bUnion_diff_bUnion_eq Set.biUnion_diff_biUnion_eq
 
-/- warning: set.bUnion_eq_sigma_of_disjoint -> Set.bunionᵢEqSigmaOfDisjoint is a dubious translation:
+/- warning: set.bUnion_eq_sigma_of_disjoint -> Set.biUnionEqSigmaOfDisjoint is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Type.{u2}} {s : Set.{u2} ι} {f : ι -> (Set.{u1} α)}, (Set.PairwiseDisjoint.{u1, u2} (Set.{u1} α) ι (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))) s f) -> (Equiv.{succ u1, max (succ u2) (succ u1)} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.unionᵢ.{u1, succ u2} α ι (fun (i : ι) => Set.unionᵢ.{u1, 0} α (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i s) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i s) => f i)))) (Sigma.{u2, u1} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) (fun (i : coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) => coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (f ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (coeSubtype.{succ u2} ι (fun (x : ι) => Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) x s))))) i)))))
+  forall {α : Type.{u1}} {ι : Type.{u2}} {s : Set.{u2} ι} {f : ι -> (Set.{u1} α)}, (Set.PairwiseDisjoint.{u1, u2} (Set.{u1} α) ι (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))) s f) -> (Equiv.{succ u1, max (succ u2) (succ u1)} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.iUnion.{u1, succ u2} α ι (fun (i : ι) => Set.iUnion.{u1, 0} α (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i s) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i s) => f i)))) (Sigma.{u2, u1} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) (fun (i : coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) => coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (f ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (coeSubtype.{succ u2} ι (fun (x : ι) => Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) x s))))) i)))))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Type.{u2}} {s : Set.{u2} ι} {f : ι -> (Set.{u1} α)}, (Set.PairwiseDisjoint.{u1, u2} (Set.{u1} α) ι (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) s f) -> (Equiv.{succ u1, max (succ u1) (succ u2)} (Set.Elem.{u1} α (Set.unionᵢ.{u1, succ u2} α ι (fun (i : ι) => Set.unionᵢ.{u1, 0} α (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i s) (fun (H : Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i s) => f i)))) (Sigma.{u2, u1} (Set.Elem.{u2} ι s) (fun (i : Set.Elem.{u2} ι s) => Set.Elem.{u1} α (f (Subtype.val.{succ u2} ι (fun (x : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) x s) i)))))
-Case conversion may be inaccurate. Consider using '#align set.bUnion_eq_sigma_of_disjoint Set.bunionᵢEqSigmaOfDisjointₓ'. -/
+  forall {α : Type.{u1}} {ι : Type.{u2}} {s : Set.{u2} ι} {f : ι -> (Set.{u1} α)}, (Set.PairwiseDisjoint.{u1, u2} (Set.{u1} α) ι (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) s f) -> (Equiv.{succ u1, max (succ u1) (succ u2)} (Set.Elem.{u1} α (Set.iUnion.{u1, succ u2} α ι (fun (i : ι) => Set.iUnion.{u1, 0} α (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i s) (fun (H : Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i s) => f i)))) (Sigma.{u2, u1} (Set.Elem.{u2} ι s) (fun (i : Set.Elem.{u2} ι s) => Set.Elem.{u1} α (f (Subtype.val.{succ u2} ι (fun (x : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) x s) i)))))
+Case conversion may be inaccurate. Consider using '#align set.bUnion_eq_sigma_of_disjoint Set.biUnionEqSigmaOfDisjointₓ'. -/
 /-- Equivalence between a disjoint bounded union and a dependent sum. -/
-noncomputable def bunionᵢEqSigmaOfDisjoint {s : Set ι} {f : ι → Set α} (h : s.PairwiseDisjoint f) :
+noncomputable def biUnionEqSigmaOfDisjoint {s : Set ι} {f : ι → Set α} (h : s.PairwiseDisjoint f) :
     (⋃ i ∈ s, f i) ≃ Σi : s, f i :=
-  (Equiv.setCongr (bunionᵢ_eq_unionᵢ _ _)).trans <|
+  (Equiv.setCongr (biUnion_eq_iUnion _ _)).trans <|
     unionEqSigmaOfDisjoint fun ⟨i, hi⟩ ⟨j, hj⟩ ne => h hi hj fun eq => Ne <| Subtype.eq Eq
-#align set.bUnion_eq_sigma_of_disjoint Set.bunionᵢEqSigmaOfDisjoint
+#align set.bUnion_eq_sigma_of_disjoint Set.biUnionEqSigmaOfDisjoint
 
 end Set
 
@@ -151,13 +151,13 @@ section
 
 variable {f : ι → Set α} {s t : Set ι}
 
-/- warning: set.pairwise_disjoint.subset_of_bUnion_subset_bUnion -> Set.PairwiseDisjoint.subset_of_bunionᵢ_subset_bunionᵢ is a dubious translation:
+/- warning: set.pairwise_disjoint.subset_of_bUnion_subset_bUnion -> Set.PairwiseDisjoint.subset_of_biUnion_subset_biUnion is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Type.{u2}} {f : ι -> (Set.{u1} α)} {s : Set.{u2} ι} {t : Set.{u2} ι}, (Set.PairwiseDisjoint.{u1, u2} (Set.{u1} α) ι (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))) (Union.union.{u2} (Set.{u2} ι) (Set.hasUnion.{u2} ι) s t) f) -> (forall (i : ι), (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i s) -> (Set.Nonempty.{u1} α (f i))) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.unionᵢ.{u1, succ u2} α ι (fun (i : ι) => Set.unionᵢ.{u1, 0} α (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i s) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i s) => f i))) (Set.unionᵢ.{u1, succ u2} α ι (fun (i : ι) => Set.unionᵢ.{u1, 0} α (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i t) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i t) => f i)))) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.hasSubset.{u2} ι) s t)
+  forall {α : Type.{u1}} {ι : Type.{u2}} {f : ι -> (Set.{u1} α)} {s : Set.{u2} ι} {t : Set.{u2} ι}, (Set.PairwiseDisjoint.{u1, u2} (Set.{u1} α) ι (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))) (Union.union.{u2} (Set.{u2} ι) (Set.hasUnion.{u2} ι) s t) f) -> (forall (i : ι), (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i s) -> (Set.Nonempty.{u1} α (f i))) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.iUnion.{u1, succ u2} α ι (fun (i : ι) => Set.iUnion.{u1, 0} α (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i s) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i s) => f i))) (Set.iUnion.{u1, succ u2} α ι (fun (i : ι) => Set.iUnion.{u1, 0} α (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i t) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i t) => f i)))) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.hasSubset.{u2} ι) s t)
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Type.{u1}} {f : ι -> (Set.{u2} α)} {s : Set.{u1} ι} {t : Set.{u1} ι}, (Set.PairwiseDisjoint.{u2, u1} (Set.{u2} α) ι (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} α) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} α) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} α) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} α) (Set.instCompleteBooleanAlgebraSet.{u2} α)))))) (BoundedOrder.toOrderBot.{u2} (Set.{u2} α) (Preorder.toLE.{u2} (Set.{u2} α) (PartialOrder.toPreorder.{u2} (Set.{u2} α) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} α) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} α) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} α) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} α) (Set.instCompleteBooleanAlgebraSet.{u2} α)))))))) (CompleteLattice.toBoundedOrder.{u2} (Set.{u2} α) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} α) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} α) (Set.instCompleteBooleanAlgebraSet.{u2} α)))))) (Union.union.{u1} (Set.{u1} ι) (Set.instUnionSet.{u1} ι) s t) f) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) i s) -> (Set.Nonempty.{u2} α (f i))) -> (HasSubset.Subset.{u2} (Set.{u2} α) (Set.instHasSubsetSet.{u2} α) (Set.unionᵢ.{u2, succ u1} α ι (fun (i : ι) => Set.unionᵢ.{u2, 0} α (Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) i s) (fun (H : Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) i s) => f i))) (Set.unionᵢ.{u2, succ u1} α ι (fun (i : ι) => Set.unionᵢ.{u2, 0} α (Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) i t) (fun (H : Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) i t) => f i)))) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.instHasSubsetSet.{u1} ι) s t)
-Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint.subset_of_bUnion_subset_bUnion Set.PairwiseDisjoint.subset_of_bunionᵢ_subset_bunionᵢₓ'. -/
-theorem Set.PairwiseDisjoint.subset_of_bunionᵢ_subset_bunionᵢ (h₀ : (s ∪ t).PairwiseDisjoint f)
+  forall {α : Type.{u2}} {ι : Type.{u1}} {f : ι -> (Set.{u2} α)} {s : Set.{u1} ι} {t : Set.{u1} ι}, (Set.PairwiseDisjoint.{u2, u1} (Set.{u2} α) ι (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} α) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} α) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} α) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} α) (Set.instCompleteBooleanAlgebraSet.{u2} α)))))) (BoundedOrder.toOrderBot.{u2} (Set.{u2} α) (Preorder.toLE.{u2} (Set.{u2} α) (PartialOrder.toPreorder.{u2} (Set.{u2} α) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} α) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} α) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} α) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} α) (Set.instCompleteBooleanAlgebraSet.{u2} α)))))))) (CompleteLattice.toBoundedOrder.{u2} (Set.{u2} α) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} α) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} α) (Set.instCompleteBooleanAlgebraSet.{u2} α)))))) (Union.union.{u1} (Set.{u1} ι) (Set.instUnionSet.{u1} ι) s t) f) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) i s) -> (Set.Nonempty.{u2} α (f i))) -> (HasSubset.Subset.{u2} (Set.{u2} α) (Set.instHasSubsetSet.{u2} α) (Set.iUnion.{u2, succ u1} α ι (fun (i : ι) => Set.iUnion.{u2, 0} α (Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) i s) (fun (H : Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) i s) => f i))) (Set.iUnion.{u2, succ u1} α ι (fun (i : ι) => Set.iUnion.{u2, 0} α (Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) i t) (fun (H : Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) i t) => f i)))) -> (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.instHasSubsetSet.{u1} ι) s t)
+Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint.subset_of_bUnion_subset_bUnion Set.PairwiseDisjoint.subset_of_biUnion_subset_biUnionₓ'. -/
+theorem Set.PairwiseDisjoint.subset_of_biUnion_subset_biUnion (h₀ : (s ∪ t).PairwiseDisjoint f)
     (h₁ : ∀ i ∈ s, (f i).Nonempty) (h : (⋃ i ∈ s, f i) ⊆ ⋃ i ∈ t, f i) : s ⊆ t :=
   by
   rintro i hi
@@ -165,30 +165,30 @@ theorem Set.PairwiseDisjoint.subset_of_bunionᵢ_subset_bunionᵢ (h₀ : (s ∪
   obtain ⟨j, hj, haj⟩ := mem_Union₂.1 (h <| mem_Union₂_of_mem hi hai)
   rwa [h₀.eq (subset_union_left _ _ hi) (subset_union_right _ _ hj)
       (not_disjoint_iff.2 ⟨a, hai, haj⟩)]
-#align set.pairwise_disjoint.subset_of_bUnion_subset_bUnion Set.PairwiseDisjoint.subset_of_bunionᵢ_subset_bunionᵢ
+#align set.pairwise_disjoint.subset_of_bUnion_subset_bUnion Set.PairwiseDisjoint.subset_of_biUnion_subset_biUnion
 
-/- warning: pairwise.subset_of_bUnion_subset_bUnion -> Pairwise.subset_of_bunionᵢ_subset_bunionᵢ is a dubious translation:
+/- warning: pairwise.subset_of_bUnion_subset_bUnion -> Pairwise.subset_of_biUnion_subset_biUnion is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Type.{u2}} {f : ι -> (Set.{u1} α)} {s : Set.{u2} ι} {t : Set.{u2} ι}, (Pairwise.{u2} ι (Function.onFun.{succ u2, succ u1, 1} ι (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) f)) -> (forall (i : ι), (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i s) -> (Set.Nonempty.{u1} α (f i))) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.unionᵢ.{u1, succ u2} α ι (fun (i : ι) => Set.unionᵢ.{u1, 0} α (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i s) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i s) => f i))) (Set.unionᵢ.{u1, succ u2} α ι (fun (i : ι) => Set.unionᵢ.{u1, 0} α (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i t) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i t) => f i)))) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.hasSubset.{u2} ι) s t)
+  forall {α : Type.{u1}} {ι : Type.{u2}} {f : ι -> (Set.{u1} α)} {s : Set.{u2} ι} {t : Set.{u2} ι}, (Pairwise.{u2} ι (Function.onFun.{succ u2, succ u1, 1} ι (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) f)) -> (forall (i : ι), (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i s) -> (Set.Nonempty.{u1} α (f i))) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.iUnion.{u1, succ u2} α ι (fun (i : ι) => Set.iUnion.{u1, 0} α (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i s) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i s) => f i))) (Set.iUnion.{u1, succ u2} α ι (fun (i : ι) => Set.iUnion.{u1, 0} α (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i t) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i t) => f i)))) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.hasSubset.{u2} ι) s t)
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Type.{u2}} {f : ι -> (Set.{u1} α)} {s : Set.{u2} ι} {t : Set.{u2} ι}, (Pairwise.{u2} ι (Function.onFun.{succ u2, succ u1, 1} ι (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α))))))) f)) -> (forall (i : ι), (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i s) -> (Set.Nonempty.{u1} α (f i))) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.unionᵢ.{u1, succ u2} α ι (fun (i : ι) => Set.unionᵢ.{u1, 0} α (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i s) (fun (H : Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i s) => f i))) (Set.unionᵢ.{u1, succ u2} α ι (fun (i : ι) => Set.unionᵢ.{u1, 0} α (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i t) (fun (H : Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i t) => f i)))) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.instHasSubsetSet.{u2} ι) s t)
-Case conversion may be inaccurate. Consider using '#align pairwise.subset_of_bUnion_subset_bUnion Pairwise.subset_of_bunionᵢ_subset_bunionᵢₓ'. -/
-theorem Pairwise.subset_of_bunionᵢ_subset_bunionᵢ (h₀ : Pairwise (Disjoint on f))
+  forall {α : Type.{u1}} {ι : Type.{u2}} {f : ι -> (Set.{u1} α)} {s : Set.{u2} ι} {t : Set.{u2} ι}, (Pairwise.{u2} ι (Function.onFun.{succ u2, succ u1, 1} ι (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α))))))) f)) -> (forall (i : ι), (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i s) -> (Set.Nonempty.{u1} α (f i))) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.iUnion.{u1, succ u2} α ι (fun (i : ι) => Set.iUnion.{u1, 0} α (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i s) (fun (H : Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i s) => f i))) (Set.iUnion.{u1, succ u2} α ι (fun (i : ι) => Set.iUnion.{u1, 0} α (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i t) (fun (H : Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i t) => f i)))) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.instHasSubsetSet.{u2} ι) s t)
+Case conversion may be inaccurate. Consider using '#align pairwise.subset_of_bUnion_subset_bUnion Pairwise.subset_of_biUnion_subset_biUnionₓ'. -/
+theorem Pairwise.subset_of_biUnion_subset_biUnion (h₀ : Pairwise (Disjoint on f))
     (h₁ : ∀ i ∈ s, (f i).Nonempty) (h : (⋃ i ∈ s, f i) ⊆ ⋃ i ∈ t, f i) : s ⊆ t :=
-  Set.PairwiseDisjoint.subset_of_bunionᵢ_subset_bunionᵢ (h₀.set_pairwise _) h₁ h
-#align pairwise.subset_of_bUnion_subset_bUnion Pairwise.subset_of_bunionᵢ_subset_bunionᵢ
+  Set.PairwiseDisjoint.subset_of_biUnion_subset_biUnion (h₀.set_pairwise _) h₁ h
+#align pairwise.subset_of_bUnion_subset_bUnion Pairwise.subset_of_biUnion_subset_biUnion
 
-/- warning: pairwise.bUnion_injective -> Pairwise.bunionᵢ_injective is a dubious translation:
+/- warning: pairwise.bUnion_injective -> Pairwise.biUnion_injective is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Type.{u2}} {f : ι -> (Set.{u1} α)}, (Pairwise.{u2} ι (Function.onFun.{succ u2, succ u1, 1} ι (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) f)) -> (forall (i : ι), Set.Nonempty.{u1} α (f i)) -> (Function.Injective.{succ u2, succ u1} (Set.{u2} ι) (Set.{u1} α) (fun (s : Set.{u2} ι) => Set.unionᵢ.{u1, succ u2} α ι (fun (i : ι) => Set.unionᵢ.{u1, 0} α (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i s) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i s) => f i))))
+  forall {α : Type.{u1}} {ι : Type.{u2}} {f : ι -> (Set.{u1} α)}, (Pairwise.{u2} ι (Function.onFun.{succ u2, succ u1, 1} ι (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) f)) -> (forall (i : ι), Set.Nonempty.{u1} α (f i)) -> (Function.Injective.{succ u2, succ u1} (Set.{u2} ι) (Set.{u1} α) (fun (s : Set.{u2} ι) => Set.iUnion.{u1, succ u2} α ι (fun (i : ι) => Set.iUnion.{u1, 0} α (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i s) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i s) => f i))))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Type.{u2}} {f : ι -> (Set.{u1} α)}, (Pairwise.{u2} ι (Function.onFun.{succ u2, succ u1, 1} ι (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α))))))) f)) -> (forall (i : ι), Set.Nonempty.{u1} α (f i)) -> (Function.Injective.{succ u2, succ u1} (Set.{u2} ι) (Set.{u1} α) (fun (s : Set.{u2} ι) => Set.unionᵢ.{u1, succ u2} α ι (fun (i : ι) => Set.unionᵢ.{u1, 0} α (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i s) (fun (H : Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i s) => f i))))
-Case conversion may be inaccurate. Consider using '#align pairwise.bUnion_injective Pairwise.bunionᵢ_injectiveₓ'. -/
-theorem Pairwise.bunionᵢ_injective (h₀ : Pairwise (Disjoint on f)) (h₁ : ∀ i, (f i).Nonempty) :
+  forall {α : Type.{u1}} {ι : Type.{u2}} {f : ι -> (Set.{u1} α)}, (Pairwise.{u2} ι (Function.onFun.{succ u2, succ u1, 1} ι (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α))))))) f)) -> (forall (i : ι), Set.Nonempty.{u1} α (f i)) -> (Function.Injective.{succ u2, succ u1} (Set.{u2} ι) (Set.{u1} α) (fun (s : Set.{u2} ι) => Set.iUnion.{u1, succ u2} α ι (fun (i : ι) => Set.iUnion.{u1, 0} α (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i s) (fun (H : Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i s) => f i))))
+Case conversion may be inaccurate. Consider using '#align pairwise.bUnion_injective Pairwise.biUnion_injectiveₓ'. -/
+theorem Pairwise.biUnion_injective (h₀ : Pairwise (Disjoint on f)) (h₁ : ∀ i, (f i).Nonempty) :
     Injective fun s : Set ι => ⋃ i ∈ s, f i := fun s t h =>
-  ((h₀.subset_of_bunionᵢ_subset_bunionᵢ fun _ _ => h₁ _) <| h.Subset).antisymm <|
-    (h₀.subset_of_bunionᵢ_subset_bunionᵢ fun _ _ => h₁ _) <| h.Superset
-#align pairwise.bUnion_injective Pairwise.bunionᵢ_injective
+  ((h₀.subset_of_biUnion_subset_biUnion fun _ _ => h₁ _) <| h.Subset).antisymm <|
+    (h₀.subset_of_biUnion_subset_biUnion fun _ _ => h₁ _) <| h.Superset
+#align pairwise.bUnion_injective Pairwise.biUnion_injective
 
 end

bump to nightly-2023-04-04-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/3cacc945118c8c637d89950af01da78307f59325

2ee17135

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
 
 ! This file was ported from Lean 3 source module data.set.pairwise.lattice
-! leanprover-community/mathlib commit c227d107bbada5d0d9d20287e3282c0a7f1651a0
+! leanprover-community/mathlib commit 31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Data.Set.Pairwise.Basic
 /-!
 # Relations holding pairwise
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we prove many facts about `pairwise` and the set lattice.
 -/

bump to nightly-2023-03-28-00

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

e9532e35

Diff

@@ -32,7 +32,7 @@ namespace Set
 lean 3 declaration is
   forall {α : Type.{u1}} {ι : Type.{u2}} {r : α -> α -> Prop} {f : ι -> (Set.{u1} α)}, (Directed.{u1, succ u2} (Set.{u1} α) ι (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α)) f) -> (Iff (Set.Pairwise.{u1} α (Set.unionᵢ.{u1, succ u2} α ι (fun (n : ι) => f n)) r) (forall (n : ι), Set.Pairwise.{u1} α (f n) r))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Type.{u1}} {r : α -> α -> Prop} {f : ι -> (Set.{u2} α)}, (Directed.{u2, succ u1} (Set.{u2} α) ι (fun (x._@.Mathlib.Data.Set.Pairwise._hyg.2714 : Set.{u2} α) (x._@.Mathlib.Data.Set.Pairwise._hyg.2716 : Set.{u2} α) => HasSubset.Subset.{u2} (Set.{u2} α) (Set.instHasSubsetSet.{u2} α) x._@.Mathlib.Data.Set.Pairwise._hyg.2714 x._@.Mathlib.Data.Set.Pairwise._hyg.2716) f) -> (Iff (Set.Pairwise.{u2} α (Set.unionᵢ.{u2, succ u1} α ι (fun (n : ι) => f n)) r) (forall (n : ι), Set.Pairwise.{u2} α (f n) r))
+  forall {α : Type.{u2}} {ι : Type.{u1}} {r : α -> α -> Prop} {f : ι -> (Set.{u2} α)}, (Directed.{u2, succ u1} (Set.{u2} α) ι (fun (x._@.Mathlib.Data.Set.Pairwise.Lattice._hyg.120 : Set.{u2} α) (x._@.Mathlib.Data.Set.Pairwise.Lattice._hyg.122 : Set.{u2} α) => HasSubset.Subset.{u2} (Set.{u2} α) (Set.instHasSubsetSet.{u2} α) x._@.Mathlib.Data.Set.Pairwise.Lattice._hyg.120 x._@.Mathlib.Data.Set.Pairwise.Lattice._hyg.122) f) -> (Iff (Set.Pairwise.{u2} α (Set.unionᵢ.{u2, succ u1} α ι (fun (n : ι) => f n)) r) (forall (n : ι), Set.Pairwise.{u2} α (f n) r))
 Case conversion may be inaccurate. Consider using '#align set.pairwise_Union Set.pairwise_unionᵢₓ'. -/
 theorem pairwise_unionᵢ {f : ι → Set α} (h : Directed (· ⊆ ·) f) :
     (⋃ n, f n).Pairwise r ↔ ∀ n, (f n).Pairwise r :=
@@ -70,7 +70,7 @@ variable [PartialOrder α] [OrderBot α] {s t : Set ι} {f g : ι → α}
 lean 3 declaration is
   forall {α : Type.{u1}} {ι : Type.{u2}} {ι' : Type.{u3}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {f : ι -> α} {g : ι' -> (Set.{u2} ι)}, (Directed.{u2, succ u3} (Set.{u2} ι) ι' (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.hasSubset.{u2} ι)) g) -> (Iff (Set.PairwiseDisjoint.{u1, u2} α ι _inst_1 _inst_2 (Set.unionᵢ.{u2, succ u3} ι ι' (fun (n : ι') => g n)) f) (forall {{n : ι'}}, Set.PairwiseDisjoint.{u1, u2} α ι _inst_1 _inst_2 (g n) f))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Type.{u3}} {ι' : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {f : ι -> α} {g : ι' -> (Set.{u3} ι)}, (Directed.{u3, succ u2} (Set.{u3} ι) ι' (fun (x._@.Mathlib.Data.Set.Pairwise._hyg.4274 : Set.{u3} ι) (x._@.Mathlib.Data.Set.Pairwise._hyg.4276 : Set.{u3} ι) => HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) x._@.Mathlib.Data.Set.Pairwise._hyg.4274 x._@.Mathlib.Data.Set.Pairwise._hyg.4276) g) -> (Iff (Set.PairwiseDisjoint.{u1, u3} α ι _inst_1 _inst_2 (Set.unionᵢ.{u3, succ u2} ι ι' (fun (n : ι') => g n)) f) (forall {{n : ι'}}, Set.PairwiseDisjoint.{u1, u3} α ι _inst_1 _inst_2 (g n) f))
+  forall {α : Type.{u1}} {ι : Type.{u3}} {ι' : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {f : ι -> α} {g : ι' -> (Set.{u3} ι)}, (Directed.{u3, succ u2} (Set.{u3} ι) ι' (fun (x._@.Mathlib.Data.Set.Pairwise.Lattice._hyg.443 : Set.{u3} ι) (x._@.Mathlib.Data.Set.Pairwise.Lattice._hyg.445 : Set.{u3} ι) => HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) x._@.Mathlib.Data.Set.Pairwise.Lattice._hyg.443 x._@.Mathlib.Data.Set.Pairwise.Lattice._hyg.445) g) -> (Iff (Set.PairwiseDisjoint.{u1, u3} α ι _inst_1 _inst_2 (Set.unionᵢ.{u3, succ u2} ι ι' (fun (n : ι') => g n)) f) (forall {{n : ι'}}, Set.PairwiseDisjoint.{u1, u3} α ι _inst_1 _inst_2 (g n) f))
 Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Union Set.pairwiseDisjoint_unionᵢₓ'. -/
 theorem pairwiseDisjoint_unionᵢ {g : ι' → Set ι} (h : Directed (· ⊆ ·) g) :
     (⋃ n, g n).PairwiseDisjoint f ↔ ∀ ⦃n⦄, (g n).PairwiseDisjoint f :=

bump to nightly-2023-03-27-02

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

0e4ebd8c

Changes in mathlib4

mathlib3

mathlib4

style: replace '.-/' by '. -/' (#11938)

Purely automatic replacement. If this is in any way controversial; I'm happy to just close this PR.

3556ded2

Diff

@@ -164,7 +164,7 @@ theorem Pairwise.biUnion_injective (h₀ : Pairwise (Disjoint on f)) (h₁ : ∀
     (h₀.subset_of_biUnion_subset_biUnion fun _ _ => h₁ _) <| h.superset
 #align pairwise.bUnion_injective Pairwise.biUnion_injective
 
-/-- In a disjoint union we can identify the unique set an element belongs to.-/
+/-- In a disjoint union we can identify the unique set an element belongs to. -/
 theorem pairwiseDisjoint_unique {y : α}
     (h_disjoint : PairwiseDisjoint s f)
     (hy : y ∈ (⋃ i ∈ s, f i)) : ∃! i, i ∈ s ∧ y ∈ f i := by

feat(Data/Setoid): another way to define piecewise functions (#7273)

Use IndexedPartition to define piecewise functions. This is natural for piecewise functions that are split into many pieces.

e7fd6c92

Diff

@@ -164,4 +164,13 @@ theorem Pairwise.biUnion_injective (h₀ : Pairwise (Disjoint on f)) (h₁ : ∀
     (h₀.subset_of_biUnion_subset_biUnion fun _ _ => h₁ _) <| h.superset
 #align pairwise.bUnion_injective Pairwise.biUnion_injective
 
+/-- In a disjoint union we can identify the unique set an element belongs to.-/
+theorem pairwiseDisjoint_unique {y : α}
+    (h_disjoint : PairwiseDisjoint s f)
+    (hy : y ∈ (⋃ i ∈ s, f i)) : ∃! i, i ∈ s ∧ y ∈ f i := by
+  refine exists_unique_of_exists_of_unique ?ex ?unique
+  · simpa only [mem_iUnion, exists_prop] using hy
+  · rintro i j ⟨his, hi⟩ ⟨hjs, hj⟩
+    exact h_disjoint.elim his hjs <| not_disjoint_iff.mpr ⟨y, ⟨hi, hj⟩⟩
+
 end

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

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

This has nice performance benefits.

32de3f67

Diff

@@ -17,7 +17,7 @@ In this file we prove many facts about `Pairwise` and the set lattice.
 
 open Function Set Order
 
-variable {α β γ ι ι' : Type _} {κ : Sort _} {r p q : α → α → Prop}
+variable {α β γ ι ι' : Type*} {κ : Sort*} {r p q : α → α → Prop}
 section Pairwise
 
 variable {f g : ι → α} {s t u : Set α} {a b : α}

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

depends on: #5966

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

89aa3a3b

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
-
-! This file was ported from Lean 3 source module data.set.pairwise.lattice
-! leanprover-community/mathlib commit c4c2ed622f43768eff32608d4a0f8a6cec1c047d
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Set.Lattice
 import Mathlib.Data.Set.Pairwise.Basic
 
+#align_import data.set.pairwise.lattice from "leanprover-community/mathlib"@"c4c2ed622f43768eff32608d4a0f8a6cec1c047d"
+
 /-!
 # Relations holding pairwise

fix: precedences of ⨆⋃⋂⨅ (#5614)

e3c8f983

Diff

@@ -148,7 +148,7 @@ section
 variable {f : ι → Set α} {s t : Set ι}
 
 theorem Set.PairwiseDisjoint.subset_of_biUnion_subset_biUnion (h₀ : (s ∪ t).PairwiseDisjoint f)
-    (h₁ : ∀ i ∈ s, (f i).Nonempty) (h : (⋃ i ∈ s, f i) ⊆ ⋃ i ∈ t, f i) : s ⊆ t := by
+    (h₁ : ∀ i ∈ s, (f i).Nonempty) (h : ⋃ i ∈ s, f i ⊆ ⋃ i ∈ t, f i) : s ⊆ t := by
   rintro i hi
   obtain ⟨a, hai⟩ := h₁ i hi
   obtain ⟨j, hj, haj⟩ := mem_iUnion₂.1 (h <| mem_iUnion₂_of_mem hi hai)
@@ -157,7 +157,7 @@ theorem Set.PairwiseDisjoint.subset_of_biUnion_subset_biUnion (h₀ : (s ∪ t).
 #align set.pairwise_disjoint.subset_of_bUnion_subset_bUnion Set.PairwiseDisjoint.subset_of_biUnion_subset_biUnion
 
 theorem Pairwise.subset_of_biUnion_subset_biUnion (h₀ : Pairwise (Disjoint on f))
-    (h₁ : ∀ i ∈ s, (f i).Nonempty) (h : (⋃ i ∈ s, f i) ⊆ ⋃ i ∈ t, f i) : s ⊆ t :=
+    (h₁ : ∀ i ∈ s, (f i).Nonempty) (h : ⋃ i ∈ s, f i ⊆ ⋃ i ∈ t, f i) : s ⊆ t :=
   Set.PairwiseDisjoint.subset_of_biUnion_subset_biUnion (h₀.set_pairwise _) h₁ h
 #align pairwise.subset_of_bUnion_subset_bUnion Pairwise.subset_of_biUnion_subset_biUnion

Match https://github.com/leanprover-community/mathlib/pull/11932

feat: More sup_indep lemmas (#5196)

Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

e266a22f

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
 
 ! This file was ported from Lean 3 source module data.set.pairwise.lattice
-! leanprover-community/mathlib commit c227d107bbada5d0d9d20287e3282c0a7f1651a0
+! leanprover-community/mathlib commit c4c2ed622f43768eff32608d4a0f8a6cec1c047d
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -18,17 +18,16 @@ In this file we prove many facts about `Pairwise` and the set lattice.
 -/
 
 
-open Set Function
-
-variable {α β γ ι ι' : Type _} {r p q : α → α → Prop}
+open Function Set Order
 
+variable {α β γ ι ι' : Type _} {κ : Sort _} {r p q : α → α → Prop}
 section Pairwise
 
 variable {f g : ι → α} {s t u : Set α} {a b : α}
 
 namespace Set
 
-theorem pairwise_iUnion {f : ι → Set α} (h : Directed (· ⊆ ·) f) :
+theorem pairwise_iUnion {f : κ → Set α} (h : Directed (· ⊆ ·) f) :
     (⋃ n, f n).Pairwise r ↔ ∀ n, (f n).Pairwise r := by
   constructor
   · intro H n
@@ -69,8 +68,7 @@ end PartialOrderBot
 
 section CompleteLattice
 
-variable [CompleteLattice α]
-
+variable [CompleteLattice α] {s : Set ι} {t : Set ι'}
 
 /-- Bind operation for `Set.PairwiseDisjoint`. If you want to only consider finsets of indices, you
 can use `Set.PairwiseDisjoint.biUnion_finset`. -/
@@ -89,8 +87,43 @@ theorem PairwiseDisjoint.biUnion {s : Set ι'} {g : ι' → Set ι} {f : ι →
       (le_iSup₂ (f := fun i (_ : i ∈ g d) => f i) b hb)
 #align set.pairwise_disjoint.bUnion Set.PairwiseDisjoint.biUnion
 
+/-- If the suprema of columns are pairwise disjoint and suprema of rows as well, then everything is
+pairwise disjoint. Not to be confused with `Set.PairwiseDisjoint.prod`. -/
+theorem PairwiseDisjoint.prod_left {f : ι × ι' → α}
+    (hs : s.PairwiseDisjoint fun i => ⨆ i' ∈ t, f (i, i'))
+    (ht : t.PairwiseDisjoint fun i' => ⨆ i ∈ s, f (i, i')) :
+    (s ×ˢ t : Set (ι × ι')).PairwiseDisjoint f := by
+  rintro ⟨i, i'⟩ hi ⟨j, j'⟩ hj h
+  rw [mem_prod] at hi hj
+  obtain rfl | hij := eq_or_ne i j
+  · refine' (ht hi.2 hj.2 <| (Prod.mk.inj_left _).ne_iff.1 h).mono _ _
+    · convert le_iSup₂ (α := α) i hi.1; rfl
+    · convert le_iSup₂ (α := α) i hj.1; rfl
+  · refine' (hs hi.1 hj.1 hij).mono _ _
+    · convert le_iSup₂ (α := α) i' hi.2; rfl
+    · convert le_iSup₂ (α := α) j' hj.2; rfl
+#align set.pairwise_disjoint.prod_left Set.PairwiseDisjoint.prod_left
+
 end CompleteLattice
 
+section Frame
+
+variable [Frame α]
+
+theorem pairwiseDisjoint_prod_left {s : Set ι} {t : Set ι'} {f : ι × ι' → α} :
+    (s ×ˢ t : Set (ι × ι')).PairwiseDisjoint f ↔
+      (s.PairwiseDisjoint fun i => ⨆ i' ∈ t, f (i, i')) ∧
+        t.PairwiseDisjoint fun i' => ⨆ i ∈ s, f (i, i') := by
+  refine'
+        ⟨fun h => ⟨fun i hi j hj hij => _, fun i hi j hj hij => _⟩, fun h => h.1.prod_left h.2⟩ <;>
+      simp_rw [Function.onFun, iSup_disjoint_iff, disjoint_iSup_iff] <;>
+    intro i' hi' j' hj'
+  · exact h (mk_mem_prod hi hi') (mk_mem_prod hj hj') (ne_of_apply_ne Prod.fst hij)
+  · exact h (mk_mem_prod hi' hi) (mk_mem_prod hj' hj) (ne_of_apply_ne Prod.snd hij)
+#align set.pairwise_disjoint_prod_left Set.pairwiseDisjoint_prod_left
+
+end Frame
+
 theorem biUnion_diff_biUnion_eq {s t : Set ι} {f : ι → Set α} (h : (s ∪ t).PairwiseDisjoint f) :
     ((⋃ i ∈ s, f i) \ ⋃ i ∈ t, f i) = ⋃ i ∈ s \ t, f i := by
   refine'

chore: fix upper/lowercase in comments (#4360)

Run a non-interactive version of fix-comments.py on all files.
Go through the diff and manually add/discard/edit chunks.

27d257fc

Diff

@@ -14,7 +14,7 @@ import Mathlib.Data.Set.Pairwise.Basic
 /-!
 # Relations holding pairwise
 
-In this file we prove many facts about `pairwise` and the set lattice.
+In this file we prove many facts about `Pairwise` and the set lattice.
 -/
 
 
@@ -72,8 +72,8 @@ section CompleteLattice
 variable [CompleteLattice α]
 
 
-/-- Bind operation for `set.pairwise_disjoint`. If you want to only consider finsets of indices, you
-can use `set.pairwise_disjoint.bUnion_finset`. -/
+/-- Bind operation for `Set.PairwiseDisjoint`. If you want to only consider finsets of indices, you
+can use `Set.PairwiseDisjoint.biUnion_finset`. -/
 theorem PairwiseDisjoint.biUnion {s : Set ι'} {g : ι' → Set ι} {f : ι → α}
     (hs : s.PairwiseDisjoint fun i' : ι' => ⨆ i ∈ g i', f i)
     (hg : ∀ i ∈ s, (g i).PairwiseDisjoint f) : (⋃ i ∈ s, g i).PairwiseDisjoint f := by

chore: Rename to sSup/iSup (#3938)

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>

d1eb6264

Diff

@@ -28,22 +28,22 @@ variable {f g : ι → α} {s t u : Set α} {a b : α}
 
 namespace Set
 
-theorem pairwise_unionᵢ {f : ι → Set α} (h : Directed (· ⊆ ·) f) :
+theorem pairwise_iUnion {f : ι → Set α} (h : Directed (· ⊆ ·) f) :
     (⋃ n, f n).Pairwise r ↔ ∀ n, (f n).Pairwise r := by
   constructor
   · intro H n
-    exact Pairwise.mono (subset_unionᵢ _ _) H
+    exact Pairwise.mono (subset_iUnion _ _) H
   · intro H i hi j hj hij
-    rcases mem_unionᵢ.1 hi with ⟨m, hm⟩
-    rcases mem_unionᵢ.1 hj with ⟨n, hn⟩
+    rcases mem_iUnion.1 hi with ⟨m, hm⟩
+    rcases mem_iUnion.1 hj with ⟨n, hn⟩
     rcases h m n with ⟨p, mp, np⟩
     exact H p (mp hm) (np hn) hij
-#align set.pairwise_Union Set.pairwise_unionᵢ
+#align set.pairwise_Union Set.pairwise_iUnion
 
-theorem pairwise_unionₛ {r : α → α → Prop} {s : Set (Set α)} (h : DirectedOn (· ⊆ ·) s) :
+theorem pairwise_sUnion {r : α → α → Prop} {s : Set (Set α)} (h : DirectedOn (· ⊆ ·) s) :
     (⋃₀ s).Pairwise r ↔ ∀ a ∈ s, Set.Pairwise a r := by
-  rw [unionₛ_eq_unionᵢ, pairwise_unionᵢ h.directed_val, SetCoe.forall]
-#align set.pairwise_sUnion Set.pairwise_unionₛ
+  rw [sUnion_eq_iUnion, pairwise_iUnion h.directed_val, SetCoe.forall]
+#align set.pairwise_sUnion Set.pairwise_sUnion
 
 end Set
 
@@ -55,15 +55,15 @@ section PartialOrderBot
 
 variable [PartialOrder α] [OrderBot α] {s t : Set ι} {f g : ι → α}
 
-theorem pairwiseDisjoint_unionᵢ {g : ι' → Set ι} (h : Directed (· ⊆ ·) g) :
+theorem pairwiseDisjoint_iUnion {g : ι' → Set ι} (h : Directed (· ⊆ ·) g) :
     (⋃ n, g n).PairwiseDisjoint f ↔ ∀ ⦃n⦄, (g n).PairwiseDisjoint f :=
-  pairwise_unionᵢ h
-#align set.pairwise_disjoint_Union Set.pairwiseDisjoint_unionᵢ
+  pairwise_iUnion h
+#align set.pairwise_disjoint_Union Set.pairwiseDisjoint_iUnion
 
-theorem pairwiseDisjoint_unionₛ {s : Set (Set ι)} (h : DirectedOn (· ⊆ ·) s) :
+theorem pairwiseDisjoint_sUnion {s : Set (Set ι)} (h : DirectedOn (· ⊆ ·) s) :
     (⋃₀ s).PairwiseDisjoint f ↔ ∀ ⦃a⦄, a ∈ s → Set.PairwiseDisjoint a f :=
-  pairwise_unionₛ h
-#align set.pairwise_disjoint_sUnion Set.pairwiseDisjoint_unionₛ
+  pairwise_sUnion h
+#align set.pairwise_disjoint_sUnion Set.pairwiseDisjoint_sUnion
 
 end PartialOrderBot
 
@@ -74,39 +74,39 @@ variable [CompleteLattice α]
 
 /-- Bind operation for `set.pairwise_disjoint`. If you want to only consider finsets of indices, you
 can use `set.pairwise_disjoint.bUnion_finset`. -/
-theorem PairwiseDisjoint.bunionᵢ {s : Set ι'} {g : ι' → Set ι} {f : ι → α}
+theorem PairwiseDisjoint.biUnion {s : Set ι'} {g : ι' → Set ι} {f : ι → α}
     (hs : s.PairwiseDisjoint fun i' : ι' => ⨆ i ∈ g i', f i)
     (hg : ∀ i ∈ s, (g i).PairwiseDisjoint f) : (⋃ i ∈ s, g i).PairwiseDisjoint f := by
   rintro a ha b hb hab
-  simp_rw [Set.mem_unionᵢ] at ha hb
+  simp_rw [Set.mem_iUnion] at ha hb
   obtain ⟨c, hc, ha⟩ := ha
   obtain ⟨d, hd, hb⟩ := hb
   obtain hcd | hcd := eq_or_ne (g c) (g d)
   · exact hg d hd (hcd.subst ha) hb hab
   -- Porting note: the elaborator couldn't figure out `f` here.
   · exact (hs hc hd <| ne_of_apply_ne _ hcd).mono
-      (le_supᵢ₂ (f := fun i (_ : i ∈ g c) => f i) a ha)
-      (le_supᵢ₂ (f := fun i (_ : i ∈ g d) => f i) b hb)
-#align set.pairwise_disjoint.bUnion Set.PairwiseDisjoint.bunionᵢ
+      (le_iSup₂ (f := fun i (_ : i ∈ g c) => f i) a ha)
+      (le_iSup₂ (f := fun i (_ : i ∈ g d) => f i) b hb)
+#align set.pairwise_disjoint.bUnion Set.PairwiseDisjoint.biUnion
 
 end CompleteLattice
 
-theorem bunionᵢ_diff_bunionᵢ_eq {s t : Set ι} {f : ι → Set α} (h : (s ∪ t).PairwiseDisjoint f) :
+theorem biUnion_diff_biUnion_eq {s t : Set ι} {f : ι → Set α} (h : (s ∪ t).PairwiseDisjoint f) :
     ((⋃ i ∈ s, f i) \ ⋃ i ∈ t, f i) = ⋃ i ∈ s \ t, f i := by
   refine'
-    (bunionᵢ_diff_bunionᵢ_subset f s t).antisymm
-      (unionᵢ₂_subset fun i hi a ha => (mem_diff _).2 ⟨mem_bunionᵢ hi.1 ha, _⟩)
-  rw [mem_unionᵢ₂]; rintro ⟨j, hj, haj⟩
+    (biUnion_diff_biUnion_subset f s t).antisymm
+      (iUnion₂_subset fun i hi a ha => (mem_diff _).2 ⟨mem_biUnion hi.1 ha, _⟩)
+  rw [mem_iUnion₂]; rintro ⟨j, hj, haj⟩
   exact (h (Or.inl hi.1) (Or.inr hj) (ne_of_mem_of_not_mem hj hi.2).symm).le_bot ⟨ha, haj⟩
-#align set.bUnion_diff_bUnion_eq Set.bunionᵢ_diff_bunionᵢ_eq
+#align set.bUnion_diff_bUnion_eq Set.biUnion_diff_biUnion_eq
 
 
 /-- Equivalence between a disjoint bounded union and a dependent sum. -/
-noncomputable def bunionᵢEqSigmaOfDisjoint {s : Set ι} {f : ι → Set α} (h : s.PairwiseDisjoint f) :
+noncomputable def biUnionEqSigmaOfDisjoint {s : Set ι} {f : ι → Set α} (h : s.PairwiseDisjoint f) :
     (⋃ i ∈ s, f i) ≃ Σi : s, f i :=
-  (Equiv.setCongr (bunionᵢ_eq_unionᵢ _ _)).trans <|
+  (Equiv.setCongr (biUnion_eq_iUnion _ _)).trans <|
     unionEqSigmaOfDisjoint fun ⟨_i, hi⟩ ⟨_j, hj⟩ ne => h hi hj fun eq => ne <| Subtype.eq eq
-#align set.bUnion_eq_sigma_of_disjoint Set.bunionᵢEqSigmaOfDisjoint
+#align set.bUnion_eq_sigma_of_disjoint Set.biUnionEqSigmaOfDisjoint
 
 end Set
 
@@ -114,24 +114,24 @@ section
 
 variable {f : ι → Set α} {s t : Set ι}
 
-theorem Set.PairwiseDisjoint.subset_of_bunionᵢ_subset_bunionᵢ (h₀ : (s ∪ t).PairwiseDisjoint f)
+theorem Set.PairwiseDisjoint.subset_of_biUnion_subset_biUnion (h₀ : (s ∪ t).PairwiseDisjoint f)
     (h₁ : ∀ i ∈ s, (f i).Nonempty) (h : (⋃ i ∈ s, f i) ⊆ ⋃ i ∈ t, f i) : s ⊆ t := by
   rintro i hi
   obtain ⟨a, hai⟩ := h₁ i hi
-  obtain ⟨j, hj, haj⟩ := mem_unionᵢ₂.1 (h <| mem_unionᵢ₂_of_mem hi hai)
+  obtain ⟨j, hj, haj⟩ := mem_iUnion₂.1 (h <| mem_iUnion₂_of_mem hi hai)
   rwa [h₀.eq (subset_union_left _ _ hi) (subset_union_right _ _ hj)
       (not_disjoint_iff.2 ⟨a, hai, haj⟩)]
-#align set.pairwise_disjoint.subset_of_bUnion_subset_bUnion Set.PairwiseDisjoint.subset_of_bunionᵢ_subset_bunionᵢ
+#align set.pairwise_disjoint.subset_of_bUnion_subset_bUnion Set.PairwiseDisjoint.subset_of_biUnion_subset_biUnion
 
-theorem Pairwise.subset_of_bunionᵢ_subset_bunionᵢ (h₀ : Pairwise (Disjoint on f))
+theorem Pairwise.subset_of_biUnion_subset_biUnion (h₀ : Pairwise (Disjoint on f))
     (h₁ : ∀ i ∈ s, (f i).Nonempty) (h : (⋃ i ∈ s, f i) ⊆ ⋃ i ∈ t, f i) : s ⊆ t :=
-  Set.PairwiseDisjoint.subset_of_bunionᵢ_subset_bunionᵢ (h₀.set_pairwise _) h₁ h
-#align pairwise.subset_of_bUnion_subset_bUnion Pairwise.subset_of_bunionᵢ_subset_bunionᵢ
+  Set.PairwiseDisjoint.subset_of_biUnion_subset_biUnion (h₀.set_pairwise _) h₁ h
+#align pairwise.subset_of_bUnion_subset_bUnion Pairwise.subset_of_biUnion_subset_biUnion
 
-theorem Pairwise.bunionᵢ_injective (h₀ : Pairwise (Disjoint on f)) (h₁ : ∀ i, (f i).Nonempty) :
+theorem Pairwise.biUnion_injective (h₀ : Pairwise (Disjoint on f)) (h₁ : ∀ i, (f i).Nonempty) :
     Injective fun s : Set ι => ⋃ i ∈ s, f i := fun _s _t h =>
-  ((h₀.subset_of_bunionᵢ_subset_bunionᵢ fun _ _ => h₁ _) <| h.subset).antisymm <|
-    (h₀.subset_of_bunionᵢ_subset_bunionᵢ fun _ _ => h₁ _) <| h.superset
-#align pairwise.bUnion_injective Pairwise.bunionᵢ_injective
+  ((h₀.subset_of_biUnion_subset_biUnion fun _ _ => h₁ _) <| h.subset).antisymm <|
+    (h₀.subset_of_biUnion_subset_biUnion fun _ _ => h₁ _) <| h.superset
+#align pairwise.bUnion_injective Pairwise.biUnion_injective
 
 end