data.set.basic | Mathlib porting status

(last sync)

feat(probability/independence): Independence of singletons (#18506)

Characterisation of independence in terms of measure distributing over finite intersections, and lemmas connecting the different concepts of independence.

Also add supporting measurable_space and set.preimage lemmas

Diff

@@ -1906,3 +1906,6 @@ lemma subset_right_of_subset_union (h : s ⊆ t ∪ u) (hab : disjoint s t) : s
 hab.left_le_of_le_sup_left h
 
 end disjoint
+
+@[simp] lemma Prop.compl_singleton (p : Prop) : ({p}ᶜ : set Prop) = {¬ p} :=
+ext $ λ q, by simpa [@iff.comm q] using not_iff

refactor(*): move all mk_simp_attribute commands to 1 file (#19223)

Diff

@@ -409,7 +409,7 @@ Mathematically it is the same as `α` but it has a different type.
 
 @[simp] theorem set_of_true : {x : α | true} = univ := rfl
 
-@[simp] theorem mem_univ (x : α) : x ∈ @univ α := trivial
+@[simp, mfld_simps] theorem mem_univ (x : α) : x ∈ @univ α := trivial
 
 @[simp] lemma univ_eq_empty_iff : (univ : set α) = ∅ ↔ is_empty α :=
 eq_empty_iff_forall_not_mem.trans ⟨λ H, ⟨λ x, H x trivial⟩, λ H x _, @is_empty.false α H x⟩
@@ -541,7 +541,8 @@ by simp only [← subset_empty_iff]; exact union_subset_iff
 
 theorem inter_def {s₁ s₂ : set α} : s₁ ∩ s₂ = {a | a ∈ s₁ ∧ a ∈ s₂} := rfl
 
-@[simp] theorem mem_inter_iff (x : α) (a b : set α) : x ∈ a ∩ b ↔ (x ∈ a ∧ x ∈ b) := iff.rfl
+@[simp, mfld_simps]
+theorem mem_inter_iff (x : α) (a b : set α) : x ∈ a ∩ b ↔ (x ∈ a ∧ x ∈ b) := iff.rfl
 
 theorem mem_inter {x : α} {a b : set α} (ha : x ∈ a) (hb : x ∈ b) : x ∈ a ∩ b := ⟨ha, hb⟩
 
@@ -569,7 +570,7 @@ ext $ λ x, and.left_comm
 theorem inter_right_comm (s₁ s₂ s₃ : set α) : (s₁ ∩ s₂) ∩ s₃ = (s₁ ∩ s₃) ∩ s₂ :=
 ext $ λ x, and.right_comm
 
-@[simp] theorem inter_subset_left (s t : set α) : s ∩ t ⊆ s := λ x, and.left
+@[simp, mfld_simps] theorem inter_subset_left (s t : set α) : s ∩ t ⊆ s := λ x, and.left
 
 @[simp] theorem inter_subset_right (s t : set α) : s ∩ t ⊆ t := λ x, and.right
 
@@ -596,9 +597,9 @@ lemma inter_congr_right (hs : t ∩ u ⊆ s) (ht : s ∩ u ⊆ t) : s ∩ u = t
 lemma inter_eq_inter_iff_left : s ∩ t = s ∩ u ↔ s ∩ u ⊆ t ∧ s ∩ t ⊆ u := inf_eq_inf_iff_left
 lemma inter_eq_inter_iff_right : s ∩ u = t ∩ u ↔ t ∩ u ⊆ s ∧ s ∩ u ⊆ t := inf_eq_inf_iff_right
 
-@[simp] theorem inter_univ (a : set α) : a ∩ univ = a := inf_top_eq
+@[simp, mfld_simps] theorem inter_univ (a : set α) : a ∩ univ = a := inf_top_eq
 
-@[simp] theorem univ_inter (a : set α) : univ ∩ a = a := top_inf_eq
+@[simp, mfld_simps] theorem univ_inter (a : set α) : univ ∩ a = a := top_inf_eq
 
 theorem inter_subset_inter {s₁ s₂ t₁ t₂ : set α}
   (h₁ : s₁ ⊆ t₁) (h₂ : s₂ ⊆ t₂) : s₁ ∩ s₂ ⊆ t₁ ∩ t₂ := λ x, and.imp (@h₁ _) (@h₂ _)

feat(data/finset/basic): insert and erase lemmas (#18729)

Interaction of insert and erase with inter, union and disjoint.

Co-authored-by: Eric Rodriguez <ericrboidi@gmail.com>

Diff

@@ -960,6 +960,11 @@ disjoint_sup_right
 lemma disjoint_sdiff_left : disjoint (t \ s) s := disjoint_sdiff_self_left
 lemma disjoint_sdiff_right : disjoint s (t \ s) := disjoint_sdiff_self_right
 
+lemma diff_union_diff_cancel (hts : t ⊆ s) (hut : u ⊆ t) : s \ t ∪ t \ u = s \ u :=
+sdiff_sup_sdiff_cancel hts hut
+
+lemma diff_diff_eq_sdiff_union (h : u ⊆ s) : s \ (t \ u) = s \ t ∪ u := sdiff_sdiff_eq_sdiff_sup h
+
 @[simp] lemma disjoint_singleton_left : disjoint {a} s ↔ a ∉ s :=
 by simp [set.disjoint_iff, subset_def]; exact iff.rfl

chore(*): Miscellaneous lemmas (#18677)

algebra.support: support n = univ if n ≠ 0, mul_support n = univ if n ≠ 1
data.int.char_zero: ↑n = 1 ↔ n = 1
data.real.ennreal: of_real a.to_real = a ↔ a ≠ ⊤, (of_real a).to_real = a ↔ 0 ≤ a
data.set.basic: s ∩ {a | p a} = {a ∈ s | p a}
logic.function.basic: on_fun f g a b = f (g a) (g b)
order.conditionally_complete_lattice.basic: Lemmas unfolding the definition of Sup/Inf on with_top/with_bot

Diff

@@ -615,6 +615,10 @@ inter_eq_self_of_subset_right $ subset_union_left _ _
 theorem union_inter_cancel_right {s t : set α} : (s ∪ t) ∩ t = t :=
 inter_eq_self_of_subset_right $ subset_union_right _ _
 
+lemma inter_set_of_eq_sep (s : set α) (p : α → Prop) : s ∩ {a | p a} = {a ∈ s | p a} := rfl
+lemma set_of_inter_eq_sep (p : α → Prop) (s : set α) : {a | p a} ∩ s = {a ∈ s | p a} :=
+inter_comm _ _
+
 /-! ### Distributivity laws -/
 
 theorem inter_distrib_left (s t u : set α) : s ∩ (t ∪ u) = (s ∩ t) ∪ (s ∩ u) :=
@@ -783,6 +787,8 @@ theorem insert_eq (x : α) (s : set α) : insert x s = ({x} : set α) ∪ s := r
 
 @[simp] theorem singleton_subset_iff {a : α} {s : set α} : {a} ⊆ s ↔ a ∈ s := forall_eq
 
+lemma singleton_subset_singleton : ({a} : set α) ⊆ {b} ↔ a = b := by simp
+
 theorem set_compr_eq_eq_singleton {a : α} : {b | b = a} = {a} := rfl
 
 @[simp] theorem singleton_union : {a} ∪ s = insert a s := rfl
@@ -965,6 +971,12 @@ by rw [disjoint_singleton_left, mem_singleton_iff]
 
 lemma subset_diff : s ⊆ t \ u ↔ s ⊆ t ∧ disjoint s u := le_iff_subset.symm.trans le_sdiff
 
+lemma inter_diff_distrib_left (s t u : set α) : s ∩ (t \ u) = (s ∩ t) \ (s ∩ u) :=
+inf_sdiff_distrib_left _ _ _
+
+lemma inter_diff_distrib_right (s t u : set α) : s \ t ∩ u = (s ∩ u) \ (t ∩ u) :=
+inf_sdiff_distrib_right _ _ _
+
 /-! ### Lemmas about complement -/
 
 lemma compl_def (s : set α) : sᶜ = {x | x ∉ s} := rfl
@@ -1227,10 +1239,18 @@ sdiff_inf_self_right _ _
 @[simp] theorem diff_singleton_eq_self {a : α} {s : set α} (h : a ∉ s) : s \ {a} = s :=
 sdiff_eq_self_iff_disjoint.2 $ by simp [h]
 
+@[simp] lemma diff_singleton_ssubset {s : set α} {a : α} : s \ {a} ⊂ s ↔ a ∈ s :=
+sdiff_le.lt_iff_ne.trans $ sdiff_eq_left.not.trans $ by simp
+
 @[simp] theorem insert_diff_singleton {a : α} {s : set α} :
   insert a (s \ {a}) = insert a s :=
 by simp [insert_eq, union_diff_self, -union_singleton, -singleton_union]
 
+lemma insert_diff_singleton_comm (hab : a ≠ b) (s : set α) :
+  insert a (s \ {b}) = insert a s \ {b} :=
+by simp_rw [←union_singleton, union_diff_distrib,
+  diff_singleton_eq_self (mem_singleton_iff.not.2 hab.symm)]
+
 @[simp] lemma diff_self {s : set α} : s \ s = ∅ := sdiff_self
 
 lemma diff_diff_right_self (s t : set α)  : s \ (s \ t) = s ∩ t := sdiff_sdiff_right_self

chore(data/set/basic): Golf #18356 (#18491)

and fix a docstring that was made a comment

Diff

@@ -698,21 +698,8 @@ begin
   exacts [(ha hx).elim, hxt]
 end
 
-theorem subset_insert_iff_of_not_mem {s t : set α} {a : α} (h : a ∉ s) :
-  s ⊆ insert a t ↔ s ⊆ t :=
-begin
-  constructor,
-  { intros g y hy,
-    specialize g hy,
-    rw [mem_insert_iff] at g,
-    rcases g with g | g,
-    { rw [g] at hy,
-      contradiction },
-    { assumption }},
-  { intros g y hy,
-    specialize g hy,
-    exact mem_insert_of_mem _ g }
-end
+theorem subset_insert_iff_of_not_mem (ha : a ∉ s) : s ⊆ insert a t ↔ s ⊆ t :=
+forall₂_congr $ λ b hb, or_iff_right $ ne_of_mem_of_not_mem hb ha
 
 theorem ssubset_iff_insert {s t : set α} : s ⊂ t ↔ ∃ a ∉ s, insert a s ⊆ t :=
 begin
@@ -1317,7 +1304,7 @@ ext $ λ s, subset_empty_iff
 @[simp] theorem powerset_univ : 𝒫 (univ : set α) = univ :=
 eq_univ_of_forall subset_univ
 
-/- The powerset of a singleton contains only `∅` and the singleton itself. -/
+/-- The powerset of a singleton contains only `∅` and the singleton itself. -/
 theorem powerset_singleton (x : α) : 𝒫 ({x} : set α) = {∅, {x}} :=
 by { ext y, rw [mem_powerset_iff, subset_singleton_iff_eq, mem_insert_iff, mem_singleton_iff] }

45501380

feat(data/set): add lemmas about powerset of insert and singleton (#18356)

Add lemmas about 𝒫 {x} and 𝒫 (insert x A).

Mathlib4 pair : leanprover-community/mathlib4/pull/2000

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

Diff

@@ -698,6 +698,22 @@ begin
   exacts [(ha hx).elim, hxt]
 end
 
+theorem subset_insert_iff_of_not_mem {s t : set α} {a : α} (h : a ∉ s) :
+  s ⊆ insert a t ↔ s ⊆ t :=
+begin
+  constructor,
+  { intros g y hy,
+    specialize g hy,
+    rw [mem_insert_iff] at g,
+    rcases g with g | g,
+    { rw [g] at hy,
+      contradiction },
+    { assumption }},
+  { intros g y hy,
+    specialize g hy,
+    exact mem_insert_of_mem _ g }
+end
+
 theorem ssubset_iff_insert {s t : set α} : s ⊂ t ↔ ∃ a ∉ s, insert a s ⊆ t :=
 begin
   simp only [insert_subset, exists_and_distrib_right, ssubset_def, not_subset],
@@ -1301,6 +1317,10 @@ ext $ λ s, subset_empty_iff
 @[simp] theorem powerset_univ : 𝒫 (univ : set α) = univ :=
 eq_univ_of_forall subset_univ
 
+/- The powerset of a singleton contains only `∅` and the singleton itself. -/
+theorem powerset_singleton (x : α) : 𝒫 ({x} : set α) = {∅, {x}} :=
+by { ext y, rw [mem_powerset_iff, subset_singleton_iff_eq, mem_insert_iff, mem_singleton_iff] }
+
 /-! ### Sets defined as an if-then-else -/
 
 lemma mem_dite_univ_right (p : Prop) [decidable p] (t : p → set α) (x : α) :

b875cbb7

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bc7d81be

feat(data/{set,finset}/basic): Convenience lemmas (#17957)

Add a few convenient corollaries to existing lemmas.

Diff

@@ -162,7 +162,7 @@ lemma eq.subset {α} {s t : set α} : s = t → s ⊆ t := eq.subset'
 
 namespace set
 
-variables {α : Type u} {β : Type v} {γ : Type w} {ι : Sort x} {a b : α} {s t u : set α}
+variables {α : Type u} {β : Type v} {γ : Type w} {ι : Sort x} {a b : α} {s s₁ s₂ t t₁ t₂ u : set α}
 
 instance : inhabited (set α) := ⟨∅⟩
 
@@ -914,6 +914,54 @@ lemma disjoint_left : disjoint s t ↔ ∀ ⦃a⦄, a ∈ s → a ∉ t :=
 disjoint_iff_inf_le.trans $ forall_congr $ λ _, not_and
 lemma disjoint_right : disjoint s t ↔ ∀ ⦃a⦄, a ∈ t → a ∉ s := by rw [disjoint.comm, disjoint_left]
 
+lemma not_disjoint_iff : ¬disjoint s t ↔ ∃ x, x ∈ s ∧ x ∈ t :=
+set.disjoint_iff.not.trans $ not_forall.trans $ exists_congr $ λ x, not_not
+
+lemma not_disjoint_iff_nonempty_inter : ¬disjoint s t ↔ (s ∩ t).nonempty := not_disjoint_iff
+
+alias not_disjoint_iff_nonempty_inter ↔ _ nonempty.not_disjoint
+
+lemma disjoint_or_nonempty_inter (s t : set α) : disjoint s t ∨ (s ∩ t).nonempty :=
+(em _).imp_right not_disjoint_iff_nonempty_inter.mp
+
+lemma disjoint_iff_forall_ne : disjoint s t ↔ ∀ (x ∈ s) (y ∈ t), x ≠ y :=
+by simp only [ne.def, disjoint_left, @imp_not_comm _ (_ = _), forall_eq']
+
+lemma _root_.disjoint.ne_of_mem (h : disjoint s t) {x y} (hx : x ∈ s) (hy : y ∈ t) : x ≠ y :=
+disjoint_iff_forall_ne.mp h x hx y hy
+
+lemma disjoint_of_subset_left (hs : s₁ ⊆ s₂) (h : disjoint s₂ t) : disjoint s₁ t := h.mono_left hs
+lemma disjoint_of_subset_right (ht : t₁ ⊆ t₂) (h : disjoint s t₂) : disjoint s t₁ := h.mono_right ht
+
+lemma disjoint_of_subset (hs : s₁ ⊆ s₂) (ht : t₁ ⊆ t₂) (h : disjoint s₂ t₂) : disjoint s₁ t₁ :=
+h.mono hs ht
+
+@[simp] lemma disjoint_union_left : disjoint (s ∪ t) u ↔ disjoint s u ∧ disjoint t u :=
+disjoint_sup_left
+
+@[simp] lemma disjoint_union_right : disjoint s (t ∪ u) ↔ disjoint s t ∧ disjoint s u :=
+disjoint_sup_right
+
+@[simp] lemma disjoint_empty (s : set α) : disjoint s ∅ := disjoint_bot_right
+@[simp] lemma empty_disjoint (s : set α) : disjoint ∅ s := disjoint_bot_left
+
+@[simp] lemma univ_disjoint : disjoint univ s ↔ s = ∅ := top_disjoint
+@[simp] lemma disjoint_univ : disjoint s univ ↔ s = ∅ := disjoint_top
+
+lemma disjoint_sdiff_left : disjoint (t \ s) s := disjoint_sdiff_self_left
+lemma disjoint_sdiff_right : disjoint s (t \ s) := disjoint_sdiff_self_right
+
+@[simp] lemma disjoint_singleton_left : disjoint {a} s ↔ a ∉ s :=
+by simp [set.disjoint_iff, subset_def]; exact iff.rfl
+
+@[simp] lemma disjoint_singleton_right : disjoint s {a} ↔ a ∉ s :=
+disjoint.comm.trans disjoint_singleton_left
+
+@[simp] lemma disjoint_singleton : disjoint ({a} : set α) {b} ↔ a ≠ b :=
+by rw [disjoint_singleton_left, mem_singleton_iff]
+
+lemma subset_diff : s ⊆ t \ u ↔ s ⊆ t ∧ disjoint s u := le_iff_subset.symm.trans le_sdiff
+
 /-! ### Lemmas about complement -/
 
 lemma compl_def (s : set α) : sᶜ = {x | x ∉ s} := rfl
@@ -1173,11 +1221,8 @@ sdiff_inf_self_right _ _
 
 @[simp] theorem diff_self_inter {s t : set α} : s \ (s ∩ t) = s \ t := sdiff_inf_self_left _ _
 
-@[simp] theorem diff_eq_self {s t : set α} : s \ t = s ↔ t ∩ s ⊆ ∅ :=
-show s \ t = s ↔ t ⊓ s ≤ ⊥, from sdiff_eq_self_iff_disjoint.trans disjoint_iff_inf_le
-
 @[simp] theorem diff_singleton_eq_self {a : α} {s : set α} (h : a ∉ s) : s \ {a} = s :=
-diff_eq_self.2 $ by simp [singleton_inter_eq_empty.2 h]
+sdiff_eq_self_iff_disjoint.2 $ by simp [h]
 
 @[simp] theorem insert_diff_singleton {a : α} {s : set α} :
   insert a (s \ {a}) = insert a s :=
@@ -1558,6 +1603,12 @@ by simp [or_iff_not_imp_right]
 lemma eq_singleton_or_nontrivial (ha : a ∈ s) : s = {a} ∨ s.nontrivial :=
 by { rw ←subsingleton_iff_singleton ha, exact s.subsingleton_or_nontrivial }
 
+lemma nontrivial_iff_ne_singleton (ha : a ∈ s) : s.nontrivial ↔ s ≠ {a} :=
+⟨nontrivial.ne_singleton, (eq_singleton_or_nontrivial ha).resolve_left⟩
+
+lemma nonempty.exists_eq_singleton_or_nontrivial : s.nonempty → (∃ a, s = {a}) ∨ s.nontrivial :=
+λ ⟨a, ha⟩, (eq_singleton_or_nontrivial ha).imp_left $ exists.intro a
+
 theorem univ_eq_true_false : univ = ({true, false} : set Prop) :=
 eq.symm $ eq_univ_of_forall $ classical.cases (by simp) (by simp)
 
@@ -1793,8 +1844,6 @@ end monotone
 
 /-! ### Disjoint sets -/
 
-section disjoint
-
 variables {α β : Type*} {s t u : set α} {f : α → β}
 
 namespace disjoint
@@ -1824,70 +1873,3 @@ lemma subset_right_of_subset_union (h : s ⊆ t ∪ u) (hab : disjoint s t) : s
 hab.left_le_of_le_sup_left h
 
 end disjoint
-
-namespace set
-
-lemma not_disjoint_iff : ¬disjoint s t ↔ ∃ x, x ∈ s ∧ x ∈ t :=
-set.disjoint_iff.not.trans $ not_forall.trans $ exists_congr $ λ x, not_not
-
-lemma not_disjoint_iff_nonempty_inter : ¬disjoint s t ↔ (s ∩ t).nonempty :=
-not_disjoint_iff
-
-alias not_disjoint_iff_nonempty_inter ↔ _ nonempty.not_disjoint
-
-lemma disjoint_or_nonempty_inter (s t : set α) : disjoint s t ∨ (s ∩ t).nonempty :=
-(em _).imp_right not_disjoint_iff_nonempty_inter.mp
-
-lemma disjoint_iff_forall_ne : disjoint s t ↔ ∀ (x ∈ s) (y ∈ t), x ≠ y :=
-by simp only [ne.def, disjoint_left, @imp_not_comm _ (_ = _), forall_eq']
-
-lemma _root_.disjoint.ne_of_mem (h : disjoint s t) {x y} (hx : x ∈ s) (hy : y ∈ t) : x ≠ y :=
-disjoint_iff_forall_ne.mp h x hx y hy
-
-theorem disjoint_of_subset_left (h : s ⊆ u) (d : disjoint u t) : disjoint s t :=
-d.mono_left h
-
-theorem disjoint_of_subset_right (h : t ⊆ u) (d : disjoint s u) : disjoint s t :=
-d.mono_right h
-
-theorem disjoint_of_subset {s t u v : set α} (h1 : s ⊆ u) (h2 : t ⊆ v) (d : disjoint u v) :
-  disjoint s t :=
-d.mono h1 h2
-
-@[simp] theorem disjoint_union_left :
-  disjoint (s ∪ t) u ↔ disjoint s u ∧ disjoint t u :=
-disjoint_sup_left
-
-@[simp] theorem disjoint_union_right :
-  disjoint s (t ∪ u) ↔ disjoint s t ∧ disjoint s u :=
-disjoint_sup_right
-
-theorem disjoint_diff {a b : set α} : disjoint a (b \ a) :=
-disjoint_iff.2 (inter_diff_self _ _)
-
-@[simp] theorem disjoint_empty (s : set α) : disjoint s ∅ := disjoint_bot_right
-
-@[simp] theorem empty_disjoint (s : set α) : disjoint ∅ s := disjoint_bot_left
-
-@[simp] lemma univ_disjoint {s : set α} : disjoint univ s ↔ s = ∅ :=
-top_disjoint
-
-@[simp] lemma disjoint_univ {s : set α} : disjoint s univ ↔ s = ∅ :=
-disjoint_top
-
-@[simp] theorem disjoint_singleton_left {a : α} {s : set α} : disjoint {a} s ↔ a ∉ s :=
-by simp [set.disjoint_iff, subset_def]; exact iff.rfl
-
-@[simp] theorem disjoint_singleton_right {a : α} {s : set α} : disjoint s {a} ↔ a ∉ s :=
-by rw [disjoint.comm]; exact disjoint_singleton_left
-
-@[simp] lemma disjoint_singleton {a b : α} : disjoint ({a} : set α) {b} ↔ a ≠ b :=
-by rw [disjoint_singleton_left, mem_singleton_iff]
-
-lemma subset_diff {s t u : set α} : s ⊆ t \ u ↔ s ⊆ t ∧ disjoint s u :=
-⟨λ h, ⟨λ x hxs, (h hxs).1, disjoint_iff_inf_le.mpr $ λ x ⟨hxs, hxu⟩, (h hxs).2 hxu⟩,
-λ ⟨h1, h2⟩ x hxs, ⟨h1 hxs, λ hxu, h2.le_bot ⟨hxs, hxu⟩⟩⟩
-
-end set
-
-end disjoint

chore(data/set/lattice): move basic lemmas to basic files (#17882)

This PR moves some lemmas in data.set.lattice to data.set.basic, data.set.image, and data.set.function. They are basic enough and do not depend on the set lattice. This also helps #17880 to split data.set.pairwise and reduce the dependency of many files.

mathlib4 PR: https://github.com/leanprover-community/mathlib4/pull/1109

Diff

@@ -1736,3 +1736,159 @@ instance decidable_set_of (p : α → Prop) [decidable (p a)] : decidable (a ∈
 by assumption
 
 end set
+
+/-! ### Monotone lemmas for sets -/
+
+section monotone
+variables {α β : Type*}
+
+theorem monotone.inter [preorder β] {f g : β → set α}
+  (hf : monotone f) (hg : monotone g) : monotone (λ x, f x ∩ g x) :=
+hf.inf hg
+
+theorem monotone_on.inter [preorder β] {f g : β → set α} {s : set β}
+  (hf : monotone_on f s) (hg : monotone_on g s) : monotone_on (λ x, f x ∩ g x) s :=
+hf.inf hg
+
+theorem antitone.inter [preorder β] {f g : β → set α}
+  (hf : antitone f) (hg : antitone g) : antitone (λ x, f x ∩ g x) :=
+hf.inf hg
+
+theorem antitone_on.inter [preorder β] {f g : β → set α} {s : set β}
+  (hf : antitone_on f s) (hg : antitone_on g s) : antitone_on (λ x, f x ∩ g x) s :=
+hf.inf hg
+
+theorem monotone.union [preorder β] {f g : β → set α}
+  (hf : monotone f) (hg : monotone g) : monotone (λ x, f x ∪ g x) :=
+hf.sup hg
+
+theorem monotone_on.union [preorder β] {f g : β → set α} {s : set β}
+  (hf : monotone_on f s) (hg : monotone_on g s) : monotone_on (λ x, f x ∪ g x) s :=
+hf.sup hg
+
+theorem antitone.union [preorder β] {f g : β → set α}
+  (hf : antitone f) (hg : antitone g) : antitone (λ x, f x ∪ g x) :=
+hf.sup hg
+
+theorem antitone_on.union [preorder β] {f g : β → set α} {s : set β}
+  (hf : antitone_on f s) (hg : antitone_on g s) : antitone_on (λ x, f x ∪ g x) s :=
+hf.sup hg
+
+namespace set
+
+theorem monotone_set_of [preorder α] {p : α → β → Prop}
+  (hp : ∀ b, monotone (λ a, p a b)) : monotone (λ a, {b | p a b}) :=
+λ a a' h b, hp b h
+
+theorem antitone_set_of [preorder α] {p : α → β → Prop}
+  (hp : ∀ b, antitone (λ a, p a b)) : antitone (λ a, {b | p a b}) :=
+λ a a' h b, hp b h
+
+/-- Quantifying over a set is antitone in the set -/
+lemma antitone_bforall {P : α → Prop} : antitone (λ s : set α, ∀ x ∈ s, P x) :=
+λ s t hst h x hx, h x $ hst hx
+
+end set
+
+end monotone
+
+/-! ### Disjoint sets -/
+
+section disjoint
+
+variables {α β : Type*} {s t u : set α} {f : α → β}
+
+namespace disjoint
+
+theorem union_left (hs : disjoint s u) (ht : disjoint t u) : disjoint (s ∪ t) u :=
+hs.sup_left ht
+
+theorem union_right (ht : disjoint s t) (hu : disjoint s u) : disjoint s (t ∪ u) :=
+ht.sup_right hu
+
+lemma inter_left (u : set α) (h : disjoint s t) : disjoint (s ∩ u) t :=
+h.inf_left u
+
+lemma inter_left' (u : set α) (h : disjoint s t) : disjoint (u ∩ s) t :=
+h.inf_left' _
+
+lemma inter_right (u : set α) (h : disjoint s t) : disjoint s (t ∩ u) :=
+h.inf_right _
+
+lemma inter_right' (u : set α) (h : disjoint s t) : disjoint s (u ∩ t) :=
+h.inf_right' _
+
+lemma subset_left_of_subset_union (h : s ⊆ t ∪ u) (hac : disjoint s u) : s ⊆ t :=
+hac.left_le_of_le_sup_right h
+
+lemma subset_right_of_subset_union (h : s ⊆ t ∪ u) (hab : disjoint s t) : s ⊆ u :=
+hab.left_le_of_le_sup_left h
+
+end disjoint
+
+namespace set
+
+lemma not_disjoint_iff : ¬disjoint s t ↔ ∃ x, x ∈ s ∧ x ∈ t :=
+set.disjoint_iff.not.trans $ not_forall.trans $ exists_congr $ λ x, not_not
+
+lemma not_disjoint_iff_nonempty_inter : ¬disjoint s t ↔ (s ∩ t).nonempty :=
+not_disjoint_iff
+
+alias not_disjoint_iff_nonempty_inter ↔ _ nonempty.not_disjoint
+
+lemma disjoint_or_nonempty_inter (s t : set α) : disjoint s t ∨ (s ∩ t).nonempty :=
+(em _).imp_right not_disjoint_iff_nonempty_inter.mp
+
+lemma disjoint_iff_forall_ne : disjoint s t ↔ ∀ (x ∈ s) (y ∈ t), x ≠ y :=
+by simp only [ne.def, disjoint_left, @imp_not_comm _ (_ = _), forall_eq']
+
+lemma _root_.disjoint.ne_of_mem (h : disjoint s t) {x y} (hx : x ∈ s) (hy : y ∈ t) : x ≠ y :=
+disjoint_iff_forall_ne.mp h x hx y hy
+
+theorem disjoint_of_subset_left (h : s ⊆ u) (d : disjoint u t) : disjoint s t :=
+d.mono_left h
+
+theorem disjoint_of_subset_right (h : t ⊆ u) (d : disjoint s u) : disjoint s t :=
+d.mono_right h
+
+theorem disjoint_of_subset {s t u v : set α} (h1 : s ⊆ u) (h2 : t ⊆ v) (d : disjoint u v) :
+  disjoint s t :=
+d.mono h1 h2
+
+@[simp] theorem disjoint_union_left :
+  disjoint (s ∪ t) u ↔ disjoint s u ∧ disjoint t u :=
+disjoint_sup_left
+
+@[simp] theorem disjoint_union_right :
+  disjoint s (t ∪ u) ↔ disjoint s t ∧ disjoint s u :=
+disjoint_sup_right
+
+theorem disjoint_diff {a b : set α} : disjoint a (b \ a) :=
+disjoint_iff.2 (inter_diff_self _ _)
+
+@[simp] theorem disjoint_empty (s : set α) : disjoint s ∅ := disjoint_bot_right
+
+@[simp] theorem empty_disjoint (s : set α) : disjoint ∅ s := disjoint_bot_left
+
+@[simp] lemma univ_disjoint {s : set α} : disjoint univ s ↔ s = ∅ :=
+top_disjoint
+
+@[simp] lemma disjoint_univ {s : set α} : disjoint s univ ↔ s = ∅ :=
+disjoint_top
+
+@[simp] theorem disjoint_singleton_left {a : α} {s : set α} : disjoint {a} s ↔ a ∉ s :=
+by simp [set.disjoint_iff, subset_def]; exact iff.rfl
+
+@[simp] theorem disjoint_singleton_right {a : α} {s : set α} : disjoint s {a} ↔ a ∉ s :=
+by rw [disjoint.comm]; exact disjoint_singleton_left
+
+@[simp] lemma disjoint_singleton {a b : α} : disjoint ({a} : set α) {b} ↔ a ≠ b :=
+by rw [disjoint_singleton_left, mem_singleton_iff]
+
+lemma subset_diff {s t u : set α} : s ⊆ t \ u ↔ s ⊆ t ∧ disjoint s u :=
+⟨λ h, ⟨λ x hxs, (h hxs).1, disjoint_iff_inf_le.mpr $ λ x ⟨hxs, hxu⟩, (h hxs).2 hxu⟩,
+λ ⟨h1, h2⟩ x hxs, ⟨h1 hxs, λ hxu, h2.le_bot ⟨hxs, hxu⟩⟩⟩
+
+end set
+
+end disjoint

bd59f822

feat(data/set/basic): A set is either a subsingleton or nontrivial (#17901)

Also make the argument to set.finite_or_infinite explicit.

Diff

@@ -1549,6 +1549,12 @@ iff.not_left not_subsingleton_iff.symm
 alias not_nontrivial_iff ↔ _ subsingleton.not_nontrivial
 alias not_subsingleton_iff ↔ _ nontrivial.not_subsingleton
 
+protected lemma subsingleton_or_nontrivial (s : set α) : s.subsingleton ∨ s.nontrivial :=
+by simp [or_iff_not_imp_right]
+
+lemma eq_singleton_or_nontrivial (ha : a ∈ s) : s = {a} ∨ s.nontrivial :=
+by { rw ←subsingleton_iff_singleton ha, exact s.subsingleton_or_nontrivial }
+
 theorem univ_eq_true_false : univ = ({true, false} : set Prop) :=
 eq.symm $ eq_univ_of_forall $ classical.cases (by simp) (by simp)

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

bump to nightly-2024-04-25-08

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

ad7a2212

Diff

@@ -658,7 +658,7 @@ theorem inter_nonempty_iff_exists_left : (s ∩ t).Nonempty ↔ ∃ x ∈ s, x 
 
 #print Set.inter_nonempty_iff_exists_right /-
 theorem inter_nonempty_iff_exists_right : (s ∩ t).Nonempty ↔ ∃ x ∈ t, x ∈ s := by
-  simp_rw [inter_nonempty, exists_prop, and_comm']
+  simp_rw [inter_nonempty, exists_prop, and_comm]
 #align set.inter_nonempty_iff_exists_right Set.inter_nonempty_iff_exists_right
 -/
 
@@ -1592,7 +1592,7 @@ theorem subset_insert_iff_of_not_mem (ha : a ∉ s) : s ⊆ insert a t ↔ s ⊆
 theorem ssubset_iff_insert {s t : Set α} : s ⊂ t ↔ ∃ (a : _) (_ : a ∉ s), insert a s ⊆ t :=
   by
   simp only [insert_subset, exists_and_right, ssubset_def, not_subset]
-  simp only [exists_prop, and_comm']
+  simp only [exists_prop, and_comm]
 #align set.ssubset_iff_insert Set.ssubset_iff_insert
 -/
 
@@ -3759,7 +3759,7 @@ theorem not_monotoneOn_not_antitoneOn_iff_exists_le_le :
       ∃ (a : _) (_ : a ∈ s) (b : _) (_ : b ∈ s) (c : _) (_ : c ∈ s),
         a ≤ b ∧ b ≤ c ∧ (f a < f b ∧ f c < f b ∨ f b < f a ∧ f b < f c) :=
   by
-  simp [monotone_on_iff_monotone, antitone_on_iff_antitone, and_assoc', exists_and_left,
+  simp [monotone_on_iff_monotone, antitone_on_iff_antitone, and_assoc, exists_and_left,
     not_monotone_not_antitone_iff_exists_le_le, @and_left_comm (_ ∈ s)]
 #align set.not_monotone_on_not_antitone_on_iff_exists_le_le Set.not_monotoneOn_not_antitoneOn_iff_exists_le_le
 -/
@@ -3773,7 +3773,7 @@ theorem not_monotoneOn_not_antitoneOn_iff_exists_lt_lt :
       ∃ (a : _) (_ : a ∈ s) (b : _) (_ : b ∈ s) (c : _) (_ : c ∈ s),
         a < b ∧ b < c ∧ (f a < f b ∧ f c < f b ∨ f b < f a ∧ f b < f c) :=
   by
-  simp [monotone_on_iff_monotone, antitone_on_iff_antitone, and_assoc', exists_and_left,
+  simp [monotone_on_iff_monotone, antitone_on_iff_antitone, and_assoc, exists_and_left,
     not_monotone_not_antitone_iff_exists_lt_lt, @and_left_comm (_ ∈ s)]
 #align set.not_monotone_on_not_antitone_on_iff_exists_lt_lt Set.not_monotoneOn_not_antitoneOn_iff_exists_lt_lt
 -/

bump to nightly-2024-04-10-08

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

cd0c1af5

Diff

@@ -806,10 +806,10 @@ theorem subset_eq_empty {s t : Set α} (h : t ⊆ s) (e : s = ∅) : t = ∅ :=
 #align set.subset_eq_empty Set.subset_eq_empty
 -/
 
-#print Set.ball_empty_iff /-
-theorem ball_empty_iff {p : α → Prop} : (∀ x ∈ (∅ : Set α), p x) ↔ True :=
+#print Set.forall_mem_empty /-
+theorem forall_mem_empty {p : α → Prop} : (∀ x ∈ (∅ : Set α), p x) ↔ True :=
   iff_true_intro fun x => False.elim
-#align set.ball_empty_iff Set.ball_empty_iff
+#align set.ball_empty_iff Set.forall_mem_empty
 -/
 
 instance (α : Type u) : IsEmpty.{u + 1} (∅ : Set α) :=
@@ -1671,18 +1671,18 @@ theorem forall_insert_of_forall {P : α → Prop} {a : α} {s : Set α} (H : ∀
 #align set.forall_insert_of_forall Set.forall_insert_of_forall
 -/
 
-#print Set.bex_insert_iff /-
-theorem bex_insert_iff {P : α → Prop} {a : α} {s : Set α} :
+#print Set.exists_mem_insert /-
+theorem exists_mem_insert {P : α → Prop} {a : α} {s : Set α} :
     (∃ x ∈ insert a s, P x) ↔ P a ∨ ∃ x ∈ s, P x :=
-  bex_or_left.trans <| or_congr_left bex_eq_left
-#align set.bex_insert_iff Set.bex_insert_iff
+  exists_mem_or_left.trans <| or_congr_left bex_eq_left
+#align set.bex_insert_iff Set.exists_mem_insert
 -/
 
-#print Set.ball_insert_iff /-
-theorem ball_insert_iff {P : α → Prop} {a : α} {s : Set α} :
+#print Set.forall_mem_insert /-
+theorem forall_mem_insert {P : α → Prop} {a : α} {s : Set α} :
     (∀ x ∈ insert a s, P x) ↔ P a ∧ ∀ x ∈ s, P x :=
-  ball_or_left.trans <| and_congr_left' forall_eq
-#align set.ball_insert_iff Set.ball_insert_iff
+  forall₂_or_left.trans <| and_congr_left' forall_eq
+#align set.ball_insert_iff Set.forall_mem_insert
 -/
 
 /-! ### Lemmas about singletons -/

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -1387,48 +1387,56 @@ theorem setOf_inter_eq_sep (p : α → Prop) (s : Set α) : {a | p a} ∩ s = {a
 /-! ### Distributivity laws -/
 
 
-#print Set.inter_distrib_left /-
-theorem inter_distrib_left (s t u : Set α) : s ∩ (t ∪ u) = s ∩ t ∪ s ∩ u :=
+#print Set.inter_union_distrib_left /-
+theorem inter_union_distrib_left (s t u : Set α) : s ∩ (t ∪ u) = s ∩ t ∪ s ∩ u :=
   inf_sup_left
-#align set.inter_distrib_left Set.inter_distrib_left
+#align set.inter_distrib_left Set.inter_union_distrib_left
 -/
 
+/- warning: set.inter_union_distrib_left clashes with set.inter_distrib_left -> Set.inter_union_distrib_left
+Case conversion may be inaccurate. Consider using '#align set.inter_union_distrib_left Set.inter_union_distrib_leftₓ'. -/
 #print Set.inter_union_distrib_left /-
 theorem inter_union_distrib_left {s t u : Set α} : s ∩ (t ∪ u) = s ∩ t ∪ s ∩ u :=
   inf_sup_left
 #align set.inter_union_distrib_left Set.inter_union_distrib_left
 -/
 
-#print Set.inter_distrib_right /-
-theorem inter_distrib_right (s t u : Set α) : (s ∪ t) ∩ u = s ∩ u ∪ t ∩ u :=
+#print Set.union_inter_distrib_right /-
+theorem union_inter_distrib_right (s t u : Set α) : (s ∪ t) ∩ u = s ∩ u ∪ t ∩ u :=
   inf_sup_right
-#align set.inter_distrib_right Set.inter_distrib_right
+#align set.inter_distrib_right Set.union_inter_distrib_right
 -/
 
+/- warning: set.union_inter_distrib_right clashes with set.inter_distrib_right -> Set.union_inter_distrib_right
+Case conversion may be inaccurate. Consider using '#align set.union_inter_distrib_right Set.union_inter_distrib_rightₓ'. -/
 #print Set.union_inter_distrib_right /-
 theorem union_inter_distrib_right {s t u : Set α} : (s ∪ t) ∩ u = s ∩ u ∪ t ∩ u :=
   inf_sup_right
 #align set.union_inter_distrib_right Set.union_inter_distrib_right
 -/
 
-#print Set.union_distrib_left /-
-theorem union_distrib_left (s t u : Set α) : s ∪ t ∩ u = (s ∪ t) ∩ (s ∪ u) :=
+#print Set.union_inter_distrib_left /-
+theorem union_inter_distrib_left (s t u : Set α) : s ∪ t ∩ u = (s ∪ t) ∩ (s ∪ u) :=
   sup_inf_left
-#align set.union_distrib_left Set.union_distrib_left
+#align set.union_distrib_left Set.union_inter_distrib_left
 -/
 
+/- warning: set.union_inter_distrib_left clashes with set.union_distrib_left -> Set.union_inter_distrib_left
+Case conversion may be inaccurate. Consider using '#align set.union_inter_distrib_left Set.union_inter_distrib_leftₓ'. -/
 #print Set.union_inter_distrib_left /-
 theorem union_inter_distrib_left {s t u : Set α} : s ∪ t ∩ u = (s ∪ t) ∩ (s ∪ u) :=
   sup_inf_left
 #align set.union_inter_distrib_left Set.union_inter_distrib_left
 -/
 
-#print Set.union_distrib_right /-
-theorem union_distrib_right (s t u : Set α) : s ∩ t ∪ u = (s ∪ u) ∩ (t ∪ u) :=
+#print Set.inter_union_distrib_right /-
+theorem inter_union_distrib_right (s t u : Set α) : s ∩ t ∪ u = (s ∪ u) ∩ (t ∪ u) :=
   sup_inf_right
-#align set.union_distrib_right Set.union_distrib_right
+#align set.union_distrib_right Set.inter_union_distrib_right
 -/
 
+/- warning: set.inter_union_distrib_right clashes with set.union_distrib_right -> Set.inter_union_distrib_right
+Case conversion may be inaccurate. Consider using '#align set.inter_union_distrib_right Set.inter_union_distrib_rightₓ'. -/
 #print Set.inter_union_distrib_right /-
 theorem inter_union_distrib_right {s t u : Set α} : s ∩ t ∪ u = (s ∪ u) ∩ (t ∪ u) :=
   sup_inf_right
@@ -1579,7 +1587,7 @@ theorem subset_insert_iff_of_not_mem (ha : a ∉ s) : s ⊆ insert a t ↔ s ⊆
 #align set.subset_insert_iff_of_not_mem Set.subset_insert_iff_of_not_mem
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (a «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (a «expr ∉ » s) -/
 #print Set.ssubset_iff_insert /-
 theorem ssubset_iff_insert {s t : Set α} : s ⊂ t ↔ ∃ (a : _) (_ : a ∉ s), insert a s ⊆ t :=
   by
@@ -3367,7 +3375,7 @@ instance subsingleton_coe_of_subsingleton [Subsingleton α] {s : Set α} : Subsi
 /-! ### Nontrivial -/
 
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Nontrivial /-
 /-- A set `s` is `nontrivial` if it has at least two distinct elements. -/
 protected def Nontrivial (s : Set α) : Prop :=
@@ -3472,7 +3480,7 @@ theorem nontrivial_of_lt [Preorder α] {x y} (hx : x ∈ s) (hy : y ∈ s) (hxy
 #align set.nontrivial_of_lt Set.nontrivial_of_lt
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.nontrivial_of_exists_lt /-
 theorem nontrivial_of_exists_lt [Preorder α]
     (H : ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s), x < y) : s.Nontrivial :=
@@ -3481,7 +3489,7 @@ theorem nontrivial_of_exists_lt [Preorder α]
 #align set.nontrivial_of_exists_lt Set.nontrivial_of_exists_lt
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Nontrivial.exists_lt /-
 theorem Nontrivial.exists_lt [LinearOrder α] (hs : s.Nontrivial) :
     ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s), x < y :=
@@ -3490,7 +3498,7 @@ theorem Nontrivial.exists_lt [LinearOrder α] (hs : s.Nontrivial) :
 #align set.nontrivial.exists_lt Set.Nontrivial.exists_lt
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.nontrivial_iff_exists_lt /-
 theorem nontrivial_iff_exists_lt [LinearOrder α] :
     s.Nontrivial ↔ ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s), x < y :=
@@ -3742,7 +3750,7 @@ section LinearOrder
 
 variable [LinearOrder α] [LinearOrder β] {f : α → β}
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (a b c «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (a b c «expr ∈ » s) -/
 #print Set.not_monotoneOn_not_antitoneOn_iff_exists_le_le /-
 /-- A function between linear orders which is neither monotone nor antitone makes a dent upright or
 downright. -/
@@ -3756,7 +3764,7 @@ theorem not_monotoneOn_not_antitoneOn_iff_exists_le_le :
 #align set.not_monotone_on_not_antitone_on_iff_exists_le_le Set.not_monotoneOn_not_antitoneOn_iff_exists_le_le
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (a b c «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (a b c «expr ∈ » s) -/
 #print Set.not_monotoneOn_not_antitoneOn_iff_exists_lt_lt /-
 /-- A function between linear orders which is neither monotone nor antitone makes a dent upright or
 downright. -/

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -2754,7 +2754,7 @@ theorem insert_diff_of_not_mem (s) (h : a ∉ t) : insert a s \ t = insert a (s
   by_cases h' : x ∈ t
   · have : x ≠ a := by
       intro H
-      rw [H] at h' 
+      rw [H] at h'
       exact h h'
     simp [h, h', this]
   · simp [h, h']
@@ -3452,9 +3452,9 @@ theorem nontrivial_of_exists_ne {x} (hx : x ∈ s) (h : ∃ y ∈ s, y ≠ x) :
 #print Set.Nontrivial.exists_ne /-
 theorem Nontrivial.exists_ne (hs : s.Nontrivial) (z) : ∃ x ∈ s, x ≠ z :=
   by
-  by_contra H; push_neg at H 
+  by_contra H; push_neg at H
   rcases hs with ⟨x, hx, y, hy, hxy⟩
-  rw [H x hx, H y hy] at hxy 
+  rw [H x hx, H y hy] at hxy
   exact hxy rfl
 #align set.nontrivial.exists_ne Set.Nontrivial.exists_ne
 -/
@@ -3527,7 +3527,7 @@ theorem not_nontrivial_empty : ¬(∅ : Set α).Nontrivial := fun h => h.ne_empt
 @[simp]
 theorem not_nontrivial_singleton {x} : ¬({x} : Set α).Nontrivial := fun H =>
   by
-  rw [nontrivial_iff_exists_ne (mem_singleton x)] at H 
+  rw [nontrivial_iff_exists_ne (mem_singleton x)] at H
   exact
     let ⟨y, hy, hya⟩ := H
     hya (mem_singleton_iff.1 hy)
@@ -3535,7 +3535,7 @@ theorem not_nontrivial_singleton {x} : ¬({x} : Set α).Nontrivial := fun H =>
 -/
 
 #print Set.Nontrivial.ne_singleton /-
-theorem Nontrivial.ne_singleton {x} (hs : s.Nontrivial) : s ≠ {x} := fun H => by rw [H] at hs ;
+theorem Nontrivial.ne_singleton {x} (hs : s.Nontrivial) : s ≠ {x} := fun H => by rw [H] at hs;
   exact not_nontrivial_singleton hs
 #align set.nontrivial.ne_singleton Set.Nontrivial.ne_singleton
 -/

bump to nightly-2024-02-23-08

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

ac9421d6

Diff

@@ -1013,13 +1013,13 @@ theorem union_assoc (a b c : Set α) : a ∪ b ∪ c = a ∪ (b ∪ c) :=
 -/
 
 #print Set.union_isAssoc /-
-instance union_isAssoc : IsAssociative (Set α) (· ∪ ·) :=
+instance union_isAssoc : Std.Associative (Set α) (· ∪ ·) :=
   ⟨union_assoc⟩
 #align set.union_is_assoc Set.union_isAssoc
 -/
 
 #print Set.union_isComm /-
-instance union_isComm : IsCommutative (Set α) (· ∪ ·) :=
+instance union_isComm : Std.Commutative (Set α) (· ∪ ·) :=
   ⟨union_comm⟩
 #align set.union_is_comm Set.union_isComm
 -/
@@ -1230,13 +1230,13 @@ theorem inter_assoc (a b c : Set α) : a ∩ b ∩ c = a ∩ (b ∩ c) :=
 -/
 
 #print Set.inter_isAssoc /-
-instance inter_isAssoc : IsAssociative (Set α) (· ∩ ·) :=
+instance inter_isAssoc : Std.Associative (Set α) (· ∩ ·) :=
   ⟨inter_assoc⟩
 #align set.inter_is_assoc Set.inter_isAssoc
 -/
 
 #print Set.inter_isComm /-
-instance inter_isComm : IsCommutative (Set α) (· ∩ ·) :=
+instance inter_isComm : Std.Commutative (Set α) (· ∩ ·) :=
   ⟨inter_comm⟩
 #align set.inter_is_comm Set.inter_isComm
 -/

bump to nightly-2024-02-01-06

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

5433bded

Diff

@@ -2748,7 +2748,16 @@ theorem insert_diff_of_mem (s) (h : a ∈ t) : insert a s \ t = s \ t := by ext;
 -/
 
 #print Set.insert_diff_of_not_mem /-
-theorem insert_diff_of_not_mem (s) (h : a ∉ t) : insert a s \ t = insert a (s \ t) := by classical
+theorem insert_diff_of_not_mem (s) (h : a ∉ t) : insert a s \ t = insert a (s \ t) := by
+  classical
+  ext x
+  by_cases h' : x ∈ t
+  · have : x ≠ a := by
+      intro H
+      rw [H] at h' 
+      exact h h'
+    simp [h, h', this]
+  · simp [h, h']
 #align set.insert_diff_of_not_mem Set.insert_diff_of_not_mem
 -/

bump to nightly-2024-01-31-06

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

61100fe9

Diff

@@ -2748,16 +2748,7 @@ theorem insert_diff_of_mem (s) (h : a ∈ t) : insert a s \ t = s \ t := by ext;
 -/
 
 #print Set.insert_diff_of_not_mem /-
-theorem insert_diff_of_not_mem (s) (h : a ∉ t) : insert a s \ t = insert a (s \ t) := by
-  classical
-  ext x
-  by_cases h' : x ∈ t
-  · have : x ≠ a := by
-      intro H
-      rw [H] at h' 
-      exact h h'
-    simp [h, h', this]
-  · simp [h, h']
+theorem insert_diff_of_not_mem (s) (h : a ∉ t) : insert a s \ t = insert a (s \ t) := by classical
 #align set.insert_diff_of_not_mem Set.insert_diff_of_not_mem
 -/

bump to nightly-2023-11-05-06

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

acc3325f

Diff

@@ -796,7 +796,7 @@ theorem isEmpty_coe_sort {s : Set α} : IsEmpty ↥s ↔ s = ∅ :=
 
 #print Set.eq_empty_or_nonempty /-
 theorem eq_empty_or_nonempty (s : Set α) : s = ∅ ∨ s.Nonempty :=
-  or_iff_not_imp_left.2 nonempty_iff_ne_empty.2
+  Classical.or_iff_not_imp_left.2 nonempty_iff_ne_empty.2
 #align set.eq_empty_or_nonempty Set.eq_empty_or_nonempty
 -/
 
@@ -2452,7 +2452,7 @@ theorem subset_union_compl_iff_inter_subset {s t u : Set α} : s ⊆ t ∪ uᶜ
 
 #print Set.compl_subset_iff_union /-
 theorem compl_subset_iff_union {s t : Set α} : sᶜ ⊆ t ↔ s ∪ t = univ :=
-  Iff.symm <| eq_univ_iff_forall.trans <| forall_congr' fun a => or_iff_not_imp_left
+  Iff.symm <| eq_univ_iff_forall.trans <| forall_congr' fun a => Classical.or_iff_not_imp_left
 #align set.compl_subset_iff_union Set.compl_subset_iff_union
 -/
 
@@ -3623,7 +3623,7 @@ alias ⟨_, nontrivial.not_subsingleton⟩ := not_subsingleton_iff
 
 #print Set.subsingleton_or_nontrivial /-
 protected theorem subsingleton_or_nontrivial (s : Set α) : s.Subsingleton ∨ s.Nontrivial := by
-  simp [or_iff_not_imp_right]
+  simp [Classical.or_iff_not_imp_right]
 #align set.subsingleton_or_nontrivial Set.subsingleton_or_nontrivial
 -/

bump to nightly-2023-10-21-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/b1abe23ae96fef89ad30d9f4362c307f72a55010

a2dc86f8

Diff

@@ -470,7 +470,7 @@ theorem not_mem_subset (h : s ⊆ t) : a ∉ t → a ∉ s :=
 -/
 
 #print Set.not_subset /-
-theorem not_subset : ¬s ⊆ t ↔ ∃ a ∈ s, a ∉ t := by simp only [subset_def, not_forall]
+theorem not_subset : ¬s ⊆ t ↔ ∃ a ∈ s, a ∉ t := by simp only [subset_def, Classical.not_forall]
 #align set.not_subset Set.not_subset
 -/
 
@@ -910,7 +910,7 @@ theorem exists_mem_of_nonempty (α) : ∀ [Nonempty α], ∃ x : α, x ∈ (univ
 
 #print Set.ne_univ_iff_exists_not_mem /-
 theorem ne_univ_iff_exists_not_mem {α : Type _} (s : Set α) : s ≠ univ ↔ ∃ a, a ∉ s := by
-  rw [← not_forall, ← eq_univ_iff_forall]
+  rw [← Classical.not_forall, ← eq_univ_iff_forall]
 #align set.ne_univ_iff_exists_not_mem Set.ne_univ_iff_exists_not_mem
 -/
 
@@ -2083,7 +2083,8 @@ theorem disjoint_right : Disjoint s t ↔ ∀ ⦃a⦄, a ∈ t → a ∉ s := by
 
 #print Set.not_disjoint_iff /-
 theorem not_disjoint_iff : ¬Disjoint s t ↔ ∃ x, x ∈ s ∧ x ∈ t :=
-  Set.disjoint_iff.Not.trans <| not_forall.trans <| exists_congr fun x => Classical.not_not
+  Set.disjoint_iff.Not.trans <|
+    Classical.not_forall.trans <| exists_congr fun x => Classical.not_not
 #align set.not_disjoint_iff Set.not_disjoint_iff
 -/
 
@@ -3603,7 +3604,7 @@ theorem nontrivial_mono {α : Type _} {s t : Set α} (hst : s ⊆ t) (hs : Nontr
 #print Set.not_subsingleton_iff /-
 @[simp]
 theorem not_subsingleton_iff : ¬s.Subsingleton ↔ s.Nontrivial := by
-  simp_rw [Set.Subsingleton, Set.Nontrivial, not_forall]
+  simp_rw [Set.Subsingleton, Set.Nontrivial, Classical.not_forall]
 #align set.not_subsingleton_iff Set.not_subsingleton_iff
 -/

bump to nightly-2023-10-09-06

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

ec4e4d0e

Diff

@@ -1036,25 +1036,29 @@ theorem union_right_comm (s₁ s₂ s₃ : Set α) : s₁ ∪ s₂ ∪ s₃ = s
 #align set.union_right_comm Set.union_right_comm
 -/
 
+#print Set.union_eq_left /-
 @[simp]
-theorem union_eq_left_iff_subset {s t : Set α} : s ∪ t = s ↔ t ⊆ s :=
+theorem union_eq_left {s t : Set α} : s ∪ t = s ↔ t ⊆ s :=
   sup_eq_left
-#align set.union_eq_left_iff_subset Set.union_eq_left_iff_subset
+#align set.union_eq_left_iff_subset Set.union_eq_left
+-/
 
+#print Set.union_eq_right /-
 @[simp]
-theorem union_eq_right_iff_subset {s t : Set α} : s ∪ t = t ↔ s ⊆ t :=
+theorem union_eq_right {s t : Set α} : s ∪ t = t ↔ s ⊆ t :=
   sup_eq_right
-#align set.union_eq_right_iff_subset Set.union_eq_right_iff_subset
+#align set.union_eq_right_iff_subset Set.union_eq_right
+-/
 
 #print Set.union_eq_self_of_subset_left /-
 theorem union_eq_self_of_subset_left {s t : Set α} (h : s ⊆ t) : s ∪ t = t :=
-  union_eq_right_iff_subset.mpr h
+  union_eq_right.mpr h
 #align set.union_eq_self_of_subset_left Set.union_eq_self_of_subset_left
 -/
 
 #print Set.union_eq_self_of_subset_right /-
 theorem union_eq_self_of_subset_right {s t : Set α} (h : t ⊆ s) : s ∪ t = s :=
-  union_eq_left_iff_subset.mpr h
+  union_eq_left.mpr h
 #align set.union_eq_self_of_subset_right Set.union_eq_self_of_subset_right
 -/

bump to nightly-2023-10-03-06

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

4daf4174

Diff

@@ -1036,19 +1036,15 @@ theorem union_right_comm (s₁ s₂ s₃ : Set α) : s₁ ∪ s₂ ∪ s₃ = s
 #align set.union_right_comm Set.union_right_comm
 -/
 
-#print Set.union_eq_left_iff_subset /-
 @[simp]
 theorem union_eq_left_iff_subset {s t : Set α} : s ∪ t = s ↔ t ⊆ s :=
   sup_eq_left
 #align set.union_eq_left_iff_subset Set.union_eq_left_iff_subset
--/
 
-#print Set.union_eq_right_iff_subset /-
 @[simp]
 theorem union_eq_right_iff_subset {s t : Set α} : s ∪ t = t ↔ s ⊆ t :=
   sup_eq_right
 #align set.union_eq_right_iff_subset Set.union_eq_right_iff_subset
--/
 
 #print Set.union_eq_self_of_subset_left /-
 theorem union_eq_self_of_subset_left {s t : Set α} (h : s ⊆ t) : s ∪ t = t :=
@@ -1278,29 +1274,29 @@ theorem subset_inter_iff {s t r : Set α} : r ⊆ s ∩ t ↔ r ⊆ s ∧ r ⊆
 #align set.subset_inter_iff Set.subset_inter_iff
 -/
 
-#print Set.inter_eq_left_iff_subset /-
+#print Set.inter_eq_left /-
 @[simp]
-theorem inter_eq_left_iff_subset {s t : Set α} : s ∩ t = s ↔ s ⊆ t :=
+theorem inter_eq_left {s t : Set α} : s ∩ t = s ↔ s ⊆ t :=
   inf_eq_left
-#align set.inter_eq_left_iff_subset Set.inter_eq_left_iff_subset
+#align set.inter_eq_left_iff_subset Set.inter_eq_left
 -/
 
-#print Set.inter_eq_right_iff_subset /-
+#print Set.inter_eq_right /-
 @[simp]
-theorem inter_eq_right_iff_subset {s t : Set α} : s ∩ t = t ↔ t ⊆ s :=
+theorem inter_eq_right {s t : Set α} : s ∩ t = t ↔ t ⊆ s :=
   inf_eq_right
-#align set.inter_eq_right_iff_subset Set.inter_eq_right_iff_subset
+#align set.inter_eq_right_iff_subset Set.inter_eq_right
 -/
 
 #print Set.inter_eq_self_of_subset_left /-
 theorem inter_eq_self_of_subset_left {s t : Set α} : s ⊆ t → s ∩ t = s :=
-  inter_eq_left_iff_subset.mpr
+  inter_eq_left.mpr
 #align set.inter_eq_self_of_subset_left Set.inter_eq_self_of_subset_left
 -/
 
 #print Set.inter_eq_self_of_subset_right /-
 theorem inter_eq_self_of_subset_right {s t : Set α} : t ⊆ s → s ∩ t = t :=
-  inter_eq_right_iff_subset.mpr
+  inter_eq_right.mpr
 #align set.inter_eq_self_of_subset_right Set.inter_eq_self_of_subset_right
 -/

bump to nightly-2023-09-28-06

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

5aabfdf4

Diff

@@ -4092,8 +4092,10 @@ theorem subset_right_of_subset_union (h : s ⊆ t ∪ u) (hab : Disjoint s t) :
 
 end Disjoint
 
+#print Prop.compl_singleton /-
 @[simp]
 theorem Prop.compl_singleton (p : Prop) : ({p}ᶜ : Set Prop) = {¬p} :=
   ext fun q => by simpa [@Iff.comm q] using not_iff
 #align Prop.compl_singleton Prop.compl_singleton
+-/

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) 2014 Jeremy Avigad. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Leonardo de Moura
 -/
-import Mathbin.Order.SymmDiff
-import Mathbin.Logic.Function.Iterate
+import Order.SymmDiff
+import Logic.Function.Iterate
 
 #align_import data.set.basic from "leanprover-community/mathlib"@"001ffdc42920050657fd45bd2b8bfbec8eaaeb29"
 
@@ -1579,7 +1579,7 @@ theorem subset_insert_iff_of_not_mem (ha : a ∉ s) : s ⊆ insert a t ↔ s ⊆
 #align set.subset_insert_iff_of_not_mem Set.subset_insert_iff_of_not_mem
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (a «expr ∉ » s) -/
 #print Set.ssubset_iff_insert /-
 theorem ssubset_iff_insert {s t : Set α} : s ⊂ t ↔ ∃ (a : _) (_ : a ∉ s), insert a s ⊆ t :=
   by
@@ -3366,7 +3366,7 @@ instance subsingleton_coe_of_subsingleton [Subsingleton α] {s : Set α} : Subsi
 /-! ### Nontrivial -/
 
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Nontrivial /-
 /-- A set `s` is `nontrivial` if it has at least two distinct elements. -/
 protected def Nontrivial (s : Set α) : Prop :=
@@ -3471,7 +3471,7 @@ theorem nontrivial_of_lt [Preorder α] {x y} (hx : x ∈ s) (hy : y ∈ s) (hxy
 #align set.nontrivial_of_lt Set.nontrivial_of_lt
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.nontrivial_of_exists_lt /-
 theorem nontrivial_of_exists_lt [Preorder α]
     (H : ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s), x < y) : s.Nontrivial :=
@@ -3480,7 +3480,7 @@ theorem nontrivial_of_exists_lt [Preorder α]
 #align set.nontrivial_of_exists_lt Set.nontrivial_of_exists_lt
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Nontrivial.exists_lt /-
 theorem Nontrivial.exists_lt [LinearOrder α] (hs : s.Nontrivial) :
     ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s), x < y :=
@@ -3489,7 +3489,7 @@ theorem Nontrivial.exists_lt [LinearOrder α] (hs : s.Nontrivial) :
 #align set.nontrivial.exists_lt Set.Nontrivial.exists_lt
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.nontrivial_iff_exists_lt /-
 theorem nontrivial_iff_exists_lt [LinearOrder α] :
     s.Nontrivial ↔ ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s), x < y :=
@@ -3741,7 +3741,7 @@ section LinearOrder
 
 variable [LinearOrder α] [LinearOrder β] {f : α → β}
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a b c «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (a b c «expr ∈ » s) -/
 #print Set.not_monotoneOn_not_antitoneOn_iff_exists_le_le /-
 /-- A function between linear orders which is neither monotone nor antitone makes a dent upright or
 downright. -/
@@ -3755,7 +3755,7 @@ theorem not_monotoneOn_not_antitoneOn_iff_exists_le_le :
 #align set.not_monotone_on_not_antitone_on_iff_exists_le_le Set.not_monotoneOn_not_antitoneOn_iff_exists_le_le
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a b c «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (a b c «expr ∈ » s) -/
 #print Set.not_monotoneOn_not_antitoneOn_iff_exists_lt_lt /-
 /-- A function between linear orders which is neither monotone nor antitone makes a dent upright or
 downright. -/

bump to nightly-2023-09-14-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/001ffdc42920050657fd45bd2b8bfbec8eaaeb29

4e7aae4f

Diff

@@ -6,7 +6,7 @@ Authors: Jeremy Avigad, Leonardo de Moura
 import Mathbin.Order.SymmDiff
 import Mathbin.Logic.Function.Iterate
 
-#align_import data.set.basic from "leanprover-community/mathlib"@"48fb5b5280e7c81672afc9524185ae994553ebf4"
+#align_import data.set.basic from "leanprover-community/mathlib"@"001ffdc42920050657fd45bd2b8bfbec8eaaeb29"
 
 /-!
 # Basic properties of sets
@@ -4092,3 +4092,8 @@ theorem subset_right_of_subset_union (h : s ⊆ t ∪ u) (hab : Disjoint s t) :
 
 end Disjoint
 
+@[simp]
+theorem Prop.compl_singleton (p : Prop) : ({p}ᶜ : Set Prop) = {¬p} :=
+  ext fun q => by simpa [@Iff.comm q] using not_iff
+#align Prop.compl_singleton Prop.compl_singleton
+

bump to nightly-2023-08-23-23

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

f612b9e0

Diff

@@ -159,11 +159,11 @@ theorem lt_iff_ssubset : s < t ↔ s ⊂ t :=
 #align set.lt_iff_ssubset Set.lt_iff_ssubset
 -/
 
-alias le_iff_subset ↔ _root_.has_le.le.subset _root_.has_subset.subset.le
+alias ⟨_root_.has_le.le.subset, _root_.has_subset.subset.le⟩ := le_iff_subset
 #align has_le.le.subset LE.le.subset
 #align has_subset.subset.le HasSubset.Subset.le
 
-alias lt_iff_ssubset ↔ _root_.has_lt.lt.ssubset _root_.has_ssubset.ssubset.lt
+alias ⟨_root_.has_lt.lt.ssubset, _root_.has_ssubset.ssubset.lt⟩ := lt_iff_ssubset
 #align has_lt.lt.ssubset LT.lt.sSubset
 #align has_ssubset.ssubset.lt HasSSubset.SSubset.lt
 
@@ -547,7 +547,7 @@ theorem nonempty_coe_sort {s : Set α} : Nonempty ↥s ↔ s.Nonempty :=
 #align set.nonempty_coe_sort Set.nonempty_coe_sort
 -/
 
-alias nonempty_coe_sort ↔ _ nonempty.coe_sort
+alias ⟨_, nonempty.coe_sort⟩ := nonempty_coe_sort
 #align set.nonempty.coe_sort Set.Nonempty.coe_sort
 
 #print Set.nonempty_def /-
@@ -778,7 +778,7 @@ theorem nonempty_iff_ne_empty : s.Nonempty ↔ s ≠ ∅ :=
 #align set.nonempty_iff_ne_empty Set.nonempty_iff_ne_empty
 -/
 
-alias nonempty_iff_ne_empty ↔ nonempty.ne_empty _
+alias ⟨nonempty.ne_empty, _⟩ := nonempty_iff_ne_empty
 #align set.nonempty.ne_empty Set.Nonempty.ne_empty
 
 #print Set.not_nonempty_empty /-
@@ -822,7 +822,7 @@ theorem empty_ssubset : ∅ ⊂ s ↔ s.Nonempty :=
 #align set.empty_ssubset Set.empty_ssubset
 -/
 
-alias empty_ssubset ↔ _ nonempty.empty_ssubset
+alias ⟨_, nonempty.empty_ssubset⟩ := empty_ssubset
 #align set.nonempty.empty_ssubset Set.Nonempty.empty_ssubset
 
 /-!
@@ -875,7 +875,7 @@ theorem univ_subset_iff {s : Set α} : univ ⊆ s ↔ s = univ :=
 #align set.univ_subset_iff Set.univ_subset_iff
 -/
 
-alias univ_subset_iff ↔ eq_univ_of_univ_subset _
+alias ⟨eq_univ_of_univ_subset, _⟩ := univ_subset_iff
 #align set.eq_univ_of_univ_subset Set.eq_univ_of_univ_subset
 
 #print Set.eq_univ_iff_forall /-
@@ -2093,7 +2093,7 @@ theorem not_disjoint_iff_nonempty_inter : ¬Disjoint s t ↔ (s ∩ t).Nonempty
 #align set.not_disjoint_iff_nonempty_inter Set.not_disjoint_iff_nonempty_inter
 -/
 
-alias not_disjoint_iff_nonempty_inter ↔ _ nonempty.not_disjoint
+alias ⟨_, nonempty.not_disjoint⟩ := not_disjoint_iff_nonempty_inter
 #align set.nonempty.not_disjoint Set.Nonempty.not_disjoint
 
 #print Set.disjoint_or_nonempty_inter /-
@@ -2431,16 +2431,16 @@ theorem disjoint_compl_right_iff_subset : Disjoint s (tᶜ) ↔ s ⊆ t :=
 #align set.disjoint_compl_right_iff_subset Set.disjoint_compl_right_iff_subset
 -/
 
-alias subset_compl_iff_disjoint_right ↔ _ _root_.disjoint.subset_compl_right
+alias ⟨_, _root_.disjoint.subset_compl_right⟩ := subset_compl_iff_disjoint_right
 #align disjoint.subset_compl_right Disjoint.subset_compl_right
 
-alias subset_compl_iff_disjoint_left ↔ _ _root_.disjoint.subset_compl_left
+alias ⟨_, _root_.disjoint.subset_compl_left⟩ := subset_compl_iff_disjoint_left
 #align disjoint.subset_compl_left Disjoint.subset_compl_left
 
-alias disjoint_compl_left_iff_subset ↔ _ _root_.has_subset.subset.disjoint_compl_left
+alias ⟨_, _root_.has_subset.subset.disjoint_compl_left⟩ := disjoint_compl_left_iff_subset
 #align has_subset.subset.disjoint_compl_left HasSubset.Subset.disjoint_compl_left
 
-alias disjoint_compl_right_iff_subset ↔ _ _root_.has_subset.subset.disjoint_compl_right
+alias ⟨_, _root_.has_subset.subset.disjoint_compl_right⟩ := disjoint_compl_right_iff_subset
 #align has_subset.subset.disjoint_compl_right HasSubset.Subset.disjoint_compl_right
 
 #print Set.subset_union_compl_iff_inter_subset /-
@@ -3582,7 +3582,7 @@ theorem nontrivial_coe_sort {s : Set α} : Nontrivial s ↔ s.Nontrivial := by
 #align set.nontrivial_coe_sort Set.nontrivial_coe_sort
 -/
 
-alias nontrivial_coe_sort ↔ _ nontrivial.coe_sort
+alias ⟨_, nontrivial.coe_sort⟩ := nontrivial_coe_sort
 #align set.nontrivial.coe_sort Set.Nontrivial.coe_sort
 
 #print Set.nontrivial_of_nontrivial_coe /-
@@ -3614,10 +3614,10 @@ theorem not_nontrivial_iff : ¬s.Nontrivial ↔ s.Subsingleton :=
 #align set.not_nontrivial_iff Set.not_nontrivial_iff
 -/
 
-alias not_nontrivial_iff ↔ _ subsingleton.not_nontrivial
+alias ⟨_, subsingleton.not_nontrivial⟩ := not_nontrivial_iff
 #align set.subsingleton.not_nontrivial Set.Subsingleton.not_nontrivial
 
-alias not_subsingleton_iff ↔ _ nontrivial.not_subsingleton
+alias ⟨_, nontrivial.not_subsingleton⟩ := not_subsingleton_iff
 #align set.nontrivial.not_subsingleton Set.Nontrivial.not_subsingleton
 
 #print Set.subsingleton_or_nontrivial /-

bump to nightly-2023-08-02-01

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

7aca3f15

Diff

@@ -2023,7 +2023,7 @@ theorem subset_singleton_iff {α : Type _} {s : Set α} {x : α} : s ⊆ {x} ↔
 theorem subset_singleton_iff_eq {s : Set α} {x : α} : s ⊆ {x} ↔ s = ∅ ∨ s = {x} :=
   by
   obtain rfl | hs := s.eq_empty_or_nonempty
-  use ⟨fun _ => Or.inl rfl, fun _ => empty_subset _⟩
+  use⟨fun _ => Or.inl rfl, fun _ => empty_subset _⟩
   simp [eq_singleton_iff_nonempty_unique_mem, hs, hs.ne_empty]
 #align set.subset_singleton_iff_eq Set.subset_singleton_iff_eq
 -/

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) 2014 Jeremy Avigad. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Leonardo de Moura
-
-! This file was ported from Lean 3 source module data.set.basic
-! leanprover-community/mathlib commit 48fb5b5280e7c81672afc9524185ae994553ebf4
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Order.SymmDiff
 import Mathbin.Logic.Function.Iterate
 
+#align_import data.set.basic from "leanprover-community/mathlib"@"48fb5b5280e7c81672afc9524185ae994553ebf4"
+
 /-!
 # Basic properties of sets
 
@@ -1582,7 +1579,7 @@ theorem subset_insert_iff_of_not_mem (ha : a ∉ s) : s ⊆ insert a t ↔ s ⊆
 #align set.subset_insert_iff_of_not_mem Set.subset_insert_iff_of_not_mem
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (a «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a «expr ∉ » s) -/
 #print Set.ssubset_iff_insert /-
 theorem ssubset_iff_insert {s t : Set α} : s ⊂ t ↔ ∃ (a : _) (_ : a ∉ s), insert a s ⊆ t :=
   by
@@ -3369,7 +3366,7 @@ instance subsingleton_coe_of_subsingleton [Subsingleton α] {s : Set α} : Subsi
 /-! ### Nontrivial -/
 
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Nontrivial /-
 /-- A set `s` is `nontrivial` if it has at least two distinct elements. -/
 protected def Nontrivial (s : Set α) : Prop :=
@@ -3474,7 +3471,7 @@ theorem nontrivial_of_lt [Preorder α] {x y} (hx : x ∈ s) (hy : y ∈ s) (hxy
 #align set.nontrivial_of_lt Set.nontrivial_of_lt
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.nontrivial_of_exists_lt /-
 theorem nontrivial_of_exists_lt [Preorder α]
     (H : ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s), x < y) : s.Nontrivial :=
@@ -3483,7 +3480,7 @@ theorem nontrivial_of_exists_lt [Preorder α]
 #align set.nontrivial_of_exists_lt Set.nontrivial_of_exists_lt
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Nontrivial.exists_lt /-
 theorem Nontrivial.exists_lt [LinearOrder α] (hs : s.Nontrivial) :
     ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s), x < y :=
@@ -3492,7 +3489,7 @@ theorem Nontrivial.exists_lt [LinearOrder α] (hs : s.Nontrivial) :
 #align set.nontrivial.exists_lt Set.Nontrivial.exists_lt
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.nontrivial_iff_exists_lt /-
 theorem nontrivial_iff_exists_lt [LinearOrder α] :
     s.Nontrivial ↔ ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s), x < y :=
@@ -3744,7 +3741,7 @@ section LinearOrder
 
 variable [LinearOrder α] [LinearOrder β] {f : α → β}
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (a b c «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a b c «expr ∈ » s) -/
 #print Set.not_monotoneOn_not_antitoneOn_iff_exists_le_le /-
 /-- A function between linear orders which is neither monotone nor antitone makes a dent upright or
 downright. -/
@@ -3758,7 +3755,7 @@ theorem not_monotoneOn_not_antitoneOn_iff_exists_le_le :
 #align set.not_monotone_on_not_antitone_on_iff_exists_le_le Set.not_monotoneOn_not_antitoneOn_iff_exists_le_le
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (a b c «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a b c «expr ∈ » s) -/
 #print Set.not_monotoneOn_not_antitoneOn_iff_exists_lt_lt /-
 /-- A function between linear orders which is neither monotone nor antitone makes a dent upright or
 downright. -/

bump to nightly-2023-07-04-01

mathlib commit https://github.com/leanprover-community/mathlib/commit/728ef9dbb281241906f25cbeb30f90d83e0bb451

05318d71

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Leonardo de Moura
 
 ! This file was ported from Lean 3 source module data.set.basic
-! leanprover-community/mathlib commit 9ac7c0c8c4d7a535ec3e5b34b8859aab9233b2f4
+! leanprover-community/mathlib commit 48fb5b5280e7c81672afc9524185ae994553ebf4
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -846,7 +846,7 @@ theorem setOf_true : {x : α | True} = univ :=
 -/
 
 #print Set.mem_univ /-
-@[simp]
+@[simp, mfld_simps]
 theorem mem_univ (x : α) : x ∈ @univ α :=
   trivial
 #align set.mem_univ Set.mem_univ
@@ -1175,7 +1175,7 @@ theorem inter_def {s₁ s₂ : Set α} : s₁ ∩ s₂ = {a | a ∈ s₁ ∧ a 
 -/
 
 #print Set.mem_inter_iff /-
-@[simp]
+@[simp, mfld_simps]
 theorem mem_inter_iff (x : α) (a b : Set α) : x ∈ a ∩ b ↔ x ∈ a ∧ x ∈ b :=
   Iff.rfl
 #align set.mem_inter_iff Set.mem_inter_iff
@@ -1257,7 +1257,7 @@ theorem inter_right_comm (s₁ s₂ s₃ : Set α) : s₁ ∩ s₂ ∩ s₃ = s
 -/
 
 #print Set.inter_subset_left /-
-@[simp]
+@[simp, mfld_simps]
 theorem inter_subset_left (s t : Set α) : s ∩ t ⊆ s := fun x => And.left
 #align set.inter_subset_left Set.inter_subset_left
 -/
@@ -1332,14 +1332,14 @@ theorem inter_eq_inter_iff_right : s ∩ u = t ∩ u ↔ t ∩ u ⊆ s ∧ s ∩
 -/
 
 #print Set.inter_univ /-
-@[simp]
+@[simp, mfld_simps]
 theorem inter_univ (a : Set α) : a ∩ univ = a :=
   inf_top_eq
 #align set.inter_univ Set.inter_univ
 -/
 
 #print Set.univ_inter /-
-@[simp]
+@[simp, mfld_simps]
 theorem univ_inter (a : Set α) : univ ∩ a = a :=
   top_inf_eq
 #align set.univ_inter Set.univ_inter

bump to nightly-2023-06-28-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/8b981918a93bc45a8600de608cde7944a80d92b9

79a0bd3b

Diff

@@ -1556,10 +1556,10 @@ theorem insert_ne_self : insert a s ≠ s ↔ a ∉ s :=
 #align set.insert_ne_self Set.insert_ne_self
 -/
 
-#print Set.insert_subset /-
-theorem insert_subset : insert a s ⊆ t ↔ a ∈ t ∧ s ⊆ t := by
+#print Set.insert_subset_iff /-
+theorem insert_subset_iff : insert a s ⊆ t ↔ a ∈ t ∧ s ⊆ t := by
   simp only [subset_def, or_imp, forall_and, forall_eq, mem_insert_iff]
-#align set.insert_subset Set.insert_subset
+#align set.insert_subset Set.insert_subset_iff
 -/
 
 #print Set.insert_subset_insert /-
@@ -1883,8 +1883,8 @@ theorem pair_comm (a b : α) : ({a, b} : Set α) = {b, a} :=
 theorem pair_eq_pair_iff {x y z w : α} :
     ({x, y} : Set α) = {z, w} ↔ x = z ∧ y = w ∨ x = w ∧ y = z :=
   by
-  simp only [Set.Subset.antisymm_iff, Set.insert_subset, Set.mem_insert_iff, Set.mem_singleton_iff,
-    Set.singleton_subset_iff]
+  simp only [Set.Subset.antisymm_iff, Set.insert_subset_iff, Set.mem_insert_iff,
+    Set.mem_singleton_iff, Set.singleton_subset_iff]
   constructor
   · tauto
   · rintro (⟨rfl, rfl⟩ | ⟨rfl, rfl⟩) <;> simp
@@ -3432,7 +3432,7 @@ theorem nontrivial_of_pair_subset {x y} (hxy : x ≠ y) (h : {x, y} ⊆ s) : s.N
 #print Set.Nontrivial.pair_subset /-
 theorem Nontrivial.pair_subset (hs : s.Nontrivial) : ∃ (x y : _) (hab : x ≠ y), {x, y} ⊆ s :=
   let ⟨x, hx, y, hy, hxy⟩ := hs
-  ⟨x, y, hxy, insert_subset.2 ⟨hx, singleton_subset_iff.2 hy⟩⟩
+  ⟨x, y, hxy, insert_subset_iff.2 ⟨hx, singleton_subset_iff.2 hy⟩⟩
 #align set.nontrivial.pair_subset Set.Nontrivial.pair_subset
 -/

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -108,25 +108,33 @@ instance : Union (Set α) :=
 instance : Inter (Set α) :=
   ⟨(· ⊓ ·)⟩
 
+#print Set.top_eq_univ /-
 @[simp]
 theorem top_eq_univ : (⊤ : Set α) = univ :=
   rfl
 #align set.top_eq_univ Set.top_eq_univ
+-/
 
+#print Set.bot_eq_empty /-
 @[simp]
 theorem bot_eq_empty : (⊥ : Set α) = ∅ :=
   rfl
 #align set.bot_eq_empty Set.bot_eq_empty
+-/
 
+#print Set.sup_eq_union /-
 @[simp]
 theorem sup_eq_union : ((· ⊔ ·) : Set α → Set α → Set α) = (· ∪ ·) :=
   rfl
 #align set.sup_eq_union Set.sup_eq_union
+-/
 
+#print Set.inf_eq_inter /-
 @[simp]
 theorem inf_eq_inter : ((· ⊓ ·) : Set α → Set α → Set α) = (· ∩ ·) :=
   rfl
 #align set.inf_eq_inter Set.inf_eq_inter
+-/
 
 #print Set.le_eq_subset /-
 @[simp]
@@ -135,10 +143,12 @@ theorem le_eq_subset : ((· ≤ ·) : Set α → Set α → Prop) = (· ⊆ ·)
 #align set.le_eq_subset Set.le_eq_subset
 -/
 
+#print Set.lt_eq_ssubset /-
 @[simp]
 theorem lt_eq_ssubset : ((· < ·) : Set α → Set α → Prop) = (· ⊂ ·) :=
   rfl
 #align set.lt_eq_ssubset Set.lt_eq_ssubset
+-/
 
 #print Set.le_iff_subset /-
 theorem le_iff_subset : s ≤ t ↔ s ⊆ t :=
@@ -146,9 +156,11 @@ theorem le_iff_subset : s ≤ t ↔ s ⊆ t :=
 #align set.le_iff_subset Set.le_iff_subset
 -/
 
+#print Set.lt_iff_ssubset /-
 theorem lt_iff_ssubset : s < t ↔ s ⊂ t :=
   Iff.rfl
 #align set.lt_iff_ssubset Set.lt_iff_ssubset
+-/
 
 alias le_iff_subset ↔ _root_.has_le.le.subset _root_.has_subset.subset.le
 #align has_le.le.subset LE.le.subset
@@ -355,13 +367,17 @@ theorem setOf_subset_setOf {p q : α → Prop} : {a | p a} ⊆ {a | q a} ↔ ∀
 #align set.set_of_subset_set_of Set.setOf_subset_setOf
 -/
 
+#print Set.setOf_and /-
 theorem setOf_and {p q : α → Prop} : {a | p a ∧ q a} = {a | p a} ∩ {a | q a} :=
   rfl
 #align set.set_of_and Set.setOf_and
+-/
 
+#print Set.setOf_or /-
 theorem setOf_or {p q : α → Prop} : {a | p a ∨ q a} = {a | p a} ∪ {a | q a} :=
   rfl
 #align set.set_of_or Set.setOf_or
+-/
 
 /-! ### Subset and strict subset relations -/
 
@@ -394,9 +410,11 @@ theorem subset_def : (s ⊆ t) = ∀ x, x ∈ s → x ∈ t :=
 #align set.subset_def Set.subset_def
 -/
 
+#print Set.ssubset_def /-
 theorem ssubset_def : (s ⊂ t) = (s ⊆ t ∧ ¬t ⊆ s) :=
   rfl
 #align set.ssubset_def Set.ssubset_def
+-/
 
 #print Set.Subset.refl /-
 @[refl]
@@ -454,37 +472,51 @@ theorem not_mem_subset (h : s ⊆ t) : a ∉ t → a ∉ s :=
 #align set.not_mem_subset Set.not_mem_subset
 -/
 
+#print Set.not_subset /-
 theorem not_subset : ¬s ⊆ t ↔ ∃ a ∈ s, a ∉ t := by simp only [subset_def, not_forall]
 #align set.not_subset Set.not_subset
+-/
 
 /-! ### Definition of strict subsets `s ⊂ t` and basic properties. -/
 
 
+#print Set.eq_or_ssubset_of_subset /-
 protected theorem eq_or_ssubset_of_subset (h : s ⊆ t) : s = t ∨ s ⊂ t :=
   eq_or_lt_of_le h
 #align set.eq_or_ssubset_of_subset Set.eq_or_ssubset_of_subset
+-/
 
+#print Set.exists_of_ssubset /-
 theorem exists_of_ssubset {s t : Set α} (h : s ⊂ t) : ∃ x ∈ t, x ∉ s :=
   not_subset.1 h.2
 #align set.exists_of_ssubset Set.exists_of_ssubset
+-/
 
+#print Set.ssubset_iff_subset_ne /-
 protected theorem ssubset_iff_subset_ne {s t : Set α} : s ⊂ t ↔ s ⊆ t ∧ s ≠ t :=
   @lt_iff_le_and_ne (Set α) _ s t
 #align set.ssubset_iff_subset_ne Set.ssubset_iff_subset_ne
+-/
 
+#print Set.ssubset_iff_of_subset /-
 theorem ssubset_iff_of_subset {s t : Set α} (h : s ⊆ t) : s ⊂ t ↔ ∃ x ∈ t, x ∉ s :=
   ⟨exists_of_ssubset, fun ⟨x, hxt, hxs⟩ => ⟨h, fun h => hxs <| h hxt⟩⟩
 #align set.ssubset_iff_of_subset Set.ssubset_iff_of_subset
+-/
 
+#print Set.ssubset_of_ssubset_of_subset /-
 protected theorem ssubset_of_ssubset_of_subset {s₁ s₂ s₃ : Set α} (hs₁s₂ : s₁ ⊂ s₂)
     (hs₂s₃ : s₂ ⊆ s₃) : s₁ ⊂ s₃ :=
   ⟨Subset.trans hs₁s₂.1 hs₂s₃, fun hs₃s₁ => hs₁s₂.2 (Subset.trans hs₂s₃ hs₃s₁)⟩
 #align set.ssubset_of_ssubset_of_subset Set.ssubset_of_ssubset_of_subset
+-/
 
+#print Set.ssubset_of_subset_of_ssubset /-
 protected theorem ssubset_of_subset_of_ssubset {s₁ s₂ s₃ : Set α} (hs₁s₂ : s₁ ⊆ s₂)
     (hs₂s₃ : s₂ ⊂ s₃) : s₁ ⊂ s₃ :=
   ⟨Subset.trans hs₁s₂ hs₂s₃.1, fun hs₃s₁ => hs₂s₃.2 (Subset.trans hs₃s₁ hs₁s₂)⟩
 #align set.ssubset_of_subset_of_ssubset Set.ssubset_of_subset_of_ssubset
+-/
 
 #print Set.not_mem_empty /-
 theorem not_mem_empty (x : α) : ¬x ∈ (∅ : Set α) :=
@@ -559,55 +591,79 @@ theorem Nonempty.mono (ht : s ⊆ t) (hs : s.Nonempty) : t.Nonempty :=
 #align set.nonempty.mono Set.Nonempty.mono
 -/
 
+#print Set.nonempty_of_not_subset /-
 theorem nonempty_of_not_subset (h : ¬s ⊆ t) : (s \ t).Nonempty :=
   let ⟨x, xs, xt⟩ := not_subset.1 h
   ⟨x, xs, xt⟩
 #align set.nonempty_of_not_subset Set.nonempty_of_not_subset
+-/
 
+#print Set.nonempty_of_ssubset /-
 theorem nonempty_of_ssubset (ht : s ⊂ t) : (t \ s).Nonempty :=
   nonempty_of_not_subset ht.2
 #align set.nonempty_of_ssubset Set.nonempty_of_ssubset
+-/
 
+#print Set.Nonempty.of_diff /-
 theorem Nonempty.of_diff (h : (s \ t).Nonempty) : s.Nonempty :=
   h.imp fun _ => And.left
 #align set.nonempty.of_diff Set.Nonempty.of_diff
+-/
 
+#print Set.nonempty_of_ssubset' /-
 theorem nonempty_of_ssubset' (ht : s ⊂ t) : t.Nonempty :=
   (nonempty_of_ssubset ht).of_diff
 #align set.nonempty_of_ssubset' Set.nonempty_of_ssubset'
+-/
 
+#print Set.Nonempty.inl /-
 theorem Nonempty.inl (hs : s.Nonempty) : (s ∪ t).Nonempty :=
   hs.imp fun _ => Or.inl
 #align set.nonempty.inl Set.Nonempty.inl
+-/
 
+#print Set.Nonempty.inr /-
 theorem Nonempty.inr (ht : t.Nonempty) : (s ∪ t).Nonempty :=
   ht.imp fun _ => Or.inr
 #align set.nonempty.inr Set.Nonempty.inr
+-/
 
+#print Set.union_nonempty /-
 @[simp]
 theorem union_nonempty : (s ∪ t).Nonempty ↔ s.Nonempty ∨ t.Nonempty :=
   exists_or
 #align set.union_nonempty Set.union_nonempty
+-/
 
+#print Set.Nonempty.left /-
 theorem Nonempty.left (h : (s ∩ t).Nonempty) : s.Nonempty :=
   h.imp fun _ => And.left
 #align set.nonempty.left Set.Nonempty.left
+-/
 
+#print Set.Nonempty.right /-
 theorem Nonempty.right (h : (s ∩ t).Nonempty) : t.Nonempty :=
   h.imp fun _ => And.right
 #align set.nonempty.right Set.Nonempty.right
+-/
 
+#print Set.inter_nonempty /-
 theorem inter_nonempty : (s ∩ t).Nonempty ↔ ∃ x, x ∈ s ∧ x ∈ t :=
   Iff.rfl
 #align set.inter_nonempty Set.inter_nonempty
+-/
 
+#print Set.inter_nonempty_iff_exists_left /-
 theorem inter_nonempty_iff_exists_left : (s ∩ t).Nonempty ↔ ∃ x ∈ s, x ∈ t := by
   simp_rw [inter_nonempty, exists_prop]
 #align set.inter_nonempty_iff_exists_left Set.inter_nonempty_iff_exists_left
+-/
 
+#print Set.inter_nonempty_iff_exists_right /-
 theorem inter_nonempty_iff_exists_right : (s ∩ t).Nonempty ↔ ∃ x ∈ t, x ∈ s := by
   simp_rw [inter_nonempty, exists_prop, and_comm']
 #align set.inter_nonempty_iff_exists_right Set.inter_nonempty_iff_exists_right
+-/
 
 #print Set.nonempty_iff_univ_nonempty /-
 theorem nonempty_iff_univ_nonempty : Nonempty α ↔ (univ : Set α).Nonempty :=
@@ -645,9 +701,11 @@ theorem nonempty_of_nonempty_subtype [Nonempty s] : s.Nonempty :=
 /-! ### Lemmas about the empty set -/
 
 
+#print Set.empty_def /-
 theorem empty_def : (∅ : Set α) = {x | False} :=
   rfl
 #align set.empty_def Set.empty_def
+-/
 
 #print Set.mem_empty_iff_false /-
 @[simp]
@@ -760,10 +818,12 @@ theorem ball_empty_iff {p : α → Prop} : (∀ x ∈ (∅ : Set α), p x) ↔ T
 instance (α : Type u) : IsEmpty.{u + 1} (∅ : Set α) :=
   ⟨fun x => x.2⟩
 
+#print Set.empty_ssubset /-
 @[simp]
 theorem empty_ssubset : ∅ ⊂ s ↔ s.Nonempty :=
   (@bot_lt_iff_ne_bot (Set α) _ _ _).trans nonempty_iff_ne_empty.symm
 #align set.empty_ssubset Set.empty_ssubset
+-/
 
 alias empty_ssubset ↔ _ nonempty.empty_ssubset
 #align set.nonempty.empty_ssubset Set.Nonempty.empty_ssubset
@@ -869,9 +929,11 @@ theorem univ_unique [Unique α] : @Set.univ α = {default} :=
 #align set.univ_unique Set.univ_unique
 -/
 
+#print Set.ssubset_univ_iff /-
 theorem ssubset_univ_iff : s ⊂ univ ↔ s ≠ univ :=
   lt_top_iff_ne_top
 #align set.ssubset_univ_iff Set.ssubset_univ_iff
+-/
 
 #print Set.nontrivial_of_nonempty /-
 instance nontrivial_of_nonempty [Nonempty α] : Nontrivial (Set α) :=
@@ -882,367 +944,535 @@ instance nontrivial_of_nonempty [Nonempty α] : Nontrivial (Set α) :=
 /-! ### Lemmas about union -/
 
 
+#print Set.union_def /-
 theorem union_def {s₁ s₂ : Set α} : s₁ ∪ s₂ = {a | a ∈ s₁ ∨ a ∈ s₂} :=
   rfl
 #align set.union_def Set.union_def
+-/
 
+#print Set.mem_union_left /-
 theorem mem_union_left {x : α} {a : Set α} (b : Set α) : x ∈ a → x ∈ a ∪ b :=
   Or.inl
 #align set.mem_union_left Set.mem_union_left
+-/
 
+#print Set.mem_union_right /-
 theorem mem_union_right {x : α} {b : Set α} (a : Set α) : x ∈ b → x ∈ a ∪ b :=
   Or.inr
 #align set.mem_union_right Set.mem_union_right
+-/
 
+#print Set.mem_or_mem_of_mem_union /-
 theorem mem_or_mem_of_mem_union {x : α} {a b : Set α} (H : x ∈ a ∪ b) : x ∈ a ∨ x ∈ b :=
   H
 #align set.mem_or_mem_of_mem_union Set.mem_or_mem_of_mem_union
+-/
 
+#print Set.MemUnion.elim /-
 theorem MemUnion.elim {x : α} {a b : Set α} {P : Prop} (H₁ : x ∈ a ∪ b) (H₂ : x ∈ a → P)
     (H₃ : x ∈ b → P) : P :=
   Or.elim H₁ H₂ H₃
 #align set.mem_union.elim Set.MemUnion.elim
+-/
 
+#print Set.mem_union /-
 @[simp]
 theorem mem_union (x : α) (a b : Set α) : x ∈ a ∪ b ↔ x ∈ a ∨ x ∈ b :=
   Iff.rfl
 #align set.mem_union Set.mem_union
+-/
 
+#print Set.union_self /-
 @[simp]
 theorem union_self (a : Set α) : a ∪ a = a :=
   ext fun x => or_self_iff _
 #align set.union_self Set.union_self
+-/
 
+#print Set.union_empty /-
 @[simp]
 theorem union_empty (a : Set α) : a ∪ ∅ = a :=
   ext fun x => or_false_iff _
 #align set.union_empty Set.union_empty
+-/
 
+#print Set.empty_union /-
 @[simp]
 theorem empty_union (a : Set α) : ∅ ∪ a = a :=
   ext fun x => false_or_iff _
 #align set.empty_union Set.empty_union
+-/
 
+#print Set.union_comm /-
 theorem union_comm (a b : Set α) : a ∪ b = b ∪ a :=
   ext fun x => or_comm
 #align set.union_comm Set.union_comm
+-/
 
+#print Set.union_assoc /-
 theorem union_assoc (a b c : Set α) : a ∪ b ∪ c = a ∪ (b ∪ c) :=
   ext fun x => or_assoc
 #align set.union_assoc Set.union_assoc
+-/
 
+#print Set.union_isAssoc /-
 instance union_isAssoc : IsAssociative (Set α) (· ∪ ·) :=
   ⟨union_assoc⟩
 #align set.union_is_assoc Set.union_isAssoc
+-/
 
+#print Set.union_isComm /-
 instance union_isComm : IsCommutative (Set α) (· ∪ ·) :=
   ⟨union_comm⟩
 #align set.union_is_comm Set.union_isComm
+-/
 
+#print Set.union_left_comm /-
 theorem union_left_comm (s₁ s₂ s₃ : Set α) : s₁ ∪ (s₂ ∪ s₃) = s₂ ∪ (s₁ ∪ s₃) :=
   ext fun x => or_left_comm
 #align set.union_left_comm Set.union_left_comm
+-/
 
+#print Set.union_right_comm /-
 theorem union_right_comm (s₁ s₂ s₃ : Set α) : s₁ ∪ s₂ ∪ s₃ = s₁ ∪ s₃ ∪ s₂ :=
   ext fun x => or_right_comm
 #align set.union_right_comm Set.union_right_comm
+-/
 
+#print Set.union_eq_left_iff_subset /-
 @[simp]
 theorem union_eq_left_iff_subset {s t : Set α} : s ∪ t = s ↔ t ⊆ s :=
   sup_eq_left
 #align set.union_eq_left_iff_subset Set.union_eq_left_iff_subset
+-/
 
+#print Set.union_eq_right_iff_subset /-
 @[simp]
 theorem union_eq_right_iff_subset {s t : Set α} : s ∪ t = t ↔ s ⊆ t :=
   sup_eq_right
 #align set.union_eq_right_iff_subset Set.union_eq_right_iff_subset
+-/
 
+#print Set.union_eq_self_of_subset_left /-
 theorem union_eq_self_of_subset_left {s t : Set α} (h : s ⊆ t) : s ∪ t = t :=
   union_eq_right_iff_subset.mpr h
 #align set.union_eq_self_of_subset_left Set.union_eq_self_of_subset_left
+-/
 
+#print Set.union_eq_self_of_subset_right /-
 theorem union_eq_self_of_subset_right {s t : Set α} (h : t ⊆ s) : s ∪ t = s :=
   union_eq_left_iff_subset.mpr h
 #align set.union_eq_self_of_subset_right Set.union_eq_self_of_subset_right
+-/
 
+#print Set.subset_union_left /-
 @[simp]
 theorem subset_union_left (s t : Set α) : s ⊆ s ∪ t := fun x => Or.inl
 #align set.subset_union_left Set.subset_union_left
+-/
 
+#print Set.subset_union_right /-
 @[simp]
 theorem subset_union_right (s t : Set α) : t ⊆ s ∪ t := fun x => Or.inr
 #align set.subset_union_right Set.subset_union_right
+-/
 
+#print Set.union_subset /-
 theorem union_subset {s t r : Set α} (sr : s ⊆ r) (tr : t ⊆ r) : s ∪ t ⊆ r := fun x =>
   Or.ndrec (@sr _) (@tr _)
 #align set.union_subset Set.union_subset
+-/
 
+#print Set.union_subset_iff /-
 @[simp]
 theorem union_subset_iff {s t u : Set α} : s ∪ t ⊆ u ↔ s ⊆ u ∧ t ⊆ u :=
   (forall_congr' fun x => or_imp).trans forall_and
 #align set.union_subset_iff Set.union_subset_iff
+-/
 
+#print Set.union_subset_union /-
 theorem union_subset_union {s₁ s₂ t₁ t₂ : Set α} (h₁ : s₁ ⊆ s₂) (h₂ : t₁ ⊆ t₂) :
     s₁ ∪ t₁ ⊆ s₂ ∪ t₂ := fun x => Or.imp (@h₁ _) (@h₂ _)
 #align set.union_subset_union Set.union_subset_union
+-/
 
+#print Set.union_subset_union_left /-
 theorem union_subset_union_left {s₁ s₂ : Set α} (t) (h : s₁ ⊆ s₂) : s₁ ∪ t ⊆ s₂ ∪ t :=
   union_subset_union h Subset.rfl
 #align set.union_subset_union_left Set.union_subset_union_left
+-/
 
+#print Set.union_subset_union_right /-
 theorem union_subset_union_right (s) {t₁ t₂ : Set α} (h : t₁ ⊆ t₂) : s ∪ t₁ ⊆ s ∪ t₂ :=
   union_subset_union Subset.rfl h
 #align set.union_subset_union_right Set.union_subset_union_right
+-/
 
+#print Set.subset_union_of_subset_left /-
 theorem subset_union_of_subset_left {s t : Set α} (h : s ⊆ t) (u : Set α) : s ⊆ t ∪ u :=
   Subset.trans h (subset_union_left t u)
 #align set.subset_union_of_subset_left Set.subset_union_of_subset_left
+-/
 
+#print Set.subset_union_of_subset_right /-
 theorem subset_union_of_subset_right {s u : Set α} (h : s ⊆ u) (t : Set α) : s ⊆ t ∪ u :=
   Subset.trans h (subset_union_right t u)
 #align set.subset_union_of_subset_right Set.subset_union_of_subset_right
+-/
 
+#print Set.union_congr_left /-
 theorem union_congr_left (ht : t ⊆ s ∪ u) (hu : u ⊆ s ∪ t) : s ∪ t = s ⊔ u :=
   sup_congr_left ht hu
 #align set.union_congr_left Set.union_congr_left
+-/
 
+#print Set.union_congr_right /-
 theorem union_congr_right (hs : s ⊆ t ∪ u) (ht : t ⊆ s ∪ u) : s ∪ u = t ∪ u :=
   sup_congr_right hs ht
 #align set.union_congr_right Set.union_congr_right
+-/
 
+#print Set.union_eq_union_iff_left /-
 theorem union_eq_union_iff_left : s ∪ t = s ∪ u ↔ t ⊆ s ∪ u ∧ u ⊆ s ∪ t :=
   sup_eq_sup_iff_left
 #align set.union_eq_union_iff_left Set.union_eq_union_iff_left
+-/
 
+#print Set.union_eq_union_iff_right /-
 theorem union_eq_union_iff_right : s ∪ u = t ∪ u ↔ s ⊆ t ∪ u ∧ t ⊆ s ∪ u :=
   sup_eq_sup_iff_right
 #align set.union_eq_union_iff_right Set.union_eq_union_iff_right
+-/
 
+#print Set.union_empty_iff /-
 @[simp]
 theorem union_empty_iff {s t : Set α} : s ∪ t = ∅ ↔ s = ∅ ∧ t = ∅ := by
   simp only [← subset_empty_iff] <;> exact union_subset_iff
 #align set.union_empty_iff Set.union_empty_iff
+-/
 
+#print Set.union_univ /-
 @[simp]
 theorem union_univ {s : Set α} : s ∪ univ = univ :=
   sup_top_eq
 #align set.union_univ Set.union_univ
+-/
 
+#print Set.univ_union /-
 @[simp]
 theorem univ_union {s : Set α} : univ ∪ s = univ :=
   top_sup_eq
 #align set.univ_union Set.univ_union
+-/
 
 /-! ### Lemmas about intersection -/
 
 
+#print Set.inter_def /-
 theorem inter_def {s₁ s₂ : Set α} : s₁ ∩ s₂ = {a | a ∈ s₁ ∧ a ∈ s₂} :=
   rfl
 #align set.inter_def Set.inter_def
+-/
 
+#print Set.mem_inter_iff /-
 @[simp]
 theorem mem_inter_iff (x : α) (a b : Set α) : x ∈ a ∩ b ↔ x ∈ a ∧ x ∈ b :=
   Iff.rfl
 #align set.mem_inter_iff Set.mem_inter_iff
+-/
 
+#print Set.mem_inter /-
 theorem mem_inter {x : α} {a b : Set α} (ha : x ∈ a) (hb : x ∈ b) : x ∈ a ∩ b :=
   ⟨ha, hb⟩
 #align set.mem_inter Set.mem_inter
+-/
 
+#print Set.mem_of_mem_inter_left /-
 theorem mem_of_mem_inter_left {x : α} {a b : Set α} (h : x ∈ a ∩ b) : x ∈ a :=
   h.left
 #align set.mem_of_mem_inter_left Set.mem_of_mem_inter_left
+-/
 
+#print Set.mem_of_mem_inter_right /-
 theorem mem_of_mem_inter_right {x : α} {a b : Set α} (h : x ∈ a ∩ b) : x ∈ b :=
   h.right
 #align set.mem_of_mem_inter_right Set.mem_of_mem_inter_right
+-/
 
+#print Set.inter_self /-
 @[simp]
 theorem inter_self (a : Set α) : a ∩ a = a :=
   ext fun x => and_self_iff _
 #align set.inter_self Set.inter_self
+-/
 
+#print Set.inter_empty /-
 @[simp]
 theorem inter_empty (a : Set α) : a ∩ ∅ = ∅ :=
   ext fun x => and_false_iff _
 #align set.inter_empty Set.inter_empty
+-/
 
+#print Set.empty_inter /-
 @[simp]
 theorem empty_inter (a : Set α) : ∅ ∩ a = ∅ :=
   ext fun x => false_and_iff _
 #align set.empty_inter Set.empty_inter
+-/
 
+#print Set.inter_comm /-
 theorem inter_comm (a b : Set α) : a ∩ b = b ∩ a :=
   ext fun x => and_comm
 #align set.inter_comm Set.inter_comm
+-/
 
+#print Set.inter_assoc /-
 theorem inter_assoc (a b c : Set α) : a ∩ b ∩ c = a ∩ (b ∩ c) :=
   ext fun x => and_assoc
 #align set.inter_assoc Set.inter_assoc
+-/
 
+#print Set.inter_isAssoc /-
 instance inter_isAssoc : IsAssociative (Set α) (· ∩ ·) :=
   ⟨inter_assoc⟩
 #align set.inter_is_assoc Set.inter_isAssoc
+-/
 
+#print Set.inter_isComm /-
 instance inter_isComm : IsCommutative (Set α) (· ∩ ·) :=
   ⟨inter_comm⟩
 #align set.inter_is_comm Set.inter_isComm
+-/
 
+#print Set.inter_left_comm /-
 theorem inter_left_comm (s₁ s₂ s₃ : Set α) : s₁ ∩ (s₂ ∩ s₃) = s₂ ∩ (s₁ ∩ s₃) :=
   ext fun x => and_left_comm
 #align set.inter_left_comm Set.inter_left_comm
+-/
 
+#print Set.inter_right_comm /-
 theorem inter_right_comm (s₁ s₂ s₃ : Set α) : s₁ ∩ s₂ ∩ s₃ = s₁ ∩ s₃ ∩ s₂ :=
   ext fun x => and_right_comm
 #align set.inter_right_comm Set.inter_right_comm
+-/
 
+#print Set.inter_subset_left /-
 @[simp]
 theorem inter_subset_left (s t : Set α) : s ∩ t ⊆ s := fun x => And.left
 #align set.inter_subset_left Set.inter_subset_left
+-/
 
+#print Set.inter_subset_right /-
 @[simp]
 theorem inter_subset_right (s t : Set α) : s ∩ t ⊆ t := fun x => And.right
 #align set.inter_subset_right Set.inter_subset_right
+-/
 
+#print Set.subset_inter /-
 theorem subset_inter {s t r : Set α} (rs : r ⊆ s) (rt : r ⊆ t) : r ⊆ s ∩ t := fun x h =>
   ⟨rs h, rt h⟩
 #align set.subset_inter Set.subset_inter
+-/
 
+#print Set.subset_inter_iff /-
 @[simp]
 theorem subset_inter_iff {s t r : Set α} : r ⊆ s ∩ t ↔ r ⊆ s ∧ r ⊆ t :=
   (forall_congr' fun x => imp_and).trans forall_and
 #align set.subset_inter_iff Set.subset_inter_iff
+-/
 
+#print Set.inter_eq_left_iff_subset /-
 @[simp]
 theorem inter_eq_left_iff_subset {s t : Set α} : s ∩ t = s ↔ s ⊆ t :=
   inf_eq_left
 #align set.inter_eq_left_iff_subset Set.inter_eq_left_iff_subset
+-/
 
+#print Set.inter_eq_right_iff_subset /-
 @[simp]
 theorem inter_eq_right_iff_subset {s t : Set α} : s ∩ t = t ↔ t ⊆ s :=
   inf_eq_right
 #align set.inter_eq_right_iff_subset Set.inter_eq_right_iff_subset
+-/
 
+#print Set.inter_eq_self_of_subset_left /-
 theorem inter_eq_self_of_subset_left {s t : Set α} : s ⊆ t → s ∩ t = s :=
   inter_eq_left_iff_subset.mpr
 #align set.inter_eq_self_of_subset_left Set.inter_eq_self_of_subset_left
+-/
 
+#print Set.inter_eq_self_of_subset_right /-
 theorem inter_eq_self_of_subset_right {s t : Set α} : t ⊆ s → s ∩ t = t :=
   inter_eq_right_iff_subset.mpr
 #align set.inter_eq_self_of_subset_right Set.inter_eq_self_of_subset_right
+-/
 
+#print Set.inter_congr_left /-
 theorem inter_congr_left (ht : s ∩ u ⊆ t) (hu : s ∩ t ⊆ u) : s ∩ t = s ∩ u :=
   inf_congr_left ht hu
 #align set.inter_congr_left Set.inter_congr_left
+-/
 
+#print Set.inter_congr_right /-
 theorem inter_congr_right (hs : t ∩ u ⊆ s) (ht : s ∩ u ⊆ t) : s ∩ u = t ∩ u :=
   inf_congr_right hs ht
 #align set.inter_congr_right Set.inter_congr_right
+-/
 
+#print Set.inter_eq_inter_iff_left /-
 theorem inter_eq_inter_iff_left : s ∩ t = s ∩ u ↔ s ∩ u ⊆ t ∧ s ∩ t ⊆ u :=
   inf_eq_inf_iff_left
 #align set.inter_eq_inter_iff_left Set.inter_eq_inter_iff_left
+-/
 
+#print Set.inter_eq_inter_iff_right /-
 theorem inter_eq_inter_iff_right : s ∩ u = t ∩ u ↔ t ∩ u ⊆ s ∧ s ∩ u ⊆ t :=
   inf_eq_inf_iff_right
 #align set.inter_eq_inter_iff_right Set.inter_eq_inter_iff_right
+-/
 
+#print Set.inter_univ /-
 @[simp]
 theorem inter_univ (a : Set α) : a ∩ univ = a :=
   inf_top_eq
 #align set.inter_univ Set.inter_univ
+-/
 
+#print Set.univ_inter /-
 @[simp]
 theorem univ_inter (a : Set α) : univ ∩ a = a :=
   top_inf_eq
 #align set.univ_inter Set.univ_inter
+-/
 
+#print Set.inter_subset_inter /-
 theorem inter_subset_inter {s₁ s₂ t₁ t₂ : Set α} (h₁ : s₁ ⊆ t₁) (h₂ : s₂ ⊆ t₂) :
     s₁ ∩ s₂ ⊆ t₁ ∩ t₂ := fun x => And.imp (@h₁ _) (@h₂ _)
 #align set.inter_subset_inter Set.inter_subset_inter
+-/
 
+#print Set.inter_subset_inter_left /-
 theorem inter_subset_inter_left {s t : Set α} (u : Set α) (H : s ⊆ t) : s ∩ u ⊆ t ∩ u :=
   inter_subset_inter H Subset.rfl
 #align set.inter_subset_inter_left Set.inter_subset_inter_left
+-/
 
+#print Set.inter_subset_inter_right /-
 theorem inter_subset_inter_right {s t : Set α} (u : Set α) (H : s ⊆ t) : u ∩ s ⊆ u ∩ t :=
   inter_subset_inter Subset.rfl H
 #align set.inter_subset_inter_right Set.inter_subset_inter_right
+-/
 
+#print Set.union_inter_cancel_left /-
 theorem union_inter_cancel_left {s t : Set α} : (s ∪ t) ∩ s = s :=
   inter_eq_self_of_subset_right <| subset_union_left _ _
 #align set.union_inter_cancel_left Set.union_inter_cancel_left
+-/
 
+#print Set.union_inter_cancel_right /-
 theorem union_inter_cancel_right {s t : Set α} : (s ∪ t) ∩ t = t :=
   inter_eq_self_of_subset_right <| subset_union_right _ _
 #align set.union_inter_cancel_right Set.union_inter_cancel_right
+-/
 
+#print Set.inter_setOf_eq_sep /-
 theorem inter_setOf_eq_sep (s : Set α) (p : α → Prop) : s ∩ {a | p a} = {a ∈ s | p a} :=
   rfl
 #align set.inter_set_of_eq_sep Set.inter_setOf_eq_sep
+-/
 
+#print Set.setOf_inter_eq_sep /-
 theorem setOf_inter_eq_sep (p : α → Prop) (s : Set α) : {a | p a} ∩ s = {a ∈ s | p a} :=
   inter_comm _ _
 #align set.set_of_inter_eq_sep Set.setOf_inter_eq_sep
+-/
 
 /-! ### Distributivity laws -/
 
 
+#print Set.inter_distrib_left /-
 theorem inter_distrib_left (s t u : Set α) : s ∩ (t ∪ u) = s ∩ t ∪ s ∩ u :=
   inf_sup_left
 #align set.inter_distrib_left Set.inter_distrib_left
+-/
 
+#print Set.inter_union_distrib_left /-
 theorem inter_union_distrib_left {s t u : Set α} : s ∩ (t ∪ u) = s ∩ t ∪ s ∩ u :=
   inf_sup_left
 #align set.inter_union_distrib_left Set.inter_union_distrib_left
+-/
 
+#print Set.inter_distrib_right /-
 theorem inter_distrib_right (s t u : Set α) : (s ∪ t) ∩ u = s ∩ u ∪ t ∩ u :=
   inf_sup_right
 #align set.inter_distrib_right Set.inter_distrib_right
+-/
 
+#print Set.union_inter_distrib_right /-
 theorem union_inter_distrib_right {s t u : Set α} : (s ∪ t) ∩ u = s ∩ u ∪ t ∩ u :=
   inf_sup_right
 #align set.union_inter_distrib_right Set.union_inter_distrib_right
+-/
 
+#print Set.union_distrib_left /-
 theorem union_distrib_left (s t u : Set α) : s ∪ t ∩ u = (s ∪ t) ∩ (s ∪ u) :=
   sup_inf_left
 #align set.union_distrib_left Set.union_distrib_left
+-/
 
+#print Set.union_inter_distrib_left /-
 theorem union_inter_distrib_left {s t u : Set α} : s ∪ t ∩ u = (s ∪ t) ∩ (s ∪ u) :=
   sup_inf_left
 #align set.union_inter_distrib_left Set.union_inter_distrib_left
+-/
 
+#print Set.union_distrib_right /-
 theorem union_distrib_right (s t u : Set α) : s ∩ t ∪ u = (s ∪ u) ∩ (t ∪ u) :=
   sup_inf_right
 #align set.union_distrib_right Set.union_distrib_right
+-/
 
+#print Set.inter_union_distrib_right /-
 theorem inter_union_distrib_right {s t u : Set α} : s ∩ t ∪ u = (s ∪ u) ∩ (t ∪ u) :=
   sup_inf_right
 #align set.inter_union_distrib_right Set.inter_union_distrib_right
+-/
 
+#print Set.union_union_distrib_left /-
 theorem union_union_distrib_left (s t u : Set α) : s ∪ (t ∪ u) = s ∪ t ∪ (s ∪ u) :=
   sup_sup_distrib_left _ _ _
 #align set.union_union_distrib_left Set.union_union_distrib_left
+-/
 
+#print Set.union_union_distrib_right /-
 theorem union_union_distrib_right (s t u : Set α) : s ∪ t ∪ u = s ∪ u ∪ (t ∪ u) :=
   sup_sup_distrib_right _ _ _
 #align set.union_union_distrib_right Set.union_union_distrib_right
+-/
 
+#print Set.inter_inter_distrib_left /-
 theorem inter_inter_distrib_left (s t u : Set α) : s ∩ (t ∩ u) = s ∩ t ∩ (s ∩ u) :=
   inf_inf_distrib_left _ _ _
 #align set.inter_inter_distrib_left Set.inter_inter_distrib_left
+-/
 
+#print Set.inter_inter_distrib_right /-
 theorem inter_inter_distrib_right (s t u : Set α) : s ∩ t ∩ u = s ∩ u ∩ (t ∩ u) :=
   inf_inf_distrib_right _ _ _
 #align set.inter_inter_distrib_right Set.inter_inter_distrib_right
+-/
 
+#print Set.union_union_union_comm /-
 theorem union_union_union_comm (s t u v : Set α) : s ∪ t ∪ (u ∪ v) = s ∪ u ∪ (t ∪ v) :=
   sup_sup_sup_comm _ _ _ _
 #align set.union_union_union_comm Set.union_union_union_comm
+-/
 
+#print Set.inter_inter_inter_comm /-
 theorem inter_inter_inter_comm (s t u v : Set α) : s ∩ t ∩ (u ∩ v) = s ∩ u ∩ (t ∩ v) :=
   inf_inf_inf_comm _ _ _ _
 #align set.inter_inter_inter_comm Set.inter_inter_inter_comm
+-/
 
 /-!
 ### Lemmas about `insert`
@@ -1353,15 +1583,19 @@ theorem subset_insert_iff_of_not_mem (ha : a ∉ s) : s ⊆ insert a t ↔ s ⊆
 -/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (a «expr ∉ » s) -/
+#print Set.ssubset_iff_insert /-
 theorem ssubset_iff_insert {s t : Set α} : s ⊂ t ↔ ∃ (a : _) (_ : a ∉ s), insert a s ⊆ t :=
   by
   simp only [insert_subset, exists_and_right, ssubset_def, not_subset]
   simp only [exists_prop, and_comm']
 #align set.ssubset_iff_insert Set.ssubset_iff_insert
+-/
 
+#print Set.ssubset_insert /-
 theorem ssubset_insert {s : Set α} {a : α} (h : a ∉ s) : s ⊂ insert a s :=
   ssubset_iff_insert.2 ⟨a, h, Subset.rfl⟩
 #align set.ssubset_insert Set.ssubset_insert
+-/
 
 #print Set.insert_comm /-
 theorem insert_comm (a b : α) (s : Set α) : insert a (insert b s) = insert b (insert a s) :=
@@ -1376,14 +1610,18 @@ theorem insert_idem (a : α) (s : Set α) : insert a (insert a s) = insert a s :
 #align set.insert_idem Set.insert_idem
 -/
 
+#print Set.insert_union /-
 theorem insert_union : insert a s ∪ t = insert a (s ∪ t) :=
   ext fun x => or_assoc
 #align set.insert_union Set.insert_union
+-/
 
+#print Set.union_insert /-
 @[simp]
 theorem union_insert : s ∪ insert a t = insert a (s ∪ t) :=
   ext fun x => or_left_comm
 #align set.union_insert Set.union_insert
+-/
 
 #print Set.insert_nonempty /-
 @[simp]
@@ -1395,13 +1633,17 @@ theorem insert_nonempty (a : α) (s : Set α) : (insert a s).Nonempty :=
 instance (a : α) (s : Set α) : Nonempty (insert a s : Set α) :=
   (insert_nonempty a s).to_subtype
 
+#print Set.insert_inter_distrib /-
 theorem insert_inter_distrib (a : α) (s t : Set α) : insert a (s ∩ t) = insert a s ∩ insert a t :=
   ext fun y => or_and_left
 #align set.insert_inter_distrib Set.insert_inter_distrib
+-/
 
+#print Set.insert_union_distrib /-
 theorem insert_union_distrib (a : α) (s t : Set α) : insert a (s ∪ t) = insert a s ∪ insert a t :=
   ext fun _ => or_or_distrib_left _ _ _
 #align set.insert_union_distrib Set.insert_union_distrib
+-/
 
 #print Set.insert_inj /-
 theorem insert_inj (ha : a ∉ s) : insert a s = insert b s ↔ a = b :=
@@ -1424,10 +1666,12 @@ theorem forall_insert_of_forall {P : α → Prop} {a : α} {s : Set α} (H : ∀
 #align set.forall_insert_of_forall Set.forall_insert_of_forall
 -/
 
+#print Set.bex_insert_iff /-
 theorem bex_insert_iff {P : α → Prop} {a : α} {s : Set α} :
     (∃ x ∈ insert a s, P x) ↔ P a ∨ ∃ x ∈ s, P x :=
   bex_or_left.trans <| or_congr_left bex_eq_left
 #align set.bex_insert_iff Set.bex_insert_iff
+-/
 
 #print Set.ball_insert_iff /-
 theorem ball_insert_iff {P : α → Prop} {a : α} {s : Set α} :
@@ -1499,9 +1743,11 @@ theorem mem_singleton_of_eq {x y : α} (H : x = y) : x ∈ ({y} : Set α) :=
 #align set.mem_singleton_of_eq Set.mem_singleton_of_eq
 -/
 
+#print Set.insert_eq /-
 theorem insert_eq (x : α) (s : Set α) : insert x s = ({x} : Set α) ∪ s :=
   rfl
 #align set.insert_eq Set.insert_eq
+-/
 
 #print Set.singleton_nonempty /-
 @[simp]
@@ -1517,10 +1763,12 @@ theorem singleton_ne_empty (a : α) : ({a} : Set α) ≠ ∅ :=
 #align set.singleton_ne_empty Set.singleton_ne_empty
 -/
 
+#print Set.empty_ssubset_singleton /-
 @[simp]
 theorem empty_ssubset_singleton : (∅ : Set α) ⊂ {a} :=
   (singleton_nonempty _).empty_ssubset
 #align set.empty_ssubset_singleton Set.empty_ssubset_singleton
+-/
 
 #print Set.singleton_subset_iff /-
 @[simp]
@@ -1540,35 +1788,47 @@ theorem set_compr_eq_eq_singleton {a : α} : {b | b = a} = {a} :=
 #align set.set_compr_eq_eq_singleton Set.set_compr_eq_eq_singleton
 -/
 
+#print Set.singleton_union /-
 @[simp]
 theorem singleton_union : {a} ∪ s = insert a s :=
   rfl
 #align set.singleton_union Set.singleton_union
+-/
 
+#print Set.union_singleton /-
 @[simp]
 theorem union_singleton : s ∪ {a} = insert a s :=
   union_comm _ _
 #align set.union_singleton Set.union_singleton
+-/
 
+#print Set.singleton_inter_nonempty /-
 @[simp]
 theorem singleton_inter_nonempty : ({a} ∩ s).Nonempty ↔ a ∈ s := by
   simp only [Set.Nonempty, mem_inter_iff, mem_singleton_iff, exists_eq_left]
 #align set.singleton_inter_nonempty Set.singleton_inter_nonempty
+-/
 
+#print Set.inter_singleton_nonempty /-
 @[simp]
 theorem inter_singleton_nonempty : (s ∩ {a}).Nonempty ↔ a ∈ s := by
   rw [inter_comm, singleton_inter_nonempty]
 #align set.inter_singleton_nonempty Set.inter_singleton_nonempty
+-/
 
+#print Set.singleton_inter_eq_empty /-
 @[simp]
 theorem singleton_inter_eq_empty : {a} ∩ s = ∅ ↔ a ∉ s :=
   not_nonempty_iff_eq_empty.symm.trans singleton_inter_nonempty.Not
 #align set.singleton_inter_eq_empty Set.singleton_inter_eq_empty
+-/
 
+#print Set.inter_singleton_eq_empty /-
 @[simp]
 theorem inter_singleton_eq_empty : s ∩ {a} = ∅ ↔ a ∉ s := by
   rw [inter_comm, singleton_inter_eq_empty]
 #align set.inter_singleton_eq_empty Set.inter_singleton_eq_empty
+-/
 
 #print Set.nmem_singleton_empty /-
 theorem nmem_singleton_empty {s : Set α} : s ∉ ({∅} : Set (Set α)) ↔ s.Nonempty :=
@@ -1644,10 +1904,12 @@ theorem mem_sep (xs : x ∈ s) (px : p x) : x ∈ {x ∈ s | p x} :=
 #align set.mem_sep Set.mem_sep
 -/
 
+#print Set.sep_mem_eq /-
 @[simp]
 theorem sep_mem_eq : {x ∈ s | x ∈ t} = s ∩ t :=
   rfl
 #align set.sep_mem_eq Set.sep_mem_eq
+-/
 
 #print Set.mem_sep_iff /-
 @[simp]
@@ -1716,25 +1978,33 @@ theorem sep_univ : {x ∈ (univ : Set α) | p x} = {x | p x} :=
 #align set.sep_univ Set.sep_univ
 -/
 
+#print Set.sep_union /-
 @[simp]
 theorem sep_union : {x ∈ s ∪ t | p x} = {x ∈ s | p x} ∪ {x ∈ t | p x} :=
   union_inter_distrib_right
 #align set.sep_union Set.sep_union
+-/
 
+#print Set.sep_inter /-
 @[simp]
 theorem sep_inter : {x ∈ s ∩ t | p x} = {x ∈ s | p x} ∩ {x ∈ t | p x} :=
   inter_inter_distrib_right s t p
 #align set.sep_inter Set.sep_inter
+-/
 
+#print Set.sep_and /-
 @[simp]
 theorem sep_and : {x ∈ s | p x ∧ q x} = {x ∈ s | p x} ∩ {x ∈ s | q x} :=
   inter_inter_distrib_left s p q
 #align set.sep_and Set.sep_and
+-/
 
+#print Set.sep_or /-
 @[simp]
 theorem sep_or : {x ∈ s | p x ∨ q x} = {x ∈ s | p x} ∪ {x ∈ s | q x} :=
   inter_union_distrib_left
 #align set.sep_or Set.sep_or
+-/
 
 #print Set.sep_setOf /-
 @[simp]
@@ -1767,280 +2037,402 @@ theorem Nonempty.subset_singleton_iff (h : s.Nonempty) : s ⊆ {a} ↔ s = {a} :
 #align set.nonempty.subset_singleton_iff Set.Nonempty.subset_singleton_iff
 -/
 
+#print Set.ssubset_singleton_iff /-
 theorem ssubset_singleton_iff {s : Set α} {x : α} : s ⊂ {x} ↔ s = ∅ :=
   by
   rw [ssubset_iff_subset_ne, subset_singleton_iff_eq, or_and_right, and_not_self_iff, or_false_iff,
     and_iff_left_iff_imp]
   exact fun h => ne_of_eq_of_ne h (singleton_ne_empty _).symm
 #align set.ssubset_singleton_iff Set.ssubset_singleton_iff
+-/
 
+#print Set.eq_empty_of_ssubset_singleton /-
 theorem eq_empty_of_ssubset_singleton {s : Set α} {x : α} (hs : s ⊂ {x}) : s = ∅ :=
   ssubset_singleton_iff.1 hs
 #align set.eq_empty_of_ssubset_singleton Set.eq_empty_of_ssubset_singleton
+-/
 
 /-! ### Disjointness -/
 
 
+#print Set.disjoint_iff /-
 protected theorem disjoint_iff : Disjoint s t ↔ s ∩ t ⊆ ∅ :=
   disjoint_iff_inf_le
 #align set.disjoint_iff Set.disjoint_iff
+-/
 
+#print Set.disjoint_iff_inter_eq_empty /-
 theorem disjoint_iff_inter_eq_empty : Disjoint s t ↔ s ∩ t = ∅ :=
   disjoint_iff
 #align set.disjoint_iff_inter_eq_empty Set.disjoint_iff_inter_eq_empty
+-/
 
+#print Disjoint.inter_eq /-
 theorem Disjoint.inter_eq : Disjoint s t → s ∩ t = ∅ :=
   Disjoint.eq_bot
 #align disjoint.inter_eq Disjoint.inter_eq
+-/
 
+#print Set.disjoint_left /-
 theorem disjoint_left : Disjoint s t ↔ ∀ ⦃a⦄, a ∈ s → a ∉ t :=
   disjoint_iff_inf_le.trans <| forall_congr' fun _ => not_and
 #align set.disjoint_left Set.disjoint_left
+-/
 
+#print Set.disjoint_right /-
 theorem disjoint_right : Disjoint s t ↔ ∀ ⦃a⦄, a ∈ t → a ∉ s := by rw [disjoint_comm, disjoint_left]
 #align set.disjoint_right Set.disjoint_right
+-/
 
+#print Set.not_disjoint_iff /-
 theorem not_disjoint_iff : ¬Disjoint s t ↔ ∃ x, x ∈ s ∧ x ∈ t :=
   Set.disjoint_iff.Not.trans <| not_forall.trans <| exists_congr fun x => Classical.not_not
 #align set.not_disjoint_iff Set.not_disjoint_iff
+-/
 
+#print Set.not_disjoint_iff_nonempty_inter /-
 theorem not_disjoint_iff_nonempty_inter : ¬Disjoint s t ↔ (s ∩ t).Nonempty :=
   not_disjoint_iff
 #align set.not_disjoint_iff_nonempty_inter Set.not_disjoint_iff_nonempty_inter
+-/
 
 alias not_disjoint_iff_nonempty_inter ↔ _ nonempty.not_disjoint
 #align set.nonempty.not_disjoint Set.Nonempty.not_disjoint
 
+#print Set.disjoint_or_nonempty_inter /-
 theorem disjoint_or_nonempty_inter (s t : Set α) : Disjoint s t ∨ (s ∩ t).Nonempty :=
   (em _).imp_right not_disjoint_iff_nonempty_inter.mp
 #align set.disjoint_or_nonempty_inter Set.disjoint_or_nonempty_inter
+-/
 
+#print Set.disjoint_iff_forall_ne /-
 theorem disjoint_iff_forall_ne : Disjoint s t ↔ ∀ x ∈ s, ∀ y ∈ t, x ≠ y := by
   simp only [Ne.def, disjoint_left, @imp_not_comm _ (_ = _), forall_eq']
 #align set.disjoint_iff_forall_ne Set.disjoint_iff_forall_ne
+-/
 
+#print Disjoint.ne_of_mem /-
 theorem Disjoint.ne_of_mem (h : Disjoint s t) {x y} (hx : x ∈ s) (hy : y ∈ t) : x ≠ y :=
   disjoint_iff_forall_ne.mp h x hx y hy
 #align disjoint.ne_of_mem Disjoint.ne_of_mem
+-/
 
+#print Set.disjoint_of_subset_left /-
 theorem disjoint_of_subset_left (hs : s₁ ⊆ s₂) (h : Disjoint s₂ t) : Disjoint s₁ t :=
   h.mono_left hs
 #align set.disjoint_of_subset_left Set.disjoint_of_subset_left
+-/
 
+#print Set.disjoint_of_subset_right /-
 theorem disjoint_of_subset_right (ht : t₁ ⊆ t₂) (h : Disjoint s t₂) : Disjoint s t₁ :=
   h.mono_right ht
 #align set.disjoint_of_subset_right Set.disjoint_of_subset_right
+-/
 
+#print Set.disjoint_of_subset /-
 theorem disjoint_of_subset (hs : s₁ ⊆ s₂) (ht : t₁ ⊆ t₂) (h : Disjoint s₂ t₂) : Disjoint s₁ t₁ :=
   h.mono hs ht
 #align set.disjoint_of_subset Set.disjoint_of_subset
+-/
 
+#print Set.disjoint_union_left /-
 @[simp]
 theorem disjoint_union_left : Disjoint (s ∪ t) u ↔ Disjoint s u ∧ Disjoint t u :=
   disjoint_sup_left
 #align set.disjoint_union_left Set.disjoint_union_left
+-/
 
+#print Set.disjoint_union_right /-
 @[simp]
 theorem disjoint_union_right : Disjoint s (t ∪ u) ↔ Disjoint s t ∧ Disjoint s u :=
   disjoint_sup_right
 #align set.disjoint_union_right Set.disjoint_union_right
+-/
 
+#print Set.disjoint_empty /-
 @[simp]
 theorem disjoint_empty (s : Set α) : Disjoint s ∅ :=
   disjoint_bot_right
 #align set.disjoint_empty Set.disjoint_empty
+-/
 
+#print Set.empty_disjoint /-
 @[simp]
 theorem empty_disjoint (s : Set α) : Disjoint ∅ s :=
   disjoint_bot_left
 #align set.empty_disjoint Set.empty_disjoint
+-/
 
+#print Set.univ_disjoint /-
 @[simp]
 theorem univ_disjoint : Disjoint univ s ↔ s = ∅ :=
   top_disjoint
 #align set.univ_disjoint Set.univ_disjoint
+-/
 
+#print Set.disjoint_univ /-
 @[simp]
 theorem disjoint_univ : Disjoint s univ ↔ s = ∅ :=
   disjoint_top
 #align set.disjoint_univ Set.disjoint_univ
+-/
 
+#print Set.disjoint_sdiff_left /-
 theorem disjoint_sdiff_left : Disjoint (t \ s) s :=
   disjoint_sdiff_self_left
 #align set.disjoint_sdiff_left Set.disjoint_sdiff_left
+-/
 
+#print Set.disjoint_sdiff_right /-
 theorem disjoint_sdiff_right : Disjoint s (t \ s) :=
   disjoint_sdiff_self_right
 #align set.disjoint_sdiff_right Set.disjoint_sdiff_right
+-/
 
+#print Set.diff_union_diff_cancel /-
 theorem diff_union_diff_cancel (hts : t ⊆ s) (hut : u ⊆ t) : s \ t ∪ t \ u = s \ u :=
   sdiff_sup_sdiff_cancel hts hut
 #align set.diff_union_diff_cancel Set.diff_union_diff_cancel
+-/
 
+#print Set.diff_diff_eq_sdiff_union /-
 theorem diff_diff_eq_sdiff_union (h : u ⊆ s) : s \ (t \ u) = s \ t ∪ u :=
   sdiff_sdiff_eq_sdiff_sup h
 #align set.diff_diff_eq_sdiff_union Set.diff_diff_eq_sdiff_union
+-/
 
+#print Set.disjoint_singleton_left /-
 @[simp]
 theorem disjoint_singleton_left : Disjoint {a} s ↔ a ∉ s := by
   simp [Set.disjoint_iff, subset_def] <;> exact Iff.rfl
 #align set.disjoint_singleton_left Set.disjoint_singleton_left
+-/
 
+#print Set.disjoint_singleton_right /-
 @[simp]
 theorem disjoint_singleton_right : Disjoint s {a} ↔ a ∉ s :=
   disjoint_comm.trans disjoint_singleton_left
 #align set.disjoint_singleton_right Set.disjoint_singleton_right
+-/
 
+#print Set.disjoint_singleton /-
 @[simp]
 theorem disjoint_singleton : Disjoint ({a} : Set α) {b} ↔ a ≠ b := by
   rw [disjoint_singleton_left, mem_singleton_iff]
 #align set.disjoint_singleton Set.disjoint_singleton
+-/
 
+#print Set.subset_diff /-
 theorem subset_diff : s ⊆ t \ u ↔ s ⊆ t ∧ Disjoint s u :=
   le_iff_subset.symm.trans le_sdiff
 #align set.subset_diff Set.subset_diff
+-/
 
+#print Set.inter_diff_distrib_left /-
 theorem inter_diff_distrib_left (s t u : Set α) : s ∩ (t \ u) = (s ∩ t) \ (s ∩ u) :=
   inf_sdiff_distrib_left _ _ _
 #align set.inter_diff_distrib_left Set.inter_diff_distrib_left
+-/
 
+#print Set.inter_diff_distrib_right /-
 theorem inter_diff_distrib_right (s t u : Set α) : s \ t ∩ u = (s ∩ u) \ (t ∩ u) :=
   inf_sdiff_distrib_right _ _ _
 #align set.inter_diff_distrib_right Set.inter_diff_distrib_right
+-/
 
 /-! ### Lemmas about complement -/
 
 
+#print Set.compl_def /-
 theorem compl_def (s : Set α) : sᶜ = {x | x ∉ s} :=
   rfl
 #align set.compl_def Set.compl_def
+-/
 
+#print Set.mem_compl /-
 theorem mem_compl {s : Set α} {x : α} (h : x ∉ s) : x ∈ sᶜ :=
   h
 #align set.mem_compl Set.mem_compl
+-/
 
+#print Set.compl_setOf /-
 theorem compl_setOf {α} (p : α → Prop) : {a | p a}ᶜ = {a | ¬p a} :=
   rfl
 #align set.compl_set_of Set.compl_setOf
+-/
 
+#print Set.not_mem_of_mem_compl /-
 theorem not_mem_of_mem_compl {s : Set α} {x : α} (h : x ∈ sᶜ) : x ∉ s :=
   h
 #align set.not_mem_of_mem_compl Set.not_mem_of_mem_compl
+-/
 
+#print Set.mem_compl_iff /-
 @[simp]
 theorem mem_compl_iff (s : Set α) (x : α) : x ∈ sᶜ ↔ x ∉ s :=
   Iff.rfl
 #align set.mem_compl_iff Set.mem_compl_iff
+-/
 
+#print Set.not_mem_compl_iff /-
 theorem not_mem_compl_iff {x : α} : x ∉ sᶜ ↔ x ∈ s :=
   Classical.not_not
 #align set.not_mem_compl_iff Set.not_mem_compl_iff
+-/
 
+#print Set.inter_compl_self /-
 @[simp]
 theorem inter_compl_self (s : Set α) : s ∩ sᶜ = ∅ :=
   inf_compl_eq_bot
 #align set.inter_compl_self Set.inter_compl_self
+-/
 
+#print Set.compl_inter_self /-
 @[simp]
 theorem compl_inter_self (s : Set α) : sᶜ ∩ s = ∅ :=
   compl_inf_eq_bot
 #align set.compl_inter_self Set.compl_inter_self
+-/
 
+#print Set.compl_empty /-
 @[simp]
 theorem compl_empty : (∅ : Set α)ᶜ = univ :=
   compl_bot
 #align set.compl_empty Set.compl_empty
+-/
 
+#print Set.compl_union /-
 @[simp]
 theorem compl_union (s t : Set α) : (s ∪ t)ᶜ = sᶜ ∩ tᶜ :=
   compl_sup
 #align set.compl_union Set.compl_union
+-/
 
+#print Set.compl_inter /-
 theorem compl_inter (s t : Set α) : (s ∩ t)ᶜ = sᶜ ∪ tᶜ :=
   compl_inf
 #align set.compl_inter Set.compl_inter
+-/
 
+#print Set.compl_univ /-
 @[simp]
 theorem compl_univ : (univ : Set α)ᶜ = ∅ :=
   compl_top
 #align set.compl_univ Set.compl_univ
+-/
 
+#print Set.compl_empty_iff /-
 @[simp]
 theorem compl_empty_iff {s : Set α} : sᶜ = ∅ ↔ s = univ :=
   compl_eq_bot
 #align set.compl_empty_iff Set.compl_empty_iff
+-/
 
+#print Set.compl_univ_iff /-
 @[simp]
 theorem compl_univ_iff {s : Set α} : sᶜ = univ ↔ s = ∅ :=
   compl_eq_top
 #align set.compl_univ_iff Set.compl_univ_iff
+-/
 
+#print Set.compl_ne_univ /-
 theorem compl_ne_univ : sᶜ ≠ univ ↔ s.Nonempty :=
   compl_univ_iff.Not.trans nonempty_iff_ne_empty.symm
 #align set.compl_ne_univ Set.compl_ne_univ
+-/
 
+#print Set.nonempty_compl /-
 theorem nonempty_compl : sᶜ.Nonempty ↔ s ≠ univ :=
   (ne_univ_iff_exists_not_mem s).symm
 #align set.nonempty_compl Set.nonempty_compl
+-/
 
+#print Set.mem_compl_singleton_iff /-
 theorem mem_compl_singleton_iff {a x : α} : x ∈ ({a} : Set α)ᶜ ↔ x ≠ a :=
   Iff.rfl
 #align set.mem_compl_singleton_iff Set.mem_compl_singleton_iff
+-/
 
+#print Set.compl_singleton_eq /-
 theorem compl_singleton_eq (a : α) : ({a} : Set α)ᶜ = {x | x ≠ a} :=
   rfl
 #align set.compl_singleton_eq Set.compl_singleton_eq
+-/
 
+#print Set.compl_ne_eq_singleton /-
 @[simp]
 theorem compl_ne_eq_singleton (a : α) : ({x | x ≠ a} : Set α)ᶜ = {a} :=
   compl_compl _
 #align set.compl_ne_eq_singleton Set.compl_ne_eq_singleton
+-/
 
+#print Set.union_eq_compl_compl_inter_compl /-
 theorem union_eq_compl_compl_inter_compl (s t : Set α) : s ∪ t = (sᶜ ∩ tᶜ)ᶜ :=
   ext fun x => or_iff_not_and_not
 #align set.union_eq_compl_compl_inter_compl Set.union_eq_compl_compl_inter_compl
+-/
 
+#print Set.inter_eq_compl_compl_union_compl /-
 theorem inter_eq_compl_compl_union_compl (s t : Set α) : s ∩ t = (sᶜ ∪ tᶜ)ᶜ :=
   ext fun x => and_iff_not_or_not
 #align set.inter_eq_compl_compl_union_compl Set.inter_eq_compl_compl_union_compl
+-/
 
+#print Set.union_compl_self /-
 @[simp]
 theorem union_compl_self (s : Set α) : s ∪ sᶜ = univ :=
   eq_univ_iff_forall.2 fun x => em _
 #align set.union_compl_self Set.union_compl_self
+-/
 
+#print Set.compl_union_self /-
 @[simp]
 theorem compl_union_self (s : Set α) : sᶜ ∪ s = univ := by rw [union_comm, union_compl_self]
 #align set.compl_union_self Set.compl_union_self
+-/
 
+#print Set.compl_subset_comm /-
 theorem compl_subset_comm : sᶜ ⊆ t ↔ tᶜ ⊆ s :=
   @compl_le_iff_compl_le _ s _ _
 #align set.compl_subset_comm Set.compl_subset_comm
+-/
 
+#print Set.subset_compl_comm /-
 theorem subset_compl_comm : s ⊆ tᶜ ↔ t ⊆ sᶜ :=
   @le_compl_iff_le_compl _ _ _ t
 #align set.subset_compl_comm Set.subset_compl_comm
+-/
 
+#print Set.compl_subset_compl /-
 @[simp]
 theorem compl_subset_compl : sᶜ ⊆ tᶜ ↔ t ⊆ s :=
   @compl_le_compl_iff_le (Set α) _ _ _
 #align set.compl_subset_compl Set.compl_subset_compl
+-/
 
+#print Set.subset_compl_iff_disjoint_left /-
 theorem subset_compl_iff_disjoint_left : s ⊆ tᶜ ↔ Disjoint t s :=
   @le_compl_iff_disjoint_left (Set α) _ _ _
 #align set.subset_compl_iff_disjoint_left Set.subset_compl_iff_disjoint_left
+-/
 
+#print Set.subset_compl_iff_disjoint_right /-
 theorem subset_compl_iff_disjoint_right : s ⊆ tᶜ ↔ Disjoint s t :=
   @le_compl_iff_disjoint_right (Set α) _ _ _
 #align set.subset_compl_iff_disjoint_right Set.subset_compl_iff_disjoint_right
+-/
 
+#print Set.disjoint_compl_left_iff_subset /-
 theorem disjoint_compl_left_iff_subset : Disjoint (sᶜ) t ↔ t ⊆ s :=
   disjoint_compl_left_iff
 #align set.disjoint_compl_left_iff_subset Set.disjoint_compl_left_iff_subset
+-/
 
+#print Set.disjoint_compl_right_iff_subset /-
 theorem disjoint_compl_right_iff_subset : Disjoint s (tᶜ) ↔ s ⊆ t :=
   disjoint_compl_right_iff
 #align set.disjoint_compl_right_iff_subset Set.disjoint_compl_right_iff_subset
+-/
 
 alias subset_compl_iff_disjoint_right ↔ _ _root_.disjoint.subset_compl_right
 #align disjoint.subset_compl_right Disjoint.subset_compl_right
@@ -2054,213 +2446,310 @@ alias disjoint_compl_left_iff_subset ↔ _ _root_.has_subset.subset.disjoint_com
 alias disjoint_compl_right_iff_subset ↔ _ _root_.has_subset.subset.disjoint_compl_right
 #align has_subset.subset.disjoint_compl_right HasSubset.Subset.disjoint_compl_right
 
+#print Set.subset_union_compl_iff_inter_subset /-
 theorem subset_union_compl_iff_inter_subset {s t u : Set α} : s ⊆ t ∪ uᶜ ↔ s ∩ u ⊆ t :=
   (@isCompl_compl _ u _).le_sup_right_iff_inf_left_le
 #align set.subset_union_compl_iff_inter_subset Set.subset_union_compl_iff_inter_subset
+-/
 
+#print Set.compl_subset_iff_union /-
 theorem compl_subset_iff_union {s t : Set α} : sᶜ ⊆ t ↔ s ∪ t = univ :=
   Iff.symm <| eq_univ_iff_forall.trans <| forall_congr' fun a => or_iff_not_imp_left
 #align set.compl_subset_iff_union Set.compl_subset_iff_union
+-/
 
+#print Set.subset_compl_singleton_iff /-
 @[simp]
 theorem subset_compl_singleton_iff {a : α} {s : Set α} : s ⊆ {a}ᶜ ↔ a ∉ s :=
   subset_compl_comm.trans singleton_subset_iff
 #align set.subset_compl_singleton_iff Set.subset_compl_singleton_iff
+-/
 
+#print Set.inter_subset /-
 theorem inter_subset (a b c : Set α) : a ∩ b ⊆ c ↔ a ⊆ bᶜ ∪ c :=
   forall_congr' fun x => and_imp.trans <| imp_congr_right fun _ => imp_iff_not_or
 #align set.inter_subset Set.inter_subset
+-/
 
+#print Set.inter_compl_nonempty_iff /-
 theorem inter_compl_nonempty_iff {s t : Set α} : (s ∩ tᶜ).Nonempty ↔ ¬s ⊆ t :=
   (not_subset.trans <| exists_congr fun x => by simp [mem_compl]).symm
 #align set.inter_compl_nonempty_iff Set.inter_compl_nonempty_iff
+-/
 
 /-! ### Lemmas about set difference -/
 
 
+#print Set.diff_eq /-
 theorem diff_eq (s t : Set α) : s \ t = s ∩ tᶜ :=
   rfl
 #align set.diff_eq Set.diff_eq
+-/
 
+#print Set.mem_diff /-
 @[simp]
 theorem mem_diff {s t : Set α} (x : α) : x ∈ s \ t ↔ x ∈ s ∧ x ∉ t :=
   Iff.rfl
 #align set.mem_diff Set.mem_diff
+-/
 
+#print Set.mem_diff_of_mem /-
 theorem mem_diff_of_mem {s t : Set α} {x : α} (h1 : x ∈ s) (h2 : x ∉ t) : x ∈ s \ t :=
   ⟨h1, h2⟩
 #align set.mem_diff_of_mem Set.mem_diff_of_mem
+-/
 
+#print Set.not_mem_diff_of_mem /-
 theorem not_mem_diff_of_mem {s t : Set α} {x : α} (hx : x ∈ t) : x ∉ s \ t := fun h => h.2 hx
 #align set.not_mem_diff_of_mem Set.not_mem_diff_of_mem
+-/
 
+#print Set.mem_of_mem_diff /-
 theorem mem_of_mem_diff {s t : Set α} {x : α} (h : x ∈ s \ t) : x ∈ s :=
   h.left
 #align set.mem_of_mem_diff Set.mem_of_mem_diff
+-/
 
+#print Set.not_mem_of_mem_diff /-
 theorem not_mem_of_mem_diff {s t : Set α} {x : α} (h : x ∈ s \ t) : x ∉ t :=
   h.right
 #align set.not_mem_of_mem_diff Set.not_mem_of_mem_diff
+-/
 
+#print Set.diff_eq_compl_inter /-
 theorem diff_eq_compl_inter {s t : Set α} : s \ t = tᶜ ∩ s := by rw [diff_eq, inter_comm]
 #align set.diff_eq_compl_inter Set.diff_eq_compl_inter
+-/
 
+#print Set.nonempty_diff /-
 theorem nonempty_diff {s t : Set α} : (s \ t).Nonempty ↔ ¬s ⊆ t :=
   inter_compl_nonempty_iff
 #align set.nonempty_diff Set.nonempty_diff
+-/
 
+#print Set.diff_subset /-
 theorem diff_subset (s t : Set α) : s \ t ⊆ s :=
   show s \ t ≤ s from sdiff_le
 #align set.diff_subset Set.diff_subset
+-/
 
+#print Set.union_diff_cancel' /-
 theorem union_diff_cancel' {s t u : Set α} (h₁ : s ⊆ t) (h₂ : t ⊆ u) : t ∪ u \ s = u :=
   sup_sdiff_cancel' h₁ h₂
 #align set.union_diff_cancel' Set.union_diff_cancel'
+-/
 
+#print Set.union_diff_cancel /-
 theorem union_diff_cancel {s t : Set α} (h : s ⊆ t) : s ∪ t \ s = t :=
   sup_sdiff_cancel_right h
 #align set.union_diff_cancel Set.union_diff_cancel
+-/
 
+#print Set.union_diff_cancel_left /-
 theorem union_diff_cancel_left {s t : Set α} (h : s ∩ t ⊆ ∅) : (s ∪ t) \ s = t :=
   Disjoint.sup_sdiff_cancel_left <| disjoint_iff_inf_le.2 h
 #align set.union_diff_cancel_left Set.union_diff_cancel_left
+-/
 
+#print Set.union_diff_cancel_right /-
 theorem union_diff_cancel_right {s t : Set α} (h : s ∩ t ⊆ ∅) : (s ∪ t) \ t = s :=
   Disjoint.sup_sdiff_cancel_right <| disjoint_iff_inf_le.2 h
 #align set.union_diff_cancel_right Set.union_diff_cancel_right
+-/
 
+#print Set.union_diff_left /-
 @[simp]
 theorem union_diff_left {s t : Set α} : (s ∪ t) \ s = t \ s :=
   sup_sdiff_left_self
 #align set.union_diff_left Set.union_diff_left
+-/
 
+#print Set.union_diff_right /-
 @[simp]
 theorem union_diff_right {s t : Set α} : (s ∪ t) \ t = s \ t :=
   sup_sdiff_right_self
 #align set.union_diff_right Set.union_diff_right
+-/
 
+#print Set.union_diff_distrib /-
 theorem union_diff_distrib {s t u : Set α} : (s ∪ t) \ u = s \ u ∪ t \ u :=
   sup_sdiff
 #align set.union_diff_distrib Set.union_diff_distrib
+-/
 
+#print Set.inter_diff_assoc /-
 theorem inter_diff_assoc (a b c : Set α) : (a ∩ b) \ c = a ∩ (b \ c) :=
   inf_sdiff_assoc
 #align set.inter_diff_assoc Set.inter_diff_assoc
+-/
 
+#print Set.inter_diff_self /-
 @[simp]
 theorem inter_diff_self (a b : Set α) : a ∩ (b \ a) = ∅ :=
   inf_sdiff_self_right
 #align set.inter_diff_self Set.inter_diff_self
+-/
 
+#print Set.inter_union_diff /-
 @[simp]
 theorem inter_union_diff (s t : Set α) : s ∩ t ∪ s \ t = s :=
   sup_inf_sdiff s t
 #align set.inter_union_diff Set.inter_union_diff
+-/
 
+#print Set.diff_union_inter /-
 @[simp]
 theorem diff_union_inter (s t : Set α) : s \ t ∪ s ∩ t = s := by rw [union_comm];
   exact sup_inf_sdiff _ _
 #align set.diff_union_inter Set.diff_union_inter
+-/
 
+#print Set.inter_union_compl /-
 @[simp]
 theorem inter_union_compl (s t : Set α) : s ∩ t ∪ s ∩ tᶜ = s :=
   inter_union_diff _ _
 #align set.inter_union_compl Set.inter_union_compl
+-/
 
+#print Set.diff_subset_diff /-
 theorem diff_subset_diff {s₁ s₂ t₁ t₂ : Set α} : s₁ ⊆ s₂ → t₂ ⊆ t₁ → s₁ \ t₁ ⊆ s₂ \ t₂ :=
   show s₁ ≤ s₂ → t₂ ≤ t₁ → s₁ \ t₁ ≤ s₂ \ t₂ from sdiff_le_sdiff
 #align set.diff_subset_diff Set.diff_subset_diff
+-/
 
+#print Set.diff_subset_diff_left /-
 theorem diff_subset_diff_left {s₁ s₂ t : Set α} (h : s₁ ⊆ s₂) : s₁ \ t ⊆ s₂ \ t :=
   sdiff_le_sdiff_right ‹s₁ ≤ s₂›
 #align set.diff_subset_diff_left Set.diff_subset_diff_left
+-/
 
+#print Set.diff_subset_diff_right /-
 theorem diff_subset_diff_right {s t u : Set α} (h : t ⊆ u) : s \ u ⊆ s \ t :=
   sdiff_le_sdiff_left ‹t ≤ u›
 #align set.diff_subset_diff_right Set.diff_subset_diff_right
+-/
 
+#print Set.compl_eq_univ_diff /-
 theorem compl_eq_univ_diff (s : Set α) : sᶜ = univ \ s :=
   top_sdiff.symm
 #align set.compl_eq_univ_diff Set.compl_eq_univ_diff
+-/
 
+#print Set.empty_diff /-
 @[simp]
 theorem empty_diff (s : Set α) : (∅ \ s : Set α) = ∅ :=
   bot_sdiff
 #align set.empty_diff Set.empty_diff
+-/
 
+#print Set.diff_eq_empty /-
 theorem diff_eq_empty {s t : Set α} : s \ t = ∅ ↔ s ⊆ t :=
   sdiff_eq_bot_iff
 #align set.diff_eq_empty Set.diff_eq_empty
+-/
 
+#print Set.diff_empty /-
 @[simp]
 theorem diff_empty {s : Set α} : s \ ∅ = s :=
   sdiff_bot
 #align set.diff_empty Set.diff_empty
+-/
 
+#print Set.diff_univ /-
 @[simp]
 theorem diff_univ (s : Set α) : s \ univ = ∅ :=
   diff_eq_empty.2 (subset_univ s)
 #align set.diff_univ Set.diff_univ
+-/
 
+#print Set.diff_diff /-
 theorem diff_diff {u : Set α} : (s \ t) \ u = s \ (t ∪ u) :=
   sdiff_sdiff_left
 #align set.diff_diff Set.diff_diff
+-/
 
+#print Set.diff_diff_comm /-
 -- the following statement contains parentheses to help the reader
 theorem diff_diff_comm {s t u : Set α} : (s \ t) \ u = (s \ u) \ t :=
   sdiff_sdiff_comm
 #align set.diff_diff_comm Set.diff_diff_comm
+-/
 
+#print Set.diff_subset_iff /-
 theorem diff_subset_iff {s t u : Set α} : s \ t ⊆ u ↔ s ⊆ t ∪ u :=
   show s \ t ≤ u ↔ s ≤ t ∪ u from sdiff_le_iff
 #align set.diff_subset_iff Set.diff_subset_iff
+-/
 
+#print Set.subset_diff_union /-
 theorem subset_diff_union (s t : Set α) : s ⊆ s \ t ∪ t :=
   show s ≤ s \ t ∪ t from le_sdiff_sup
 #align set.subset_diff_union Set.subset_diff_union
+-/
 
+#print Set.diff_union_of_subset /-
 theorem diff_union_of_subset {s t : Set α} (h : t ⊆ s) : s \ t ∪ t = s :=
   Subset.antisymm (union_subset (diff_subset _ _) h) (subset_diff_union _ _)
 #align set.diff_union_of_subset Set.diff_union_of_subset
+-/
 
+#print Set.diff_singleton_subset_iff /-
 @[simp]
 theorem diff_singleton_subset_iff {x : α} {s t : Set α} : s \ {x} ⊆ t ↔ s ⊆ insert x t := by
   rw [← union_singleton, union_comm]; apply diff_subset_iff
 #align set.diff_singleton_subset_iff Set.diff_singleton_subset_iff
+-/
 
+#print Set.subset_diff_singleton /-
 theorem subset_diff_singleton {x : α} {s t : Set α} (h : s ⊆ t) (hx : x ∉ s) : s ⊆ t \ {x} :=
   subset_inter h <| subset_compl_comm.1 <| singleton_subset_iff.2 hx
 #align set.subset_diff_singleton Set.subset_diff_singleton
+-/
 
+#print Set.subset_insert_diff_singleton /-
 theorem subset_insert_diff_singleton (x : α) (s : Set α) : s ⊆ insert x (s \ {x}) := by
   rw [← diff_singleton_subset_iff]
 #align set.subset_insert_diff_singleton Set.subset_insert_diff_singleton
+-/
 
+#print Set.diff_subset_comm /-
 theorem diff_subset_comm {s t u : Set α} : s \ t ⊆ u ↔ s \ u ⊆ t :=
   show s \ t ≤ u ↔ s \ u ≤ t from sdiff_le_comm
 #align set.diff_subset_comm Set.diff_subset_comm
+-/
 
+#print Set.diff_inter /-
 theorem diff_inter {s t u : Set α} : s \ (t ∩ u) = s \ t ∪ s \ u :=
   sdiff_inf
 #align set.diff_inter Set.diff_inter
+-/
 
+#print Set.diff_inter_diff /-
 theorem diff_inter_diff {s t u : Set α} : s \ t ∩ (s \ u) = s \ (t ∪ u) :=
   sdiff_sup.symm
 #align set.diff_inter_diff Set.diff_inter_diff
+-/
 
+#print Set.diff_compl /-
 theorem diff_compl : s \ tᶜ = s ∩ t :=
   sdiff_compl
 #align set.diff_compl Set.diff_compl
+-/
 
+#print Set.diff_diff_right /-
 theorem diff_diff_right {s t u : Set α} : s \ (t \ u) = s \ t ∪ s ∩ u :=
   sdiff_sdiff_right'
 #align set.diff_diff_right Set.diff_diff_right
+-/
 
+#print Set.insert_diff_of_mem /-
 @[simp]
 theorem insert_diff_of_mem (s) (h : a ∈ t) : insert a s \ t = s \ t := by ext;
   constructor <;> simp (config := { contextual := true }) [or_imp, h]
 #align set.insert_diff_of_mem Set.insert_diff_of_mem
+-/
 
+#print Set.insert_diff_of_not_mem /-
 theorem insert_diff_of_not_mem (s) (h : a ∉ t) : insert a s \ t = insert a (s \ t) := by
   classical
   ext x
@@ -2272,11 +2761,15 @@ theorem insert_diff_of_not_mem (s) (h : a ∉ t) : insert a s \ t = insert a (s
     simp [h, h', this]
   · simp [h, h']
 #align set.insert_diff_of_not_mem Set.insert_diff_of_not_mem
+-/
 
+#print Set.insert_diff_self_of_not_mem /-
 theorem insert_diff_self_of_not_mem {a : α} {s : Set α} (h : a ∉ s) : insert a s \ {a} = s := by
   ext; simp [and_iff_left_of_imp fun hx : x ∈ s => show x ≠ a from fun hxa => h <| hxa ▸ hx]
 #align set.insert_diff_self_of_not_mem Set.insert_diff_self_of_not_mem
+-/
 
+#print Set.insert_diff_eq_singleton /-
 @[simp]
 theorem insert_diff_eq_singleton {a : α} {s : Set α} (h : a ∉ s) : insert a s \ s = {a} :=
   by
@@ -2286,134 +2779,191 @@ theorem insert_diff_eq_singleton {a : α} {s : Set α} (h : a ∉ s) : insert a
   rintro rfl
   exact h
 #align set.insert_diff_eq_singleton Set.insert_diff_eq_singleton
+-/
 
+#print Set.inter_insert_of_mem /-
 theorem inter_insert_of_mem (h : a ∈ s) : s ∩ insert a t = insert a (s ∩ t) := by
   rw [insert_inter_distrib, insert_eq_of_mem h]
 #align set.inter_insert_of_mem Set.inter_insert_of_mem
+-/
 
+#print Set.insert_inter_of_mem /-
 theorem insert_inter_of_mem (h : a ∈ t) : insert a s ∩ t = insert a (s ∩ t) := by
   rw [insert_inter_distrib, insert_eq_of_mem h]
 #align set.insert_inter_of_mem Set.insert_inter_of_mem
+-/
 
+#print Set.inter_insert_of_not_mem /-
 theorem inter_insert_of_not_mem (h : a ∉ s) : s ∩ insert a t = s ∩ t :=
   ext fun x => and_congr_right fun hx => or_iff_right <| ne_of_mem_of_not_mem hx h
 #align set.inter_insert_of_not_mem Set.inter_insert_of_not_mem
+-/
 
+#print Set.insert_inter_of_not_mem /-
 theorem insert_inter_of_not_mem (h : a ∉ t) : insert a s ∩ t = s ∩ t :=
   ext fun x => and_congr_left fun hx => or_iff_right <| ne_of_mem_of_not_mem hx h
 #align set.insert_inter_of_not_mem Set.insert_inter_of_not_mem
+-/
 
+#print Set.union_diff_self /-
 @[simp]
 theorem union_diff_self {s t : Set α} : s ∪ t \ s = s ∪ t :=
   sup_sdiff_self _ _
 #align set.union_diff_self Set.union_diff_self
+-/
 
+#print Set.diff_union_self /-
 @[simp]
 theorem diff_union_self {s t : Set α} : s \ t ∪ t = s ∪ t :=
   sdiff_sup_self _ _
 #align set.diff_union_self Set.diff_union_self
+-/
 
+#print Set.diff_inter_self /-
 @[simp]
 theorem diff_inter_self {a b : Set α} : b \ a ∩ a = ∅ :=
   inf_sdiff_self_left
 #align set.diff_inter_self Set.diff_inter_self
+-/
 
+#print Set.diff_inter_self_eq_diff /-
 @[simp]
 theorem diff_inter_self_eq_diff {s t : Set α} : s \ (t ∩ s) = s \ t :=
   sdiff_inf_self_right _ _
 #align set.diff_inter_self_eq_diff Set.diff_inter_self_eq_diff
+-/
 
+#print Set.diff_self_inter /-
 @[simp]
 theorem diff_self_inter {s t : Set α} : s \ (s ∩ t) = s \ t :=
   sdiff_inf_self_left _ _
 #align set.diff_self_inter Set.diff_self_inter
+-/
 
+#print Set.diff_singleton_eq_self /-
 @[simp]
 theorem diff_singleton_eq_self {a : α} {s : Set α} (h : a ∉ s) : s \ {a} = s :=
   sdiff_eq_self_iff_disjoint.2 <| by simp [h]
 #align set.diff_singleton_eq_self Set.diff_singleton_eq_self
+-/
 
+#print Set.diff_singleton_sSubset /-
 @[simp]
 theorem diff_singleton_sSubset {s : Set α} {a : α} : s \ {a} ⊂ s ↔ a ∈ s :=
   sdiff_le.lt_iff_ne.trans <| sdiff_eq_left.Not.trans <| by simp
 #align set.diff_singleton_ssubset Set.diff_singleton_sSubset
+-/
 
+#print Set.insert_diff_singleton /-
 @[simp]
 theorem insert_diff_singleton {a : α} {s : Set α} : insert a (s \ {a}) = insert a s := by
   simp [insert_eq, union_diff_self, -union_singleton, -singleton_union]
 #align set.insert_diff_singleton Set.insert_diff_singleton
+-/
 
+#print Set.insert_diff_singleton_comm /-
 theorem insert_diff_singleton_comm (hab : a ≠ b) (s : Set α) :
     insert a (s \ {b}) = insert a s \ {b} := by
   simp_rw [← union_singleton, union_diff_distrib,
     diff_singleton_eq_self (mem_singleton_iff.not.2 hab.symm)]
 #align set.insert_diff_singleton_comm Set.insert_diff_singleton_comm
+-/
 
+#print Set.diff_self /-
 @[simp]
 theorem diff_self {s : Set α} : s \ s = ∅ :=
   sdiff_self
 #align set.diff_self Set.diff_self
+-/
 
+#print Set.diff_diff_right_self /-
 theorem diff_diff_right_self (s t : Set α) : s \ (s \ t) = s ∩ t :=
   sdiff_sdiff_right_self
 #align set.diff_diff_right_self Set.diff_diff_right_self
+-/
 
+#print Set.diff_diff_cancel_left /-
 theorem diff_diff_cancel_left {s t : Set α} (h : s ⊆ t) : t \ (t \ s) = s :=
   sdiff_sdiff_eq_self h
 #align set.diff_diff_cancel_left Set.diff_diff_cancel_left
+-/
 
+#print Set.mem_diff_singleton /-
 theorem mem_diff_singleton {x y : α} {s : Set α} : x ∈ s \ {y} ↔ x ∈ s ∧ x ≠ y :=
   Iff.rfl
 #align set.mem_diff_singleton Set.mem_diff_singleton
+-/
 
+#print Set.mem_diff_singleton_empty /-
 theorem mem_diff_singleton_empty {t : Set (Set α)} : s ∈ t \ {∅} ↔ s ∈ t ∧ s.Nonempty :=
   mem_diff_singleton.trans <| and_congr_right' nonempty_iff_ne_empty.symm
 #align set.mem_diff_singleton_empty Set.mem_diff_singleton_empty
+-/
 
+#print Set.union_eq_diff_union_diff_union_inter /-
 theorem union_eq_diff_union_diff_union_inter (s t : Set α) : s ∪ t = s \ t ∪ t \ s ∪ s ∩ t :=
   sup_eq_sdiff_sup_sdiff_sup_inf
 #align set.union_eq_diff_union_diff_union_inter Set.union_eq_diff_union_diff_union_inter
+-/
 
 /-! ### Symmetric difference -/
 
 
+#print Set.mem_symmDiff /-
 theorem mem_symmDiff : a ∈ s ∆ t ↔ a ∈ s ∧ a ∉ t ∨ a ∈ t ∧ a ∉ s :=
   Iff.rfl
 #align set.mem_symm_diff Set.mem_symmDiff
+-/
 
+#print Set.symmDiff_def /-
 protected theorem symmDiff_def (s t : Set α) : s ∆ t = s \ t ∪ t \ s :=
   rfl
 #align set.symm_diff_def Set.symmDiff_def
+-/
 
+#print Set.symmDiff_subset_union /-
 theorem symmDiff_subset_union : s ∆ t ⊆ s ∪ t :=
   @symmDiff_le_sup (Set α) _ _ _
 #align set.symm_diff_subset_union Set.symmDiff_subset_union
+-/
 
+#print Set.symmDiff_eq_empty /-
 @[simp]
 theorem symmDiff_eq_empty : s ∆ t = ∅ ↔ s = t :=
   symmDiff_eq_bot
 #align set.symm_diff_eq_empty Set.symmDiff_eq_empty
+-/
 
+#print Set.symmDiff_nonempty /-
 @[simp]
 theorem symmDiff_nonempty : (s ∆ t).Nonempty ↔ s ≠ t :=
   nonempty_iff_ne_empty.trans symmDiff_eq_empty.Not
 #align set.symm_diff_nonempty Set.symmDiff_nonempty
+-/
 
+#print Set.inter_symmDiff_distrib_left /-
 theorem inter_symmDiff_distrib_left (s t u : Set α) : s ∩ t ∆ u = (s ∩ t) ∆ (s ∩ u) :=
   inf_symmDiff_distrib_left _ _ _
 #align set.inter_symm_diff_distrib_left Set.inter_symmDiff_distrib_left
+-/
 
+#print Set.inter_symmDiff_distrib_right /-
 theorem inter_symmDiff_distrib_right (s t u : Set α) : s ∆ t ∩ u = (s ∩ u) ∆ (t ∩ u) :=
   inf_symmDiff_distrib_right _ _ _
 #align set.inter_symm_diff_distrib_right Set.inter_symmDiff_distrib_right
+-/
 
+#print Set.subset_symmDiff_union_symmDiff_left /-
 theorem subset_symmDiff_union_symmDiff_left (h : Disjoint s t) : u ⊆ s ∆ u ∪ t ∆ u :=
   h.le_symmDiff_sup_symmDiff_left
 #align set.subset_symm_diff_union_symm_diff_left Set.subset_symmDiff_union_symmDiff_left
+-/
 
+#print Set.subset_symmDiff_union_symmDiff_right /-
 theorem subset_symmDiff_union_symmDiff_right (h : Disjoint t u) : s ⊆ s ∆ t ∪ s ∆ u :=
   h.le_symmDiff_sup_symmDiff_right
 #align set.subset_symm_diff_union_symm_diff_right Set.subset_symmDiff_union_symmDiff_right
+-/
 
 /-! ### Powerset -/
 
@@ -2444,9 +2994,11 @@ theorem mem_powerset_iff (x s : Set α) : x ∈ 𝒫 s ↔ x ⊆ s :=
 #align set.mem_powerset_iff Set.mem_powerset_iff
 -/
 
+#print Set.powerset_inter /-
 theorem powerset_inter (s t : Set α) : 𝒫(s ∩ t) = 𝒫 s ∩ 𝒫 t :=
   ext fun u => subset_inter_iff
 #align set.powerset_inter Set.powerset_inter
+-/
 
 #print Set.powerset_mono /-
 @[simp]
@@ -2455,8 +3007,10 @@ theorem powerset_mono : 𝒫 s ⊆ 𝒫 t ↔ s ⊆ t :=
 #align set.powerset_mono Set.powerset_mono
 -/
 
+#print Set.monotone_powerset /-
 theorem monotone_powerset : Monotone (powerset : Set α → Set (Set α)) := fun s t => powerset_mono.2
 #align set.monotone_powerset Set.monotone_powerset
+-/
 
 #print Set.powerset_nonempty /-
 @[simp]
@@ -2554,25 +3108,33 @@ protected def ite (t s s' : Set α) : Set α :=
 #align set.ite Set.ite
 -/
 
+#print Set.ite_inter_self /-
 @[simp]
 theorem ite_inter_self (t s s' : Set α) : t.ite s s' ∩ t = s ∩ t := by
   rw [Set.ite, union_inter_distrib_right, diff_inter_self, inter_assoc, inter_self, union_empty]
 #align set.ite_inter_self Set.ite_inter_self
+-/
 
+#print Set.ite_compl /-
 @[simp]
 theorem ite_compl (t s s' : Set α) : tᶜ.ite s s' = t.ite s' s := by
   rw [Set.ite, Set.ite, diff_compl, union_comm, diff_eq]
 #align set.ite_compl Set.ite_compl
+-/
 
+#print Set.ite_inter_compl_self /-
 @[simp]
 theorem ite_inter_compl_self (t s s' : Set α) : t.ite s s' ∩ tᶜ = s' ∩ tᶜ := by
   rw [← ite_compl, ite_inter_self]
 #align set.ite_inter_compl_self Set.ite_inter_compl_self
+-/
 
+#print Set.ite_diff_self /-
 @[simp]
 theorem ite_diff_self (t s s' : Set α) : t.ite s s' \ t = s' \ t :=
   ite_inter_compl_self t s s'
 #align set.ite_diff_self Set.ite_diff_self
+-/
 
 #print Set.ite_same /-
 @[simp]
@@ -2581,13 +3143,17 @@ theorem ite_same (t s : Set α) : t.ite s s = s :=
 #align set.ite_same Set.ite_same
 -/
 
+#print Set.ite_left /-
 @[simp]
 theorem ite_left (s t : Set α) : s.ite s t = s ∪ t := by simp [Set.ite]
 #align set.ite_left Set.ite_left
+-/
 
+#print Set.ite_right /-
 @[simp]
 theorem ite_right (s t : Set α) : s.ite t s = t ∩ s := by simp [Set.ite]
 #align set.ite_right Set.ite_right
+-/
 
 #print Set.ite_empty /-
 @[simp]
@@ -2601,13 +3167,17 @@ theorem ite_univ (s s' : Set α) : Set.ite univ s s' = s := by simp [Set.ite]
 #align set.ite_univ Set.ite_univ
 -/
 
+#print Set.ite_empty_left /-
 @[simp]
 theorem ite_empty_left (t s : Set α) : t.ite ∅ s = s \ t := by simp [Set.ite]
 #align set.ite_empty_left Set.ite_empty_left
+-/
 
+#print Set.ite_empty_right /-
 @[simp]
 theorem ite_empty_right (t s : Set α) : t.ite s ∅ = s ∩ t := by simp [Set.ite]
 #align set.ite_empty_right Set.ite_empty_right
+-/
 
 #print Set.ite_mono /-
 theorem ite_mono (t : Set α) {s₁ s₁' s₂ s₂' : Set α} (h : s₁ ⊆ s₂) (h' : s₁' ⊆ s₂') :
@@ -2616,33 +3186,45 @@ theorem ite_mono (t : Set α) {s₁ s₁' s₂ s₂' : Set α} (h : s₁ ⊆ s
 #align set.ite_mono Set.ite_mono
 -/
 
+#print Set.ite_subset_union /-
 theorem ite_subset_union (t s s' : Set α) : t.ite s s' ⊆ s ∪ s' :=
   union_subset_union (inter_subset_left _ _) (diff_subset _ _)
 #align set.ite_subset_union Set.ite_subset_union
+-/
 
+#print Set.inter_subset_ite /-
 theorem inter_subset_ite (t s s' : Set α) : s ∩ s' ⊆ t.ite s s' :=
   ite_same t (s ∩ s') ▸ ite_mono _ (inter_subset_left _ _) (inter_subset_right _ _)
 #align set.inter_subset_ite Set.inter_subset_ite
+-/
 
+#print Set.ite_inter_inter /-
 theorem ite_inter_inter (t s₁ s₂ s₁' s₂' : Set α) :
     t.ite (s₁ ∩ s₂) (s₁' ∩ s₂') = t.ite s₁ s₁' ∩ t.ite s₂ s₂' := by ext x;
   simp only [Set.ite, Set.mem_inter_iff, Set.mem_diff, Set.mem_union]; itauto
 #align set.ite_inter_inter Set.ite_inter_inter
+-/
 
+#print Set.ite_inter /-
 theorem ite_inter (t s₁ s₂ s : Set α) : t.ite (s₁ ∩ s) (s₂ ∩ s) = t.ite s₁ s₂ ∩ s := by
   rw [ite_inter_inter, ite_same]
 #align set.ite_inter Set.ite_inter
+-/
 
+#print Set.ite_inter_of_inter_eq /-
 theorem ite_inter_of_inter_eq (t : Set α) {s₁ s₂ s : Set α} (h : s₁ ∩ s = s₂ ∩ s) :
     t.ite s₁ s₂ ∩ s = s₁ ∩ s := by rw [← ite_inter, ← h, ite_same]
 #align set.ite_inter_of_inter_eq Set.ite_inter_of_inter_eq
+-/
 
+#print Set.subset_ite /-
 theorem subset_ite {t s s' u : Set α} : u ⊆ t.ite s s' ↔ u ∩ t ⊆ s ∧ u \ t ⊆ s' :=
   by
   simp only [subset_def, ← forall_and]
   refine' forall_congr' fun x => _
   by_cases hx : x ∈ t <;> simp [*, Set.ite]
 #align set.subset_ite Set.subset_ite
+-/
 
 /-! ### Subsingleton -/
 
@@ -2862,11 +3444,14 @@ theorem nontrivial_iff_pair_subset : s.Nontrivial ↔ ∃ (x y : _) (hxy : x ≠
 #align set.nontrivial_iff_pair_subset Set.nontrivial_iff_pair_subset
 -/
 
+#print Set.nontrivial_of_exists_ne /-
 theorem nontrivial_of_exists_ne {x} (hx : x ∈ s) (h : ∃ y ∈ s, y ≠ x) : s.Nontrivial :=
   let ⟨y, hy, hyx⟩ := h
   ⟨y, hy, x, hx, hyx⟩
 #align set.nontrivial_of_exists_ne Set.nontrivial_of_exists_ne
+-/
 
+#print Set.Nontrivial.exists_ne /-
 theorem Nontrivial.exists_ne (hs : s.Nontrivial) (z) : ∃ x ∈ s, x ≠ z :=
   by
   by_contra H; push_neg at H 
@@ -2874,10 +3459,13 @@ theorem Nontrivial.exists_ne (hs : s.Nontrivial) (z) : ∃ x ∈ s, x ≠ z :=
   rw [H x hx, H y hy] at hxy 
   exact hxy rfl
 #align set.nontrivial.exists_ne Set.Nontrivial.exists_ne
+-/
 
+#print Set.nontrivial_iff_exists_ne /-
 theorem nontrivial_iff_exists_ne {x} (hx : x ∈ s) : s.Nontrivial ↔ ∃ y ∈ s, y ≠ x :=
   ⟨fun H => H.exists_ne _, nontrivial_of_exists_ne hx⟩
 #align set.nontrivial_iff_exists_ne Set.nontrivial_iff_exists_ne
+-/
 
 #print Set.nontrivial_of_lt /-
 theorem nontrivial_of_lt [Preorder α] {x y} (hx : x ∈ s) (hy : y ∈ s) (hxy : x < y) :
@@ -3194,10 +3782,12 @@ namespace Function
 
 variable {ι : Sort _} {α : Type _} {β : Type _} {f : α → β}
 
+#print Function.Injective.nonempty_apply_iff /-
 theorem Injective.nonempty_apply_iff {f : Set α → Set β} (hf : Injective f) (h2 : f ∅ = ∅)
     {s : Set α} : (f s).Nonempty ↔ s.Nonempty := by
   rw [nonempty_iff_ne_empty, ← h2, nonempty_iff_ne_empty, hf.ne_iff]
 #align function.injective.nonempty_apply_iff Function.Injective.nonempty_apply_iff
+-/
 
 end Function
 
@@ -3317,21 +3907,29 @@ namespace Set
 
 variable {α : Type u} (s t : Set α) (a : α)
 
+#print Set.decidableSdiff /-
 instance decidableSdiff [Decidable (a ∈ s)] [Decidable (a ∈ t)] : Decidable (a ∈ s \ t) :=
   (by infer_instance : Decidable (a ∈ s ∧ a ∉ t))
 #align set.decidable_sdiff Set.decidableSdiff
+-/
 
+#print Set.decidableInter /-
 instance decidableInter [Decidable (a ∈ s)] [Decidable (a ∈ t)] : Decidable (a ∈ s ∩ t) :=
   (by infer_instance : Decidable (a ∈ s ∧ a ∈ t))
 #align set.decidable_inter Set.decidableInter
+-/
 
+#print Set.decidableUnion /-
 instance decidableUnion [Decidable (a ∈ s)] [Decidable (a ∈ t)] : Decidable (a ∈ s ∪ t) :=
   (by infer_instance : Decidable (a ∈ s ∨ a ∈ t))
 #align set.decidable_union Set.decidableUnion
+-/
 
+#print Set.decidableCompl /-
 instance decidableCompl [Decidable (a ∈ s)] : Decidable (a ∈ sᶜ) :=
   (by infer_instance : Decidable (a ∉ s))
 #align set.decidable_compl Set.decidableCompl
+-/
 
 #print Set.decidableEmptyset /-
 instance decidableEmptyset : DecidablePred (· ∈ (∅ : Set α)) := fun _ => Decidable.isFalse (by simp)
@@ -3359,60 +3957,82 @@ section Monotone
 
 variable {α β : Type _}
 
+#print Monotone.inter /-
 theorem Monotone.inter [Preorder β] {f g : β → Set α} (hf : Monotone f) (hg : Monotone g) :
     Monotone fun x => f x ∩ g x :=
   hf.inf hg
 #align monotone.inter Monotone.inter
+-/
 
+#print MonotoneOn.inter /-
 theorem MonotoneOn.inter [Preorder β] {f g : β → Set α} {s : Set β} (hf : MonotoneOn f s)
     (hg : MonotoneOn g s) : MonotoneOn (fun x => f x ∩ g x) s :=
   hf.inf hg
 #align monotone_on.inter MonotoneOn.inter
+-/
 
+#print Antitone.inter /-
 theorem Antitone.inter [Preorder β] {f g : β → Set α} (hf : Antitone f) (hg : Antitone g) :
     Antitone fun x => f x ∩ g x :=
   hf.inf hg
 #align antitone.inter Antitone.inter
+-/
 
+#print AntitoneOn.inter /-
 theorem AntitoneOn.inter [Preorder β] {f g : β → Set α} {s : Set β} (hf : AntitoneOn f s)
     (hg : AntitoneOn g s) : AntitoneOn (fun x => f x ∩ g x) s :=
   hf.inf hg
 #align antitone_on.inter AntitoneOn.inter
+-/
 
+#print Monotone.union /-
 theorem Monotone.union [Preorder β] {f g : β → Set α} (hf : Monotone f) (hg : Monotone g) :
     Monotone fun x => f x ∪ g x :=
   hf.sup hg
 #align monotone.union Monotone.union
+-/
 
+#print MonotoneOn.union /-
 theorem MonotoneOn.union [Preorder β] {f g : β → Set α} {s : Set β} (hf : MonotoneOn f s)
     (hg : MonotoneOn g s) : MonotoneOn (fun x => f x ∪ g x) s :=
   hf.sup hg
 #align monotone_on.union MonotoneOn.union
+-/
 
+#print Antitone.union /-
 theorem Antitone.union [Preorder β] {f g : β → Set α} (hf : Antitone f) (hg : Antitone g) :
     Antitone fun x => f x ∪ g x :=
   hf.sup hg
 #align antitone.union Antitone.union
+-/
 
+#print AntitoneOn.union /-
 theorem AntitoneOn.union [Preorder β] {f g : β → Set α} {s : Set β} (hf : AntitoneOn f s)
     (hg : AntitoneOn g s) : AntitoneOn (fun x => f x ∪ g x) s :=
   hf.sup hg
 #align antitone_on.union AntitoneOn.union
+-/
 
 namespace Set
 
+#print Set.monotone_setOf /-
 theorem monotone_setOf [Preorder α] {p : α → β → Prop} (hp : ∀ b, Monotone fun a => p a b) :
     Monotone fun a => {b | p a b} := fun a a' h b => hp b h
 #align set.monotone_set_of Set.monotone_setOf
+-/
 
+#print Set.antitone_setOf /-
 theorem antitone_setOf [Preorder α] {p : α → β → Prop} (hp : ∀ b, Antitone fun a => p a b) :
     Antitone fun a => {b | p a b} := fun a a' h b => hp b h
 #align set.antitone_set_of Set.antitone_setOf
+-/
 
+#print Set.antitone_bforall /-
 /-- Quantifying over a set is antitone in the set -/
 theorem antitone_bforall {P : α → Prop} : Antitone fun s : Set α => ∀ x ∈ s, P x :=
   fun s t hst h x hx => h x <| hst hx
 #align set.antitone_bforall Set.antitone_bforall
+-/
 
 end Set
 
@@ -3425,37 +4045,53 @@ variable {α β : Type _} {s t u : Set α} {f : α → β}
 
 namespace Disjoint
 
+#print Disjoint.union_left /-
 theorem union_left (hs : Disjoint s u) (ht : Disjoint t u) : Disjoint (s ∪ t) u :=
   hs.sup_left ht
 #align disjoint.union_left Disjoint.union_left
+-/
 
+#print Disjoint.union_right /-
 theorem union_right (ht : Disjoint s t) (hu : Disjoint s u) : Disjoint s (t ∪ u) :=
   ht.sup_right hu
 #align disjoint.union_right Disjoint.union_right
+-/
 
+#print Disjoint.inter_left /-
 theorem inter_left (u : Set α) (h : Disjoint s t) : Disjoint (s ∩ u) t :=
   h.inf_left u
 #align disjoint.inter_left Disjoint.inter_left
+-/
 
+#print Disjoint.inter_left' /-
 theorem inter_left' (u : Set α) (h : Disjoint s t) : Disjoint (u ∩ s) t :=
   h.inf_left' _
 #align disjoint.inter_left' Disjoint.inter_left'
+-/
 
+#print Disjoint.inter_right /-
 theorem inter_right (u : Set α) (h : Disjoint s t) : Disjoint s (t ∩ u) :=
   h.inf_right _
 #align disjoint.inter_right Disjoint.inter_right
+-/
 
+#print Disjoint.inter_right' /-
 theorem inter_right' (u : Set α) (h : Disjoint s t) : Disjoint s (u ∩ t) :=
   h.inf_right' _
 #align disjoint.inter_right' Disjoint.inter_right'
+-/
 
+#print Disjoint.subset_left_of_subset_union /-
 theorem subset_left_of_subset_union (h : s ⊆ t ∪ u) (hac : Disjoint s u) : s ⊆ t :=
   hac.left_le_of_le_sup_right h
 #align disjoint.subset_left_of_subset_union Disjoint.subset_left_of_subset_union
+-/
 
+#print Disjoint.subset_right_of_subset_union /-
 theorem subset_right_of_subset_union (h : s ⊆ t ∪ u) (hab : Disjoint s t) : s ⊆ u :=
   hab.left_le_of_le_sup_left h
 #align disjoint.subset_right_of_subset_union Disjoint.subset_right_of_subset_union
+-/
 
 end Disjoint

bump to nightly-2023-06-08-23

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

d3cfe2e3

Diff

@@ -1352,7 +1352,7 @@ theorem subset_insert_iff_of_not_mem (ha : a ∉ s) : s ⊆ insert a t ↔ s ⊆
 #align set.subset_insert_iff_of_not_mem Set.subset_insert_iff_of_not_mem
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (a «expr ∉ » s) -/
 theorem ssubset_iff_insert {s t : Set α} : s ⊂ t ↔ ∃ (a : _) (_ : a ∉ s), insert a s ⊆ t :=
   by
   simp only [insert_subset, exists_and_right, ssubset_def, not_subset]
@@ -2787,7 +2787,7 @@ instance subsingleton_coe_of_subsingleton [Subsingleton α] {s : Set α} : Subsi
 /-! ### Nontrivial -/
 
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Nontrivial /-
 /-- A set `s` is `nontrivial` if it has at least two distinct elements. -/
 protected def Nontrivial (s : Set α) : Prop :=
@@ -2886,7 +2886,7 @@ theorem nontrivial_of_lt [Preorder α] {x y} (hx : x ∈ s) (hy : y ∈ s) (hxy
 #align set.nontrivial_of_lt Set.nontrivial_of_lt
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.nontrivial_of_exists_lt /-
 theorem nontrivial_of_exists_lt [Preorder α]
     (H : ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s), x < y) : s.Nontrivial :=
@@ -2895,7 +2895,7 @@ theorem nontrivial_of_exists_lt [Preorder α]
 #align set.nontrivial_of_exists_lt Set.nontrivial_of_exists_lt
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Nontrivial.exists_lt /-
 theorem Nontrivial.exists_lt [LinearOrder α] (hs : s.Nontrivial) :
     ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s), x < y :=
@@ -2904,7 +2904,7 @@ theorem Nontrivial.exists_lt [LinearOrder α] (hs : s.Nontrivial) :
 #align set.nontrivial.exists_lt Set.Nontrivial.exists_lt
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.nontrivial_iff_exists_lt /-
 theorem nontrivial_iff_exists_lt [LinearOrder α] :
     s.Nontrivial ↔ ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s), x < y :=
@@ -3156,7 +3156,7 @@ section LinearOrder
 
 variable [LinearOrder α] [LinearOrder β] {f : α → β}
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a b c «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (a b c «expr ∈ » s) -/
 #print Set.not_monotoneOn_not_antitoneOn_iff_exists_le_le /-
 /-- A function between linear orders which is neither monotone nor antitone makes a dent upright or
 downright. -/
@@ -3170,7 +3170,7 @@ theorem not_monotoneOn_not_antitoneOn_iff_exists_le_le :
 #align set.not_monotone_on_not_antitone_on_iff_exists_le_le Set.not_monotoneOn_not_antitoneOn_iff_exists_le_le
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a b c «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (a b c «expr ∈ » s) -/
 #print Set.not_monotoneOn_not_antitoneOn_iff_exists_lt_lt /-
 /-- A function between linear orders which is neither monotone nor antitone makes a dent upright or
 downright. -/

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -89,16 +89,15 @@ instance : HasSubset (Set α) :=
 instance {α : Type _} : BooleanAlgebra (Set α) :=
   {
     (inferInstance :
-      BooleanAlgebra (α →
-          Prop)) with
-    sup := fun s t => { x | x ∈ s ∨ x ∈ t }
+      BooleanAlgebra (α → Prop)) with
+    sup := fun s t => {x | x ∈ s ∨ x ∈ t}
     le := (· ≤ ·)
     lt := fun s t => s ⊆ t ∧ ¬t ⊆ s
-    inf := fun s t => { x | x ∈ s ∧ x ∈ t }
+    inf := fun s t => {x | x ∈ s ∧ x ∈ t}
     bot := ∅
-    compl := fun s => { x | x ∉ s }
+    compl := fun s => {x | x ∉ s}
     top := univ
-    sdiff := fun s t => { x | x ∈ s ∧ x ∉ t } }
+    sdiff := fun s t => {x | x ∈ s ∧ x ∉ t} }
 
 instance : HasSSubset (Set α) :=
   ⟨(· < ·)⟩
@@ -191,7 +190,7 @@ theorem Set.coe_eq_subtype (s : Set α) : ↥s = { x // x ∈ s } :=
 
 #print Set.coe_setOf /-
 @[simp]
-theorem Set.coe_setOf (p : α → Prop) : ↥{ x | p x } = { x // p x } :=
+theorem Set.coe_setOf (p : α → Prop) : ↥{x | p x} = { x // p x } :=
   rfl
 #align set.coe_set_of Set.coe_setOf
 -/
@@ -298,7 +297,7 @@ theorem forall_in_swap {p : α → β → Prop} : (∀ a ∈ s, ∀ (b), p a b)
 
 
 #print Set.mem_setOf /-
-theorem mem_setOf {a : α} {p : α → Prop} : a ∈ { x | p x } ↔ p a :=
+theorem mem_setOf {a : α} {p : α → Prop} : a ∈ {x | p x} ↔ p a :=
   Iff.rfl
 #align set.mem_set_of Set.mem_setOf
 -/
@@ -307,20 +306,20 @@ theorem mem_setOf {a : α} {p : α → Prop} : a ∈ { x | p x } ↔ p a :=
 /-- If `h : a ∈ {x | p x}` then `h.out : p x`. These are definitionally equal, but this can
 nevertheless be useful for various reasons, e.g. to apply further projection notation or in an
 argument to `simp`. -/
-theorem Membership.mem.out {p : α → Prop} {a : α} (h : a ∈ { x | p x }) : p a :=
+theorem Membership.mem.out {p : α → Prop} {a : α} (h : a ∈ {x | p x}) : p a :=
   h
 #align has_mem.mem.out Membership.mem.out
 -/
 
 #print Set.nmem_setOf_iff /-
-theorem nmem_setOf_iff {a : α} {p : α → Prop} : a ∉ { x | p x } ↔ ¬p a :=
+theorem nmem_setOf_iff {a : α} {p : α → Prop} : a ∉ {x | p x} ↔ ¬p a :=
   Iff.rfl
 #align set.nmem_set_of_iff Set.nmem_setOf_iff
 -/
 
 #print Set.setOf_mem_eq /-
 @[simp]
-theorem setOf_mem_eq {s : Set α} : { x | x ∈ s } = s :=
+theorem setOf_mem_eq {s : Set α} : {x | x ∈ s} = s :=
   rfl
 #align set.set_of_mem_eq Set.setOf_mem_eq
 -/
@@ -332,7 +331,7 @@ theorem setOf_set {s : Set α} : setOf s = s :=
 -/
 
 #print Set.setOf_app_iff /-
-theorem setOf_app_iff {p : α → Prop} {x : α} : { x | p x } x ↔ p x :=
+theorem setOf_app_iff {p : α → Prop} {x : α} : {x | p x} x ↔ p x :=
   Iff.rfl
 #align set.set_of_app_iff Set.setOf_app_iff
 -/
@@ -351,16 +350,16 @@ theorem setOf_bijective : Bijective (setOf : (α → Prop) → Set α) :=
 
 #print Set.setOf_subset_setOf /-
 @[simp]
-theorem setOf_subset_setOf {p q : α → Prop} : { a | p a } ⊆ { a | q a } ↔ ∀ a, p a → q a :=
+theorem setOf_subset_setOf {p q : α → Prop} : {a | p a} ⊆ {a | q a} ↔ ∀ a, p a → q a :=
   Iff.rfl
 #align set.set_of_subset_set_of Set.setOf_subset_setOf
 -/
 
-theorem setOf_and {p q : α → Prop} : { a | p a ∧ q a } = { a | p a } ∩ { a | q a } :=
+theorem setOf_and {p q : α → Prop} : {a | p a ∧ q a} = {a | p a} ∩ {a | q a} :=
   rfl
 #align set.set_of_and Set.setOf_and
 
-theorem setOf_or {p q : α → Prop} : { a | p a ∨ q a } = { a | p a } ∪ { a | q a } :=
+theorem setOf_or {p q : α → Prop} : {a | p a ∨ q a} = {a | p a} ∪ {a | q a} :=
   rfl
 #align set.set_of_or Set.setOf_or
 
@@ -646,7 +645,7 @@ theorem nonempty_of_nonempty_subtype [Nonempty s] : s.Nonempty :=
 /-! ### Lemmas about the empty set -/
 
 
-theorem empty_def : (∅ : Set α) = { x | False } :=
+theorem empty_def : (∅ : Set α) = {x | False} :=
   rfl
 #align set.empty_def Set.empty_def
 
@@ -659,7 +658,7 @@ theorem mem_empty_iff_false (x : α) : x ∈ (∅ : Set α) ↔ False :=
 
 #print Set.setOf_false /-
 @[simp]
-theorem setOf_false : { a : α | False } = ∅ :=
+theorem setOf_false : {a : α | False} = ∅ :=
   rfl
 #align set.set_of_false Set.setOf_false
 -/
@@ -781,7 +780,7 @@ Mathematically it is the same as `α` but it has a different type.
 
 #print Set.setOf_true /-
 @[simp]
-theorem setOf_true : { x : α | True } = univ :=
+theorem setOf_true : {x : α | True} = univ :=
   rfl
 #align set.set_of_true Set.setOf_true
 -/
@@ -883,7 +882,7 @@ instance nontrivial_of_nonempty [Nonempty α] : Nontrivial (Set α) :=
 /-! ### Lemmas about union -/
 
 
-theorem union_def {s₁ s₂ : Set α} : s₁ ∪ s₂ = { a | a ∈ s₁ ∨ a ∈ s₂ } :=
+theorem union_def {s₁ s₂ : Set α} : s₁ ∪ s₂ = {a | a ∈ s₁ ∨ a ∈ s₂} :=
   rfl
 #align set.union_def Set.union_def
 
@@ -1037,7 +1036,7 @@ theorem univ_union {s : Set α} : univ ∪ s = univ :=
 /-! ### Lemmas about intersection -/
 
 
-theorem inter_def {s₁ s₂ : Set α} : s₁ ∩ s₂ = { a | a ∈ s₁ ∧ a ∈ s₂ } :=
+theorem inter_def {s₁ s₂ : Set α} : s₁ ∩ s₂ = {a | a ∈ s₁ ∧ a ∈ s₂} :=
   rfl
 #align set.inter_def Set.inter_def
 
@@ -1178,11 +1177,11 @@ theorem union_inter_cancel_right {s t : Set α} : (s ∪ t) ∩ t = t :=
   inter_eq_self_of_subset_right <| subset_union_right _ _
 #align set.union_inter_cancel_right Set.union_inter_cancel_right
 
-theorem inter_setOf_eq_sep (s : Set α) (p : α → Prop) : s ∩ { a | p a } = { a ∈ s | p a } :=
+theorem inter_setOf_eq_sep (s : Set α) (p : α → Prop) : s ∩ {a | p a} = {a ∈ s | p a} :=
   rfl
 #align set.inter_set_of_eq_sep Set.inter_setOf_eq_sep
 
-theorem setOf_inter_eq_sep (p : α → Prop) (s : Set α) : { a | p a } ∩ s = { a ∈ s | p a } :=
+theorem setOf_inter_eq_sep (p : α → Prop) (s : Set α) : {a | p a} ∩ s = {a ∈ s | p a} :=
   inter_comm _ _
 #align set.set_of_inter_eq_sep Set.setOf_inter_eq_sep
 
@@ -1253,7 +1252,7 @@ theorem inter_inter_inter_comm (s t u v : Set α) : s ∩ t ∩ (u ∩ v) = s 
 
 
 #print Set.insert_def /-
-theorem insert_def (x : α) (s : Set α) : insert x s = { y | y = x ∨ y ∈ s } :=
+theorem insert_def (x : α) (s : Set α) : insert x s = {y | y = x ∨ y ∈ s} :=
   rfl
 #align set.insert_def Set.insert_def
 -/
@@ -1455,14 +1454,14 @@ theorem mem_singleton_iff {a b : α} : a ∈ ({b} : Set α) ↔ a = b :=
 
 #print Set.setOf_eq_eq_singleton /-
 @[simp]
-theorem setOf_eq_eq_singleton {a : α} : { n | n = a } = {a} :=
+theorem setOf_eq_eq_singleton {a : α} : {n | n = a} = {a} :=
   rfl
 #align set.set_of_eq_eq_singleton Set.setOf_eq_eq_singleton
 -/
 
 #print Set.setOf_eq_eq_singleton' /-
 @[simp]
-theorem setOf_eq_eq_singleton' {a : α} : { x | a = x } = {a} :=
+theorem setOf_eq_eq_singleton' {a : α} : {x | a = x} = {a} :=
   ext fun x => eq_comm
 #align set.set_of_eq_eq_singleton' Set.setOf_eq_eq_singleton'
 -/
@@ -1536,7 +1535,7 @@ theorem singleton_subset_singleton : ({a} : Set α) ⊆ {b} ↔ a = b := by simp
 -/
 
 #print Set.set_compr_eq_eq_singleton /-
-theorem set_compr_eq_eq_singleton {a : α} : { b | b = a } = {a} :=
+theorem set_compr_eq_eq_singleton {a : α} : {b | b = a} = {a} :=
   rfl
 #align set.set_compr_eq_eq_singleton Set.set_compr_eq_eq_singleton
 -/
@@ -1640,106 +1639,106 @@ section Sep
 variable {p q : α → Prop} {x : α}
 
 #print Set.mem_sep /-
-theorem mem_sep (xs : x ∈ s) (px : p x) : x ∈ { x ∈ s | p x } :=
+theorem mem_sep (xs : x ∈ s) (px : p x) : x ∈ {x ∈ s | p x} :=
   ⟨xs, px⟩
 #align set.mem_sep Set.mem_sep
 -/
 
 @[simp]
-theorem sep_mem_eq : { x ∈ s | x ∈ t } = s ∩ t :=
+theorem sep_mem_eq : {x ∈ s | x ∈ t} = s ∩ t :=
   rfl
 #align set.sep_mem_eq Set.sep_mem_eq
 
 #print Set.mem_sep_iff /-
 @[simp]
-theorem mem_sep_iff : x ∈ { x ∈ s | p x } ↔ x ∈ s ∧ p x :=
+theorem mem_sep_iff : x ∈ {x ∈ s | p x} ↔ x ∈ s ∧ p x :=
   Iff.rfl
 #align set.mem_sep_iff Set.mem_sep_iff
 -/
 
 #print Set.sep_ext_iff /-
-theorem sep_ext_iff : { x ∈ s | p x } = { x ∈ s | q x } ↔ ∀ x ∈ s, p x ↔ q x := by
+theorem sep_ext_iff : {x ∈ s | p x} = {x ∈ s | q x} ↔ ∀ x ∈ s, p x ↔ q x := by
   simp_rw [ext_iff, mem_sep_iff, and_congr_right_iff]
 #align set.sep_ext_iff Set.sep_ext_iff
 -/
 
 #print Set.sep_eq_of_subset /-
-theorem sep_eq_of_subset (h : s ⊆ t) : { x ∈ t | x ∈ s } = s :=
+theorem sep_eq_of_subset (h : s ⊆ t) : {x ∈ t | x ∈ s} = s :=
   inter_eq_self_of_subset_right h
 #align set.sep_eq_of_subset Set.sep_eq_of_subset
 -/
 
 #print Set.sep_subset /-
 @[simp]
-theorem sep_subset (s : Set α) (p : α → Prop) : { x ∈ s | p x } ⊆ s := fun x => And.left
+theorem sep_subset (s : Set α) (p : α → Prop) : {x ∈ s | p x} ⊆ s := fun x => And.left
 #align set.sep_subset Set.sep_subset
 -/
 
 #print Set.sep_eq_self_iff_mem_true /-
 @[simp]
-theorem sep_eq_self_iff_mem_true : { x ∈ s | p x } = s ↔ ∀ x ∈ s, p x := by
+theorem sep_eq_self_iff_mem_true : {x ∈ s | p x} = s ↔ ∀ x ∈ s, p x := by
   simp_rw [ext_iff, mem_sep_iff, and_iff_left_iff_imp]
 #align set.sep_eq_self_iff_mem_true Set.sep_eq_self_iff_mem_true
 -/
 
 #print Set.sep_eq_empty_iff_mem_false /-
 @[simp]
-theorem sep_eq_empty_iff_mem_false : { x ∈ s | p x } = ∅ ↔ ∀ x ∈ s, ¬p x := by
+theorem sep_eq_empty_iff_mem_false : {x ∈ s | p x} = ∅ ↔ ∀ x ∈ s, ¬p x := by
   simp_rw [ext_iff, mem_sep_iff, mem_empty_iff_false, iff_false_iff, not_and]
 #align set.sep_eq_empty_iff_mem_false Set.sep_eq_empty_iff_mem_false
 -/
 
 #print Set.sep_true /-
 @[simp]
-theorem sep_true : { x ∈ s | True } = s :=
+theorem sep_true : {x ∈ s | True} = s :=
   inter_univ s
 #align set.sep_true Set.sep_true
 -/
 
 #print Set.sep_false /-
 @[simp]
-theorem sep_false : { x ∈ s | False } = ∅ :=
+theorem sep_false : {x ∈ s | False} = ∅ :=
   inter_empty s
 #align set.sep_false Set.sep_false
 -/
 
 #print Set.sep_empty /-
 @[simp]
-theorem sep_empty (p : α → Prop) : { x ∈ (∅ : Set α) | p x } = ∅ :=
+theorem sep_empty (p : α → Prop) : {x ∈ (∅ : Set α) | p x} = ∅ :=
   empty_inter p
 #align set.sep_empty Set.sep_empty
 -/
 
 #print Set.sep_univ /-
 @[simp]
-theorem sep_univ : { x ∈ (univ : Set α) | p x } = { x | p x } :=
+theorem sep_univ : {x ∈ (univ : Set α) | p x} = {x | p x} :=
   univ_inter p
 #align set.sep_univ Set.sep_univ
 -/
 
 @[simp]
-theorem sep_union : { x ∈ s ∪ t | p x } = { x ∈ s | p x } ∪ { x ∈ t | p x } :=
+theorem sep_union : {x ∈ s ∪ t | p x} = {x ∈ s | p x} ∪ {x ∈ t | p x} :=
   union_inter_distrib_right
 #align set.sep_union Set.sep_union
 
 @[simp]
-theorem sep_inter : { x ∈ s ∩ t | p x } = { x ∈ s | p x } ∩ { x ∈ t | p x } :=
+theorem sep_inter : {x ∈ s ∩ t | p x} = {x ∈ s | p x} ∩ {x ∈ t | p x} :=
   inter_inter_distrib_right s t p
 #align set.sep_inter Set.sep_inter
 
 @[simp]
-theorem sep_and : { x ∈ s | p x ∧ q x } = { x ∈ s | p x } ∩ { x ∈ s | q x } :=
+theorem sep_and : {x ∈ s | p x ∧ q x} = {x ∈ s | p x} ∩ {x ∈ s | q x} :=
   inter_inter_distrib_left s p q
 #align set.sep_and Set.sep_and
 
 @[simp]
-theorem sep_or : { x ∈ s | p x ∨ q x } = { x ∈ s | p x } ∪ { x ∈ s | q x } :=
+theorem sep_or : {x ∈ s | p x ∨ q x} = {x ∈ s | p x} ∪ {x ∈ s | q x} :=
   inter_union_distrib_left
 #align set.sep_or Set.sep_or
 
 #print Set.sep_setOf /-
 @[simp]
-theorem sep_setOf : { x ∈ { y | p y } | q x } = { x | p x ∧ q x } :=
+theorem sep_setOf : {x ∈ {y | p y} | q x} = {x | p x ∧ q x} :=
   rfl
 #align set.sep_set_of Set.sep_setOf
 -/
@@ -1912,7 +1911,7 @@ theorem inter_diff_distrib_right (s t u : Set α) : s \ t ∩ u = (s ∩ u) \ (t
 /-! ### Lemmas about complement -/
 
 
-theorem compl_def (s : Set α) : sᶜ = { x | x ∉ s } :=
+theorem compl_def (s : Set α) : sᶜ = {x | x ∉ s} :=
   rfl
 #align set.compl_def Set.compl_def
 
@@ -1920,7 +1919,7 @@ theorem mem_compl {s : Set α} {x : α} (h : x ∉ s) : x ∈ sᶜ :=
   h
 #align set.mem_compl Set.mem_compl
 
-theorem compl_setOf {α} (p : α → Prop) : { a | p a }ᶜ = { a | ¬p a } :=
+theorem compl_setOf {α} (p : α → Prop) : {a | p a}ᶜ = {a | ¬p a} :=
   rfl
 #align set.compl_set_of Set.compl_setOf
 
@@ -1988,12 +1987,12 @@ theorem mem_compl_singleton_iff {a x : α} : x ∈ ({a} : Set α)ᶜ ↔ x ≠ a
   Iff.rfl
 #align set.mem_compl_singleton_iff Set.mem_compl_singleton_iff
 
-theorem compl_singleton_eq (a : α) : ({a} : Set α)ᶜ = { x | x ≠ a } :=
+theorem compl_singleton_eq (a : α) : ({a} : Set α)ᶜ = {x | x ≠ a} :=
   rfl
 #align set.compl_singleton_eq Set.compl_singleton_eq
 
 @[simp]
-theorem compl_ne_eq_singleton (a : α) : ({ x | x ≠ a } : Set α)ᶜ = {a} :=
+theorem compl_ne_eq_singleton (a : α) : ({x | x ≠ a} : Set α)ᶜ = {a} :=
   compl_compl _
 #align set.compl_ne_eq_singleton Set.compl_ne_eq_singleton
 
@@ -2264,14 +2263,14 @@ theorem insert_diff_of_mem (s) (h : a ∈ t) : insert a s \ t = s \ t := by ext;
 
 theorem insert_diff_of_not_mem (s) (h : a ∉ t) : insert a s \ t = insert a (s \ t) := by
   classical
-    ext x
-    by_cases h' : x ∈ t
-    · have : x ≠ a := by
-        intro H
-        rw [H] at h' 
-        exact h h'
-      simp [h, h', this]
-    · simp [h, h']
+  ext x
+  by_cases h' : x ∈ t
+  · have : x ≠ a := by
+      intro H
+      rw [H] at h' 
+      exact h h'
+    simp [h, h', this]
+  · simp [h, h']
 #align set.insert_diff_of_not_mem Set.insert_diff_of_not_mem
 
 theorem insert_diff_self_of_not_mem {a : α} {s : Set α} (h : a ∉ s) : insert a s \ {a} = s := by
@@ -2422,7 +2421,7 @@ theorem subset_symmDiff_union_symmDiff_right (h : Disjoint t u) : s ⊆ s ∆ t
 #print Set.powerset /-
 /-- `𝒫 s = set.powerset s` is the set of all subsets of `s`. -/
 def powerset (s : Set α) : Set (Set α) :=
-  { t | t ⊆ s }
+  {t | t ⊆ s}
 #align set.powerset Set.powerset
 -/
 
@@ -2737,13 +2736,13 @@ theorem subsingleton_of_subsingleton [Subsingleton α] {s : Set α} : Set.Subsin
 -/
 
 #print Set.subsingleton_isTop /-
-theorem subsingleton_isTop (α : Type _) [PartialOrder α] : Set.Subsingleton { x : α | IsTop x } :=
+theorem subsingleton_isTop (α : Type _) [PartialOrder α] : Set.Subsingleton {x : α | IsTop x} :=
   fun x hx y hy => hx.IsMax.eq_of_le (hy x)
 #align set.subsingleton_is_top Set.subsingleton_isTop
 -/
 
 #print Set.subsingleton_isBot /-
-theorem subsingleton_isBot (α : Type _) [PartialOrder α] : Set.Subsingleton { x : α | IsBot x } :=
+theorem subsingleton_isBot (α : Type _) [PartialOrder α] : Set.Subsingleton {x : α | IsBot x} :=
   fun x hx y hy => hx.IsMin.eq_of_ge (hy x)
 #align set.subsingleton_is_bot Set.subsingleton_isBot
 -/
@@ -2870,7 +2869,7 @@ theorem nontrivial_of_exists_ne {x} (hx : x ∈ s) (h : ∃ y ∈ s, y ≠ x) :
 
 theorem Nontrivial.exists_ne (hs : s.Nontrivial) (z) : ∃ x ∈ s, x ≠ z :=
   by
-  by_contra H; push_neg  at H 
+  by_contra H; push_neg at H 
   rcases hs with ⟨x, hx, y, hy, hxy⟩
   rw [H x hx, H y hy] at hxy 
   exact hxy rfl
@@ -3346,7 +3345,7 @@ instance decidableUniv : DecidablePred (· ∈ (Set.univ : Set α)) := fun _ =>
 -/
 
 #print Set.decidableSetOf /-
-instance decidableSetOf (p : α → Prop) [Decidable (p a)] : Decidable (a ∈ { a | p a }) := by
+instance decidableSetOf (p : α → Prop) [Decidable (p a)] : Decidable (a ∈ {a | p a}) := by
   assumption
 #align set.decidable_set_of Set.decidableSetOf
 -/
@@ -3403,11 +3402,11 @@ theorem AntitoneOn.union [Preorder β] {f g : β → Set α} {s : Set β} (hf :
 namespace Set
 
 theorem monotone_setOf [Preorder α] {p : α → β → Prop} (hp : ∀ b, Monotone fun a => p a b) :
-    Monotone fun a => { b | p a b } := fun a a' h b => hp b h
+    Monotone fun a => {b | p a b} := fun a a' h b => hp b h
 #align set.monotone_set_of Set.monotone_setOf
 
 theorem antitone_setOf [Preorder α] {p : α → β → Prop} (hp : ∀ b, Antitone fun a => p a b) :
-    Antitone fun a => { b | p a b } := fun a a' h b => hp b h
+    Antitone fun a => {b | p a b} := fun a a' h b => hp b h
 #align set.antitone_set_of Set.antitone_setOf
 
 /-- Quantifying over a set is antitone in the set -/

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -206,14 +206,14 @@ theorem SetCoe.forall {s : Set α} {p : s → Prop} : (∀ x : s, p x) ↔ ∀ (
 #print SetCoe.exists /-
 @[simp]
 theorem SetCoe.exists {s : Set α} {p : s → Prop} :
-    (∃ x : s, p x) ↔ ∃ (x : _)(h : x ∈ s), p ⟨x, h⟩ :=
+    (∃ x : s, p x) ↔ ∃ (x : _) (h : x ∈ s), p ⟨x, h⟩ :=
   Subtype.exists
 #align set_coe.exists SetCoe.exists
 -/
 
 #print SetCoe.exists' /-
 theorem SetCoe.exists' {s : Set α} {p : ∀ x, x ∈ s → Prop} :
-    (∃ (x : _)(h : x ∈ s), p x h) ↔ ∃ x : s, p x x.2 :=
+    (∃ (x : _) (h : x ∈ s), p x h) ↔ ∃ x : s, p x x.2 :=
   (@SetCoe.exists _ _ fun x => p x.1 x.2).symm
 #align set_coe.exists' SetCoe.exists'
 -/
@@ -1343,7 +1343,7 @@ theorem insert_subset_insert_iff (ha : a ∉ s) : insert a s ⊆ insert a t ↔
   by
   refine' ⟨fun h x hx => _, insert_subset_insert⟩
   rcases h (subset_insert _ _ hx) with (rfl | hxt)
-  exacts[(ha hx).elim, hxt]
+  exacts [(ha hx).elim, hxt]
 #align set.insert_subset_insert_iff Set.insert_subset_insert_iff
 -/
 
@@ -1354,7 +1354,7 @@ theorem subset_insert_iff_of_not_mem (ha : a ∉ s) : s ⊆ insert a t ↔ s ⊆
 -/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a «expr ∉ » s) -/
-theorem ssubset_iff_insert {s t : Set α} : s ⊂ t ↔ ∃ (a : _)(_ : a ∉ s), insert a s ⊆ t :=
+theorem ssubset_iff_insert {s t : Set α} : s ⊂ t ↔ ∃ (a : _) (_ : a ∉ s), insert a s ⊆ t :=
   by
   simp only [insert_subset, exists_and_right, ssubset_def, not_subset]
   simp only [exists_prop, and_comm']
@@ -2268,7 +2268,7 @@ theorem insert_diff_of_not_mem (s) (h : a ∉ t) : insert a s \ t = insert a (s
     by_cases h' : x ∈ t
     · have : x ≠ a := by
         intro H
-        rw [H] at h'
+        rw [H] at h' 
         exact h h'
       simp [h, h', this]
     · simp [h, h']
@@ -2707,7 +2707,7 @@ theorem Subsingleton.eq_empty_or_singleton (hs : s.Subsingleton) : s = ∅ ∨ 
 #print Set.Subsingleton.induction_on /-
 theorem Subsingleton.induction_on {p : Set α → Prop} (hs : s.Subsingleton) (he : p ∅)
     (h₁ : ∀ x, p {x}) : p s := by rcases hs.eq_empty_or_singleton with (rfl | ⟨x, rfl⟩);
-  exacts[he, h₁ _]
+  exacts [he, h₁ _]
 #align set.subsingleton.induction_on Set.Subsingleton.induction_on
 -/
 
@@ -2792,7 +2792,7 @@ instance subsingleton_coe_of_subsingleton [Subsingleton α] {s : Set α} : Subsi
 #print Set.Nontrivial /-
 /-- A set `s` is `nontrivial` if it has at least two distinct elements. -/
 protected def Nontrivial (s : Set α) : Prop :=
-  ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s), x ≠ y
+  ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s), x ≠ y
 #align set.nontrivial Set.Nontrivial
 -/
 
@@ -2849,14 +2849,14 @@ theorem nontrivial_of_pair_subset {x y} (hxy : x ≠ y) (h : {x, y} ⊆ s) : s.N
 -/
 
 #print Set.Nontrivial.pair_subset /-
-theorem Nontrivial.pair_subset (hs : s.Nontrivial) : ∃ (x y : _)(hab : x ≠ y), {x, y} ⊆ s :=
+theorem Nontrivial.pair_subset (hs : s.Nontrivial) : ∃ (x y : _) (hab : x ≠ y), {x, y} ⊆ s :=
   let ⟨x, hx, y, hy, hxy⟩ := hs
   ⟨x, y, hxy, insert_subset.2 ⟨hx, singleton_subset_iff.2 hy⟩⟩
 #align set.nontrivial.pair_subset Set.Nontrivial.pair_subset
 -/
 
 #print Set.nontrivial_iff_pair_subset /-
-theorem nontrivial_iff_pair_subset : s.Nontrivial ↔ ∃ (x y : _)(hxy : x ≠ y), {x, y} ⊆ s :=
+theorem nontrivial_iff_pair_subset : s.Nontrivial ↔ ∃ (x y : _) (hxy : x ≠ y), {x, y} ⊆ s :=
   ⟨Nontrivial.pair_subset, fun H =>
     let ⟨x, y, hxy, h⟩ := H
     nontrivial_of_pair_subset hxy h⟩
@@ -2870,9 +2870,9 @@ theorem nontrivial_of_exists_ne {x} (hx : x ∈ s) (h : ∃ y ∈ s, y ≠ x) :
 
 theorem Nontrivial.exists_ne (hs : s.Nontrivial) (z) : ∃ x ∈ s, x ≠ z :=
   by
-  by_contra H; push_neg  at H
+  by_contra H; push_neg  at H 
   rcases hs with ⟨x, hx, y, hy, hxy⟩
-  rw [H x hx, H y hy] at hxy
+  rw [H x hx, H y hy] at hxy 
   exact hxy rfl
 #align set.nontrivial.exists_ne Set.Nontrivial.exists_ne
 
@@ -2889,8 +2889,8 @@ theorem nontrivial_of_lt [Preorder α] {x y} (hx : x ∈ s) (hy : y ∈ s) (hxy
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.nontrivial_of_exists_lt /-
-theorem nontrivial_of_exists_lt [Preorder α] (H : ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s), x < y) :
-    s.Nontrivial :=
+theorem nontrivial_of_exists_lt [Preorder α]
+    (H : ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s), x < y) : s.Nontrivial :=
   let ⟨x, hx, y, hy, hxy⟩ := H
   nontrivial_of_lt hx hy hxy
 #align set.nontrivial_of_exists_lt Set.nontrivial_of_exists_lt
@@ -2899,7 +2899,7 @@ theorem nontrivial_of_exists_lt [Preorder α] (H : ∃ (x : _)(_ : x ∈ s)(y :
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Nontrivial.exists_lt /-
 theorem Nontrivial.exists_lt [LinearOrder α] (hs : s.Nontrivial) :
-    ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s), x < y :=
+    ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s), x < y :=
   let ⟨x, hx, y, hy, hxy⟩ := hs
   Or.elim (lt_or_gt_of_ne hxy) (fun H => ⟨x, hx, y, hy, H⟩) fun H => ⟨y, hy, x, hx, H⟩
 #align set.nontrivial.exists_lt Set.Nontrivial.exists_lt
@@ -2908,7 +2908,7 @@ theorem Nontrivial.exists_lt [LinearOrder α] (hs : s.Nontrivial) :
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.nontrivial_iff_exists_lt /-
 theorem nontrivial_iff_exists_lt [LinearOrder α] :
-    s.Nontrivial ↔ ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s), x < y :=
+    s.Nontrivial ↔ ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s), x < y :=
   ⟨Nontrivial.exists_lt, nontrivial_of_exists_lt⟩
 #align set.nontrivial_iff_exists_lt Set.nontrivial_iff_exists_lt
 -/
@@ -2942,7 +2942,7 @@ theorem not_nontrivial_empty : ¬(∅ : Set α).Nontrivial := fun h => h.ne_empt
 @[simp]
 theorem not_nontrivial_singleton {x} : ¬({x} : Set α).Nontrivial := fun H =>
   by
-  rw [nontrivial_iff_exists_ne (mem_singleton x)] at H
+  rw [nontrivial_iff_exists_ne (mem_singleton x)] at H 
   exact
     let ⟨y, hy, hya⟩ := H
     hya (mem_singleton_iff.1 hy)
@@ -2950,7 +2950,7 @@ theorem not_nontrivial_singleton {x} : ¬({x} : Set α).Nontrivial := fun H =>
 -/
 
 #print Set.Nontrivial.ne_singleton /-
-theorem Nontrivial.ne_singleton {x} (hs : s.Nontrivial) : s ≠ {x} := fun H => by rw [H] at hs;
+theorem Nontrivial.ne_singleton {x} (hs : s.Nontrivial) : s ≠ {x} := fun H => by rw [H] at hs ;
   exact not_nontrivial_singleton hs
 #align set.nontrivial.ne_singleton Set.Nontrivial.ne_singleton
 -/
@@ -3163,7 +3163,7 @@ variable [LinearOrder α] [LinearOrder β] {f : α → β}
 downright. -/
 theorem not_monotoneOn_not_antitoneOn_iff_exists_le_le :
     ¬MonotoneOn f s ∧ ¬AntitoneOn f s ↔
-      ∃ (a : _)(_ : a ∈ s)(b : _)(_ : b ∈ s)(c : _)(_ : c ∈ s),
+      ∃ (a : _) (_ : a ∈ s) (b : _) (_ : b ∈ s) (c : _) (_ : c ∈ s),
         a ≤ b ∧ b ≤ c ∧ (f a < f b ∧ f c < f b ∨ f b < f a ∧ f b < f c) :=
   by
   simp [monotone_on_iff_monotone, antitone_on_iff_antitone, and_assoc', exists_and_left,
@@ -3177,7 +3177,7 @@ theorem not_monotoneOn_not_antitoneOn_iff_exists_le_le :
 downright. -/
 theorem not_monotoneOn_not_antitoneOn_iff_exists_lt_lt :
     ¬MonotoneOn f s ∧ ¬AntitoneOn f s ↔
-      ∃ (a : _)(_ : a ∈ s)(b : _)(_ : b ∈ s)(c : _)(_ : c ∈ s),
+      ∃ (a : _) (_ : a ∈ s) (b : _) (_ : b ∈ s) (c : _) (_ : c ∈ s),
         a < b ∧ b < c ∧ (f a < f b ∧ f c < f b ∨ f b < f a ∧ f b < f c) :=
   by
   simp [monotone_on_iff_monotone, antitone_on_iff_antitone, and_assoc', exists_and_left,

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -2736,13 +2736,17 @@ theorem subsingleton_of_subsingleton [Subsingleton α] {s : Set α} : Set.Subsin
 #align set.subsingleton_of_subsingleton Set.subsingleton_of_subsingleton
 -/
 
+#print Set.subsingleton_isTop /-
 theorem subsingleton_isTop (α : Type _) [PartialOrder α] : Set.Subsingleton { x : α | IsTop x } :=
   fun x hx y hy => hx.IsMax.eq_of_le (hy x)
 #align set.subsingleton_is_top Set.subsingleton_isTop
+-/
 
+#print Set.subsingleton_isBot /-
 theorem subsingleton_isBot (α : Type _) [PartialOrder α] : Set.Subsingleton { x : α | IsBot x } :=
   fun x hx y hy => hx.IsMin.eq_of_ge (hy x)
 #align set.subsingleton_is_bot Set.subsingleton_isBot
+-/
 
 #print Set.exists_eq_singleton_iff_nonempty_subsingleton /-
 theorem exists_eq_singleton_iff_nonempty_subsingleton :
@@ -2876,30 +2880,38 @@ theorem nontrivial_iff_exists_ne {x} (hx : x ∈ s) : s.Nontrivial ↔ ∃ y ∈
   ⟨fun H => H.exists_ne _, nontrivial_of_exists_ne hx⟩
 #align set.nontrivial_iff_exists_ne Set.nontrivial_iff_exists_ne
 
+#print Set.nontrivial_of_lt /-
 theorem nontrivial_of_lt [Preorder α] {x y} (hx : x ∈ s) (hy : y ∈ s) (hxy : x < y) :
     s.Nontrivial :=
   ⟨x, hx, y, hy, ne_of_lt hxy⟩
 #align set.nontrivial_of_lt Set.nontrivial_of_lt
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+#print Set.nontrivial_of_exists_lt /-
 theorem nontrivial_of_exists_lt [Preorder α] (H : ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s), x < y) :
     s.Nontrivial :=
   let ⟨x, hx, y, hy, hxy⟩ := H
   nontrivial_of_lt hx hy hxy
 #align set.nontrivial_of_exists_lt Set.nontrivial_of_exists_lt
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+#print Set.Nontrivial.exists_lt /-
 theorem Nontrivial.exists_lt [LinearOrder α] (hs : s.Nontrivial) :
     ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s), x < y :=
   let ⟨x, hx, y, hy, hxy⟩ := hs
   Or.elim (lt_or_gt_of_ne hxy) (fun H => ⟨x, hx, y, hy, H⟩) fun H => ⟨y, hy, x, hx, H⟩
 #align set.nontrivial.exists_lt Set.Nontrivial.exists_lt
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+#print Set.nontrivial_iff_exists_lt /-
 theorem nontrivial_iff_exists_lt [LinearOrder α] :
     s.Nontrivial ↔ ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s), x < y :=
   ⟨Nontrivial.exists_lt, nontrivial_of_exists_lt⟩
 #align set.nontrivial_iff_exists_lt Set.nontrivial_iff_exists_lt
+-/
 
 #print Set.Nontrivial.nonempty /-
 protected theorem Nontrivial.nonempty (hs : s.Nontrivial) : s.Nonempty :=
@@ -3146,6 +3158,7 @@ section LinearOrder
 variable [LinearOrder α] [LinearOrder β] {f : α → β}
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a b c «expr ∈ » s) -/
+#print Set.not_monotoneOn_not_antitoneOn_iff_exists_le_le /-
 /-- A function between linear orders which is neither monotone nor antitone makes a dent upright or
 downright. -/
 theorem not_monotoneOn_not_antitoneOn_iff_exists_le_le :
@@ -3156,8 +3169,10 @@ theorem not_monotoneOn_not_antitoneOn_iff_exists_le_le :
   simp [monotone_on_iff_monotone, antitone_on_iff_antitone, and_assoc', exists_and_left,
     not_monotone_not_antitone_iff_exists_le_le, @and_left_comm (_ ∈ s)]
 #align set.not_monotone_on_not_antitone_on_iff_exists_le_le Set.not_monotoneOn_not_antitoneOn_iff_exists_le_le
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a b c «expr ∈ » s) -/
+#print Set.not_monotoneOn_not_antitoneOn_iff_exists_lt_lt /-
 /-- A function between linear orders which is neither monotone nor antitone makes a dent upright or
 downright. -/
 theorem not_monotoneOn_not_antitoneOn_iff_exists_lt_lt :
@@ -3168,6 +3183,7 @@ theorem not_monotoneOn_not_antitoneOn_iff_exists_lt_lt :
   simp [monotone_on_iff_monotone, antitone_on_iff_antitone, and_assoc', exists_and_left,
     not_monotone_not_antitone_iff_exists_lt_lt, @and_left_comm (_ ∈ s)]
 #align set.not_monotone_on_not_antitone_on_iff_exists_lt_lt Set.not_monotoneOn_not_antitoneOn_iff_exists_lt_lt
+-/
 
 end LinearOrder

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -109,45 +109,21 @@ instance : Union (Set α) :=
 instance : Inter (Set α) :=
   ⟨(· ⊓ ·)⟩
 
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-Case conversion may be inaccurate. Consider using '#align set.top_eq_univ Set.top_eq_univₓ'. -/
 @[simp]
 theorem top_eq_univ : (⊤ : Set α) = univ :=
   rfl
 #align set.top_eq_univ Set.top_eq_univ
 
-/- warning: set.bot_eq_empty -> Set.bot_eq_empty is a dubious translation:
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.bot_eq_empty Set.bot_eq_emptyₓ'. -/
 @[simp]
 theorem bot_eq_empty : (⊥ : Set α) = ∅ :=
   rfl
 #align set.bot_eq_empty Set.bot_eq_empty
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.sup_eq_union Set.sup_eq_unionₓ'. -/
 @[simp]
 theorem sup_eq_union : ((· ⊔ ·) : Set α → Set α → Set α) = (· ∪ ·) :=
   rfl
 #align set.sup_eq_union Set.sup_eq_union
 
-/- warning: set.inf_eq_inter -> Set.inf_eq_inter is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.inf_eq_inter Set.inf_eq_interₓ'. -/
 @[simp]
 theorem inf_eq_inter : ((· ⊓ ·) : Set α → Set α → Set α) = (· ∩ ·) :=
   rfl
@@ -160,12 +136,6 @@ theorem le_eq_subset : ((· ≤ ·) : Set α → Set α → Prop) = (· ⊆ ·)
 #align set.le_eq_subset Set.le_eq_subset
 -/
 
-/- warning: set.lt_eq_ssubset -> Set.lt_eq_ssubset is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.lt_eq_ssubset Set.lt_eq_ssubsetₓ'. -/
 @[simp]
 theorem lt_eq_ssubset : ((· < ·) : Set α → Set α → Prop) = (· ⊂ ·) :=
   rfl
@@ -177,12 +147,6 @@ theorem le_iff_subset : s ≤ t ↔ s ⊆ t :=
 #align set.le_iff_subset Set.le_iff_subset
 -/
 
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 theorem lt_iff_ssubset : s < t ↔ s ⊂ t :=
   Iff.rfl
 #align set.lt_iff_ssubset Set.lt_iff_ssubset
@@ -191,12 +155,6 @@ alias le_iff_subset ↔ _root_.has_le.le.subset _root_.has_subset.subset.le
 #align has_le.le.subset LE.le.subset
 #align has_subset.subset.le HasSubset.Subset.le
 
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 alias lt_iff_ssubset ↔ _root_.has_lt.lt.ssubset _root_.has_ssubset.ssubset.lt
 #align has_lt.lt.ssubset LT.lt.sSubset
 #align has_ssubset.ssubset.lt HasSSubset.SSubset.lt
@@ -398,22 +356,10 @@ theorem setOf_subset_setOf {p q : α → Prop} : { a | p a } ⊆ { a | q a } ↔
 #align set.set_of_subset_set_of Set.setOf_subset_setOf
 -/
 
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 theorem setOf_and {p q : α → Prop} : { a | p a ∧ q a } = { a | p a } ∩ { a | q a } :=
   rfl
 #align set.set_of_and Set.setOf_and
 
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-Case conversion may be inaccurate. Consider using '#align set.set_of_or Set.setOf_orₓ'. -/
 theorem setOf_or {p q : α → Prop} : { a | p a ∨ q a } = { a | p a } ∪ { a | q a } :=
   rfl
 #align set.set_of_or Set.setOf_or
@@ -449,12 +395,6 @@ theorem subset_def : (s ⊆ t) = ∀ x, x ∈ s → x ∈ t :=
 #align set.subset_def Set.subset_def
 -/
 
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-Case conversion may be inaccurate. Consider using '#align set.ssubset_def Set.ssubset_defₓ'. -/
 theorem ssubset_def : (s ⊂ t) = (s ⊆ t ∧ ¬t ⊆ s) :=
   rfl
 #align set.ssubset_def Set.ssubset_def
@@ -515,75 +455,33 @@ theorem not_mem_subset (h : s ⊆ t) : a ∉ t → a ∉ s :=
 #align set.not_mem_subset Set.not_mem_subset
 -/
 
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-Case conversion may be inaccurate. Consider using '#align set.not_subset Set.not_subsetₓ'. -/
 theorem not_subset : ¬s ⊆ t ↔ ∃ a ∈ s, a ∉ t := by simp only [subset_def, not_forall]
 #align set.not_subset Set.not_subset
 
 /-! ### Definition of strict subsets `s ⊂ t` and basic properties. -/
 
 
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-Case conversion may be inaccurate. Consider using '#align set.eq_or_ssubset_of_subset Set.eq_or_ssubset_of_subsetₓ'. -/
 protected theorem eq_or_ssubset_of_subset (h : s ⊆ t) : s = t ∨ s ⊂ t :=
   eq_or_lt_of_le h
 #align set.eq_or_ssubset_of_subset Set.eq_or_ssubset_of_subset
 
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-Case conversion may be inaccurate. Consider using '#align set.exists_of_ssubset Set.exists_of_ssubsetₓ'. -/
 theorem exists_of_ssubset {s t : Set α} (h : s ⊂ t) : ∃ x ∈ t, x ∉ s :=
   not_subset.1 h.2
 #align set.exists_of_ssubset Set.exists_of_ssubset
 
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-Case conversion may be inaccurate. Consider using '#align set.ssubset_iff_subset_ne Set.ssubset_iff_subset_neₓ'. -/
 protected theorem ssubset_iff_subset_ne {s t : Set α} : s ⊂ t ↔ s ⊆ t ∧ s ≠ t :=
   @lt_iff_le_and_ne (Set α) _ s t
 #align set.ssubset_iff_subset_ne Set.ssubset_iff_subset_ne
 
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-Case conversion may be inaccurate. Consider using '#align set.ssubset_iff_of_subset Set.ssubset_iff_of_subsetₓ'. -/
 theorem ssubset_iff_of_subset {s t : Set α} (h : s ⊆ t) : s ⊂ t ↔ ∃ x ∈ t, x ∉ s :=
   ⟨exists_of_ssubset, fun ⟨x, hxt, hxs⟩ => ⟨h, fun h => hxs <| h hxt⟩⟩
 #align set.ssubset_iff_of_subset Set.ssubset_iff_of_subset
 
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-Case conversion may be inaccurate. Consider using '#align set.ssubset_of_ssubset_of_subset Set.ssubset_of_ssubset_of_subsetₓ'. -/
 protected theorem ssubset_of_ssubset_of_subset {s₁ s₂ s₃ : Set α} (hs₁s₂ : s₁ ⊂ s₂)
     (hs₂s₃ : s₂ ⊆ s₃) : s₁ ⊂ s₃ :=
   ⟨Subset.trans hs₁s₂.1 hs₂s₃, fun hs₃s₁ => hs₁s₂.2 (Subset.trans hs₂s₃ hs₃s₁)⟩
 #align set.ssubset_of_ssubset_of_subset Set.ssubset_of_ssubset_of_subset
 
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-Case conversion may be inaccurate. Consider using '#align set.ssubset_of_subset_of_ssubset Set.ssubset_of_subset_of_ssubsetₓ'. -/
 protected theorem ssubset_of_subset_of_ssubset {s₁ s₂ s₃ : Set α} (hs₁s₂ : s₁ ⊆ s₂)
     (hs₂s₃ : s₂ ⊂ s₃) : s₁ ⊂ s₃ :=
   ⟨Subset.trans hs₁s₂ hs₂s₃.1, fun hs₃s₁ => hs₂s₃.2 (Subset.trans hs₃s₁ hs₁s₂)⟩
@@ -662,124 +560,52 @@ theorem Nonempty.mono (ht : s ⊆ t) (hs : s.Nonempty) : t.Nonempty :=
 #align set.nonempty.mono Set.Nonempty.mono
 -/
 
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-Case conversion may be inaccurate. Consider using '#align set.nonempty_of_not_subset Set.nonempty_of_not_subsetₓ'. -/
 theorem nonempty_of_not_subset (h : ¬s ⊆ t) : (s \ t).Nonempty :=
   let ⟨x, xs, xt⟩ := not_subset.1 h
   ⟨x, xs, xt⟩
 #align set.nonempty_of_not_subset Set.nonempty_of_not_subset
 
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-Case conversion may be inaccurate. Consider using '#align set.nonempty_of_ssubset Set.nonempty_of_ssubsetₓ'. -/
 theorem nonempty_of_ssubset (ht : s ⊂ t) : (t \ s).Nonempty :=
   nonempty_of_not_subset ht.2
 #align set.nonempty_of_ssubset Set.nonempty_of_ssubset
 
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-Case conversion may be inaccurate. Consider using '#align set.nonempty.of_diff Set.Nonempty.of_diffₓ'. -/
 theorem Nonempty.of_diff (h : (s \ t).Nonempty) : s.Nonempty :=
   h.imp fun _ => And.left
 #align set.nonempty.of_diff Set.Nonempty.of_diff
 
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-Case conversion may be inaccurate. Consider using '#align set.nonempty_of_ssubset' Set.nonempty_of_ssubset'ₓ'. -/
 theorem nonempty_of_ssubset' (ht : s ⊂ t) : t.Nonempty :=
   (nonempty_of_ssubset ht).of_diff
 #align set.nonempty_of_ssubset' Set.nonempty_of_ssubset'
 
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-Case conversion may be inaccurate. Consider using '#align set.nonempty.inl Set.Nonempty.inlₓ'. -/
 theorem Nonempty.inl (hs : s.Nonempty) : (s ∪ t).Nonempty :=
   hs.imp fun _ => Or.inl
 #align set.nonempty.inl Set.Nonempty.inl
 
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-Case conversion may be inaccurate. Consider using '#align set.nonempty.inr Set.Nonempty.inrₓ'. -/
 theorem Nonempty.inr (ht : t.Nonempty) : (s ∪ t).Nonempty :=
   ht.imp fun _ => Or.inr
 #align set.nonempty.inr Set.Nonempty.inr
 
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 @[simp]
 theorem union_nonempty : (s ∪ t).Nonempty ↔ s.Nonempty ∨ t.Nonempty :=
   exists_or
 #align set.union_nonempty Set.union_nonempty
 
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-Case conversion may be inaccurate. Consider using '#align set.nonempty.left Set.Nonempty.leftₓ'. -/
 theorem Nonempty.left (h : (s ∩ t).Nonempty) : s.Nonempty :=
   h.imp fun _ => And.left
 #align set.nonempty.left Set.Nonempty.left
 
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-Case conversion may be inaccurate. Consider using '#align set.nonempty.right Set.Nonempty.rightₓ'. -/
 theorem Nonempty.right (h : (s ∩ t).Nonempty) : t.Nonempty :=
   h.imp fun _ => And.right
 #align set.nonempty.right Set.Nonempty.right
 
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-Case conversion may be inaccurate. Consider using '#align set.inter_nonempty Set.inter_nonemptyₓ'. -/
 theorem inter_nonempty : (s ∩ t).Nonempty ↔ ∃ x, x ∈ s ∧ x ∈ t :=
   Iff.rfl
 #align set.inter_nonempty Set.inter_nonempty
 
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-Case conversion may be inaccurate. Consider using '#align set.inter_nonempty_iff_exists_left Set.inter_nonempty_iff_exists_leftₓ'. -/
 theorem inter_nonempty_iff_exists_left : (s ∩ t).Nonempty ↔ ∃ x ∈ s, x ∈ t := by
   simp_rw [inter_nonempty, exists_prop]
 #align set.inter_nonempty_iff_exists_left Set.inter_nonempty_iff_exists_left
 
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-Case conversion may be inaccurate. Consider using '#align set.inter_nonempty_iff_exists_right Set.inter_nonempty_iff_exists_rightₓ'. -/
 theorem inter_nonempty_iff_exists_right : (s ∩ t).Nonempty ↔ ∃ x ∈ t, x ∈ s := by
   simp_rw [inter_nonempty, exists_prop, and_comm']
 #align set.inter_nonempty_iff_exists_right Set.inter_nonempty_iff_exists_right
@@ -820,12 +646,6 @@ theorem nonempty_of_nonempty_subtype [Nonempty s] : s.Nonempty :=
 /-! ### Lemmas about the empty set -/
 
 
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-Case conversion may be inaccurate. Consider using '#align set.empty_def Set.empty_defₓ'. -/
 theorem empty_def : (∅ : Set α) = { x | False } :=
   rfl
 #align set.empty_def Set.empty_def
@@ -941,23 +761,11 @@ theorem ball_empty_iff {p : α → Prop} : (∀ x ∈ (∅ : Set α), p x) ↔ T
 instance (α : Type u) : IsEmpty.{u + 1} (∅ : Set α) :=
   ⟨fun x => x.2⟩
 
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-Case conversion may be inaccurate. Consider using '#align set.empty_ssubset Set.empty_ssubsetₓ'. -/
 @[simp]
 theorem empty_ssubset : ∅ ⊂ s ↔ s.Nonempty :=
   (@bot_lt_iff_ne_bot (Set α) _ _ _).trans nonempty_iff_ne_empty.symm
 #align set.empty_ssubset Set.empty_ssubset
 
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-Case conversion may be inaccurate. Consider using '#align set.nonempty.empty_ssubset Set.Nonempty.empty_ssubsetₓ'. -/
 alias empty_ssubset ↔ _ nonempty.empty_ssubset
 #align set.nonempty.empty_ssubset Set.Nonempty.empty_ssubset
 
@@ -1062,12 +870,6 @@ theorem univ_unique [Unique α] : @Set.univ α = {default} :=
 #align set.univ_unique Set.univ_unique
 -/
 
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-Case conversion may be inaccurate. Consider using '#align set.ssubset_univ_iff Set.ssubset_univ_iffₓ'. -/
 theorem ssubset_univ_iff : s ⊂ univ ↔ s ≠ univ :=
   lt_top_iff_ne_top
 #align set.ssubset_univ_iff Set.ssubset_univ_iff
@@ -1081,362 +883,152 @@ instance nontrivial_of_nonempty [Nonempty α] : Nontrivial (Set α) :=
 /-! ### Lemmas about union -/
 
 
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-Case conversion may be inaccurate. Consider using '#align set.union_def Set.union_defₓ'. -/
 theorem union_def {s₁ s₂ : Set α} : s₁ ∪ s₂ = { a | a ∈ s₁ ∨ a ∈ s₂ } :=
   rfl
 #align set.union_def Set.union_def
 
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-Case conversion may be inaccurate. Consider using '#align set.mem_union_left Set.mem_union_leftₓ'. -/
 theorem mem_union_left {x : α} {a : Set α} (b : Set α) : x ∈ a → x ∈ a ∪ b :=
   Or.inl
 #align set.mem_union_left Set.mem_union_left
 
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-Case conversion may be inaccurate. Consider using '#align set.mem_union_right Set.mem_union_rightₓ'. -/
 theorem mem_union_right {x : α} {b : Set α} (a : Set α) : x ∈ b → x ∈ a ∪ b :=
   Or.inr
 #align set.mem_union_right Set.mem_union_right
 
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-Case conversion may be inaccurate. Consider using '#align set.mem_or_mem_of_mem_union Set.mem_or_mem_of_mem_unionₓ'. -/
 theorem mem_or_mem_of_mem_union {x : α} {a b : Set α} (H : x ∈ a ∪ b) : x ∈ a ∨ x ∈ b :=
   H
 #align set.mem_or_mem_of_mem_union Set.mem_or_mem_of_mem_union
 
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-Case conversion may be inaccurate. Consider using '#align set.mem_union.elim Set.MemUnion.elimₓ'. -/
 theorem MemUnion.elim {x : α} {a b : Set α} {P : Prop} (H₁ : x ∈ a ∪ b) (H₂ : x ∈ a → P)
     (H₃ : x ∈ b → P) : P :=
   Or.elim H₁ H₂ H₃
 #align set.mem_union.elim Set.MemUnion.elim
 
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 @[simp]
 theorem mem_union (x : α) (a b : Set α) : x ∈ a ∪ b ↔ x ∈ a ∨ x ∈ b :=
   Iff.rfl
 #align set.mem_union Set.mem_union
 
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 @[simp]
 theorem union_self (a : Set α) : a ∪ a = a :=
   ext fun x => or_self_iff _
 #align set.union_self Set.union_self
 
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 @[simp]
 theorem union_empty (a : Set α) : a ∪ ∅ = a :=
   ext fun x => or_false_iff _
 #align set.union_empty Set.union_empty
 
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 @[simp]
 theorem empty_union (a : Set α) : ∅ ∪ a = a :=
   ext fun x => false_or_iff _
 #align set.empty_union Set.empty_union
 
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 theorem union_comm (a b : Set α) : a ∪ b = b ∪ a :=
   ext fun x => or_comm
 #align set.union_comm Set.union_comm
 
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 theorem union_assoc (a b c : Set α) : a ∪ b ∪ c = a ∪ (b ∪ c) :=
   ext fun x => or_assoc
 #align set.union_assoc Set.union_assoc
 
-/- warning: set.union_is_assoc -> Set.union_isAssoc is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}}, IsAssociative.{u1} (Set.{u1} α) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α))
-but is expected to have type
-  forall {α : Type.{u1}}, IsAssociative.{u1} (Set.{u1} α) (fun (x._@.Mathlib.Data.Set.Basic._hyg.7931 : Set.{u1} α) (x._@.Mathlib.Data.Set.Basic._hyg.7933 : Set.{u1} α) => Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) x._@.Mathlib.Data.Set.Basic._hyg.7931 x._@.Mathlib.Data.Set.Basic._hyg.7933)
-Case conversion may be inaccurate. Consider using '#align set.union_is_assoc Set.union_isAssocₓ'. -/
 instance union_isAssoc : IsAssociative (Set α) (· ∪ ·) :=
   ⟨union_assoc⟩
 #align set.union_is_assoc Set.union_isAssoc
 
-/- warning: set.union_is_comm -> Set.union_isComm is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}}, IsCommutative.{u1} (Set.{u1} α) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α))
-but is expected to have type
-  forall {α : Type.{u1}}, IsCommutative.{u1} (Set.{u1} α) (fun (x._@.Mathlib.Data.Set.Basic._hyg.7976 : Set.{u1} α) (x._@.Mathlib.Data.Set.Basic._hyg.7978 : Set.{u1} α) => Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) x._@.Mathlib.Data.Set.Basic._hyg.7976 x._@.Mathlib.Data.Set.Basic._hyg.7978)
-Case conversion may be inaccurate. Consider using '#align set.union_is_comm Set.union_isCommₓ'. -/
 instance union_isComm : IsCommutative (Set α) (· ∪ ·) :=
   ⟨union_comm⟩
 #align set.union_is_comm Set.union_isComm
 
-/- warning: set.union_left_comm -> Set.union_left_comm is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} (s₁ : Set.{u1} α) (s₂ : Set.{u1} α) (s₃ : Set.{u1} α), Eq.{succ u1} (Set.{u1} α) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s₁ (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s₂ s₃)) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s₂ (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s₁ s₃))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.union_left_comm Set.union_left_commₓ'. -/
 theorem union_left_comm (s₁ s₂ s₃ : Set α) : s₁ ∪ (s₂ ∪ s₃) = s₂ ∪ (s₁ ∪ s₃) :=
   ext fun x => or_left_comm
 #align set.union_left_comm Set.union_left_comm
 
-/- warning: set.union_right_comm -> Set.union_right_comm is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} (s₁ : Set.{u1} α) (s₂ : Set.{u1} α) (s₃ : Set.{u1} α), Eq.{succ u1} (Set.{u1} α) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s₁ s₂) s₃) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s₁ s₃) s₂)
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.union_right_comm Set.union_right_commₓ'. -/
 theorem union_right_comm (s₁ s₂ s₃ : Set α) : s₁ ∪ s₂ ∪ s₃ = s₁ ∪ s₃ ∪ s₂ :=
   ext fun x => or_right_comm
 #align set.union_right_comm Set.union_right_comm
 
-/- warning: set.union_eq_left_iff_subset -> Set.union_eq_left_iff_subset is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.union_eq_left_iff_subset Set.union_eq_left_iff_subsetₓ'. -/
 @[simp]
 theorem union_eq_left_iff_subset {s t : Set α} : s ∪ t = s ↔ t ⊆ s :=
   sup_eq_left
 #align set.union_eq_left_iff_subset Set.union_eq_left_iff_subset
 
-/- warning: set.union_eq_right_iff_subset -> Set.union_eq_right_iff_subset is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {s : Set.{u1} α} {t : Set.{u1} α}, Iff (Eq.{succ u1} (Set.{u1} α) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t) t) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s t)
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.union_eq_right_iff_subset Set.union_eq_right_iff_subsetₓ'. -/
 @[simp]
 theorem union_eq_right_iff_subset {s t : Set α} : s ∪ t = t ↔ s ⊆ t :=
   sup_eq_right
 #align set.union_eq_right_iff_subset Set.union_eq_right_iff_subset
 
-/- warning: set.union_eq_self_of_subset_left -> Set.union_eq_self_of_subset_left is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s t) -> (Eq.{succ u1} (Set.{u1} α) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t) t)
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.union_eq_self_of_subset_left Set.union_eq_self_of_subset_leftₓ'. -/
 theorem union_eq_self_of_subset_left {s t : Set α} (h : s ⊆ t) : s ∪ t = t :=
   union_eq_right_iff_subset.mpr h
 #align set.union_eq_self_of_subset_left Set.union_eq_self_of_subset_left
 
-/- warning: set.union_eq_self_of_subset_right -> Set.union_eq_self_of_subset_right is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t s) -> (Eq.{succ u1} (Set.{u1} α) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t) s)
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.union_eq_self_of_subset_right Set.union_eq_self_of_subset_rightₓ'. -/
 theorem union_eq_self_of_subset_right {s t : Set α} (h : t ⊆ s) : s ∪ t = s :=
   union_eq_left_iff_subset.mpr h
 #align set.union_eq_self_of_subset_right Set.union_eq_self_of_subset_right
 
-/- warning: set.subset_union_left -> Set.subset_union_left is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} (s : Set.{u1} α) (t : Set.{u1} α), HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.subset_union_left Set.subset_union_leftₓ'. -/
 @[simp]
 theorem subset_union_left (s t : Set α) : s ⊆ s ∪ t := fun x => Or.inl
 #align set.subset_union_left Set.subset_union_left
 
-/- warning: set.subset_union_right -> Set.subset_union_right is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} (s : Set.{u1} α) (t : Set.{u1} α), HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.subset_union_right Set.subset_union_rightₓ'. -/
 @[simp]
 theorem subset_union_right (s t : Set α) : t ⊆ s ∪ t := fun x => Or.inr
 #align set.subset_union_right Set.subset_union_right
 
-/- warning: set.union_subset -> Set.union_subset is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {s : Set.{u1} α} {t : Set.{u1} α} {r : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s r) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t r) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t) r)
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.union_subset Set.union_subsetₓ'. -/
 theorem union_subset {s t r : Set α} (sr : s ⊆ r) (tr : t ⊆ r) : s ∪ t ⊆ r := fun x =>
   Or.ndrec (@sr _) (@tr _)
 #align set.union_subset Set.union_subset
 
-/- warning: set.union_subset_iff -> Set.union_subset_iff is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.union_subset_iff Set.union_subset_iffₓ'. -/
 @[simp]
 theorem union_subset_iff {s t u : Set α} : s ∪ t ⊆ u ↔ s ⊆ u ∧ t ⊆ u :=
   (forall_congr' fun x => or_imp).trans forall_and
 #align set.union_subset_iff Set.union_subset_iff
 
-/- warning: set.union_subset_union -> Set.union_subset_union is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.union_subset_union Set.union_subset_unionₓ'. -/
 theorem union_subset_union {s₁ s₂ t₁ t₂ : Set α} (h₁ : s₁ ⊆ s₂) (h₂ : t₁ ⊆ t₂) :
     s₁ ∪ t₁ ⊆ s₂ ∪ t₂ := fun x => Or.imp (@h₁ _) (@h₂ _)
 #align set.union_subset_union Set.union_subset_union
 
-/- warning: set.union_subset_union_left -> Set.union_subset_union_left is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.union_subset_union_left Set.union_subset_union_leftₓ'. -/
 theorem union_subset_union_left {s₁ s₂ : Set α} (t) (h : s₁ ⊆ s₂) : s₁ ∪ t ⊆ s₂ ∪ t :=
   union_subset_union h Subset.rfl
 #align set.union_subset_union_left Set.union_subset_union_left
 
-/- warning: set.union_subset_union_right -> Set.union_subset_union_right is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} (s : Set.{u1} α) {t₁ : Set.{u1} α} {t₂ : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t₁ t₂) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t₁) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t₂))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.union_subset_union_right Set.union_subset_union_rightₓ'. -/
 theorem union_subset_union_right (s) {t₁ t₂ : Set α} (h : t₁ ⊆ t₂) : s ∪ t₁ ⊆ s ∪ t₂ :=
   union_subset_union Subset.rfl h
 #align set.union_subset_union_right Set.union_subset_union_right
 
-/- warning: set.subset_union_of_subset_left -> Set.subset_union_of_subset_left is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.subset_union_of_subset_left Set.subset_union_of_subset_leftₓ'. -/
 theorem subset_union_of_subset_left {s t : Set α} (h : s ⊆ t) (u : Set α) : s ⊆ t ∪ u :=
   Subset.trans h (subset_union_left t u)
 #align set.subset_union_of_subset_left Set.subset_union_of_subset_left
 
-/- warning: set.subset_union_of_subset_right -> Set.subset_union_of_subset_right is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {s : Set.{u1} α} {u : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s u) -> (forall (t : Set.{u1} α), HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) t u))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.subset_union_of_subset_right Set.subset_union_of_subset_rightₓ'. -/
 theorem subset_union_of_subset_right {s u : Set α} (h : s ⊆ u) (t : Set α) : s ⊆ t ∪ u :=
   Subset.trans h (subset_union_right t u)
 #align set.subset_union_of_subset_right Set.subset_union_of_subset_right
 
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 theorem union_congr_left (ht : t ⊆ s ∪ u) (hu : u ⊆ s ∪ t) : s ∪ t = s ⊔ u :=
   sup_congr_left ht hu
 #align set.union_congr_left Set.union_congr_left
 
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-Case conversion may be inaccurate. Consider using '#align set.union_congr_right Set.union_congr_rightₓ'. -/
 theorem union_congr_right (hs : s ⊆ t ∪ u) (ht : t ⊆ s ∪ u) : s ∪ u = t ∪ u :=
   sup_congr_right hs ht
 #align set.union_congr_right Set.union_congr_right
 
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 theorem union_eq_union_iff_left : s ∪ t = s ∪ u ↔ t ⊆ s ∪ u ∧ u ⊆ s ∪ t :=
   sup_eq_sup_iff_left
 #align set.union_eq_union_iff_left Set.union_eq_union_iff_left
 
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 theorem union_eq_union_iff_right : s ∪ u = t ∪ u ↔ s ⊆ t ∪ u ∧ t ⊆ s ∪ u :=
   sup_eq_sup_iff_right
 #align set.union_eq_union_iff_right Set.union_eq_union_iff_right
 
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-Case conversion may be inaccurate. Consider using '#align set.union_empty_iff Set.union_empty_iffₓ'. -/
 @[simp]
 theorem union_empty_iff {s t : Set α} : s ∪ t = ∅ ↔ s = ∅ ∧ t = ∅ := by
   simp only [← subset_empty_iff] <;> exact union_subset_iff
 #align set.union_empty_iff Set.union_empty_iff
 
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 @[simp]
 theorem union_univ {s : Set α} : s ∪ univ = univ :=
   sup_top_eq
 #align set.union_univ Set.union_univ
 
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 @[simp]
 theorem univ_union {s : Set α} : univ ∪ s = univ :=
   top_sup_eq
@@ -1445,361 +1037,151 @@ theorem univ_union {s : Set α} : univ ∪ s = univ :=
 /-! ### Lemmas about intersection -/
 
 
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 theorem inter_def {s₁ s₂ : Set α} : s₁ ∩ s₂ = { a | a ∈ s₁ ∧ a ∈ s₂ } :=
   rfl
 #align set.inter_def Set.inter_def
 
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 @[simp]
 theorem mem_inter_iff (x : α) (a b : Set α) : x ∈ a ∩ b ↔ x ∈ a ∧ x ∈ b :=
   Iff.rfl
 #align set.mem_inter_iff Set.mem_inter_iff
 
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 theorem mem_inter {x : α} {a b : Set α} (ha : x ∈ a) (hb : x ∈ b) : x ∈ a ∩ b :=
   ⟨ha, hb⟩
 #align set.mem_inter Set.mem_inter
 
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 theorem mem_of_mem_inter_left {x : α} {a b : Set α} (h : x ∈ a ∩ b) : x ∈ a :=
   h.left
 #align set.mem_of_mem_inter_left Set.mem_of_mem_inter_left
 
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 theorem mem_of_mem_inter_right {x : α} {a b : Set α} (h : x ∈ a ∩ b) : x ∈ b :=
   h.right
 #align set.mem_of_mem_inter_right Set.mem_of_mem_inter_right
 
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 @[simp]
 theorem inter_self (a : Set α) : a ∩ a = a :=
   ext fun x => and_self_iff _
 #align set.inter_self Set.inter_self
 
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 @[simp]
 theorem inter_empty (a : Set α) : a ∩ ∅ = ∅ :=
   ext fun x => and_false_iff _
 #align set.inter_empty Set.inter_empty
 
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 @[simp]
 theorem empty_inter (a : Set α) : ∅ ∩ a = ∅ :=
   ext fun x => false_and_iff _
 #align set.empty_inter Set.empty_inter
 
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-Case conversion may be inaccurate. Consider using '#align set.inter_comm Set.inter_commₓ'. -/
 theorem inter_comm (a b : Set α) : a ∩ b = b ∩ a :=
   ext fun x => and_comm
 #align set.inter_comm Set.inter_comm
 
-/- warning: set.inter_assoc -> Set.inter_assoc is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.inter_assoc Set.inter_assocₓ'. -/
 theorem inter_assoc (a b c : Set α) : a ∩ b ∩ c = a ∩ (b ∩ c) :=
   ext fun x => and_assoc
 #align set.inter_assoc Set.inter_assoc
 
-/- warning: set.inter_is_assoc -> Set.inter_isAssoc is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.inter_is_assoc Set.inter_isAssocₓ'. -/
 instance inter_isAssoc : IsAssociative (Set α) (· ∩ ·) :=
   ⟨inter_assoc⟩
 #align set.inter_is_assoc Set.inter_isAssoc
 
-/- warning: set.inter_is_comm -> Set.inter_isComm is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.inter_is_comm Set.inter_isCommₓ'. -/
 instance inter_isComm : IsCommutative (Set α) (· ∩ ·) :=
   ⟨inter_comm⟩
 #align set.inter_is_comm Set.inter_isComm
 
-/- warning: set.inter_left_comm -> Set.inter_left_comm is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.inter_left_comm Set.inter_left_commₓ'. -/
 theorem inter_left_comm (s₁ s₂ s₃ : Set α) : s₁ ∩ (s₂ ∩ s₃) = s₂ ∩ (s₁ ∩ s₃) :=
   ext fun x => and_left_comm
 #align set.inter_left_comm Set.inter_left_comm
 
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-Case conversion may be inaccurate. Consider using '#align set.inter_right_comm Set.inter_right_commₓ'. -/
 theorem inter_right_comm (s₁ s₂ s₃ : Set α) : s₁ ∩ s₂ ∩ s₃ = s₁ ∩ s₃ ∩ s₂ :=
   ext fun x => and_right_comm
 #align set.inter_right_comm Set.inter_right_comm
 
-/- warning: set.inter_subset_left -> Set.inter_subset_left is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align set.inter_subset_left Set.inter_subset_leftₓ'. -/
 @[simp]
 theorem inter_subset_left (s t : Set α) : s ∩ t ⊆ s := fun x => And.left
 #align set.inter_subset_left Set.inter_subset_left
 
-/- warning: set.inter_subset_right -> Set.inter_subset_right is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.inter_subset_right Set.inter_subset_rightₓ'. -/
 @[simp]
 theorem inter_subset_right (s t : Set α) : s ∩ t ⊆ t := fun x => And.right
 #align set.inter_subset_right Set.inter_subset_right
 
-/- warning: set.subset_inter -> Set.subset_inter is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.subset_inter Set.subset_interₓ'. -/
 theorem subset_inter {s t r : Set α} (rs : r ⊆ s) (rt : r ⊆ t) : r ⊆ s ∩ t := fun x h =>
   ⟨rs h, rt h⟩
 #align set.subset_inter Set.subset_inter
 
-/- warning: set.subset_inter_iff -> Set.subset_inter_iff is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.subset_inter_iff Set.subset_inter_iffₓ'. -/
 @[simp]
 theorem subset_inter_iff {s t r : Set α} : r ⊆ s ∩ t ↔ r ⊆ s ∧ r ⊆ t :=
   (forall_congr' fun x => imp_and).trans forall_and
 #align set.subset_inter_iff Set.subset_inter_iff
 
-/- warning: set.inter_eq_left_iff_subset -> Set.inter_eq_left_iff_subset is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.inter_eq_left_iff_subset Set.inter_eq_left_iff_subsetₓ'. -/
 @[simp]
 theorem inter_eq_left_iff_subset {s t : Set α} : s ∩ t = s ↔ s ⊆ t :=
   inf_eq_left
 #align set.inter_eq_left_iff_subset Set.inter_eq_left_iff_subset
 
-/- warning: set.inter_eq_right_iff_subset -> Set.inter_eq_right_iff_subset is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.inter_eq_right_iff_subset Set.inter_eq_right_iff_subsetₓ'. -/
 @[simp]
 theorem inter_eq_right_iff_subset {s t : Set α} : s ∩ t = t ↔ t ⊆ s :=
   inf_eq_right
 #align set.inter_eq_right_iff_subset Set.inter_eq_right_iff_subset
 
-/- warning: set.inter_eq_self_of_subset_left -> Set.inter_eq_self_of_subset_left is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.inter_eq_self_of_subset_left Set.inter_eq_self_of_subset_leftₓ'. -/
 theorem inter_eq_self_of_subset_left {s t : Set α} : s ⊆ t → s ∩ t = s :=
   inter_eq_left_iff_subset.mpr
 #align set.inter_eq_self_of_subset_left Set.inter_eq_self_of_subset_left
 
-/- warning: set.inter_eq_self_of_subset_right -> Set.inter_eq_self_of_subset_right is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.inter_eq_self_of_subset_right Set.inter_eq_self_of_subset_rightₓ'. -/
 theorem inter_eq_self_of_subset_right {s t : Set α} : t ⊆ s → s ∩ t = t :=
   inter_eq_right_iff_subset.mpr
 #align set.inter_eq_self_of_subset_right Set.inter_eq_self_of_subset_right
 
-/- warning: set.inter_congr_left -> Set.inter_congr_left is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.inter_congr_left Set.inter_congr_leftₓ'. -/
 theorem inter_congr_left (ht : s ∩ u ⊆ t) (hu : s ∩ t ⊆ u) : s ∩ t = s ∩ u :=
   inf_congr_left ht hu
 #align set.inter_congr_left Set.inter_congr_left
 
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-Case conversion may be inaccurate. Consider using '#align set.inter_congr_right Set.inter_congr_rightₓ'. -/
 theorem inter_congr_right (hs : t ∩ u ⊆ s) (ht : s ∩ u ⊆ t) : s ∩ u = t ∩ u :=
   inf_congr_right hs ht
 #align set.inter_congr_right Set.inter_congr_right
 
-/- warning: set.inter_eq_inter_iff_left -> Set.inter_eq_inter_iff_left is a dubious translation:
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 theorem inter_eq_inter_iff_left : s ∩ t = s ∩ u ↔ s ∩ u ⊆ t ∧ s ∩ t ⊆ u :=
   inf_eq_inf_iff_left
 #align set.inter_eq_inter_iff_left Set.inter_eq_inter_iff_left
 
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-Case conversion may be inaccurate. Consider using '#align set.inter_eq_inter_iff_right Set.inter_eq_inter_iff_rightₓ'. -/
 theorem inter_eq_inter_iff_right : s ∩ u = t ∩ u ↔ t ∩ u ⊆ s ∧ s ∩ u ⊆ t :=
   inf_eq_inf_iff_right
 #align set.inter_eq_inter_iff_right Set.inter_eq_inter_iff_right
 
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-Case conversion may be inaccurate. Consider using '#align set.inter_univ Set.inter_univₓ'. -/
 @[simp]
 theorem inter_univ (a : Set α) : a ∩ univ = a :=
   inf_top_eq
 #align set.inter_univ Set.inter_univ
 
-/- warning: set.univ_inter -> Set.univ_inter is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.univ_inter Set.univ_interₓ'. -/
 @[simp]
 theorem univ_inter (a : Set α) : univ ∩ a = a :=
   top_inf_eq
 #align set.univ_inter Set.univ_inter
 
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-Case conversion may be inaccurate. Consider using '#align set.inter_subset_inter Set.inter_subset_interₓ'. -/
 theorem inter_subset_inter {s₁ s₂ t₁ t₂ : Set α} (h₁ : s₁ ⊆ t₁) (h₂ : s₂ ⊆ t₂) :
     s₁ ∩ s₂ ⊆ t₁ ∩ t₂ := fun x => And.imp (@h₁ _) (@h₂ _)
 #align set.inter_subset_inter Set.inter_subset_inter
 
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 theorem inter_subset_inter_left {s t : Set α} (u : Set α) (H : s ⊆ t) : s ∩ u ⊆ t ∩ u :=
   inter_subset_inter H Subset.rfl
 #align set.inter_subset_inter_left Set.inter_subset_inter_left
 
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 theorem inter_subset_inter_right {s t : Set α} (u : Set α) (H : s ⊆ t) : u ∩ s ⊆ u ∩ t :=
   inter_subset_inter Subset.rfl H
 #align set.inter_subset_inter_right Set.inter_subset_inter_right
 
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 theorem union_inter_cancel_left {s t : Set α} : (s ∪ t) ∩ s = s :=
   inter_eq_self_of_subset_right <| subset_union_left _ _
 #align set.union_inter_cancel_left Set.union_inter_cancel_left
 
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 theorem union_inter_cancel_right {s t : Set α} : (s ∪ t) ∩ t = t :=
   inter_eq_self_of_subset_right <| subset_union_right _ _
 #align set.union_inter_cancel_right Set.union_inter_cancel_right
 
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 theorem inter_setOf_eq_sep (s : Set α) (p : α → Prop) : s ∩ { a | p a } = { a ∈ s | p a } :=
   rfl
 #align set.inter_set_of_eq_sep Set.inter_setOf_eq_sep
 
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 theorem setOf_inter_eq_sep (p : α → Prop) (s : Set α) : { a | p a } ∩ s = { a ∈ s | p a } :=
   inter_comm _ _
 #align set.set_of_inter_eq_sep Set.setOf_inter_eq_sep
@@ -1807,142 +1189,58 @@ theorem setOf_inter_eq_sep (p : α → Prop) (s : Set α) : { a | p a } ∩ s =
 /-! ### Distributivity laws -/
 
 
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 theorem inter_distrib_left (s t u : Set α) : s ∩ (t ∪ u) = s ∩ t ∪ s ∩ u :=
   inf_sup_left
 #align set.inter_distrib_left Set.inter_distrib_left
 
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 theorem inter_union_distrib_left {s t u : Set α} : s ∩ (t ∪ u) = s ∩ t ∪ s ∩ u :=
   inf_sup_left
 #align set.inter_union_distrib_left Set.inter_union_distrib_left
 
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 theorem inter_distrib_right (s t u : Set α) : (s ∪ t) ∩ u = s ∩ u ∪ t ∩ u :=
   inf_sup_right
 #align set.inter_distrib_right Set.inter_distrib_right
 
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 theorem union_inter_distrib_right {s t u : Set α} : (s ∪ t) ∩ u = s ∩ u ∪ t ∩ u :=
   inf_sup_right
 #align set.union_inter_distrib_right Set.union_inter_distrib_right
 
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-Case conversion may be inaccurate. Consider using '#align set.union_distrib_left Set.union_distrib_leftₓ'. -/
 theorem union_distrib_left (s t u : Set α) : s ∪ t ∩ u = (s ∪ t) ∩ (s ∪ u) :=
   sup_inf_left
 #align set.union_distrib_left Set.union_distrib_left
 
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-Case conversion may be inaccurate. Consider using '#align set.union_inter_distrib_left Set.union_inter_distrib_leftₓ'. -/
 theorem union_inter_distrib_left {s t u : Set α} : s ∪ t ∩ u = (s ∪ t) ∩ (s ∪ u) :=
   sup_inf_left
 #align set.union_inter_distrib_left Set.union_inter_distrib_left
 
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-Case conversion may be inaccurate. Consider using '#align set.union_distrib_right Set.union_distrib_rightₓ'. -/
 theorem union_distrib_right (s t u : Set α) : s ∩ t ∪ u = (s ∪ u) ∩ (t ∪ u) :=
   sup_inf_right
 #align set.union_distrib_right Set.union_distrib_right
 
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-Case conversion may be inaccurate. Consider using '#align set.inter_union_distrib_right Set.inter_union_distrib_rightₓ'. -/
 theorem inter_union_distrib_right {s t u : Set α} : s ∩ t ∪ u = (s ∪ u) ∩ (t ∪ u) :=
   sup_inf_right
 #align set.inter_union_distrib_right Set.inter_union_distrib_right
 
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-Case conversion may be inaccurate. Consider using '#align set.union_union_distrib_left Set.union_union_distrib_leftₓ'. -/
 theorem union_union_distrib_left (s t u : Set α) : s ∪ (t ∪ u) = s ∪ t ∪ (s ∪ u) :=
   sup_sup_distrib_left _ _ _
 #align set.union_union_distrib_left Set.union_union_distrib_left
 
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-Case conversion may be inaccurate. Consider using '#align set.union_union_distrib_right Set.union_union_distrib_rightₓ'. -/
 theorem union_union_distrib_right (s t u : Set α) : s ∪ t ∪ u = s ∪ u ∪ (t ∪ u) :=
   sup_sup_distrib_right _ _ _
 #align set.union_union_distrib_right Set.union_union_distrib_right
 
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-Case conversion may be inaccurate. Consider using '#align set.inter_inter_distrib_left Set.inter_inter_distrib_leftₓ'. -/
 theorem inter_inter_distrib_left (s t u : Set α) : s ∩ (t ∩ u) = s ∩ t ∩ (s ∩ u) :=
   inf_inf_distrib_left _ _ _
 #align set.inter_inter_distrib_left Set.inter_inter_distrib_left
 
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 theorem inter_inter_distrib_right (s t u : Set α) : s ∩ t ∩ u = s ∩ u ∩ (t ∩ u) :=
   inf_inf_distrib_right _ _ _
 #align set.inter_inter_distrib_right Set.inter_inter_distrib_right
 
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-Case conversion may be inaccurate. Consider using '#align set.union_union_union_comm Set.union_union_union_commₓ'. -/
 theorem union_union_union_comm (s t u v : Set α) : s ∪ t ∪ (u ∪ v) = s ∪ u ∪ (t ∪ v) :=
   sup_sup_sup_comm _ _ _ _
 #align set.union_union_union_comm Set.union_union_union_comm
 
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 theorem inter_inter_inter_comm (s t u v : Set α) : s ∩ t ∩ (u ∩ v) = s ∩ u ∩ (t ∩ v) :=
   inf_inf_inf_comm _ _ _ _
 #align set.inter_inter_inter_comm Set.inter_inter_inter_comm
@@ -2055,12 +1353,6 @@ theorem subset_insert_iff_of_not_mem (ha : a ∉ s) : s ⊆ insert a t ↔ s ⊆
 #align set.subset_insert_iff_of_not_mem Set.subset_insert_iff_of_not_mem
 -/
 
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 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a «expr ∉ » s) -/
 theorem ssubset_iff_insert {s t : Set α} : s ⊂ t ↔ ∃ (a : _)(_ : a ∉ s), insert a s ⊆ t :=
   by
@@ -2068,12 +1360,6 @@ theorem ssubset_iff_insert {s t : Set α} : s ⊂ t ↔ ∃ (a : _)(_ : a ∉ s)
   simp only [exists_prop, and_comm']
 #align set.ssubset_iff_insert Set.ssubset_iff_insert
 
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 theorem ssubset_insert {s : Set α} {a : α} (h : a ∉ s) : s ⊂ insert a s :=
   ssubset_iff_insert.2 ⟨a, h, Subset.rfl⟩
 #align set.ssubset_insert Set.ssubset_insert
@@ -2091,22 +1377,10 @@ theorem insert_idem (a : α) (s : Set α) : insert a (insert a s) = insert a s :
 #align set.insert_idem Set.insert_idem
 -/
 
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-Case conversion may be inaccurate. Consider using '#align set.insert_union Set.insert_unionₓ'. -/
 theorem insert_union : insert a s ∪ t = insert a (s ∪ t) :=
   ext fun x => or_assoc
 #align set.insert_union Set.insert_union
 
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-Case conversion may be inaccurate. Consider using '#align set.union_insert Set.union_insertₓ'. -/
 @[simp]
 theorem union_insert : s ∪ insert a t = insert a (s ∪ t) :=
   ext fun x => or_left_comm
@@ -2122,22 +1396,10 @@ theorem insert_nonempty (a : α) (s : Set α) : (insert a s).Nonempty :=
 instance (a : α) (s : Set α) : Nonempty (insert a s : Set α) :=
   (insert_nonempty a s).to_subtype
 
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-Case conversion may be inaccurate. Consider using '#align set.insert_inter_distrib Set.insert_inter_distribₓ'. -/
 theorem insert_inter_distrib (a : α) (s t : Set α) : insert a (s ∩ t) = insert a s ∩ insert a t :=
   ext fun y => or_and_left
 #align set.insert_inter_distrib Set.insert_inter_distrib
 
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-Case conversion may be inaccurate. Consider using '#align set.insert_union_distrib Set.insert_union_distribₓ'. -/
 theorem insert_union_distrib (a : α) (s t : Set α) : insert a (s ∪ t) = insert a s ∪ insert a t :=
   ext fun _ => or_or_distrib_left _ _ _
 #align set.insert_union_distrib Set.insert_union_distrib
@@ -2163,12 +1425,6 @@ theorem forall_insert_of_forall {P : α → Prop} {a : α} {s : Set α} (H : ∀
 #align set.forall_insert_of_forall Set.forall_insert_of_forall
 -/
 
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-Case conversion may be inaccurate. Consider using '#align set.bex_insert_iff Set.bex_insert_iffₓ'. -/
 theorem bex_insert_iff {P : α → Prop} {a : α} {s : Set α} :
     (∃ x ∈ insert a s, P x) ↔ P a ∨ ∃ x ∈ s, P x :=
   bex_or_left.trans <| or_congr_left bex_eq_left
@@ -2244,12 +1500,6 @@ theorem mem_singleton_of_eq {x y : α} (H : x = y) : x ∈ ({y} : Set α) :=
 #align set.mem_singleton_of_eq Set.mem_singleton_of_eq
 -/
 
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-Case conversion may be inaccurate. Consider using '#align set.insert_eq Set.insert_eqₓ'. -/
 theorem insert_eq (x : α) (s : Set α) : insert x s = ({x} : Set α) ∪ s :=
   rfl
 #align set.insert_eq Set.insert_eq
@@ -2268,12 +1518,6 @@ theorem singleton_ne_empty (a : α) : ({a} : Set α) ≠ ∅ :=
 #align set.singleton_ne_empty Set.singleton_ne_empty
 -/
 
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 @[simp]
 theorem empty_ssubset_singleton : (∅ : Set α) ⊂ {a} :=
   (singleton_nonempty _).empty_ssubset
@@ -2297,67 +1541,31 @@ theorem set_compr_eq_eq_singleton {a : α} : { b | b = a } = {a} :=
 #align set.set_compr_eq_eq_singleton Set.set_compr_eq_eq_singleton
 -/
 
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 @[simp]
 theorem singleton_union : {a} ∪ s = insert a s :=
   rfl
 #align set.singleton_union Set.singleton_union
 
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 @[simp]
 theorem union_singleton : s ∪ {a} = insert a s :=
   union_comm _ _
 #align set.union_singleton Set.union_singleton
 
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 @[simp]
 theorem singleton_inter_nonempty : ({a} ∩ s).Nonempty ↔ a ∈ s := by
   simp only [Set.Nonempty, mem_inter_iff, mem_singleton_iff, exists_eq_left]
 #align set.singleton_inter_nonempty Set.singleton_inter_nonempty
 
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 @[simp]
 theorem inter_singleton_nonempty : (s ∩ {a}).Nonempty ↔ a ∈ s := by
   rw [inter_comm, singleton_inter_nonempty]
 #align set.inter_singleton_nonempty Set.inter_singleton_nonempty
 
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 @[simp]
 theorem singleton_inter_eq_empty : {a} ∩ s = ∅ ↔ a ∉ s :=
   not_nonempty_iff_eq_empty.symm.trans singleton_inter_nonempty.Not
 #align set.singleton_inter_eq_empty Set.singleton_inter_eq_empty
 
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 @[simp]
 theorem inter_singleton_eq_empty : s ∩ {a} = ∅ ↔ a ∉ s := by
   rw [inter_comm, singleton_inter_eq_empty]
@@ -2437,12 +1645,6 @@ theorem mem_sep (xs : x ∈ s) (px : p x) : x ∈ { x ∈ s | p x } :=
 #align set.mem_sep Set.mem_sep
 -/
 
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 @[simp]
 theorem sep_mem_eq : { x ∈ s | x ∈ t } = s ∩ t :=
   rfl
@@ -2515,45 +1717,21 @@ theorem sep_univ : { x ∈ (univ : Set α) | p x } = { x | p x } :=
 #align set.sep_univ Set.sep_univ
 -/
 
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 @[simp]
 theorem sep_union : { x ∈ s ∪ t | p x } = { x ∈ s | p x } ∪ { x ∈ t | p x } :=
   union_inter_distrib_right
 #align set.sep_union Set.sep_union
 
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 @[simp]
 theorem sep_inter : { x ∈ s ∩ t | p x } = { x ∈ s | p x } ∩ { x ∈ t | p x } :=
   inter_inter_distrib_right s t p
 #align set.sep_inter Set.sep_inter
 
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 @[simp]
 theorem sep_and : { x ∈ s | p x ∧ q x } = { x ∈ s | p x } ∩ { x ∈ s | q x } :=
   inter_inter_distrib_left s p q
 #align set.sep_and Set.sep_and
 
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 @[simp]
 theorem sep_or : { x ∈ s | p x ∨ q x } = { x ∈ s | p x } ∪ { x ∈ s | q x } :=
   inter_union_distrib_left
@@ -2590,12 +1768,6 @@ theorem Nonempty.subset_singleton_iff (h : s.Nonempty) : s ⊆ {a} ↔ s = {a} :
 #align set.nonempty.subset_singleton_iff Set.Nonempty.subset_singleton_iff
 -/
 
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 theorem ssubset_singleton_iff {s : Set α} {x : α} : s ⊂ {x} ↔ s = ∅ :=
   by
   rw [ssubset_iff_subset_ne, subset_singleton_iff_eq, or_and_right, and_not_self_iff, or_false_iff,
@@ -2603,12 +1775,6 @@ theorem ssubset_singleton_iff {s : Set α} {x : α} : s ⊂ {x} ↔ s = ∅ :=
   exact fun h => ne_of_eq_of_ne h (singleton_ne_empty _).symm
 #align set.ssubset_singleton_iff Set.ssubset_singleton_iff
 
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 theorem eq_empty_of_ssubset_singleton {s : Set α} {x : α} (hs : s ⊂ {x}) : s = ∅ :=
   ssubset_singleton_iff.1 hs
 #align set.eq_empty_of_ssubset_singleton Set.eq_empty_of_ssubset_singleton
@@ -2616,309 +1782,129 @@ theorem eq_empty_of_ssubset_singleton {s : Set α} {x : α} (hs : s ⊂ {x}) : s
 /-! ### Disjointness -/
 
 
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 protected theorem disjoint_iff : Disjoint s t ↔ s ∩ t ⊆ ∅ :=
   disjoint_iff_inf_le
 #align set.disjoint_iff Set.disjoint_iff
 
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 theorem disjoint_iff_inter_eq_empty : Disjoint s t ↔ s ∩ t = ∅ :=
   disjoint_iff
 #align set.disjoint_iff_inter_eq_empty Set.disjoint_iff_inter_eq_empty
 
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 theorem Disjoint.inter_eq : Disjoint s t → s ∩ t = ∅ :=
   Disjoint.eq_bot
 #align disjoint.inter_eq Disjoint.inter_eq
 
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 theorem disjoint_left : Disjoint s t ↔ ∀ ⦃a⦄, a ∈ s → a ∉ t :=
   disjoint_iff_inf_le.trans <| forall_congr' fun _ => not_and
 #align set.disjoint_left Set.disjoint_left
 
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 theorem disjoint_right : Disjoint s t ↔ ∀ ⦃a⦄, a ∈ t → a ∉ s := by rw [disjoint_comm, disjoint_left]
 #align set.disjoint_right Set.disjoint_right
 
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 theorem not_disjoint_iff : ¬Disjoint s t ↔ ∃ x, x ∈ s ∧ x ∈ t :=
   Set.disjoint_iff.Not.trans <| not_forall.trans <| exists_congr fun x => Classical.not_not
 #align set.not_disjoint_iff Set.not_disjoint_iff
 
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 theorem not_disjoint_iff_nonempty_inter : ¬Disjoint s t ↔ (s ∩ t).Nonempty :=
   not_disjoint_iff
 #align set.not_disjoint_iff_nonempty_inter Set.not_disjoint_iff_nonempty_inter
 
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 alias not_disjoint_iff_nonempty_inter ↔ _ nonempty.not_disjoint
 #align set.nonempty.not_disjoint Set.Nonempty.not_disjoint
 
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 theorem disjoint_or_nonempty_inter (s t : Set α) : Disjoint s t ∨ (s ∩ t).Nonempty :=
   (em _).imp_right not_disjoint_iff_nonempty_inter.mp
 #align set.disjoint_or_nonempty_inter Set.disjoint_or_nonempty_inter
 
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 theorem disjoint_iff_forall_ne : Disjoint s t ↔ ∀ x ∈ s, ∀ y ∈ t, x ≠ y := by
   simp only [Ne.def, disjoint_left, @imp_not_comm _ (_ = _), forall_eq']
 #align set.disjoint_iff_forall_ne Set.disjoint_iff_forall_ne
 
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 theorem Disjoint.ne_of_mem (h : Disjoint s t) {x y} (hx : x ∈ s) (hy : y ∈ t) : x ≠ y :=
   disjoint_iff_forall_ne.mp h x hx y hy
 #align disjoint.ne_of_mem Disjoint.ne_of_mem
 
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 theorem disjoint_of_subset_left (hs : s₁ ⊆ s₂) (h : Disjoint s₂ t) : Disjoint s₁ t :=
   h.mono_left hs
 #align set.disjoint_of_subset_left Set.disjoint_of_subset_left
 
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 theorem disjoint_of_subset_right (ht : t₁ ⊆ t₂) (h : Disjoint s t₂) : Disjoint s t₁ :=
   h.mono_right ht
 #align set.disjoint_of_subset_right Set.disjoint_of_subset_right
 
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 theorem disjoint_of_subset (hs : s₁ ⊆ s₂) (ht : t₁ ⊆ t₂) (h : Disjoint s₂ t₂) : Disjoint s₁ t₁ :=
   h.mono hs ht
 #align set.disjoint_of_subset Set.disjoint_of_subset
 
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 @[simp]
 theorem disjoint_union_left : Disjoint (s ∪ t) u ↔ Disjoint s u ∧ Disjoint t u :=
   disjoint_sup_left
 #align set.disjoint_union_left Set.disjoint_union_left
 
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 @[simp]
 theorem disjoint_union_right : Disjoint s (t ∪ u) ↔ Disjoint s t ∧ Disjoint s u :=
   disjoint_sup_right
 #align set.disjoint_union_right Set.disjoint_union_right
 
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 @[simp]
 theorem disjoint_empty (s : Set α) : Disjoint s ∅ :=
   disjoint_bot_right
 #align set.disjoint_empty Set.disjoint_empty
 
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 @[simp]
 theorem empty_disjoint (s : Set α) : Disjoint ∅ s :=
   disjoint_bot_left
 #align set.empty_disjoint Set.empty_disjoint
 
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 @[simp]
 theorem univ_disjoint : Disjoint univ s ↔ s = ∅ :=
   top_disjoint
 #align set.univ_disjoint Set.univ_disjoint
 
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 @[simp]
 theorem disjoint_univ : Disjoint s univ ↔ s = ∅ :=
   disjoint_top
 #align set.disjoint_univ Set.disjoint_univ
 
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 theorem disjoint_sdiff_left : Disjoint (t \ s) s :=
   disjoint_sdiff_self_left
 #align set.disjoint_sdiff_left Set.disjoint_sdiff_left
 
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 theorem disjoint_sdiff_right : Disjoint s (t \ s) :=
   disjoint_sdiff_self_right
 #align set.disjoint_sdiff_right Set.disjoint_sdiff_right
 
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 theorem diff_union_diff_cancel (hts : t ⊆ s) (hut : u ⊆ t) : s \ t ∪ t \ u = s \ u :=
   sdiff_sup_sdiff_cancel hts hut
 #align set.diff_union_diff_cancel Set.diff_union_diff_cancel
 
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 theorem diff_diff_eq_sdiff_union (h : u ⊆ s) : s \ (t \ u) = s \ t ∪ u :=
   sdiff_sdiff_eq_sdiff_sup h
 #align set.diff_diff_eq_sdiff_union Set.diff_diff_eq_sdiff_union
 
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 @[simp]
 theorem disjoint_singleton_left : Disjoint {a} s ↔ a ∉ s := by
   simp [Set.disjoint_iff, subset_def] <;> exact Iff.rfl
 #align set.disjoint_singleton_left Set.disjoint_singleton_left
 
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 @[simp]
 theorem disjoint_singleton_right : Disjoint s {a} ↔ a ∉ s :=
   disjoint_comm.trans disjoint_singleton_left
 #align set.disjoint_singleton_right Set.disjoint_singleton_right
 
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 @[simp]
 theorem disjoint_singleton : Disjoint ({a} : Set α) {b} ↔ a ≠ b := by
   rw [disjoint_singleton_left, mem_singleton_iff]
 #align set.disjoint_singleton Set.disjoint_singleton
 
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 theorem subset_diff : s ⊆ t \ u ↔ s ⊆ t ∧ Disjoint s u :=
   le_iff_subset.symm.trans le_sdiff
 #align set.subset_diff Set.subset_diff
 
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 theorem inter_diff_distrib_left (s t u : Set α) : s ∩ (t \ u) = (s ∩ t) \ (s ∩ u) :=
   inf_sdiff_distrib_left _ _ _
 #align set.inter_diff_distrib_left Set.inter_diff_distrib_left
 
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 theorem inter_diff_distrib_right (s t u : Set α) : s \ t ∩ u = (s ∩ u) \ (t ∩ u) :=
   inf_sdiff_distrib_right _ _ _
 #align set.inter_diff_distrib_right Set.inter_diff_distrib_right
@@ -2926,400 +1912,166 @@ theorem inter_diff_distrib_right (s t u : Set α) : s \ t ∩ u = (s ∩ u) \ (t
 /-! ### Lemmas about complement -/
 
 
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 theorem compl_def (s : Set α) : sᶜ = { x | x ∉ s } :=
   rfl
 #align set.compl_def Set.compl_def
 
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 theorem mem_compl {s : Set α} {x : α} (h : x ∉ s) : x ∈ sᶜ :=
   h
 #align set.mem_compl Set.mem_compl
 
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 theorem compl_setOf {α} (p : α → Prop) : { a | p a }ᶜ = { a | ¬p a } :=
   rfl
 #align set.compl_set_of Set.compl_setOf
 
-/- warning: set.not_mem_of_mem_compl -> Set.not_mem_of_mem_compl is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.not_mem_of_mem_compl Set.not_mem_of_mem_complₓ'. -/
 theorem not_mem_of_mem_compl {s : Set α} {x : α} (h : x ∈ sᶜ) : x ∉ s :=
   h
 #align set.not_mem_of_mem_compl Set.not_mem_of_mem_compl
 
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-Case conversion may be inaccurate. Consider using '#align set.mem_compl_iff Set.mem_compl_iffₓ'. -/
 @[simp]
 theorem mem_compl_iff (s : Set α) (x : α) : x ∈ sᶜ ↔ x ∉ s :=
   Iff.rfl
 #align set.mem_compl_iff Set.mem_compl_iff
 
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-Case conversion may be inaccurate. Consider using '#align set.not_mem_compl_iff Set.not_mem_compl_iffₓ'. -/
 theorem not_mem_compl_iff {x : α} : x ∉ sᶜ ↔ x ∈ s :=
   Classical.not_not
 #align set.not_mem_compl_iff Set.not_mem_compl_iff
 
-/- warning: set.inter_compl_self -> Set.inter_compl_self is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.inter_compl_self Set.inter_compl_selfₓ'. -/
 @[simp]
 theorem inter_compl_self (s : Set α) : s ∩ sᶜ = ∅ :=
   inf_compl_eq_bot
 #align set.inter_compl_self Set.inter_compl_self
 
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-Case conversion may be inaccurate. Consider using '#align set.compl_inter_self Set.compl_inter_selfₓ'. -/
 @[simp]
 theorem compl_inter_self (s : Set α) : sᶜ ∩ s = ∅ :=
   compl_inf_eq_bot
 #align set.compl_inter_self Set.compl_inter_self
 
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-Case conversion may be inaccurate. Consider using '#align set.compl_empty Set.compl_emptyₓ'. -/
 @[simp]
 theorem compl_empty : (∅ : Set α)ᶜ = univ :=
   compl_bot
 #align set.compl_empty Set.compl_empty
 
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-Case conversion may be inaccurate. Consider using '#align set.compl_union Set.compl_unionₓ'. -/
 @[simp]
 theorem compl_union (s t : Set α) : (s ∪ t)ᶜ = sᶜ ∩ tᶜ :=
   compl_sup
 #align set.compl_union Set.compl_union
 
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-Case conversion may be inaccurate. Consider using '#align set.compl_inter Set.compl_interₓ'. -/
 theorem compl_inter (s t : Set α) : (s ∩ t)ᶜ = sᶜ ∪ tᶜ :=
   compl_inf
 #align set.compl_inter Set.compl_inter
 
-/- warning: set.compl_univ -> Set.compl_univ is a dubious translation:
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 @[simp]
 theorem compl_univ : (univ : Set α)ᶜ = ∅ :=
   compl_top
 #align set.compl_univ Set.compl_univ
 
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 @[simp]
 theorem compl_empty_iff {s : Set α} : sᶜ = ∅ ↔ s = univ :=
   compl_eq_bot
 #align set.compl_empty_iff Set.compl_empty_iff
 
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 @[simp]
 theorem compl_univ_iff {s : Set α} : sᶜ = univ ↔ s = ∅ :=
   compl_eq_top
 #align set.compl_univ_iff Set.compl_univ_iff
 
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-Case conversion may be inaccurate. Consider using '#align set.compl_ne_univ Set.compl_ne_univₓ'. -/
 theorem compl_ne_univ : sᶜ ≠ univ ↔ s.Nonempty :=
   compl_univ_iff.Not.trans nonempty_iff_ne_empty.symm
 #align set.compl_ne_univ Set.compl_ne_univ
 
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 theorem nonempty_compl : sᶜ.Nonempty ↔ s ≠ univ :=
   (ne_univ_iff_exists_not_mem s).symm
 #align set.nonempty_compl Set.nonempty_compl
 
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 theorem mem_compl_singleton_iff {a x : α} : x ∈ ({a} : Set α)ᶜ ↔ x ≠ a :=
   Iff.rfl
 #align set.mem_compl_singleton_iff Set.mem_compl_singleton_iff
 
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-Case conversion may be inaccurate. Consider using '#align set.compl_singleton_eq Set.compl_singleton_eqₓ'. -/
 theorem compl_singleton_eq (a : α) : ({a} : Set α)ᶜ = { x | x ≠ a } :=
   rfl
 #align set.compl_singleton_eq Set.compl_singleton_eq
 
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 @[simp]
 theorem compl_ne_eq_singleton (a : α) : ({ x | x ≠ a } : Set α)ᶜ = {a} :=
   compl_compl _
 #align set.compl_ne_eq_singleton Set.compl_ne_eq_singleton
 
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 theorem union_eq_compl_compl_inter_compl (s t : Set α) : s ∪ t = (sᶜ ∩ tᶜ)ᶜ :=
   ext fun x => or_iff_not_and_not
 #align set.union_eq_compl_compl_inter_compl Set.union_eq_compl_compl_inter_compl
 
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 theorem inter_eq_compl_compl_union_compl (s t : Set α) : s ∩ t = (sᶜ ∪ tᶜ)ᶜ :=
   ext fun x => and_iff_not_or_not
 #align set.inter_eq_compl_compl_union_compl Set.inter_eq_compl_compl_union_compl
 
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 @[simp]
 theorem union_compl_self (s : Set α) : s ∪ sᶜ = univ :=
   eq_univ_iff_forall.2 fun x => em _
 #align set.union_compl_self Set.union_compl_self
 
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 @[simp]
 theorem compl_union_self (s : Set α) : sᶜ ∪ s = univ := by rw [union_comm, union_compl_self]
 #align set.compl_union_self Set.compl_union_self
 
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 theorem compl_subset_comm : sᶜ ⊆ t ↔ tᶜ ⊆ s :=
   @compl_le_iff_compl_le _ s _ _
 #align set.compl_subset_comm Set.compl_subset_comm
 
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 theorem subset_compl_comm : s ⊆ tᶜ ↔ t ⊆ sᶜ :=
   @le_compl_iff_le_compl _ _ _ t
 #align set.subset_compl_comm Set.subset_compl_comm
 
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 @[simp]
 theorem compl_subset_compl : sᶜ ⊆ tᶜ ↔ t ⊆ s :=
   @compl_le_compl_iff_le (Set α) _ _ _
 #align set.compl_subset_compl Set.compl_subset_compl
 
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 theorem subset_compl_iff_disjoint_left : s ⊆ tᶜ ↔ Disjoint t s :=
   @le_compl_iff_disjoint_left (Set α) _ _ _
 #align set.subset_compl_iff_disjoint_left Set.subset_compl_iff_disjoint_left
 
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 theorem subset_compl_iff_disjoint_right : s ⊆ tᶜ ↔ Disjoint s t :=
   @le_compl_iff_disjoint_right (Set α) _ _ _
 #align set.subset_compl_iff_disjoint_right Set.subset_compl_iff_disjoint_right
 
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 theorem disjoint_compl_left_iff_subset : Disjoint (sᶜ) t ↔ t ⊆ s :=
   disjoint_compl_left_iff
 #align set.disjoint_compl_left_iff_subset Set.disjoint_compl_left_iff_subset
 
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 theorem disjoint_compl_right_iff_subset : Disjoint s (tᶜ) ↔ s ⊆ t :=
   disjoint_compl_right_iff
 #align set.disjoint_compl_right_iff_subset Set.disjoint_compl_right_iff_subset
 
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 alias subset_compl_iff_disjoint_right ↔ _ _root_.disjoint.subset_compl_right
 #align disjoint.subset_compl_right Disjoint.subset_compl_right
 
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 alias subset_compl_iff_disjoint_left ↔ _ _root_.disjoint.subset_compl_left
 #align disjoint.subset_compl_left Disjoint.subset_compl_left
 
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 alias disjoint_compl_left_iff_subset ↔ _ _root_.has_subset.subset.disjoint_compl_left
 #align has_subset.subset.disjoint_compl_left HasSubset.Subset.disjoint_compl_left
 
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 alias disjoint_compl_right_iff_subset ↔ _ _root_.has_subset.subset.disjoint_compl_right
 #align has_subset.subset.disjoint_compl_right HasSubset.Subset.disjoint_compl_right
 
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 theorem subset_union_compl_iff_inter_subset {s t u : Set α} : s ⊆ t ∪ uᶜ ↔ s ∩ u ⊆ t :=
   (@isCompl_compl _ u _).le_sup_right_iff_inf_left_le
 #align set.subset_union_compl_iff_inter_subset Set.subset_union_compl_iff_inter_subset
 
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 theorem compl_subset_iff_union {s t : Set α} : sᶜ ⊆ t ↔ s ∪ t = univ :=
   Iff.symm <| eq_univ_iff_forall.trans <| forall_congr' fun a => or_iff_not_imp_left
 #align set.compl_subset_iff_union Set.compl_subset_iff_union
 
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 @[simp]
 theorem subset_compl_singleton_iff {a : α} {s : Set α} : s ⊆ {a}ᶜ ↔ a ∉ s :=
   subset_compl_comm.trans singleton_subset_iff
 #align set.subset_compl_singleton_iff Set.subset_compl_singleton_iff
 
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 theorem inter_subset (a b c : Set α) : a ∩ b ⊆ c ↔ a ⊆ bᶜ ∪ c :=
   forall_congr' fun x => and_imp.trans <| imp_congr_right fun _ => imp_iff_not_or
 #align set.inter_subset Set.inter_subset
 
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-Case conversion may be inaccurate. Consider using '#align set.inter_compl_nonempty_iff Set.inter_compl_nonempty_iffₓ'. -/
 theorem inter_compl_nonempty_iff {s t : Set α} : (s ∩ tᶜ).Nonempty ↔ ¬s ⊆ t :=
   (not_subset.trans <| exists_congr fun x => by simp [mem_compl]).symm
 #align set.inter_compl_nonempty_iff Set.inter_compl_nonempty_iff
@@ -3327,453 +2079,189 @@ theorem inter_compl_nonempty_iff {s t : Set α} : (s ∩ tᶜ).Nonempty ↔ ¬s
 /-! ### Lemmas about set difference -/
 
 
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-Case conversion may be inaccurate. Consider using '#align set.diff_eq Set.diff_eqₓ'. -/
 theorem diff_eq (s t : Set α) : s \ t = s ∩ tᶜ :=
   rfl
 #align set.diff_eq Set.diff_eq
 
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-Case conversion may be inaccurate. Consider using '#align set.mem_diff Set.mem_diffₓ'. -/
 @[simp]
 theorem mem_diff {s t : Set α} (x : α) : x ∈ s \ t ↔ x ∈ s ∧ x ∉ t :=
   Iff.rfl
 #align set.mem_diff Set.mem_diff
 
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-Case conversion may be inaccurate. Consider using '#align set.mem_diff_of_mem Set.mem_diff_of_memₓ'. -/
 theorem mem_diff_of_mem {s t : Set α} {x : α} (h1 : x ∈ s) (h2 : x ∉ t) : x ∈ s \ t :=
   ⟨h1, h2⟩
 #align set.mem_diff_of_mem Set.mem_diff_of_mem
 
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-Case conversion may be inaccurate. Consider using '#align set.not_mem_diff_of_mem Set.not_mem_diff_of_memₓ'. -/
 theorem not_mem_diff_of_mem {s t : Set α} {x : α} (hx : x ∈ t) : x ∉ s \ t := fun h => h.2 hx
 #align set.not_mem_diff_of_mem Set.not_mem_diff_of_mem
 
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-Case conversion may be inaccurate. Consider using '#align set.mem_of_mem_diff Set.mem_of_mem_diffₓ'. -/
 theorem mem_of_mem_diff {s t : Set α} {x : α} (h : x ∈ s \ t) : x ∈ s :=
   h.left
 #align set.mem_of_mem_diff Set.mem_of_mem_diff
 
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-Case conversion may be inaccurate. Consider using '#align set.not_mem_of_mem_diff Set.not_mem_of_mem_diffₓ'. -/
 theorem not_mem_of_mem_diff {s t : Set α} {x : α} (h : x ∈ s \ t) : x ∉ t :=
   h.right
 #align set.not_mem_of_mem_diff Set.not_mem_of_mem_diff
 
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-Case conversion may be inaccurate. Consider using '#align set.diff_eq_compl_inter Set.diff_eq_compl_interₓ'. -/
 theorem diff_eq_compl_inter {s t : Set α} : s \ t = tᶜ ∩ s := by rw [diff_eq, inter_comm]
 #align set.diff_eq_compl_inter Set.diff_eq_compl_inter
 
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 theorem nonempty_diff {s t : Set α} : (s \ t).Nonempty ↔ ¬s ⊆ t :=
   inter_compl_nonempty_iff
 #align set.nonempty_diff Set.nonempty_diff
 
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 theorem diff_subset (s t : Set α) : s \ t ⊆ s :=
   show s \ t ≤ s from sdiff_le
 #align set.diff_subset Set.diff_subset
 
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 theorem union_diff_cancel' {s t u : Set α} (h₁ : s ⊆ t) (h₂ : t ⊆ u) : t ∪ u \ s = u :=
   sup_sdiff_cancel' h₁ h₂
 #align set.union_diff_cancel' Set.union_diff_cancel'
 
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 theorem union_diff_cancel {s t : Set α} (h : s ⊆ t) : s ∪ t \ s = t :=
   sup_sdiff_cancel_right h
 #align set.union_diff_cancel Set.union_diff_cancel
 
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 theorem union_diff_cancel_left {s t : Set α} (h : s ∩ t ⊆ ∅) : (s ∪ t) \ s = t :=
   Disjoint.sup_sdiff_cancel_left <| disjoint_iff_inf_le.2 h
 #align set.union_diff_cancel_left Set.union_diff_cancel_left
 
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 theorem union_diff_cancel_right {s t : Set α} (h : s ∩ t ⊆ ∅) : (s ∪ t) \ t = s :=
   Disjoint.sup_sdiff_cancel_right <| disjoint_iff_inf_le.2 h
 #align set.union_diff_cancel_right Set.union_diff_cancel_right
 
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 @[simp]
 theorem union_diff_left {s t : Set α} : (s ∪ t) \ s = t \ s :=
   sup_sdiff_left_self
 #align set.union_diff_left Set.union_diff_left
 
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-Case conversion may be inaccurate. Consider using '#align set.union_diff_right Set.union_diff_rightₓ'. -/
 @[simp]
 theorem union_diff_right {s t : Set α} : (s ∪ t) \ t = s \ t :=
   sup_sdiff_right_self
 #align set.union_diff_right Set.union_diff_right
 
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-Case conversion may be inaccurate. Consider using '#align set.union_diff_distrib Set.union_diff_distribₓ'. -/
 theorem union_diff_distrib {s t u : Set α} : (s ∪ t) \ u = s \ u ∪ t \ u :=
   sup_sdiff
 #align set.union_diff_distrib Set.union_diff_distrib
 
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-Case conversion may be inaccurate. Consider using '#align set.inter_diff_assoc Set.inter_diff_assocₓ'. -/
 theorem inter_diff_assoc (a b c : Set α) : (a ∩ b) \ c = a ∩ (b \ c) :=
   inf_sdiff_assoc
 #align set.inter_diff_assoc Set.inter_diff_assoc
 
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-Case conversion may be inaccurate. Consider using '#align set.inter_diff_self Set.inter_diff_selfₓ'. -/
 @[simp]
 theorem inter_diff_self (a b : Set α) : a ∩ (b \ a) = ∅ :=
   inf_sdiff_self_right
 #align set.inter_diff_self Set.inter_diff_self
 
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-Case conversion may be inaccurate. Consider using '#align set.inter_union_diff Set.inter_union_diffₓ'. -/
 @[simp]
 theorem inter_union_diff (s t : Set α) : s ∩ t ∪ s \ t = s :=
   sup_inf_sdiff s t
 #align set.inter_union_diff Set.inter_union_diff
 
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-Case conversion may be inaccurate. Consider using '#align set.diff_union_inter Set.diff_union_interₓ'. -/
 @[simp]
 theorem diff_union_inter (s t : Set α) : s \ t ∪ s ∩ t = s := by rw [union_comm];
   exact sup_inf_sdiff _ _
 #align set.diff_union_inter Set.diff_union_inter
 
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-Case conversion may be inaccurate. Consider using '#align set.inter_union_compl Set.inter_union_complₓ'. -/
 @[simp]
 theorem inter_union_compl (s t : Set α) : s ∩ t ∪ s ∩ tᶜ = s :=
   inter_union_diff _ _
 #align set.inter_union_compl Set.inter_union_compl
 
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-Case conversion may be inaccurate. Consider using '#align set.diff_subset_diff Set.diff_subset_diffₓ'. -/
 theorem diff_subset_diff {s₁ s₂ t₁ t₂ : Set α} : s₁ ⊆ s₂ → t₂ ⊆ t₁ → s₁ \ t₁ ⊆ s₂ \ t₂ :=
   show s₁ ≤ s₂ → t₂ ≤ t₁ → s₁ \ t₁ ≤ s₂ \ t₂ from sdiff_le_sdiff
 #align set.diff_subset_diff Set.diff_subset_diff
 
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-Case conversion may be inaccurate. Consider using '#align set.diff_subset_diff_left Set.diff_subset_diff_leftₓ'. -/
 theorem diff_subset_diff_left {s₁ s₂ t : Set α} (h : s₁ ⊆ s₂) : s₁ \ t ⊆ s₂ \ t :=
   sdiff_le_sdiff_right ‹s₁ ≤ s₂›
 #align set.diff_subset_diff_left Set.diff_subset_diff_left
 
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 theorem diff_subset_diff_right {s t u : Set α} (h : t ⊆ u) : s \ u ⊆ s \ t :=
   sdiff_le_sdiff_left ‹t ≤ u›
 #align set.diff_subset_diff_right Set.diff_subset_diff_right
 
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 theorem compl_eq_univ_diff (s : Set α) : sᶜ = univ \ s :=
   top_sdiff.symm
 #align set.compl_eq_univ_diff Set.compl_eq_univ_diff
 
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 @[simp]
 theorem empty_diff (s : Set α) : (∅ \ s : Set α) = ∅ :=
   bot_sdiff
 #align set.empty_diff Set.empty_diff
 
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 theorem diff_eq_empty {s t : Set α} : s \ t = ∅ ↔ s ⊆ t :=
   sdiff_eq_bot_iff
 #align set.diff_eq_empty Set.diff_eq_empty
 
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 @[simp]
 theorem diff_empty {s : Set α} : s \ ∅ = s :=
   sdiff_bot
 #align set.diff_empty Set.diff_empty
 
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 @[simp]
 theorem diff_univ (s : Set α) : s \ univ = ∅ :=
   diff_eq_empty.2 (subset_univ s)
 #align set.diff_univ Set.diff_univ
 
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-Case conversion may be inaccurate. Consider using '#align set.diff_diff Set.diff_diffₓ'. -/
 theorem diff_diff {u : Set α} : (s \ t) \ u = s \ (t ∪ u) :=
   sdiff_sdiff_left
 #align set.diff_diff Set.diff_diff
 
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-Case conversion may be inaccurate. Consider using '#align set.diff_diff_comm Set.diff_diff_commₓ'. -/
 -- the following statement contains parentheses to help the reader
 theorem diff_diff_comm {s t u : Set α} : (s \ t) \ u = (s \ u) \ t :=
   sdiff_sdiff_comm
 #align set.diff_diff_comm Set.diff_diff_comm
 
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-Case conversion may be inaccurate. Consider using '#align set.diff_subset_iff Set.diff_subset_iffₓ'. -/
 theorem diff_subset_iff {s t u : Set α} : s \ t ⊆ u ↔ s ⊆ t ∪ u :=
   show s \ t ≤ u ↔ s ≤ t ∪ u from sdiff_le_iff
 #align set.diff_subset_iff Set.diff_subset_iff
 
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 theorem subset_diff_union (s t : Set α) : s ⊆ s \ t ∪ t :=
   show s ≤ s \ t ∪ t from le_sdiff_sup
 #align set.subset_diff_union Set.subset_diff_union
 
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-Case conversion may be inaccurate. Consider using '#align set.diff_union_of_subset Set.diff_union_of_subsetₓ'. -/
 theorem diff_union_of_subset {s t : Set α} (h : t ⊆ s) : s \ t ∪ t = s :=
   Subset.antisymm (union_subset (diff_subset _ _) h) (subset_diff_union _ _)
 #align set.diff_union_of_subset Set.diff_union_of_subset
 
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-Case conversion may be inaccurate. Consider using '#align set.diff_singleton_subset_iff Set.diff_singleton_subset_iffₓ'. -/
 @[simp]
 theorem diff_singleton_subset_iff {x : α} {s t : Set α} : s \ {x} ⊆ t ↔ s ⊆ insert x t := by
   rw [← union_singleton, union_comm]; apply diff_subset_iff
 #align set.diff_singleton_subset_iff Set.diff_singleton_subset_iff
 
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-Case conversion may be inaccurate. Consider using '#align set.subset_diff_singleton Set.subset_diff_singletonₓ'. -/
 theorem subset_diff_singleton {x : α} {s t : Set α} (h : s ⊆ t) (hx : x ∉ s) : s ⊆ t \ {x} :=
   subset_inter h <| subset_compl_comm.1 <| singleton_subset_iff.2 hx
 #align set.subset_diff_singleton Set.subset_diff_singleton
 
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-Case conversion may be inaccurate. Consider using '#align set.subset_insert_diff_singleton Set.subset_insert_diff_singletonₓ'. -/
 theorem subset_insert_diff_singleton (x : α) (s : Set α) : s ⊆ insert x (s \ {x}) := by
   rw [← diff_singleton_subset_iff]
 #align set.subset_insert_diff_singleton Set.subset_insert_diff_singleton
 
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-Case conversion may be inaccurate. Consider using '#align set.diff_subset_comm Set.diff_subset_commₓ'. -/
 theorem diff_subset_comm {s t u : Set α} : s \ t ⊆ u ↔ s \ u ⊆ t :=
   show s \ t ≤ u ↔ s \ u ≤ t from sdiff_le_comm
 #align set.diff_subset_comm Set.diff_subset_comm
 
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-Case conversion may be inaccurate. Consider using '#align set.diff_inter Set.diff_interₓ'. -/
 theorem diff_inter {s t u : Set α} : s \ (t ∩ u) = s \ t ∪ s \ u :=
   sdiff_inf
 #align set.diff_inter Set.diff_inter
 
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-Case conversion may be inaccurate. Consider using '#align set.diff_inter_diff Set.diff_inter_diffₓ'. -/
 theorem diff_inter_diff {s t u : Set α} : s \ t ∩ (s \ u) = s \ (t ∪ u) :=
   sdiff_sup.symm
 #align set.diff_inter_diff Set.diff_inter_diff
 
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-Case conversion may be inaccurate. Consider using '#align set.diff_compl Set.diff_complₓ'. -/
 theorem diff_compl : s \ tᶜ = s ∩ t :=
   sdiff_compl
 #align set.diff_compl Set.diff_compl
 
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-Case conversion may be inaccurate. Consider using '#align set.diff_diff_right Set.diff_diff_rightₓ'. -/
 theorem diff_diff_right {s t u : Set α} : s \ (t \ u) = s \ t ∪ s ∩ u :=
   sdiff_sdiff_right'
 #align set.diff_diff_right Set.diff_diff_right
 
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 @[simp]
 theorem insert_diff_of_mem (s) (h : a ∈ t) : insert a s \ t = s \ t := by ext;
   constructor <;> simp (config := { contextual := true }) [or_imp, h]
 #align set.insert_diff_of_mem Set.insert_diff_of_mem
 
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 theorem insert_diff_of_not_mem (s) (h : a ∉ t) : insert a s \ t = insert a (s \ t) := by
   classical
     ext x
@@ -3786,22 +2274,10 @@ theorem insert_diff_of_not_mem (s) (h : a ∉ t) : insert a s \ t = insert a (s
     · simp [h, h']
 #align set.insert_diff_of_not_mem Set.insert_diff_of_not_mem
 
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 theorem insert_diff_self_of_not_mem {a : α} {s : Set α} (h : a ∉ s) : insert a s \ {a} = s := by
   ext; simp [and_iff_left_of_imp fun hx : x ∈ s => show x ≠ a from fun hxa => h <| hxa ▸ hx]
 #align set.insert_diff_self_of_not_mem Set.insert_diff_self_of_not_mem
 
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 @[simp]
 theorem insert_diff_eq_singleton {a : α} {s : Set α} (h : a ∉ s) : insert a s \ s = {a} :=
   by
@@ -3812,203 +2288,89 @@ theorem insert_diff_eq_singleton {a : α} {s : Set α} (h : a ∉ s) : insert a
   exact h
 #align set.insert_diff_eq_singleton Set.insert_diff_eq_singleton
 
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 theorem inter_insert_of_mem (h : a ∈ s) : s ∩ insert a t = insert a (s ∩ t) := by
   rw [insert_inter_distrib, insert_eq_of_mem h]
 #align set.inter_insert_of_mem Set.inter_insert_of_mem
 
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 theorem insert_inter_of_mem (h : a ∈ t) : insert a s ∩ t = insert a (s ∩ t) := by
   rw [insert_inter_distrib, insert_eq_of_mem h]
 #align set.insert_inter_of_mem Set.insert_inter_of_mem
 
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 theorem inter_insert_of_not_mem (h : a ∉ s) : s ∩ insert a t = s ∩ t :=
   ext fun x => and_congr_right fun hx => or_iff_right <| ne_of_mem_of_not_mem hx h
 #align set.inter_insert_of_not_mem Set.inter_insert_of_not_mem
 
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 theorem insert_inter_of_not_mem (h : a ∉ t) : insert a s ∩ t = s ∩ t :=
   ext fun x => and_congr_left fun hx => or_iff_right <| ne_of_mem_of_not_mem hx h
 #align set.insert_inter_of_not_mem Set.insert_inter_of_not_mem
 
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 @[simp]
 theorem union_diff_self {s t : Set α} : s ∪ t \ s = s ∪ t :=
   sup_sdiff_self _ _
 #align set.union_diff_self Set.union_diff_self
 
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 @[simp]
 theorem diff_union_self {s t : Set α} : s \ t ∪ t = s ∪ t :=
   sdiff_sup_self _ _
 #align set.diff_union_self Set.diff_union_self
 
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 @[simp]
 theorem diff_inter_self {a b : Set α} : b \ a ∩ a = ∅ :=
   inf_sdiff_self_left
 #align set.diff_inter_self Set.diff_inter_self
 
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 @[simp]
 theorem diff_inter_self_eq_diff {s t : Set α} : s \ (t ∩ s) = s \ t :=
   sdiff_inf_self_right _ _
 #align set.diff_inter_self_eq_diff Set.diff_inter_self_eq_diff
 
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 @[simp]
 theorem diff_self_inter {s t : Set α} : s \ (s ∩ t) = s \ t :=
   sdiff_inf_self_left _ _
 #align set.diff_self_inter Set.diff_self_inter
 
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 @[simp]
 theorem diff_singleton_eq_self {a : α} {s : Set α} (h : a ∉ s) : s \ {a} = s :=
   sdiff_eq_self_iff_disjoint.2 <| by simp [h]
 #align set.diff_singleton_eq_self Set.diff_singleton_eq_self
 
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-Case conversion may be inaccurate. Consider using '#align set.diff_singleton_ssubset Set.diff_singleton_sSubsetₓ'. -/
 @[simp]
 theorem diff_singleton_sSubset {s : Set α} {a : α} : s \ {a} ⊂ s ↔ a ∈ s :=
   sdiff_le.lt_iff_ne.trans <| sdiff_eq_left.Not.trans <| by simp
 #align set.diff_singleton_ssubset Set.diff_singleton_sSubset
 
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 @[simp]
 theorem insert_diff_singleton {a : α} {s : Set α} : insert a (s \ {a}) = insert a s := by
   simp [insert_eq, union_diff_self, -union_singleton, -singleton_union]
 #align set.insert_diff_singleton Set.insert_diff_singleton
 
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-Case conversion may be inaccurate. Consider using '#align set.insert_diff_singleton_comm Set.insert_diff_singleton_commₓ'. -/
 theorem insert_diff_singleton_comm (hab : a ≠ b) (s : Set α) :
     insert a (s \ {b}) = insert a s \ {b} := by
   simp_rw [← union_singleton, union_diff_distrib,
     diff_singleton_eq_self (mem_singleton_iff.not.2 hab.symm)]
 #align set.insert_diff_singleton_comm Set.insert_diff_singleton_comm
 
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 @[simp]
 theorem diff_self {s : Set α} : s \ s = ∅ :=
   sdiff_self
 #align set.diff_self Set.diff_self
 
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 theorem diff_diff_right_self (s t : Set α) : s \ (s \ t) = s ∩ t :=
   sdiff_sdiff_right_self
 #align set.diff_diff_right_self Set.diff_diff_right_self
 
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 theorem diff_diff_cancel_left {s t : Set α} (h : s ⊆ t) : t \ (t \ s) = s :=
   sdiff_sdiff_eq_self h
 #align set.diff_diff_cancel_left Set.diff_diff_cancel_left
 
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 theorem mem_diff_singleton {x y : α} {s : Set α} : x ∈ s \ {y} ↔ x ∈ s ∧ x ≠ y :=
   Iff.rfl
 #align set.mem_diff_singleton Set.mem_diff_singleton
 
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 theorem mem_diff_singleton_empty {t : Set (Set α)} : s ∈ t \ {∅} ↔ s ∈ t ∧ s.Nonempty :=
   mem_diff_singleton.trans <| and_congr_right' nonempty_iff_ne_empty.symm
 #align set.mem_diff_singleton_empty Set.mem_diff_singleton_empty
 
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 theorem union_eq_diff_union_diff_union_inter (s t : Set α) : s ∪ t = s \ t ∪ t \ s ∪ s ∩ t :=
   sup_eq_sdiff_sup_sdiff_sup_inf
 #align set.union_eq_diff_union_diff_union_inter Set.union_eq_diff_union_diff_union_inter
@@ -4016,94 +2378,40 @@ theorem union_eq_diff_union_diff_union_inter (s t : Set α) : s ∪ t = s \ t 
 /-! ### Symmetric difference -/
 
 
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 theorem mem_symmDiff : a ∈ s ∆ t ↔ a ∈ s ∧ a ∉ t ∨ a ∈ t ∧ a ∉ s :=
   Iff.rfl
 #align set.mem_symm_diff Set.mem_symmDiff
 
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 protected theorem symmDiff_def (s t : Set α) : s ∆ t = s \ t ∪ t \ s :=
   rfl
 #align set.symm_diff_def Set.symmDiff_def
 
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 theorem symmDiff_subset_union : s ∆ t ⊆ s ∪ t :=
   @symmDiff_le_sup (Set α) _ _ _
 #align set.symm_diff_subset_union Set.symmDiff_subset_union
 
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 @[simp]
 theorem symmDiff_eq_empty : s ∆ t = ∅ ↔ s = t :=
   symmDiff_eq_bot
 #align set.symm_diff_eq_empty Set.symmDiff_eq_empty
 
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 @[simp]
 theorem symmDiff_nonempty : (s ∆ t).Nonempty ↔ s ≠ t :=
   nonempty_iff_ne_empty.trans symmDiff_eq_empty.Not
 #align set.symm_diff_nonempty Set.symmDiff_nonempty
 
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 theorem inter_symmDiff_distrib_left (s t u : Set α) : s ∩ t ∆ u = (s ∩ t) ∆ (s ∩ u) :=
   inf_symmDiff_distrib_left _ _ _
 #align set.inter_symm_diff_distrib_left Set.inter_symmDiff_distrib_left
 
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 theorem inter_symmDiff_distrib_right (s t u : Set α) : s ∆ t ∩ u = (s ∩ u) ∆ (t ∩ u) :=
   inf_symmDiff_distrib_right _ _ _
 #align set.inter_symm_diff_distrib_right Set.inter_symmDiff_distrib_right
 
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 theorem subset_symmDiff_union_symmDiff_left (h : Disjoint s t) : u ⊆ s ∆ u ∪ t ∆ u :=
   h.le_symmDiff_sup_symmDiff_left
 #align set.subset_symm_diff_union_symm_diff_left Set.subset_symmDiff_union_symmDiff_left
 
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-Case conversion may be inaccurate. Consider using '#align set.subset_symm_diff_union_symm_diff_right Set.subset_symmDiff_union_symmDiff_rightₓ'. -/
 theorem subset_symmDiff_union_symmDiff_right (h : Disjoint t u) : s ⊆ s ∆ t ∪ s ∆ u :=
   h.le_symmDiff_sup_symmDiff_right
 #align set.subset_symm_diff_union_symm_diff_right Set.subset_symmDiff_union_symmDiff_right
@@ -4137,12 +2445,6 @@ theorem mem_powerset_iff (x s : Set α) : x ∈ 𝒫 s ↔ x ⊆ s :=
 #align set.mem_powerset_iff Set.mem_powerset_iff
 -/
 
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-Case conversion may be inaccurate. Consider using '#align set.powerset_inter Set.powerset_interₓ'. -/
 theorem powerset_inter (s t : Set α) : 𝒫(s ∩ t) = 𝒫 s ∩ 𝒫 t :=
   ext fun u => subset_inter_iff
 #align set.powerset_inter Set.powerset_inter
@@ -4154,12 +2456,6 @@ theorem powerset_mono : 𝒫 s ⊆ 𝒫 t ↔ s ⊆ t :=
 #align set.powerset_mono Set.powerset_mono
 -/
 
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-Case conversion may be inaccurate. Consider using '#align set.monotone_powerset Set.monotone_powersetₓ'. -/
 theorem monotone_powerset : Monotone (powerset : Set α → Set (Set α)) := fun s t => powerset_mono.2
 #align set.monotone_powerset Set.monotone_powerset
 
@@ -4259,45 +2555,21 @@ protected def ite (t s s' : Set α) : Set α :=
 #align set.ite Set.ite
 -/
 
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-Case conversion may be inaccurate. Consider using '#align set.ite_inter_self Set.ite_inter_selfₓ'. -/
 @[simp]
 theorem ite_inter_self (t s s' : Set α) : t.ite s s' ∩ t = s ∩ t := by
   rw [Set.ite, union_inter_distrib_right, diff_inter_self, inter_assoc, inter_self, union_empty]
 #align set.ite_inter_self Set.ite_inter_self
 
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 @[simp]
 theorem ite_compl (t s s' : Set α) : tᶜ.ite s s' = t.ite s' s := by
   rw [Set.ite, Set.ite, diff_compl, union_comm, diff_eq]
 #align set.ite_compl Set.ite_compl
 
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 @[simp]
 theorem ite_inter_compl_self (t s s' : Set α) : t.ite s s' ∩ tᶜ = s' ∩ tᶜ := by
   rw [← ite_compl, ite_inter_self]
 #align set.ite_inter_compl_self Set.ite_inter_compl_self
 
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 @[simp]
 theorem ite_diff_self (t s s' : Set α) : t.ite s s' \ t = s' \ t :=
   ite_inter_compl_self t s s'
@@ -4310,22 +2582,10 @@ theorem ite_same (t s : Set α) : t.ite s s = s :=
 #align set.ite_same Set.ite_same
 -/
 
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 @[simp]
 theorem ite_left (s t : Set α) : s.ite s t = s ∪ t := by simp [Set.ite]
 #align set.ite_left Set.ite_left
 
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 @[simp]
 theorem ite_right (s t : Set α) : s.ite t s = t ∩ s := by simp [Set.ite]
 #align set.ite_right Set.ite_right
@@ -4342,22 +2602,10 @@ theorem ite_univ (s s' : Set α) : Set.ite univ s s' = s := by simp [Set.ite]
 #align set.ite_univ Set.ite_univ
 -/
 
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 @[simp]
 theorem ite_empty_left (t s : Set α) : t.ite ∅ s = s \ t := by simp [Set.ite]
 #align set.ite_empty_left Set.ite_empty_left
 
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 @[simp]
 theorem ite_empty_right (t s : Set α) : t.ite s ∅ = s ∩ t := by simp [Set.ite]
 #align set.ite_empty_right Set.ite_empty_right
@@ -4369,63 +2617,27 @@ theorem ite_mono (t : Set α) {s₁ s₁' s₂ s₂' : Set α} (h : s₁ ⊆ s
 #align set.ite_mono Set.ite_mono
 -/
 
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-Case conversion may be inaccurate. Consider using '#align set.ite_subset_union Set.ite_subset_unionₓ'. -/
 theorem ite_subset_union (t s s' : Set α) : t.ite s s' ⊆ s ∪ s' :=
   union_subset_union (inter_subset_left _ _) (diff_subset _ _)
 #align set.ite_subset_union Set.ite_subset_union
 
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 theorem inter_subset_ite (t s s' : Set α) : s ∩ s' ⊆ t.ite s s' :=
   ite_same t (s ∩ s') ▸ ite_mono _ (inter_subset_left _ _) (inter_subset_right _ _)
 #align set.inter_subset_ite Set.inter_subset_ite
 
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 theorem ite_inter_inter (t s₁ s₂ s₁' s₂' : Set α) :
     t.ite (s₁ ∩ s₂) (s₁' ∩ s₂') = t.ite s₁ s₁' ∩ t.ite s₂ s₂' := by ext x;
   simp only [Set.ite, Set.mem_inter_iff, Set.mem_diff, Set.mem_union]; itauto
 #align set.ite_inter_inter Set.ite_inter_inter
 
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 theorem ite_inter (t s₁ s₂ s : Set α) : t.ite (s₁ ∩ s) (s₂ ∩ s) = t.ite s₁ s₂ ∩ s := by
   rw [ite_inter_inter, ite_same]
 #align set.ite_inter Set.ite_inter
 
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-Case conversion may be inaccurate. Consider using '#align set.ite_inter_of_inter_eq Set.ite_inter_of_inter_eqₓ'. -/
 theorem ite_inter_of_inter_eq (t : Set α) {s₁ s₂ s : Set α} (h : s₁ ∩ s = s₂ ∩ s) :
     t.ite s₁ s₂ ∩ s = s₁ ∩ s := by rw [← ite_inter, ← h, ite_same]
 #align set.ite_inter_of_inter_eq Set.ite_inter_of_inter_eq
 
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-Case conversion may be inaccurate. Consider using '#align set.subset_ite Set.subset_iteₓ'. -/
 theorem subset_ite {t s s' u : Set α} : u ⊆ t.ite s s' ↔ u ∩ t ⊆ s ∧ u \ t ⊆ s' :=
   by
   simp only [subset_def, ← forall_and]
@@ -4524,22 +2736,10 @@ theorem subsingleton_of_subsingleton [Subsingleton α] {s : Set α} : Set.Subsin
 #align set.subsingleton_of_subsingleton Set.subsingleton_of_subsingleton
 -/
 
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-Case conversion may be inaccurate. Consider using '#align set.subsingleton_is_top Set.subsingleton_isTopₓ'. -/
 theorem subsingleton_isTop (α : Type _) [PartialOrder α] : Set.Subsingleton { x : α | IsTop x } :=
   fun x hx y hy => hx.IsMax.eq_of_le (hy x)
 #align set.subsingleton_is_top Set.subsingleton_isTop
 
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-Case conversion may be inaccurate. Consider using '#align set.subsingleton_is_bot Set.subsingleton_isBotₓ'. -/
 theorem subsingleton_isBot (α : Type _) [PartialOrder α] : Set.Subsingleton { x : α | IsBot x } :=
   fun x hx y hy => hx.IsMin.eq_of_ge (hy x)
 #align set.subsingleton_is_bot Set.subsingleton_isBot
@@ -4659,23 +2859,11 @@ theorem nontrivial_iff_pair_subset : s.Nontrivial ↔ ∃ (x y : _)(hxy : x ≠
 #align set.nontrivial_iff_pair_subset Set.nontrivial_iff_pair_subset
 -/
 
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 theorem nontrivial_of_exists_ne {x} (hx : x ∈ s) (h : ∃ y ∈ s, y ≠ x) : s.Nontrivial :=
   let ⟨y, hy, hyx⟩ := h
   ⟨y, hy, x, hx, hyx⟩
 #align set.nontrivial_of_exists_ne Set.nontrivial_of_exists_ne
 
-/- warning: set.nontrivial.exists_ne -> Set.Nontrivial.exists_ne is a dubious translation:
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 theorem Nontrivial.exists_ne (hs : s.Nontrivial) (z) : ∃ x ∈ s, x ≠ z :=
   by
   by_contra H; push_neg  at H
@@ -4684,33 +2872,15 @@ theorem Nontrivial.exists_ne (hs : s.Nontrivial) (z) : ∃ x ∈ s, x ≠ z :=
   exact hxy rfl
 #align set.nontrivial.exists_ne Set.Nontrivial.exists_ne
 
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 theorem nontrivial_iff_exists_ne {x} (hx : x ∈ s) : s.Nontrivial ↔ ∃ y ∈ s, y ≠ x :=
   ⟨fun H => H.exists_ne _, nontrivial_of_exists_ne hx⟩
 #align set.nontrivial_iff_exists_ne Set.nontrivial_iff_exists_ne
 
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 theorem nontrivial_of_lt [Preorder α] {x y} (hx : x ∈ s) (hy : y ∈ s) (hxy : x < y) :
     s.Nontrivial :=
   ⟨x, hx, y, hy, ne_of_lt hxy⟩
 #align set.nontrivial_of_lt Set.nontrivial_of_lt
 
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 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem nontrivial_of_exists_lt [Preorder α] (H : ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s), x < y) :
     s.Nontrivial :=
@@ -4718,12 +2888,6 @@ theorem nontrivial_of_exists_lt [Preorder α] (H : ∃ (x : _)(_ : x ∈ s)(y :
   nontrivial_of_lt hx hy hxy
 #align set.nontrivial_of_exists_lt Set.nontrivial_of_exists_lt
 
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-Case conversion may be inaccurate. Consider using '#align set.nontrivial.exists_lt Set.Nontrivial.exists_ltₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem Nontrivial.exists_lt [LinearOrder α] (hs : s.Nontrivial) :
     ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s), x < y :=
@@ -4731,12 +2895,6 @@ theorem Nontrivial.exists_lt [LinearOrder α] (hs : s.Nontrivial) :
   Or.elim (lt_or_gt_of_ne hxy) (fun H => ⟨x, hx, y, hy, H⟩) fun H => ⟨y, hy, x, hx, H⟩
 #align set.nontrivial.exists_lt Set.Nontrivial.exists_lt
 
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 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem nontrivial_iff_exists_lt [LinearOrder α] :
     s.Nontrivial ↔ ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s), x < y :=
@@ -4987,9 +3145,6 @@ section LinearOrder
 
 variable [LinearOrder α] [LinearOrder β] {f : α → β}
 
-/- warning: set.not_monotone_on_not_antitone_on_iff_exists_le_le -> Set.not_monotoneOn_not_antitoneOn_iff_exists_le_le is a dubious translation:
-<too large>
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 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a b c «expr ∈ » s) -/
 /-- A function between linear orders which is neither monotone nor antitone makes a dent upright or
 downright. -/
@@ -5002,9 +3157,6 @@ theorem not_monotoneOn_not_antitoneOn_iff_exists_le_le :
     not_monotone_not_antitone_iff_exists_le_le, @and_left_comm (_ ∈ s)]
 #align set.not_monotone_on_not_antitone_on_iff_exists_le_le Set.not_monotoneOn_not_antitoneOn_iff_exists_le_le
 
-/- warning: set.not_monotone_on_not_antitone_on_iff_exists_lt_lt -> Set.not_monotoneOn_not_antitoneOn_iff_exists_lt_lt is a dubious translation:
-<too large>
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 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a b c «expr ∈ » s) -/
 /-- A function between linear orders which is neither monotone nor antitone makes a dent upright or
 downright. -/
@@ -5027,12 +3179,6 @@ namespace Function
 
 variable {ι : Sort _} {α : Type _} {β : Type _} {f : α → β}
 
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 theorem Injective.nonempty_apply_iff {f : Set α → Set β} (hf : Injective f) (h2 : f ∅ = ∅)
     {s : Set α} : (f s).Nonempty ↔ s.Nonempty := by
   rw [nonempty_iff_ne_empty, ← h2, nonempty_iff_ne_empty, hf.ne_iff]
@@ -5156,42 +3302,18 @@ namespace Set
 
 variable {α : Type u} (s t : Set α) (a : α)
 
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 instance decidableSdiff [Decidable (a ∈ s)] [Decidable (a ∈ t)] : Decidable (a ∈ s \ t) :=
   (by infer_instance : Decidable (a ∈ s ∧ a ∉ t))
 #align set.decidable_sdiff Set.decidableSdiff
 
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 instance decidableInter [Decidable (a ∈ s)] [Decidable (a ∈ t)] : Decidable (a ∈ s ∩ t) :=
   (by infer_instance : Decidable (a ∈ s ∧ a ∈ t))
 #align set.decidable_inter Set.decidableInter
 
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 instance decidableUnion [Decidable (a ∈ s)] [Decidable (a ∈ t)] : Decidable (a ∈ s ∪ t) :=
   (by infer_instance : Decidable (a ∈ s ∨ a ∈ t))
 #align set.decidable_union Set.decidableUnion
 
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 instance decidableCompl [Decidable (a ∈ s)] : Decidable (a ∈ sᶜ) :=
   (by infer_instance : Decidable (a ∉ s))
 #align set.decidable_compl Set.decidableCompl
@@ -5222,89 +3344,41 @@ section Monotone
 
 variable {α β : Type _}
 
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 theorem Monotone.inter [Preorder β] {f g : β → Set α} (hf : Monotone f) (hg : Monotone g) :
     Monotone fun x => f x ∩ g x :=
   hf.inf hg
 #align monotone.inter Monotone.inter
 
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-Case conversion may be inaccurate. Consider using '#align monotone_on.inter MonotoneOn.interₓ'. -/
 theorem MonotoneOn.inter [Preorder β] {f g : β → Set α} {s : Set β} (hf : MonotoneOn f s)
     (hg : MonotoneOn g s) : MonotoneOn (fun x => f x ∩ g x) s :=
   hf.inf hg
 #align monotone_on.inter MonotoneOn.inter
 
-/- warning: antitone.inter -> Antitone.inter is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align antitone.inter Antitone.interₓ'. -/
 theorem Antitone.inter [Preorder β] {f g : β → Set α} (hf : Antitone f) (hg : Antitone g) :
     Antitone fun x => f x ∩ g x :=
   hf.inf hg
 #align antitone.inter Antitone.inter
 
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-Case conversion may be inaccurate. Consider using '#align antitone_on.inter AntitoneOn.interₓ'. -/
 theorem AntitoneOn.inter [Preorder β] {f g : β → Set α} {s : Set β} (hf : AntitoneOn f s)
     (hg : AntitoneOn g s) : AntitoneOn (fun x => f x ∩ g x) s :=
   hf.inf hg
 #align antitone_on.inter AntitoneOn.inter
 
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-Case conversion may be inaccurate. Consider using '#align monotone.union Monotone.unionₓ'. -/
 theorem Monotone.union [Preorder β] {f g : β → Set α} (hf : Monotone f) (hg : Monotone g) :
     Monotone fun x => f x ∪ g x :=
   hf.sup hg
 #align monotone.union Monotone.union
 
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-Case conversion may be inaccurate. Consider using '#align monotone_on.union MonotoneOn.unionₓ'. -/
 theorem MonotoneOn.union [Preorder β] {f g : β → Set α} {s : Set β} (hf : MonotoneOn f s)
     (hg : MonotoneOn g s) : MonotoneOn (fun x => f x ∪ g x) s :=
   hf.sup hg
 #align monotone_on.union MonotoneOn.union
 
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-Case conversion may be inaccurate. Consider using '#align antitone.union Antitone.unionₓ'. -/
 theorem Antitone.union [Preorder β] {f g : β → Set α} (hf : Antitone f) (hg : Antitone g) :
     Antitone fun x => f x ∪ g x :=
   hf.sup hg
 #align antitone.union Antitone.union
 
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-Case conversion may be inaccurate. Consider using '#align antitone_on.union AntitoneOn.unionₓ'. -/
 theorem AntitoneOn.union [Preorder β] {f g : β → Set α} {s : Set β} (hf : AntitoneOn f s)
     (hg : AntitoneOn g s) : AntitoneOn (fun x => f x ∪ g x) s :=
   hf.sup hg
@@ -5312,32 +3386,14 @@ theorem AntitoneOn.union [Preorder β] {f g : β → Set α} {s : Set β} (hf :
 
 namespace Set
 
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-Case conversion may be inaccurate. Consider using '#align set.monotone_set_of Set.monotone_setOfₓ'. -/
 theorem monotone_setOf [Preorder α] {p : α → β → Prop} (hp : ∀ b, Monotone fun a => p a b) :
     Monotone fun a => { b | p a b } := fun a a' h b => hp b h
 #align set.monotone_set_of Set.monotone_setOf
 
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-Case conversion may be inaccurate. Consider using '#align set.antitone_set_of Set.antitone_setOfₓ'. -/
 theorem antitone_setOf [Preorder α] {p : α → β → Prop} (hp : ∀ b, Antitone fun a => p a b) :
     Antitone fun a => { b | p a b } := fun a a' h b => hp b h
 #align set.antitone_set_of Set.antitone_setOf
 
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-Case conversion may be inaccurate. Consider using '#align set.antitone_bforall Set.antitone_bforallₓ'. -/
 /-- Quantifying over a set is antitone in the set -/
 theorem antitone_bforall {P : α → Prop} : Antitone fun s : Set α => ∀ x ∈ s, P x :=
   fun s t hst h x hx => h x <| hst hx
@@ -5354,82 +3410,34 @@ variable {α β : Type _} {s t u : Set α} {f : α → β}
 
 namespace Disjoint
 
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-Case conversion may be inaccurate. Consider using '#align disjoint.union_left Disjoint.union_leftₓ'. -/
 theorem union_left (hs : Disjoint s u) (ht : Disjoint t u) : Disjoint (s ∪ t) u :=
   hs.sup_left ht
 #align disjoint.union_left Disjoint.union_left
 
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 theorem union_right (ht : Disjoint s t) (hu : Disjoint s u) : Disjoint s (t ∪ u) :=
   ht.sup_right hu
 #align disjoint.union_right Disjoint.union_right
 
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 theorem inter_left (u : Set α) (h : Disjoint s t) : Disjoint (s ∩ u) t :=
   h.inf_left u
 #align disjoint.inter_left Disjoint.inter_left
 
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 theorem inter_left' (u : Set α) (h : Disjoint s t) : Disjoint (u ∩ s) t :=
   h.inf_left' _
 #align disjoint.inter_left' Disjoint.inter_left'
 
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 theorem inter_right (u : Set α) (h : Disjoint s t) : Disjoint s (t ∩ u) :=
   h.inf_right _
 #align disjoint.inter_right Disjoint.inter_right
 
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-Case conversion may be inaccurate. Consider using '#align disjoint.inter_right' Disjoint.inter_right'ₓ'. -/
 theorem inter_right' (u : Set α) (h : Disjoint s t) : Disjoint s (u ∩ t) :=
   h.inf_right' _
 #align disjoint.inter_right' Disjoint.inter_right'
 
-/- warning: disjoint.subset_left_of_subset_union -> Disjoint.subset_left_of_subset_union is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {s : Set.{u1} α} {t : Set.{u1} α} {u : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) t u)) -> (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))) s u) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s t)
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align disjoint.subset_left_of_subset_union Disjoint.subset_left_of_subset_unionₓ'. -/
 theorem subset_left_of_subset_union (h : s ⊆ t ∪ u) (hac : Disjoint s u) : s ⊆ t :=
   hac.left_le_of_le_sup_right h
 #align disjoint.subset_left_of_subset_union Disjoint.subset_left_of_subset_union
 
-/- warning: disjoint.subset_right_of_subset_union -> Disjoint.subset_right_of_subset_union is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {s : Set.{u1} α} {t : Set.{u1} α} {u : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) t u)) -> (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))) s t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s u)
-but is expected to have type
-  forall {α : Type.{u1}} {s : Set.{u1} α} {t : Set.{u1} α} {u : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) t u)) -> (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))))) (BooleanAlgebra.toBoundedOrder.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))) s t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s u)
-Case conversion may be inaccurate. Consider using '#align disjoint.subset_right_of_subset_union Disjoint.subset_right_of_subset_unionₓ'. -/
 theorem subset_right_of_subset_union (h : s ⊆ t ∪ u) (hab : Disjoint s t) : s ⊆ u :=
   hab.left_le_of_le_sup_left h
 #align disjoint.subset_right_of_subset_union Disjoint.subset_right_of_subset_union

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -1027,9 +1027,7 @@ theorem eq_univ_of_forall {s : Set α} : (∀ x, x ∈ s) → s = univ :=
 -/
 
 #print Set.Nonempty.eq_univ /-
-theorem Nonempty.eq_univ [Subsingleton α] : s.Nonempty → s = univ :=
-  by
-  rintro ⟨x, hx⟩
+theorem Nonempty.eq_univ [Subsingleton α] : s.Nonempty → s = univ := by rintro ⟨x, hx⟩;
   refine' eq_univ_of_forall fun y => by rwa [Subsingleton.elim y x]
 #align set.nonempty.eq_univ Set.Nonempty.eq_univ
 -/
@@ -3529,9 +3527,7 @@ but is expected to have type
   forall {α : Type.{u1}} (s : Set.{u1} α) (t : Set.{u1} α), Eq.{succ u1} (Set.{u1} α) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) (SDiff.sdiff.{u1} (Set.{u1} α) (Set.instSDiffSet.{u1} α) s t) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s t)) s
 Case conversion may be inaccurate. Consider using '#align set.diff_union_inter Set.diff_union_interₓ'. -/
 @[simp]
-theorem diff_union_inter (s t : Set α) : s \ t ∪ s ∩ t = s :=
-  by
-  rw [union_comm]
+theorem diff_union_inter (s t : Set α) : s \ t ∪ s ∩ t = s := by rw [union_comm];
   exact sup_inf_sdiff _ _
 #align set.diff_union_inter Set.diff_union_inter
 
@@ -3687,10 +3683,8 @@ but is expected to have type
   forall {α : Type.{u1}} {x : α} {s : Set.{u1} α} {t : Set.{u1} α}, Iff (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (SDiff.sdiff.{u1} (Set.{u1} α) (Set.instSDiffSet.{u1} α) s (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) x)) t) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) x t))
 Case conversion may be inaccurate. Consider using '#align set.diff_singleton_subset_iff Set.diff_singleton_subset_iffₓ'. -/
 @[simp]
-theorem diff_singleton_subset_iff {x : α} {s t : Set α} : s \ {x} ⊆ t ↔ s ⊆ insert x t :=
-  by
-  rw [← union_singleton, union_comm]
-  apply diff_subset_iff
+theorem diff_singleton_subset_iff {x : α} {s t : Set α} : s \ {x} ⊆ t ↔ s ⊆ insert x t := by
+  rw [← union_singleton, union_comm]; apply diff_subset_iff
 #align set.diff_singleton_subset_iff Set.diff_singleton_subset_iff
 
 /- warning: set.subset_diff_singleton -> Set.subset_diff_singleton is a dubious translation:
@@ -3770,9 +3764,7 @@ but is expected to have type
   forall {α : Type.{u1}} {a : α} {t : Set.{u1} α} (s : Set.{u1} α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a t) -> (Eq.{succ u1} (Set.{u1} α) (SDiff.sdiff.{u1} (Set.{u1} α) (Set.instSDiffSet.{u1} α) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a s) t) (SDiff.sdiff.{u1} (Set.{u1} α) (Set.instSDiffSet.{u1} α) s t))
 Case conversion may be inaccurate. Consider using '#align set.insert_diff_of_mem Set.insert_diff_of_memₓ'. -/
 @[simp]
-theorem insert_diff_of_mem (s) (h : a ∈ t) : insert a s \ t = s \ t :=
-  by
-  ext
+theorem insert_diff_of_mem (s) (h : a ∈ t) : insert a s \ t = s \ t := by ext;
   constructor <;> simp (config := { contextual := true }) [or_imp, h]
 #align set.insert_diff_of_mem Set.insert_diff_of_mem
 
@@ -3800,10 +3792,8 @@ lean 3 declaration is
 but is expected to have type
   forall {α : Type.{u1}} {a : α} {s : Set.{u1} α}, (Not (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s)) -> (Eq.{succ u1} (Set.{u1} α) (SDiff.sdiff.{u1} (Set.{u1} α) (Set.instSDiffSet.{u1} α) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a s) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) a)) s)
 Case conversion may be inaccurate. Consider using '#align set.insert_diff_self_of_not_mem Set.insert_diff_self_of_not_memₓ'. -/
-theorem insert_diff_self_of_not_mem {a : α} {s : Set α} (h : a ∉ s) : insert a s \ {a} = s :=
-  by
-  ext
-  simp [and_iff_left_of_imp fun hx : x ∈ s => show x ≠ a from fun hxa => h <| hxa ▸ hx]
+theorem insert_diff_self_of_not_mem {a : α} {s : Set α} (h : a ∉ s) : insert a s \ {a} = s := by
+  ext; simp [and_iff_left_of_imp fun hx : x ∈ s => show x ≠ a from fun hxa => h <| hxa ▸ hx]
 #align set.insert_diff_self_of_not_mem Set.insert_diff_self_of_not_mem
 
 /- warning: set.insert_diff_eq_singleton -> Set.insert_diff_eq_singleton is a dubious translation:
@@ -4196,9 +4186,7 @@ theorem powerset_univ : 𝒫(univ : Set α) = univ :=
 
 #print Set.powerset_singleton /-
 /-- The powerset of a singleton contains only `∅` and the singleton itself. -/
-theorem powerset_singleton (x : α) : 𝒫({x} : Set α) = {∅, {x}} :=
-  by
-  ext y
+theorem powerset_singleton (x : α) : 𝒫({x} : Set α) = {∅, {x}} := by ext y;
   rw [mem_powerset_iff, subset_singleton_iff_eq, mem_insert_iff, mem_singleton_iff]
 #align set.powerset_singleton Set.powerset_singleton
 -/
@@ -4408,11 +4396,8 @@ but is expected to have type
   forall {α : Type.{u1}} (t : Set.{u1} α) (s₁ : Set.{u1} α) (s₂ : Set.{u1} α) (s₁' : Set.{u1} α) (s₂' : Set.{u1} α), Eq.{succ u1} (Set.{u1} α) (Set.ite.{u1} α t (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s₁ s₂) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s₁' s₂')) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) (Set.ite.{u1} α t s₁ s₁') (Set.ite.{u1} α t s₂ s₂'))
 Case conversion may be inaccurate. Consider using '#align set.ite_inter_inter Set.ite_inter_interₓ'. -/
 theorem ite_inter_inter (t s₁ s₂ s₁' s₂' : Set α) :
-    t.ite (s₁ ∩ s₂) (s₁' ∩ s₂') = t.ite s₁ s₁' ∩ t.ite s₂ s₂' :=
-  by
-  ext x
-  simp only [Set.ite, Set.mem_inter_iff, Set.mem_diff, Set.mem_union]
-  itauto
+    t.ite (s₁ ∩ s₂) (s₁' ∩ s₂') = t.ite s₁ s₁' ∩ t.ite s₂ s₂' := by ext x;
+  simp only [Set.ite, Set.mem_inter_iff, Set.mem_diff, Set.mem_union]; itauto
 #align set.ite_inter_inter Set.ite_inter_inter
 
 /- warning: set.ite_inter -> Set.ite_inter is a dubious translation:
@@ -4509,9 +4494,7 @@ theorem Subsingleton.eq_empty_or_singleton (hs : s.Subsingleton) : s = ∅ ∨ 
 
 #print Set.Subsingleton.induction_on /-
 theorem Subsingleton.induction_on {p : Set α → Prop} (hs : s.Subsingleton) (he : p ∅)
-    (h₁ : ∀ x, p {x}) : p s :=
-  by
-  rcases hs.eq_empty_or_singleton with (rfl | ⟨x, rfl⟩)
+    (h₁ : ∀ x, p {x}) : p s := by rcases hs.eq_empty_or_singleton with (rfl | ⟨x, rfl⟩);
   exacts[he, h₁ _]
 #align set.subsingleton.induction_on Set.Subsingleton.induction_on
 -/
@@ -4593,10 +4576,8 @@ theorem Subsingleton.coe_sort {s : Set α} : s.Subsingleton → Subsingleton s :
 #print Set.subsingleton_coe_of_subsingleton /-
 /-- The `coe_sort` of a set `s` in a subsingleton type is a subsingleton.
 For the corresponding result for `subtype`, see `subtype.subsingleton`. -/
-instance subsingleton_coe_of_subsingleton [Subsingleton α] {s : Set α} : Subsingleton s :=
-  by
-  rw [s.subsingleton_coe]
-  exact subsingleton_of_subsingleton
+instance subsingleton_coe_of_subsingleton [Subsingleton α] {s : Set α} : Subsingleton s := by
+  rw [s.subsingleton_coe]; exact subsingleton_of_subsingleton
 #align set.subsingleton_coe_of_subsingleton Set.subsingleton_coe_of_subsingleton
 -/
 
@@ -4799,9 +4780,7 @@ theorem not_nontrivial_singleton {x} : ¬({x} : Set α).Nontrivial := fun H =>
 -/
 
 #print Set.Nontrivial.ne_singleton /-
-theorem Nontrivial.ne_singleton {x} (hs : s.Nontrivial) : s ≠ {x} := fun H =>
-  by
-  rw [H] at hs
+theorem Nontrivial.ne_singleton {x} (hs : s.Nontrivial) : s ≠ {x} := fun H => by rw [H] at hs;
   exact not_nontrivial_singleton hs
 #align set.nontrivial.ne_singleton Set.Nontrivial.ne_singleton
 -/
@@ -4894,10 +4873,8 @@ protected theorem subsingleton_or_nontrivial (s : Set α) : s.Subsingleton ∨ s
 -/
 
 #print Set.eq_singleton_or_nontrivial /-
-theorem eq_singleton_or_nontrivial (ha : a ∈ s) : s = {a} ∨ s.Nontrivial :=
-  by
-  rw [← subsingleton_iff_singleton ha]
-  exact s.subsingleton_or_nontrivial
+theorem eq_singleton_or_nontrivial (ha : a ∈ s) : s = {a} ∨ s.Nontrivial := by
+  rw [← subsingleton_iff_singleton ha]; exact s.subsingleton_or_nontrivial
 #align set.eq_singleton_or_nontrivial Set.eq_singleton_or_nontrivial
 -/
 
@@ -5082,10 +5059,7 @@ def inclusion (h : s ⊆ t) : s → t := fun x : s => (⟨x, h x.2⟩ : t)
 
 #print Set.inclusion_self /-
 @[simp]
-theorem inclusion_self (x : s) : inclusion Subset.rfl x = x :=
-  by
-  cases x
-  rfl
+theorem inclusion_self (x : s) : inclusion Subset.rfl x = x := by cases x; rfl
 #align set.inclusion_self Set.inclusion_self
 -/
 
@@ -5103,20 +5077,15 @@ theorem inclusion_mk {h : s ⊆ t} (a : α) (ha : a ∈ s) : inclusion h ⟨a, h
 -/
 
 #print Set.inclusion_right /-
-theorem inclusion_right (h : s ⊆ t) (x : t) (m : (x : α) ∈ s) : inclusion h ⟨x, m⟩ = x :=
-  by
-  cases x
-  rfl
+theorem inclusion_right (h : s ⊆ t) (x : t) (m : (x : α) ∈ s) : inclusion h ⟨x, m⟩ = x := by
+  cases x; rfl
 #align set.inclusion_right Set.inclusion_right
 -/
 
 #print Set.inclusion_inclusion /-
 @[simp]
 theorem inclusion_inclusion (hst : s ⊆ t) (htu : t ⊆ u) (x : s) :
-    inclusion htu (inclusion hst x) = inclusion (hst.trans htu) x :=
-  by
-  cases x
-  rfl
+    inclusion htu (inclusion hst x) = inclusion (hst.trans htu) x := by cases x; rfl
 #align set.inclusion_inclusion Set.inclusion_inclusion
 -/

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -5011,10 +5011,7 @@ section LinearOrder
 variable [LinearOrder α] [LinearOrder β] {f : α → β}
 
 /- warning: set.not_monotone_on_not_antitone_on_iff_exists_le_le -> Set.not_monotoneOn_not_antitoneOn_iff_exists_le_le is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {s : Set.{u1} α} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : LinearOrder.{u2} β] {f : α -> β}, Iff (And (Not (MonotoneOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))) f s)) (Not (AntitoneOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))) f s))) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => Exists.{succ u1} α (fun (b : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => Exists.{succ u1} α (fun (c : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) c s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) c s) => And (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) (And (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) b c) (Or (And (LT.lt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))))) (f a) (f b)) (LT.lt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))))) (f c) (f b))) (And (LT.lt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))))) (f b) (f a)) (LT.lt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))))) (f b) (f c))))))))))))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} {s : Set.{u1} α} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : LinearOrder.{u2} β] {f : α -> β}, Iff (And (Not (MonotoneOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2))))) f s)) (Not (AntitoneOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2))))) f s))) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) => Exists.{succ u1} α (fun (b : α) => Exists.{0} (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) => Exists.{succ u1} α (fun (c : α) => Exists.{0} (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) c s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) c s) => And (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1)))))) a b) (And (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1)))))) b c) (Or (And (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) (f a) (f b)) (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) (f c) (f b))) (And (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) (f b) (f a)) (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) (f b) (f c))))))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align set.not_monotone_on_not_antitone_on_iff_exists_le_le Set.not_monotoneOn_not_antitoneOn_iff_exists_le_leₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a b c «expr ∈ » s) -/
 /-- A function between linear orders which is neither monotone nor antitone makes a dent upright or
@@ -5029,10 +5026,7 @@ theorem not_monotoneOn_not_antitoneOn_iff_exists_le_le :
 #align set.not_monotone_on_not_antitone_on_iff_exists_le_le Set.not_monotoneOn_not_antitoneOn_iff_exists_le_le
 
 /- warning: set.not_monotone_on_not_antitone_on_iff_exists_lt_lt -> Set.not_monotoneOn_not_antitoneOn_iff_exists_lt_lt is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {s : Set.{u1} α} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : LinearOrder.{u2} β] {f : α -> β}, Iff (And (Not (MonotoneOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))) f s)) (Not (AntitoneOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))) f s))) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => Exists.{succ u1} α (fun (b : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => Exists.{succ u1} α (fun (c : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) c s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) c s) => And (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) (And (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) b c) (Or (And (LT.lt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))))) (f a) (f b)) (LT.lt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))))) (f c) (f b))) (And (LT.lt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))))) (f b) (f a)) (LT.lt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))))) (f b) (f c))))))))))))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} {s : Set.{u1} α} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : LinearOrder.{u2} β] {f : α -> β}, Iff (And (Not (MonotoneOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2))))) f s)) (Not (AntitoneOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2))))) f s))) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) => Exists.{succ u1} α (fun (b : α) => Exists.{0} (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) => Exists.{succ u1} α (fun (c : α) => Exists.{0} (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) c s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) c s) => And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1)))))) a b) (And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1)))))) b c) (Or (And (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) (f a) (f b)) (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) (f c) (f b))) (And (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) (f b) (f a)) (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) (f b) (f c))))))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align set.not_monotone_on_not_antitone_on_iff_exists_lt_lt Set.not_monotoneOn_not_antitoneOn_iff_exists_lt_ltₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a b c «expr ∈ » s) -/
 /-- A function between linear orders which is neither monotone nor antitone makes a dent upright or

bump to nightly-2023-05-16-16

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

9cb92e8c

Diff

@@ -162,7 +162,7 @@ theorem le_eq_subset : ((· ≤ ·) : Set α → Set α → Prop) = (· ⊆ ·)
 
 /- warning: set.lt_eq_ssubset -> Set.lt_eq_ssubset is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}}, Eq.{succ u1} ((Set.{u1} α) -> (Set.{u1} α) -> Prop) (LT.lt.{u1} (Set.{u1} α) (Preorder.toLT.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))))))))) (HasSSubset.SSubset.{u1} (Set.{u1} α) (Set.hasSsubset.{u1} α))
+  forall {α : Type.{u1}}, Eq.{succ u1} ((Set.{u1} α) -> (Set.{u1} α) -> Prop) (LT.lt.{u1} (Set.{u1} α) (Preorder.toHasLt.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))))))))) (HasSSubset.SSubset.{u1} (Set.{u1} α) (Set.hasSsubset.{u1} α))
 but is expected to have type
   forall {α : Type.{u1}}, Eq.{succ u1} ((Set.{u1} α) -> (Set.{u1} α) -> Prop) (fun (x._@.Mathlib.Data.Set.Basic._hyg.488 : Set.{u1} α) (x._@.Mathlib.Data.Set.Basic._hyg.490 : Set.{u1} α) => LT.lt.{u1} (Set.{u1} α) (Preorder.toLT.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))))) x._@.Mathlib.Data.Set.Basic._hyg.488 x._@.Mathlib.Data.Set.Basic._hyg.490) (fun (x._@.Mathlib.Data.Set.Basic._hyg.503 : Set.{u1} α) (x._@.Mathlib.Data.Set.Basic._hyg.505 : Set.{u1} α) => HasSSubset.SSubset.{u1} (Set.{u1} α) (Set.instHasSSubsetSet.{u1} α) x._@.Mathlib.Data.Set.Basic._hyg.503 x._@.Mathlib.Data.Set.Basic._hyg.505)
 Case conversion may be inaccurate. Consider using '#align set.lt_eq_ssubset Set.lt_eq_ssubsetₓ'. -/
@@ -179,7 +179,7 @@ theorem le_iff_subset : s ≤ t ↔ s ⊆ t :=
 
 /- warning: set.lt_iff_ssubset -> Set.lt_iff_ssubset is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {s : Set.{u1} α} {t : Set.{u1} α}, Iff (LT.lt.{u1} (Set.{u1} α) (Preorder.toLT.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))))) s t) (HasSSubset.SSubset.{u1} (Set.{u1} α) (Set.hasSsubset.{u1} α) s t)
+  forall {α : Type.{u1}} {s : Set.{u1} α} {t : Set.{u1} α}, Iff (LT.lt.{u1} (Set.{u1} α) (Preorder.toHasLt.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))))) s t) (HasSSubset.SSubset.{u1} (Set.{u1} α) (Set.hasSsubset.{u1} α) s t)
 but is expected to have type
   forall {α : Type.{u1}} {s : Set.{u1} α} {t : Set.{u1} α}, Iff (LT.lt.{u1} (Set.{u1} α) (Preorder.toLT.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))))) s t) (HasSSubset.SSubset.{u1} (Set.{u1} α) (Set.instHasSSubsetSet.{u1} α) s t)
 Case conversion may be inaccurate. Consider using '#align set.lt_iff_ssubset Set.lt_iff_ssubsetₓ'. -/
@@ -193,7 +193,7 @@ alias le_iff_subset ↔ _root_.has_le.le.subset _root_.has_subset.subset.le
 
 /- warning: has_ssubset.ssubset.lt -> HasSSubset.SSubset.lt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {s : Set.{u1} α} {t : Set.{u1} α}, (HasSSubset.SSubset.{u1} (Set.{u1} α) (Set.hasSsubset.{u1} α) s t) -> (LT.lt.{u1} (Set.{u1} α) (Preorder.toLT.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))))) s t)
+  forall {α : Type.{u1}} {s : Set.{u1} α} {t : Set.{u1} α}, (HasSSubset.SSubset.{u1} (Set.{u1} α) (Set.hasSsubset.{u1} α) s t) -> (LT.lt.{u1} (Set.{u1} α) (Preorder.toHasLt.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))))) s t)
 but is expected to have type
   forall {α : Type.{u1}} {s : Set.{u1} α} {t : Set.{u1} α}, (HasSSubset.SSubset.{u1} (Set.{u1} α) (Set.instHasSSubsetSet.{u1} α) s t) -> (LT.lt.{u1} (Set.{u1} α) (Preorder.toLT.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))))) s t)
 Case conversion may be inaccurate. Consider using '#align has_ssubset.ssubset.lt HasSSubset.SSubset.ltₓ'. -/
@@ -4541,17 +4541,25 @@ theorem subsingleton_of_subsingleton [Subsingleton α] {s : Set α} : Set.Subsin
 #align set.subsingleton_of_subsingleton Set.subsingleton_of_subsingleton
 -/
 
-#print Set.subsingleton_isTop /-
+/- warning: set.subsingleton_is_top -> Set.subsingleton_isTop is a dubious translation:
+lean 3 declaration is
+  forall (α : Type.{u1}) [_inst_1 : PartialOrder.{u1} α], Set.Subsingleton.{u1} α (setOf.{u1} α (fun (x : α) => IsTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) x))
+but is expected to have type
+  forall (α : Type.{u1}) [_inst_1 : PartialOrder.{u1} α], Set.Subsingleton.{u1} α (setOf.{u1} α (fun (x : α) => IsTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) x))
+Case conversion may be inaccurate. Consider using '#align set.subsingleton_is_top Set.subsingleton_isTopₓ'. -/
 theorem subsingleton_isTop (α : Type _) [PartialOrder α] : Set.Subsingleton { x : α | IsTop x } :=
   fun x hx y hy => hx.IsMax.eq_of_le (hy x)
 #align set.subsingleton_is_top Set.subsingleton_isTop
--/
 
-#print Set.subsingleton_isBot /-
+/- warning: set.subsingleton_is_bot -> Set.subsingleton_isBot is a dubious translation:
+lean 3 declaration is
+  forall (α : Type.{u1}) [_inst_1 : PartialOrder.{u1} α], Set.Subsingleton.{u1} α (setOf.{u1} α (fun (x : α) => IsBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) x))
+but is expected to have type
+  forall (α : Type.{u1}) [_inst_1 : PartialOrder.{u1} α], Set.Subsingleton.{u1} α (setOf.{u1} α (fun (x : α) => IsBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) x))
+Case conversion may be inaccurate. Consider using '#align set.subsingleton_is_bot Set.subsingleton_isBotₓ'. -/
 theorem subsingleton_isBot (α : Type _) [PartialOrder α] : Set.Subsingleton { x : α | IsBot x } :=
   fun x hx y hy => hx.IsMin.eq_of_ge (hy x)
 #align set.subsingleton_is_bot Set.subsingleton_isBot
--/
 
 #print Set.exists_eq_singleton_iff_nonempty_subsingleton /-
 theorem exists_eq_singleton_iff_nonempty_subsingleton :
@@ -4705,38 +4713,54 @@ theorem nontrivial_iff_exists_ne {x} (hx : x ∈ s) : s.Nontrivial ↔ ∃ y ∈
   ⟨fun H => H.exists_ne _, nontrivial_of_exists_ne hx⟩
 #align set.nontrivial_iff_exists_ne Set.nontrivial_iff_exists_ne
 
-#print Set.nontrivial_of_lt /-
+/- warning: set.nontrivial_of_lt -> Set.nontrivial_of_lt is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {s : Set.{u1} α} [_inst_1 : Preorder.{u1} α] {x : α} {y : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_1) x y) -> (Set.Nontrivial.{u1} α s)
+but is expected to have type
+  forall {α : Type.{u1}} {s : Set.{u1} α} [_inst_1 : Preorder.{u1} α] {x : α} {y : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_1) x y) -> (Set.Nontrivial.{u1} α s)
+Case conversion may be inaccurate. Consider using '#align set.nontrivial_of_lt Set.nontrivial_of_ltₓ'. -/
 theorem nontrivial_of_lt [Preorder α] {x y} (hx : x ∈ s) (hy : y ∈ s) (hxy : x < y) :
     s.Nontrivial :=
   ⟨x, hx, y, hy, ne_of_lt hxy⟩
 #align set.nontrivial_of_lt Set.nontrivial_of_lt
--/
 
+/- warning: set.nontrivial_of_exists_lt -> Set.nontrivial_of_exists_lt is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {s : Set.{u1} α} [_inst_1 : Preorder.{u1} α], (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) => Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_1) x y))))) -> (Set.Nontrivial.{u1} α s)
+but is expected to have type
+  forall {α : Type.{u1}} {s : Set.{u1} α} [_inst_1 : Preorder.{u1} α], (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) => Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_1) x y))))) -> (Set.Nontrivial.{u1} α s)
+Case conversion may be inaccurate. Consider using '#align set.nontrivial_of_exists_lt Set.nontrivial_of_exists_ltₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
-#print Set.nontrivial_of_exists_lt /-
 theorem nontrivial_of_exists_lt [Preorder α] (H : ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s), x < y) :
     s.Nontrivial :=
   let ⟨x, hx, y, hy, hxy⟩ := H
   nontrivial_of_lt hx hy hxy
 #align set.nontrivial_of_exists_lt Set.nontrivial_of_exists_lt
--/
 
+/- warning: set.nontrivial.exists_lt -> Set.Nontrivial.exists_lt is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {s : Set.{u1} α} [_inst_1 : LinearOrder.{u1} α], (Set.Nontrivial.{u1} α s) -> (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) => Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) x y)))))
+but is expected to have type
+  forall {α : Type.{u1}} {s : Set.{u1} α} [_inst_1 : LinearOrder.{u1} α], (Set.Nontrivial.{u1} α s) -> (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) => Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1)))))) x y)))))
+Case conversion may be inaccurate. Consider using '#align set.nontrivial.exists_lt Set.Nontrivial.exists_ltₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
-#print Set.Nontrivial.exists_lt /-
 theorem Nontrivial.exists_lt [LinearOrder α] (hs : s.Nontrivial) :
     ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s), x < y :=
   let ⟨x, hx, y, hy, hxy⟩ := hs
   Or.elim (lt_or_gt_of_ne hxy) (fun H => ⟨x, hx, y, hy, H⟩) fun H => ⟨y, hy, x, hx, H⟩
 #align set.nontrivial.exists_lt Set.Nontrivial.exists_lt
--/
 
+/- warning: set.nontrivial_iff_exists_lt -> Set.nontrivial_iff_exists_lt is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {s : Set.{u1} α} [_inst_1 : LinearOrder.{u1} α], Iff (Set.Nontrivial.{u1} α s) (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) => Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) x y)))))
+but is expected to have type
+  forall {α : Type.{u1}} {s : Set.{u1} α} [_inst_1 : LinearOrder.{u1} α], Iff (Set.Nontrivial.{u1} α s) (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) => Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1)))))) x y)))))
+Case conversion may be inaccurate. Consider using '#align set.nontrivial_iff_exists_lt Set.nontrivial_iff_exists_ltₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
-#print Set.nontrivial_iff_exists_lt /-
 theorem nontrivial_iff_exists_lt [LinearOrder α] :
     s.Nontrivial ↔ ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s), x < y :=
   ⟨Nontrivial.exists_lt, nontrivial_of_exists_lt⟩
 #align set.nontrivial_iff_exists_lt Set.nontrivial_iff_exists_lt
--/
 
 #print Set.Nontrivial.nonempty /-
 protected theorem Nontrivial.nonempty (hs : s.Nontrivial) : s.Nonempty :=
@@ -4986,8 +5010,13 @@ section LinearOrder
 
 variable [LinearOrder α] [LinearOrder β] {f : α → β}
 
+/- warning: set.not_monotone_on_not_antitone_on_iff_exists_le_le -> Set.not_monotoneOn_not_antitoneOn_iff_exists_le_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {s : Set.{u1} α} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : LinearOrder.{u2} β] {f : α -> β}, Iff (And (Not (MonotoneOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))) f s)) (Not (AntitoneOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))) f s))) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => Exists.{succ u1} α (fun (b : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => Exists.{succ u1} α (fun (c : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) c s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) c s) => And (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) (And (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) b c) (Or (And (LT.lt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))))) (f a) (f b)) (LT.lt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))))) (f c) (f b))) (And (LT.lt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))))) (f b) (f a)) (LT.lt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))))) (f b) (f c))))))))))))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} {s : Set.{u1} α} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : LinearOrder.{u2} β] {f : α -> β}, Iff (And (Not (MonotoneOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2))))) f s)) (Not (AntitoneOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2))))) f s))) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) => Exists.{succ u1} α (fun (b : α) => Exists.{0} (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) => Exists.{succ u1} α (fun (c : α) => Exists.{0} (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) c s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) c s) => And (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1)))))) a b) (And (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1)))))) b c) (Or (And (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) (f a) (f b)) (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) (f c) (f b))) (And (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) (f b) (f a)) (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) (f b) (f c))))))))))))
+Case conversion may be inaccurate. Consider using '#align set.not_monotone_on_not_antitone_on_iff_exists_le_le Set.not_monotoneOn_not_antitoneOn_iff_exists_le_leₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a b c «expr ∈ » s) -/
-#print Set.not_monotoneOn_not_antitoneOn_iff_exists_le_le /-
 /-- A function between linear orders which is neither monotone nor antitone makes a dent upright or
 downright. -/
 theorem not_monotoneOn_not_antitoneOn_iff_exists_le_le :
@@ -4998,10 +5027,14 @@ theorem not_monotoneOn_not_antitoneOn_iff_exists_le_le :
   simp [monotone_on_iff_monotone, antitone_on_iff_antitone, and_assoc', exists_and_left,
     not_monotone_not_antitone_iff_exists_le_le, @and_left_comm (_ ∈ s)]
 #align set.not_monotone_on_not_antitone_on_iff_exists_le_le Set.not_monotoneOn_not_antitoneOn_iff_exists_le_le
--/
 
+/- warning: set.not_monotone_on_not_antitone_on_iff_exists_lt_lt -> Set.not_monotoneOn_not_antitoneOn_iff_exists_lt_lt is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {s : Set.{u1} α} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : LinearOrder.{u2} β] {f : α -> β}, Iff (And (Not (MonotoneOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))) f s)) (Not (AntitoneOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))) f s))) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => Exists.{succ u1} α (fun (b : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => Exists.{succ u1} α (fun (c : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) c s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) c s) => And (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) (And (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) b c) (Or (And (LT.lt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))))) (f a) (f b)) (LT.lt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))))) (f c) (f b))) (And (LT.lt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))))) (f b) (f a)) (LT.lt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))))) (f b) (f c))))))))))))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} {s : Set.{u1} α} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : LinearOrder.{u2} β] {f : α -> β}, Iff (And (Not (MonotoneOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2))))) f s)) (Not (AntitoneOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2))))) f s))) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) => Exists.{succ u1} α (fun (b : α) => Exists.{0} (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) => Exists.{succ u1} α (fun (c : α) => Exists.{0} (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) c s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) c s) => And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1)))))) a b) (And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1)))))) b c) (Or (And (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) (f a) (f b)) (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) (f c) (f b))) (And (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) (f b) (f a)) (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) (f b) (f c))))))))))))
+Case conversion may be inaccurate. Consider using '#align set.not_monotone_on_not_antitone_on_iff_exists_lt_lt Set.not_monotoneOn_not_antitoneOn_iff_exists_lt_ltₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a b c «expr ∈ » s) -/
-#print Set.not_monotoneOn_not_antitoneOn_iff_exists_lt_lt /-
 /-- A function between linear orders which is neither monotone nor antitone makes a dent upright or
 downright. -/
 theorem not_monotoneOn_not_antitoneOn_iff_exists_lt_lt :
@@ -5012,7 +5045,6 @@ theorem not_monotoneOn_not_antitoneOn_iff_exists_lt_lt :
   simp [monotone_on_iff_monotone, antitone_on_iff_antitone, and_assoc', exists_and_left,
     not_monotone_not_antitone_iff_exists_lt_lt, @and_left_comm (_ ∈ s)]
 #align set.not_monotone_on_not_antitone_on_iff_exists_lt_lt Set.not_monotoneOn_not_antitoneOn_iff_exists_lt_lt
--/
 
 end LinearOrder

bump to nightly-2023-05-03-22

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

aa7b8e08

Diff

@@ -1202,7 +1202,7 @@ theorem union_assoc (a b c : Set α) : a ∪ b ∪ c = a ∪ (b ∪ c) :=
 lean 3 declaration is
   forall {α : Type.{u1}}, IsAssociative.{u1} (Set.{u1} α) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α))
 but is expected to have type
-  forall {α : Type.{u1}}, IsAssociative.{u1} (Set.{u1} α) (fun (x._@.Mathlib.Data.Set.Basic._hyg.7936 : Set.{u1} α) (x._@.Mathlib.Data.Set.Basic._hyg.7938 : Set.{u1} α) => Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) x._@.Mathlib.Data.Set.Basic._hyg.7936 x._@.Mathlib.Data.Set.Basic._hyg.7938)
+  forall {α : Type.{u1}}, IsAssociative.{u1} (Set.{u1} α) (fun (x._@.Mathlib.Data.Set.Basic._hyg.7931 : Set.{u1} α) (x._@.Mathlib.Data.Set.Basic._hyg.7933 : Set.{u1} α) => Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) x._@.Mathlib.Data.Set.Basic._hyg.7931 x._@.Mathlib.Data.Set.Basic._hyg.7933)
 Case conversion may be inaccurate. Consider using '#align set.union_is_assoc Set.union_isAssocₓ'. -/
 instance union_isAssoc : IsAssociative (Set α) (· ∪ ·) :=
   ⟨union_assoc⟩
@@ -1212,7 +1212,7 @@ instance union_isAssoc : IsAssociative (Set α) (· ∪ ·) :=
 lean 3 declaration is
   forall {α : Type.{u1}}, IsCommutative.{u1} (Set.{u1} α) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α))
 but is expected to have type
-  forall {α : Type.{u1}}, IsCommutative.{u1} (Set.{u1} α) (fun (x._@.Mathlib.Data.Set.Basic._hyg.7981 : Set.{u1} α) (x._@.Mathlib.Data.Set.Basic._hyg.7983 : Set.{u1} α) => Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) x._@.Mathlib.Data.Set.Basic._hyg.7981 x._@.Mathlib.Data.Set.Basic._hyg.7983)
+  forall {α : Type.{u1}}, IsCommutative.{u1} (Set.{u1} α) (fun (x._@.Mathlib.Data.Set.Basic._hyg.7976 : Set.{u1} α) (x._@.Mathlib.Data.Set.Basic._hyg.7978 : Set.{u1} α) => Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) x._@.Mathlib.Data.Set.Basic._hyg.7976 x._@.Mathlib.Data.Set.Basic._hyg.7978)
 Case conversion may be inaccurate. Consider using '#align set.union_is_comm Set.union_isCommₓ'. -/
 instance union_isComm : IsCommutative (Set α) (· ∪ ·) :=
   ⟨union_comm⟩
@@ -1555,7 +1555,7 @@ theorem inter_assoc (a b c : Set α) : a ∩ b ∩ c = a ∩ (b ∩ c) :=
 lean 3 declaration is
   forall {α : Type.{u1}}, IsAssociative.{u1} (Set.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α))
 but is expected to have type
-  forall {α : Type.{u1}}, IsAssociative.{u1} (Set.{u1} α) (fun (x._@.Mathlib.Data.Set.Basic._hyg.9578 : Set.{u1} α) (x._@.Mathlib.Data.Set.Basic._hyg.9580 : Set.{u1} α) => Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) x._@.Mathlib.Data.Set.Basic._hyg.9578 x._@.Mathlib.Data.Set.Basic._hyg.9580)
+  forall {α : Type.{u1}}, IsAssociative.{u1} (Set.{u1} α) (fun (x._@.Mathlib.Data.Set.Basic._hyg.9573 : Set.{u1} α) (x._@.Mathlib.Data.Set.Basic._hyg.9575 : Set.{u1} α) => Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) x._@.Mathlib.Data.Set.Basic._hyg.9573 x._@.Mathlib.Data.Set.Basic._hyg.9575)
 Case conversion may be inaccurate. Consider using '#align set.inter_is_assoc Set.inter_isAssocₓ'. -/
 instance inter_isAssoc : IsAssociative (Set α) (· ∩ ·) :=
   ⟨inter_assoc⟩
@@ -1565,7 +1565,7 @@ instance inter_isAssoc : IsAssociative (Set α) (· ∩ ·) :=
 lean 3 declaration is
   forall {α : Type.{u1}}, IsCommutative.{u1} (Set.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α))
 but is expected to have type
-  forall {α : Type.{u1}}, IsCommutative.{u1} (Set.{u1} α) (fun (x._@.Mathlib.Data.Set.Basic._hyg.9623 : Set.{u1} α) (x._@.Mathlib.Data.Set.Basic._hyg.9625 : Set.{u1} α) => Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) x._@.Mathlib.Data.Set.Basic._hyg.9623 x._@.Mathlib.Data.Set.Basic._hyg.9625)
+  forall {α : Type.{u1}}, IsCommutative.{u1} (Set.{u1} α) (fun (x._@.Mathlib.Data.Set.Basic._hyg.9618 : Set.{u1} α) (x._@.Mathlib.Data.Set.Basic._hyg.9620 : Set.{u1} α) => Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) x._@.Mathlib.Data.Set.Basic._hyg.9618 x._@.Mathlib.Data.Set.Basic._hyg.9620)
 Case conversion may be inaccurate. Consider using '#align set.inter_is_comm Set.inter_isCommₓ'. -/
 instance inter_isComm : IsCommutative (Set α) (· ∩ ·) :=
   ⟨inter_comm⟩

bump to nightly-2023-04-24-14

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

076cf722

Diff

@@ -2842,10 +2842,22 @@ theorem disjoint_sdiff_right : Disjoint s (t \ s) :=
   disjoint_sdiff_self_right
 #align set.disjoint_sdiff_right Set.disjoint_sdiff_right
 
+/- warning: set.diff_union_diff_cancel -> Set.diff_union_diff_cancel is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {s : Set.{u1} α} {t : Set.{u1} α} {u : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) u t) -> (Eq.{succ u1} (Set.{u1} α) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) (SDiff.sdiff.{u1} (Set.{u1} α) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s t) (SDiff.sdiff.{u1} (Set.{u1} α) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) t u)) (SDiff.sdiff.{u1} (Set.{u1} α) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s u))
+but is expected to have type
+  forall {α : Type.{u1}} {s : Set.{u1} α} {t : Set.{u1} α} {u : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) t s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) u t) -> (Eq.{succ u1} (Set.{u1} α) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) (SDiff.sdiff.{u1} (Set.{u1} α) (Set.instSDiffSet.{u1} α) s t) (SDiff.sdiff.{u1} (Set.{u1} α) (Set.instSDiffSet.{u1} α) t u)) (SDiff.sdiff.{u1} (Set.{u1} α) (Set.instSDiffSet.{u1} α) s u))
+Case conversion may be inaccurate. Consider using '#align set.diff_union_diff_cancel Set.diff_union_diff_cancelₓ'. -/
 theorem diff_union_diff_cancel (hts : t ⊆ s) (hut : u ⊆ t) : s \ t ∪ t \ u = s \ u :=
   sdiff_sup_sdiff_cancel hts hut
 #align set.diff_union_diff_cancel Set.diff_union_diff_cancel
 
+/- warning: set.diff_diff_eq_sdiff_union -> Set.diff_diff_eq_sdiff_union is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {s : Set.{u1} α} {t : Set.{u1} α} {u : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) u s) -> (Eq.{succ u1} (Set.{u1} α) (SDiff.sdiff.{u1} (Set.{u1} α) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s (SDiff.sdiff.{u1} (Set.{u1} α) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) t u)) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) (SDiff.sdiff.{u1} (Set.{u1} α) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s t) u))
+but is expected to have type
+  forall {α : Type.{u1}} {s : Set.{u1} α} {t : Set.{u1} α} {u : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) u s) -> (Eq.{succ u1} (Set.{u1} α) (SDiff.sdiff.{u1} (Set.{u1} α) (Set.instSDiffSet.{u1} α) s (SDiff.sdiff.{u1} (Set.{u1} α) (Set.instSDiffSet.{u1} α) t u)) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) (SDiff.sdiff.{u1} (Set.{u1} α) (Set.instSDiffSet.{u1} α) s t) u))
+Case conversion may be inaccurate. Consider using '#align set.diff_diff_eq_sdiff_union Set.diff_diff_eq_sdiff_unionₓ'. -/
 theorem diff_diff_eq_sdiff_union (h : u ⊆ s) : s \ (t \ u) = s \ t ∪ u :=
   sdiff_sdiff_eq_sdiff_sup h
 #align set.diff_diff_eq_sdiff_union Set.diff_diff_eq_sdiff_union

bump to nightly-2023-04-21-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/246f6f7989ff86bd07e1b014846f11304f33cf9e

38c06b34

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Leonardo de Moura
 
 ! This file was ported from Lean 3 source module data.set.basic
-! leanprover-community/mathlib commit 29cb56a7b35f72758b05a30490e1f10bd62c35c1
+! leanprover-community/mathlib commit 9ac7c0c8c4d7a535ec3e5b34b8859aab9233b2f4
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -2842,6 +2842,14 @@ theorem disjoint_sdiff_right : Disjoint s (t \ s) :=
   disjoint_sdiff_self_right
 #align set.disjoint_sdiff_right Set.disjoint_sdiff_right
 
+theorem diff_union_diff_cancel (hts : t ⊆ s) (hut : u ⊆ t) : s \ t ∪ t \ u = s \ u :=
+  sdiff_sup_sdiff_cancel hts hut
+#align set.diff_union_diff_cancel Set.diff_union_diff_cancel
+
+theorem diff_diff_eq_sdiff_union (h : u ⊆ s) : s \ (t \ u) = s \ t ∪ u :=
+  sdiff_sdiff_eq_sdiff_sup h
+#align set.diff_diff_eq_sdiff_union Set.diff_diff_eq_sdiff_union
+
 /- warning: set.disjoint_singleton_left -> Set.disjoint_singleton_left is a dubious translation:
 lean 3 declaration is
   forall {α : Type.{u1}} {a : α} {s : Set.{u1} α}, Iff (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) a) s) (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s))

bump to nightly-2023-04-01-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/172bf2812857f5e56938cc148b7a539f52f84ca9

098eeca7

Diff

@@ -1786,10 +1786,22 @@ theorem union_inter_cancel_right {s t : Set α} : (s ∪ t) ∩ t = t :=
   inter_eq_self_of_subset_right <| subset_union_right _ _
 #align set.union_inter_cancel_right Set.union_inter_cancel_right
 
+/- warning: set.inter_set_of_eq_sep -> Set.inter_setOf_eq_sep is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (s : Set.{u1} α) (p : α -> Prop), Eq.{succ u1} (Set.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s (setOf.{u1} α (fun (a : α) => p a))) (Sep.sep.{u1, u1} α (Set.{u1} α) (Set.hasSep.{u1} α) (fun (a : α) => p a) s)
+but is expected to have type
+  forall {α : Type.{u1}} (s : Set.{u1} α) (p : α -> Prop), Eq.{succ u1} (Set.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s (setOf.{u1} α (fun (a : α) => p a))) (setOf.{u1} α (fun (a : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (p a)))
+Case conversion may be inaccurate. Consider using '#align set.inter_set_of_eq_sep Set.inter_setOf_eq_sepₓ'. -/
 theorem inter_setOf_eq_sep (s : Set α) (p : α → Prop) : s ∩ { a | p a } = { a ∈ s | p a } :=
   rfl
 #align set.inter_set_of_eq_sep Set.inter_setOf_eq_sep
 
+/- warning: set.set_of_inter_eq_sep -> Set.setOf_inter_eq_sep is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (p : α -> Prop) (s : Set.{u1} α), Eq.{succ u1} (Set.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) (setOf.{u1} α (fun (a : α) => p a)) s) (Sep.sep.{u1, u1} α (Set.{u1} α) (Set.hasSep.{u1} α) (fun (a : α) => p a) s)
+but is expected to have type
+  forall {α : Type.{u1}} (p : α -> Prop) (s : Set.{u1} α), Eq.{succ u1} (Set.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) (setOf.{u1} α (fun (a : α) => p a)) s) (setOf.{u1} α (fun (a : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (p a)))
+Case conversion may be inaccurate. Consider using '#align set.set_of_inter_eq_sep Set.setOf_inter_eq_sepₓ'. -/
 theorem setOf_inter_eq_sep (p : α → Prop) (s : Set α) : { a | p a } ∩ s = { a ∈ s | p a } :=
   inter_comm _ _
 #align set.set_of_inter_eq_sep Set.setOf_inter_eq_sep
@@ -2276,8 +2288,10 @@ theorem singleton_subset_iff {a : α} {s : Set α} : {a} ⊆ s ↔ a ∈ s :=
 #align set.singleton_subset_iff Set.singleton_subset_iff
 -/
 
+#print Set.singleton_subset_singleton /-
 theorem singleton_subset_singleton : ({a} : Set α) ⊆ {b} ↔ a = b := by simp
 #align set.singleton_subset_singleton Set.singleton_subset_singleton
+-/
 
 #print Set.set_compr_eq_eq_singleton /-
 theorem set_compr_eq_eq_singleton {a : α} : { b | b = a } = {a} :=
@@ -2871,10 +2885,22 @@ theorem subset_diff : s ⊆ t \ u ↔ s ⊆ t ∧ Disjoint s u :=
   le_iff_subset.symm.trans le_sdiff
 #align set.subset_diff Set.subset_diff
 
+/- warning: set.inter_diff_distrib_left -> Set.inter_diff_distrib_left is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (s : Set.{u1} α) (t : Set.{u1} α) (u : Set.{u1} α), Eq.{succ u1} (Set.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s (SDiff.sdiff.{u1} (Set.{u1} α) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) t u)) (SDiff.sdiff.{u1} (Set.{u1} α) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s u))
+but is expected to have type
+  forall {α : Type.{u1}} (s : Set.{u1} α) (t : Set.{u1} α) (u : Set.{u1} α), Eq.{succ u1} (Set.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s (SDiff.sdiff.{u1} (Set.{u1} α) (Set.instSDiffSet.{u1} α) t u)) (SDiff.sdiff.{u1} (Set.{u1} α) (Set.instSDiffSet.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s t) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s u))
+Case conversion may be inaccurate. Consider using '#align set.inter_diff_distrib_left Set.inter_diff_distrib_leftₓ'. -/
 theorem inter_diff_distrib_left (s t u : Set α) : s ∩ (t \ u) = (s ∩ t) \ (s ∩ u) :=
   inf_sdiff_distrib_left _ _ _
 #align set.inter_diff_distrib_left Set.inter_diff_distrib_left
 
+/- warning: set.inter_diff_distrib_right -> Set.inter_diff_distrib_right is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (s : Set.{u1} α) (t : Set.{u1} α) (u : Set.{u1} α), Eq.{succ u1} (Set.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) (SDiff.sdiff.{u1} (Set.{u1} α) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s t) u) (SDiff.sdiff.{u1} (Set.{u1} α) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s u) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) t u))
+but is expected to have type
+  forall {α : Type.{u1}} (s : Set.{u1} α) (t : Set.{u1} α) (u : Set.{u1} α), Eq.{succ u1} (Set.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) (SDiff.sdiff.{u1} (Set.{u1} α) (Set.instSDiffSet.{u1} α) s t) u) (SDiff.sdiff.{u1} (Set.{u1} α) (Set.instSDiffSet.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s u) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) t u))
+Case conversion may be inaccurate. Consider using '#align set.inter_diff_distrib_right Set.inter_diff_distrib_rightₓ'. -/
 theorem inter_diff_distrib_right (s t u : Set α) : s \ t ∩ u = (s ∩ u) \ (t ∩ u) :=
   inf_sdiff_distrib_right _ _ _
 #align set.inter_diff_distrib_right Set.inter_diff_distrib_right
@@ -3882,6 +3908,12 @@ theorem diff_singleton_eq_self {a : α} {s : Set α} (h : a ∉ s) : s \ {a} = s
   sdiff_eq_self_iff_disjoint.2 <| by simp [h]
 #align set.diff_singleton_eq_self Set.diff_singleton_eq_self
 
+/- warning: set.diff_singleton_ssubset -> Set.diff_singleton_sSubset is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {s : Set.{u1} α} {a : α}, Iff (HasSSubset.SSubset.{u1} (Set.{u1} α) (Set.hasSsubset.{u1} α) (SDiff.sdiff.{u1} (Set.{u1} α) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) a)) s) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s)
+but is expected to have type
+  forall {α : Type.{u1}} {s : Set.{u1} α} {a : α}, Iff (HasSSubset.SSubset.{u1} (Set.{u1} α) (Set.instHasSSubsetSet.{u1} α) (SDiff.sdiff.{u1} (Set.{u1} α) (Set.instSDiffSet.{u1} α) s (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) a)) s) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s)
+Case conversion may be inaccurate. Consider using '#align set.diff_singleton_ssubset Set.diff_singleton_sSubsetₓ'. -/
 @[simp]
 theorem diff_singleton_sSubset {s : Set α} {a : α} : s \ {a} ⊂ s ↔ a ∈ s :=
   sdiff_le.lt_iff_ne.trans <| sdiff_eq_left.Not.trans <| by simp
@@ -3898,6 +3930,12 @@ theorem insert_diff_singleton {a : α} {s : Set α} : insert a (s \ {a}) = inser
   simp [insert_eq, union_diff_self, -union_singleton, -singleton_union]
 #align set.insert_diff_singleton Set.insert_diff_singleton
 
+/- warning: set.insert_diff_singleton_comm -> Set.insert_diff_singleton_comm is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {a : α} {b : α}, (Ne.{succ u1} α a b) -> (forall (s : Set.{u1} α), Eq.{succ u1} (Set.{u1} α) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a (SDiff.sdiff.{u1} (Set.{u1} α) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) b))) (SDiff.sdiff.{u1} (Set.{u1} α) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a s) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) b)))
+but is expected to have type
+  forall {α : Type.{u1}} {a : α} {b : α}, (Ne.{succ u1} α a b) -> (forall (s : Set.{u1} α), Eq.{succ u1} (Set.{u1} α) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a (SDiff.sdiff.{u1} (Set.{u1} α) (Set.instSDiffSet.{u1} α) s (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) b))) (SDiff.sdiff.{u1} (Set.{u1} α) (Set.instSDiffSet.{u1} α) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a s) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) b)))
+Case conversion may be inaccurate. Consider using '#align set.insert_diff_singleton_comm Set.insert_diff_singleton_commₓ'. -/
 theorem insert_diff_singleton_comm (hab : a ≠ b) (s : Set α) :
     insert a (s \ {b}) = insert a s \ {b} := by
   simp_rw [← union_singleton, union_diff_distrib,

bump to nightly-2023-04-01-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/172bf2812857f5e56938cc148b7a539f52f84ca9

60c83b45

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Leonardo de Moura
 
 ! This file was ported from Lean 3 source module data.set.basic
-! leanprover-community/mathlib commit 75608affb24b4f48699fbcd38f227827f7793771
+! leanprover-community/mathlib commit 29cb56a7b35f72758b05a30490e1f10bd62c35c1
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -1786,6 +1786,14 @@ theorem union_inter_cancel_right {s t : Set α} : (s ∪ t) ∩ t = t :=
   inter_eq_self_of_subset_right <| subset_union_right _ _
 #align set.union_inter_cancel_right Set.union_inter_cancel_right
 
+theorem inter_setOf_eq_sep (s : Set α) (p : α → Prop) : s ∩ { a | p a } = { a ∈ s | p a } :=
+  rfl
+#align set.inter_set_of_eq_sep Set.inter_setOf_eq_sep
+
+theorem setOf_inter_eq_sep (p : α → Prop) (s : Set α) : { a | p a } ∩ s = { a ∈ s | p a } :=
+  inter_comm _ _
+#align set.set_of_inter_eq_sep Set.setOf_inter_eq_sep
+
 /-! ### Distributivity laws -/
 
 
@@ -2268,6 +2276,9 @@ theorem singleton_subset_iff {a : α} {s : Set α} : {a} ⊆ s ↔ a ∈ s :=
 #align set.singleton_subset_iff Set.singleton_subset_iff
 -/
 
+theorem singleton_subset_singleton : ({a} : Set α) ⊆ {b} ↔ a = b := by simp
+#align set.singleton_subset_singleton Set.singleton_subset_singleton
+
 #print Set.set_compr_eq_eq_singleton /-
 theorem set_compr_eq_eq_singleton {a : α} : { b | b = a } = {a} :=
   rfl
@@ -2860,6 +2871,14 @@ theorem subset_diff : s ⊆ t \ u ↔ s ⊆ t ∧ Disjoint s u :=
   le_iff_subset.symm.trans le_sdiff
 #align set.subset_diff Set.subset_diff
 
+theorem inter_diff_distrib_left (s t u : Set α) : s ∩ (t \ u) = (s ∩ t) \ (s ∩ u) :=
+  inf_sdiff_distrib_left _ _ _
+#align set.inter_diff_distrib_left Set.inter_diff_distrib_left
+
+theorem inter_diff_distrib_right (s t u : Set α) : s \ t ∩ u = (s ∩ u) \ (t ∩ u) :=
+  inf_sdiff_distrib_right _ _ _
+#align set.inter_diff_distrib_right Set.inter_diff_distrib_right
+
 /-! ### Lemmas about complement -/
 
 
@@ -3863,6 +3882,11 @@ theorem diff_singleton_eq_self {a : α} {s : Set α} (h : a ∉ s) : s \ {a} = s
   sdiff_eq_self_iff_disjoint.2 <| by simp [h]
 #align set.diff_singleton_eq_self Set.diff_singleton_eq_self
 
+@[simp]
+theorem diff_singleton_sSubset {s : Set α} {a : α} : s \ {a} ⊂ s ↔ a ∈ s :=
+  sdiff_le.lt_iff_ne.trans <| sdiff_eq_left.Not.trans <| by simp
+#align set.diff_singleton_ssubset Set.diff_singleton_sSubset
+
 /- warning: set.insert_diff_singleton -> Set.insert_diff_singleton is a dubious translation:
 lean 3 declaration is
   forall {α : Type.{u1}} {a : α} {s : Set.{u1} α}, Eq.{succ u1} (Set.{u1} α) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a (SDiff.sdiff.{u1} (Set.{u1} α) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) a))) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a s)
@@ -3874,6 +3898,12 @@ theorem insert_diff_singleton {a : α} {s : Set α} : insert a (s \ {a}) = inser
   simp [insert_eq, union_diff_self, -union_singleton, -singleton_union]
 #align set.insert_diff_singleton Set.insert_diff_singleton
 
+theorem insert_diff_singleton_comm (hab : a ≠ b) (s : Set α) :
+    insert a (s \ {b}) = insert a s \ {b} := by
+  simp_rw [← union_singleton, union_diff_distrib,
+    diff_singleton_eq_self (mem_singleton_iff.not.2 hab.symm)]
+#align set.insert_diff_singleton_comm Set.insert_diff_singleton_comm
+
 /- warning: set.diff_self -> Set.diff_self is a dubious translation:
 lean 3 declaration is
   forall {α : Type.{u1}} {s : Set.{u1} α}, Eq.{succ u1} (Set.{u1} α) (SDiff.sdiff.{u1} (Set.{u1} α) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s s) (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.hasEmptyc.{u1} α))

bump to nightly-2023-03-01-20

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

20cadee0

Diff

@@ -2043,7 +2043,7 @@ lean 3 declaration is
 but is expected to have type
   forall {α : Type.{u1}} {s : Set.{u1} α} {t : Set.{u1} α}, Iff (HasSSubset.SSubset.{u1} (Set.{u1} α) (Set.instHasSSubsetSet.{u1} α) s t) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Not (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s)) (fun (H : Not (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s)) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a s) t)))
 Case conversion may be inaccurate. Consider using '#align set.ssubset_iff_insert Set.ssubset_iff_insertₓ'. -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (a «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a «expr ∉ » s) -/
 theorem ssubset_iff_insert {s t : Set α} : s ⊂ t ↔ ∃ (a : _)(_ : a ∉ s), insert a s ⊆ t :=
   by
   simp only [insert_subset, exists_and_right, ssubset_def, not_subset]
@@ -4507,7 +4507,7 @@ instance subsingleton_coe_of_subsingleton [Subsingleton α] {s : Set α} : Subsi
 /-! ### Nontrivial -/
 
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Nontrivial /-
 /-- A set `s` is `nontrivial` if it has at least two distinct elements. -/
 protected def Nontrivial (s : Set α) : Prop :=
@@ -4624,7 +4624,7 @@ theorem nontrivial_of_lt [Preorder α] {x y} (hx : x ∈ s) (hy : y ∈ s) (hxy
 #align set.nontrivial_of_lt Set.nontrivial_of_lt
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.nontrivial_of_exists_lt /-
 theorem nontrivial_of_exists_lt [Preorder α] (H : ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s), x < y) :
     s.Nontrivial :=
@@ -4633,7 +4633,7 @@ theorem nontrivial_of_exists_lt [Preorder α] (H : ∃ (x : _)(_ : x ∈ s)(y :
 #align set.nontrivial_of_exists_lt Set.nontrivial_of_exists_lt
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Nontrivial.exists_lt /-
 theorem Nontrivial.exists_lt [LinearOrder α] (hs : s.Nontrivial) :
     ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s), x < y :=
@@ -4642,7 +4642,7 @@ theorem Nontrivial.exists_lt [LinearOrder α] (hs : s.Nontrivial) :
 #align set.nontrivial.exists_lt Set.Nontrivial.exists_lt
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.nontrivial_iff_exists_lt /-
 theorem nontrivial_iff_exists_lt [LinearOrder α] :
     s.Nontrivial ↔ ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s), x < y :=
@@ -4898,7 +4898,7 @@ section LinearOrder
 
 variable [LinearOrder α] [LinearOrder β] {f : α → β}
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (a b c «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a b c «expr ∈ » s) -/
 #print Set.not_monotoneOn_not_antitoneOn_iff_exists_le_le /-
 /-- A function between linear orders which is neither monotone nor antitone makes a dent upright or
 downright. -/
@@ -4912,7 +4912,7 @@ theorem not_monotoneOn_not_antitoneOn_iff_exists_le_le :
 #align set.not_monotone_on_not_antitone_on_iff_exists_le_le Set.not_monotoneOn_not_antitoneOn_iff_exists_le_le
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (a b c «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a b c «expr ∈ » s) -/
 #print Set.not_monotoneOn_not_antitoneOn_iff_exists_lt_lt /-
 /-- A function between linear orders which is neither monotone nor antitone makes a dent upright or
 downright. -/

bump to nightly-2023-02-28-04

mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211

2097f8af

Diff

@@ -133,9 +133,9 @@ theorem bot_eq_empty : (⊥ : Set α) = ∅ :=
 
 /- warning: set.sup_eq_union -> Set.sup_eq_union is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}}, Eq.{succ u1} ((Set.{u1} α) -> (Set.{u1} α) -> (Set.{u1} α)) (HasSup.sup.{u1} (Set.{u1} α) (SemilatticeSup.toHasSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))))))) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α))
+  forall {α : Type.{u1}}, Eq.{succ u1} ((Set.{u1} α) -> (Set.{u1} α) -> (Set.{u1} α)) (Sup.sup.{u1} (Set.{u1} α) (SemilatticeSup.toHasSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))))))) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α))
 but is expected to have type
-  forall {α : Type.{u1}}, Eq.{succ u1} ((Set.{u1} α) -> (Set.{u1} α) -> (Set.{u1} α)) (fun (x._@.Mathlib.Data.Set.Basic._hyg.334 : Set.{u1} α) (x._@.Mathlib.Data.Set.Basic._hyg.336 : Set.{u1} α) => HasSup.sup.{u1} (Set.{u1} α) (SemilatticeSup.toHasSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) x._@.Mathlib.Data.Set.Basic._hyg.334 x._@.Mathlib.Data.Set.Basic._hyg.336) (fun (x._@.Mathlib.Data.Set.Basic._hyg.349 : Set.{u1} α) (x._@.Mathlib.Data.Set.Basic._hyg.351 : Set.{u1} α) => Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) x._@.Mathlib.Data.Set.Basic._hyg.349 x._@.Mathlib.Data.Set.Basic._hyg.351)
+  forall {α : Type.{u1}}, Eq.{succ u1} ((Set.{u1} α) -> (Set.{u1} α) -> (Set.{u1} α)) (fun (x._@.Mathlib.Data.Set.Basic._hyg.334 : Set.{u1} α) (x._@.Mathlib.Data.Set.Basic._hyg.336 : Set.{u1} α) => Sup.sup.{u1} (Set.{u1} α) (SemilatticeSup.toSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) x._@.Mathlib.Data.Set.Basic._hyg.334 x._@.Mathlib.Data.Set.Basic._hyg.336) (fun (x._@.Mathlib.Data.Set.Basic._hyg.349 : Set.{u1} α) (x._@.Mathlib.Data.Set.Basic._hyg.351 : Set.{u1} α) => Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) x._@.Mathlib.Data.Set.Basic._hyg.349 x._@.Mathlib.Data.Set.Basic._hyg.351)
 Case conversion may be inaccurate. Consider using '#align set.sup_eq_union Set.sup_eq_unionₓ'. -/
 @[simp]
 theorem sup_eq_union : ((· ⊔ ·) : Set α → Set α → Set α) = (· ∪ ·) :=
@@ -144,9 +144,9 @@ theorem sup_eq_union : ((· ⊔ ·) : Set α → Set α → Set α) = (· ∪ ·
 
 /- warning: set.inf_eq_inter -> Set.inf_eq_inter is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}}, Eq.{succ u1} ((Set.{u1} α) -> (Set.{u1} α) -> (Set.{u1} α)) (HasInf.inf.{u1} (Set.{u1} α) (SemilatticeInf.toHasInf.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))))))) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α))
+  forall {α : Type.{u1}}, Eq.{succ u1} ((Set.{u1} α) -> (Set.{u1} α) -> (Set.{u1} α)) (Inf.inf.{u1} (Set.{u1} α) (SemilatticeInf.toHasInf.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))))))) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α))
 but is expected to have type
-  forall {α : Type.{u1}}, Eq.{succ u1} ((Set.{u1} α) -> (Set.{u1} α) -> (Set.{u1} α)) (fun (x._@.Mathlib.Data.Set.Basic._hyg.386 : Set.{u1} α) (x._@.Mathlib.Data.Set.Basic._hyg.388 : Set.{u1} α) => HasInf.inf.{u1} (Set.{u1} α) (Lattice.toHasInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)))))) x._@.Mathlib.Data.Set.Basic._hyg.386 x._@.Mathlib.Data.Set.Basic._hyg.388) (fun (x._@.Mathlib.Data.Set.Basic._hyg.401 : Set.{u1} α) (x._@.Mathlib.Data.Set.Basic._hyg.403 : Set.{u1} α) => Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) x._@.Mathlib.Data.Set.Basic._hyg.401 x._@.Mathlib.Data.Set.Basic._hyg.403)
+  forall {α : Type.{u1}}, Eq.{succ u1} ((Set.{u1} α) -> (Set.{u1} α) -> (Set.{u1} α)) (fun (x._@.Mathlib.Data.Set.Basic._hyg.386 : Set.{u1} α) (x._@.Mathlib.Data.Set.Basic._hyg.388 : Set.{u1} α) => Inf.inf.{u1} (Set.{u1} α) (Lattice.toInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)))))) x._@.Mathlib.Data.Set.Basic._hyg.386 x._@.Mathlib.Data.Set.Basic._hyg.388) (fun (x._@.Mathlib.Data.Set.Basic._hyg.401 : Set.{u1} α) (x._@.Mathlib.Data.Set.Basic._hyg.403 : Set.{u1} α) => Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) x._@.Mathlib.Data.Set.Basic._hyg.401 x._@.Mathlib.Data.Set.Basic._hyg.403)
 Case conversion may be inaccurate. Consider using '#align set.inf_eq_inter Set.inf_eq_interₓ'. -/
 @[simp]
 theorem inf_eq_inter : ((· ⊓ ·) : Set α → Set α → Set α) = (· ∩ ·) :=
@@ -1373,9 +1373,9 @@ theorem subset_union_of_subset_right {s u : Set α} (h : s ⊆ u) (t : Set α) :
 
 /- warning: set.union_congr_left -> Set.union_congr_left is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {s : Set.{u1} α} {t : Set.{u1} α} {u : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s u)) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) u (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)) -> (Eq.{succ u1} (Set.{u1} α) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t) (HasSup.sup.{u1} (Set.{u1} α) (SemilatticeSup.toHasSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) s u))
+  forall {α : Type.{u1}} {s : Set.{u1} α} {t : Set.{u1} α} {u : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s u)) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) u (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)) -> (Eq.{succ u1} (Set.{u1} α) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t) (Sup.sup.{u1} (Set.{u1} α) (SemilatticeSup.toHasSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) s u))
 but is expected to have type
-  forall {α : Type.{u1}} {s : Set.{u1} α} {t : Set.{u1} α} {u : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) t (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s u)) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) u (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s t)) -> (Eq.{succ u1} (Set.{u1} α) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s t) (HasSup.sup.{u1} (Set.{u1} α) (SemilatticeSup.toHasSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) s u))
+  forall {α : Type.{u1}} {s : Set.{u1} α} {t : Set.{u1} α} {u : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) t (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s u)) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) u (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s t)) -> (Eq.{succ u1} (Set.{u1} α) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s t) (Sup.sup.{u1} (Set.{u1} α) (SemilatticeSup.toSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) s u))
 Case conversion may be inaccurate. Consider using '#align set.union_congr_left Set.union_congr_leftₓ'. -/
 theorem union_congr_left (ht : t ⊆ s ∪ u) (hu : u ⊆ s ∪ t) : s ∪ t = s ⊔ u :=
   sup_congr_left ht hu
@@ -3942,7 +3942,7 @@ theorem union_eq_diff_union_diff_union_inter (s t : Set α) : s ∪ t = s \ t 
 lean 3 declaration is
   forall {α : Type.{u1}} {a : α} {s : Set.{u1} α} {t : Set.{u1} α}, Iff (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (symmDiff.{u1} (Set.{u1} α) (SemilatticeSup.toHasSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s t)) (Or (And (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a t))) (And (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a t) (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s))))
 but is expected to have type
-  forall {α : Type.{u1}} {a : α} {s : Set.{u1} α} {t : Set.{u1} α}, Iff (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a (symmDiff.{u1} (Set.{u1} α) (SemilatticeSup.toHasSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (Set.instSDiffSet.{u1} α) s t)) (Or (And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (Not (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a t))) (And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a t) (Not (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s))))
+  forall {α : Type.{u1}} {a : α} {s : Set.{u1} α} {t : Set.{u1} α}, Iff (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a (symmDiff.{u1} (Set.{u1} α) (SemilatticeSup.toSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (Set.instSDiffSet.{u1} α) s t)) (Or (And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (Not (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a t))) (And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a t) (Not (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s))))
 Case conversion may be inaccurate. Consider using '#align set.mem_symm_diff Set.mem_symmDiffₓ'. -/
 theorem mem_symmDiff : a ∈ s ∆ t ↔ a ∈ s ∧ a ∉ t ∨ a ∈ t ∧ a ∉ s :=
   Iff.rfl
@@ -3952,7 +3952,7 @@ theorem mem_symmDiff : a ∈ s ∆ t ↔ a ∈ s ∧ a ∉ t ∨ a ∈ t ∧ a 
 lean 3 declaration is
   forall {α : Type.{u1}} (s : Set.{u1} α) (t : Set.{u1} α), Eq.{succ u1} (Set.{u1} α) (symmDiff.{u1} (Set.{u1} α) (SemilatticeSup.toHasSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s t) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) (SDiff.sdiff.{u1} (Set.{u1} α) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s t) (SDiff.sdiff.{u1} (Set.{u1} α) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) t s))
 but is expected to have type
-  forall {α : Type.{u1}} (s : Set.{u1} α) (t : Set.{u1} α), Eq.{succ u1} (Set.{u1} α) (symmDiff.{u1} (Set.{u1} α) (SemilatticeSup.toHasSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (Set.instSDiffSet.{u1} α) s t) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) (SDiff.sdiff.{u1} (Set.{u1} α) (Set.instSDiffSet.{u1} α) s t) (SDiff.sdiff.{u1} (Set.{u1} α) (Set.instSDiffSet.{u1} α) t s))
+  forall {α : Type.{u1}} (s : Set.{u1} α) (t : Set.{u1} α), Eq.{succ u1} (Set.{u1} α) (symmDiff.{u1} (Set.{u1} α) (SemilatticeSup.toSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (Set.instSDiffSet.{u1} α) s t) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) (SDiff.sdiff.{u1} (Set.{u1} α) (Set.instSDiffSet.{u1} α) s t) (SDiff.sdiff.{u1} (Set.{u1} α) (Set.instSDiffSet.{u1} α) t s))
 Case conversion may be inaccurate. Consider using '#align set.symm_diff_def Set.symmDiff_defₓ'. -/
 protected theorem symmDiff_def (s t : Set α) : s ∆ t = s \ t ∪ t \ s :=
   rfl
@@ -3962,7 +3962,7 @@ protected theorem symmDiff_def (s t : Set α) : s ∆ t = s \ t ∪ t \ s :=
 lean 3 declaration is
   forall {α : Type.{u1}} {s : Set.{u1} α} {t : Set.{u1} α}, HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (symmDiff.{u1} (Set.{u1} α) (SemilatticeSup.toHasSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s t) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)
 but is expected to have type
-  forall {α : Type.{u1}} {s : Set.{u1} α} {t : Set.{u1} α}, HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (symmDiff.{u1} (Set.{u1} α) (SemilatticeSup.toHasSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (Set.instSDiffSet.{u1} α) s t) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s t)
+  forall {α : Type.{u1}} {s : Set.{u1} α} {t : Set.{u1} α}, HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (symmDiff.{u1} (Set.{u1} α) (SemilatticeSup.toSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (Set.instSDiffSet.{u1} α) s t) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s t)
 Case conversion may be inaccurate. Consider using '#align set.symm_diff_subset_union Set.symmDiff_subset_unionₓ'. -/
 theorem symmDiff_subset_union : s ∆ t ⊆ s ∪ t :=
   @symmDiff_le_sup (Set α) _ _ _
@@ -3972,7 +3972,7 @@ theorem symmDiff_subset_union : s ∆ t ⊆ s ∪ t :=
 lean 3 declaration is
   forall {α : Type.{u1}} {s : Set.{u1} α} {t : Set.{u1} α}, Iff (Eq.{succ u1} (Set.{u1} α) (symmDiff.{u1} (Set.{u1} α) (SemilatticeSup.toHasSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s t) (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.hasEmptyc.{u1} α))) (Eq.{succ u1} (Set.{u1} α) s t)
 but is expected to have type
-  forall {α : Type.{u1}} {s : Set.{u1} α} {t : Set.{u1} α}, Iff (Eq.{succ u1} (Set.{u1} α) (symmDiff.{u1} (Set.{u1} α) (SemilatticeSup.toHasSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (Set.instSDiffSet.{u1} α) s t) (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.instEmptyCollectionSet.{u1} α))) (Eq.{succ u1} (Set.{u1} α) s t)
+  forall {α : Type.{u1}} {s : Set.{u1} α} {t : Set.{u1} α}, Iff (Eq.{succ u1} (Set.{u1} α) (symmDiff.{u1} (Set.{u1} α) (SemilatticeSup.toSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (Set.instSDiffSet.{u1} α) s t) (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.instEmptyCollectionSet.{u1} α))) (Eq.{succ u1} (Set.{u1} α) s t)
 Case conversion may be inaccurate. Consider using '#align set.symm_diff_eq_empty Set.symmDiff_eq_emptyₓ'. -/
 @[simp]
 theorem symmDiff_eq_empty : s ∆ t = ∅ ↔ s = t :=
@@ -3983,7 +3983,7 @@ theorem symmDiff_eq_empty : s ∆ t = ∅ ↔ s = t :=
 lean 3 declaration is
   forall {α : Type.{u1}} {s : Set.{u1} α} {t : Set.{u1} α}, Iff (Set.Nonempty.{u1} α (symmDiff.{u1} (Set.{u1} α) (SemilatticeSup.toHasSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s t)) (Ne.{succ u1} (Set.{u1} α) s t)
 but is expected to have type
-  forall {α : Type.{u1}} {s : Set.{u1} α} {t : Set.{u1} α}, Iff (Set.Nonempty.{u1} α (symmDiff.{u1} (Set.{u1} α) (SemilatticeSup.toHasSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (Set.instSDiffSet.{u1} α) s t)) (Ne.{succ u1} (Set.{u1} α) s t)
+  forall {α : Type.{u1}} {s : Set.{u1} α} {t : Set.{u1} α}, Iff (Set.Nonempty.{u1} α (symmDiff.{u1} (Set.{u1} α) (SemilatticeSup.toSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (Set.instSDiffSet.{u1} α) s t)) (Ne.{succ u1} (Set.{u1} α) s t)
 Case conversion may be inaccurate. Consider using '#align set.symm_diff_nonempty Set.symmDiff_nonemptyₓ'. -/
 @[simp]
 theorem symmDiff_nonempty : (s ∆ t).Nonempty ↔ s ≠ t :=
@@ -3994,7 +3994,7 @@ theorem symmDiff_nonempty : (s ∆ t).Nonempty ↔ s ≠ t :=
 lean 3 declaration is
   forall {α : Type.{u1}} (s : Set.{u1} α) (t : Set.{u1} α) (u : Set.{u1} α), Eq.{succ u1} (Set.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s (symmDiff.{u1} (Set.{u1} α) (SemilatticeSup.toHasSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) t u)) (symmDiff.{u1} (Set.{u1} α) (SemilatticeSup.toHasSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s u))
 but is expected to have type
-  forall {α : Type.{u1}} (s : Set.{u1} α) (t : Set.{u1} α) (u : Set.{u1} α), Eq.{succ u1} (Set.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s (symmDiff.{u1} (Set.{u1} α) (SemilatticeSup.toHasSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (Set.instSDiffSet.{u1} α) t u)) (symmDiff.{u1} (Set.{u1} α) (SemilatticeSup.toHasSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (Set.instSDiffSet.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s t) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s u))
+  forall {α : Type.{u1}} (s : Set.{u1} α) (t : Set.{u1} α) (u : Set.{u1} α), Eq.{succ u1} (Set.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s (symmDiff.{u1} (Set.{u1} α) (SemilatticeSup.toSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (Set.instSDiffSet.{u1} α) t u)) (symmDiff.{u1} (Set.{u1} α) (SemilatticeSup.toSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (Set.instSDiffSet.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s t) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s u))
 Case conversion may be inaccurate. Consider using '#align set.inter_symm_diff_distrib_left Set.inter_symmDiff_distrib_leftₓ'. -/
 theorem inter_symmDiff_distrib_left (s t u : Set α) : s ∩ t ∆ u = (s ∩ t) ∆ (s ∩ u) :=
   inf_symmDiff_distrib_left _ _ _
@@ -4004,7 +4004,7 @@ theorem inter_symmDiff_distrib_left (s t u : Set α) : s ∩ t ∆ u = (s ∩ t)
 lean 3 declaration is
   forall {α : Type.{u1}} (s : Set.{u1} α) (t : Set.{u1} α) (u : Set.{u1} α), Eq.{succ u1} (Set.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) (symmDiff.{u1} (Set.{u1} α) (SemilatticeSup.toHasSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s t) u) (symmDiff.{u1} (Set.{u1} α) (SemilatticeSup.toHasSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s u) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) t u))
 but is expected to have type
-  forall {α : Type.{u1}} (s : Set.{u1} α) (t : Set.{u1} α) (u : Set.{u1} α), Eq.{succ u1} (Set.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) (symmDiff.{u1} (Set.{u1} α) (SemilatticeSup.toHasSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (Set.instSDiffSet.{u1} α) s t) u) (symmDiff.{u1} (Set.{u1} α) (SemilatticeSup.toHasSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (Set.instSDiffSet.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s u) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) t u))
+  forall {α : Type.{u1}} (s : Set.{u1} α) (t : Set.{u1} α) (u : Set.{u1} α), Eq.{succ u1} (Set.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) (symmDiff.{u1} (Set.{u1} α) (SemilatticeSup.toSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (Set.instSDiffSet.{u1} α) s t) u) (symmDiff.{u1} (Set.{u1} α) (SemilatticeSup.toSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (Set.instSDiffSet.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s u) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) t u))
 Case conversion may be inaccurate. Consider using '#align set.inter_symm_diff_distrib_right Set.inter_symmDiff_distrib_rightₓ'. -/
 theorem inter_symmDiff_distrib_right (s t u : Set α) : s ∆ t ∩ u = (s ∩ u) ∆ (t ∩ u) :=
   inf_symmDiff_distrib_right _ _ _
@@ -4014,7 +4014,7 @@ theorem inter_symmDiff_distrib_right (s t u : Set α) : s ∆ t ∩ u = (s ∩ u
 lean 3 declaration is
   forall {α : Type.{u1}} {s : Set.{u1} α} {t : Set.{u1} α} {u : Set.{u1} α}, (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))) s t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) u (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) (symmDiff.{u1} (Set.{u1} α) (SemilatticeSup.toHasSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s u) (symmDiff.{u1} (Set.{u1} α) (SemilatticeSup.toHasSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) t u)))
 but is expected to have type
-  forall {α : Type.{u1}} {s : Set.{u1} α} {t : Set.{u1} α} {u : Set.{u1} α}, (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))))) (BooleanAlgebra.toBoundedOrder.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))) s t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) u (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) (symmDiff.{u1} (Set.{u1} α) (SemilatticeSup.toHasSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (Set.instSDiffSet.{u1} α) s u) (symmDiff.{u1} (Set.{u1} α) (SemilatticeSup.toHasSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (Set.instSDiffSet.{u1} α) t u)))
+  forall {α : Type.{u1}} {s : Set.{u1} α} {t : Set.{u1} α} {u : Set.{u1} α}, (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))))) (BooleanAlgebra.toBoundedOrder.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))) s t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) u (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) (symmDiff.{u1} (Set.{u1} α) (SemilatticeSup.toSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (Set.instSDiffSet.{u1} α) s u) (symmDiff.{u1} (Set.{u1} α) (SemilatticeSup.toSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (Set.instSDiffSet.{u1} α) t u)))
 Case conversion may be inaccurate. Consider using '#align set.subset_symm_diff_union_symm_diff_left Set.subset_symmDiff_union_symmDiff_leftₓ'. -/
 theorem subset_symmDiff_union_symmDiff_left (h : Disjoint s t) : u ⊆ s ∆ u ∪ t ∆ u :=
   h.le_symmDiff_sup_symmDiff_left
@@ -4024,7 +4024,7 @@ theorem subset_symmDiff_union_symmDiff_left (h : Disjoint s t) : u ⊆ s ∆ u 
 lean 3 declaration is
   forall {α : Type.{u1}} {s : Set.{u1} α} {t : Set.{u1} α} {u : Set.{u1} α}, (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))) t u) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) (symmDiff.{u1} (Set.{u1} α) (SemilatticeSup.toHasSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s t) (symmDiff.{u1} (Set.{u1} α) (SemilatticeSup.toHasSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s u)))
 but is expected to have type
-  forall {α : Type.{u1}} {s : Set.{u1} α} {t : Set.{u1} α} {u : Set.{u1} α}, (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))))) (BooleanAlgebra.toBoundedOrder.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))) t u) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) (symmDiff.{u1} (Set.{u1} α) (SemilatticeSup.toHasSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (Set.instSDiffSet.{u1} α) s t) (symmDiff.{u1} (Set.{u1} α) (SemilatticeSup.toHasSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (Set.instSDiffSet.{u1} α) s u)))
+  forall {α : Type.{u1}} {s : Set.{u1} α} {t : Set.{u1} α} {u : Set.{u1} α}, (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))))) (BooleanAlgebra.toBoundedOrder.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))) t u) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) (symmDiff.{u1} (Set.{u1} α) (SemilatticeSup.toSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (Set.instSDiffSet.{u1} α) s t) (symmDiff.{u1} (Set.{u1} α) (SemilatticeSup.toSup.{u1} (Set.{u1} α) (Lattice.toSemilatticeSup.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (Set.instSDiffSet.{u1} α) s u)))
 Case conversion may be inaccurate. Consider using '#align set.subset_symm_diff_union_symm_diff_right Set.subset_symmDiff_union_symmDiff_rightₓ'. -/
 theorem subset_symmDiff_union_symmDiff_right (h : Disjoint t u) : s ⊆ s ∆ t ∪ s ∆ u :=
   h.le_symmDiff_sup_symmDiff_right

bump to nightly-2023-02-27-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/eb0cb4511aaef0da2462207b67358a0e1fe1e2ee

ed3e596e

Diff

@@ -2031,9 +2031,11 @@ theorem insert_subset_insert_iff (ha : a ∉ s) : insert a s ⊆ insert a t ↔
 #align set.insert_subset_insert_iff Set.insert_subset_insert_iff
 -/
 
+#print Set.subset_insert_iff_of_not_mem /-
 theorem subset_insert_iff_of_not_mem (ha : a ∉ s) : s ⊆ insert a t ↔ s ⊆ t :=
   forall₂_congr fun b hb => or_iff_right <| ne_of_mem_of_not_mem hb ha
 #align set.subset_insert_iff_of_not_mem Set.subset_insert_iff_of_not_mem
+-/
 
 /- warning: set.ssubset_iff_insert -> Set.ssubset_iff_insert is a dubious translation:
 lean 3 declaration is
@@ -4104,12 +4106,14 @@ theorem powerset_univ : 𝒫(univ : Set α) = univ :=
 #align set.powerset_univ Set.powerset_univ
 -/
 
+#print Set.powerset_singleton /-
 /-- The powerset of a singleton contains only `∅` and the singleton itself. -/
 theorem powerset_singleton (x : α) : 𝒫({x} : Set α) = {∅, {x}} :=
   by
   ext y
   rw [mem_powerset_iff, subset_singleton_iff_eq, mem_insert_iff, mem_singleton_iff]
 #align set.powerset_singleton Set.powerset_singleton
+-/
 
 /-! ### Sets defined as an if-then-else -/

bump to nightly-2023-02-25-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/271bf175e6c51b8d31d6c0107b7bb4a967c7277e

39ef98db

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Leonardo de Moura
 
 ! This file was ported from Lean 3 source module data.set.basic
-! leanprover-community/mathlib commit 4550138052d0a416b700c27056d492e2ef53214e
+! leanprover-community/mathlib commit 75608affb24b4f48699fbcd38f227827f7793771
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -2031,19 +2031,8 @@ theorem insert_subset_insert_iff (ha : a ∉ s) : insert a s ⊆ insert a t ↔
 #align set.insert_subset_insert_iff Set.insert_subset_insert_iff
 -/
 
-theorem subset_insert_iff_of_not_mem {s t : Set α} {a : α} (h : a ∉ s) : s ⊆ insert a t ↔ s ⊆ t :=
-  by
-  constructor
-  · intro g y hy
-    specialize g hy
-    rw [mem_insert_iff] at g
-    rcases g with (g | g)
-    · rw [g] at hy
-      contradiction
-    · assumption
-  · intro g y hy
-    specialize g hy
-    exact mem_insert_of_mem _ g
+theorem subset_insert_iff_of_not_mem (ha : a ∉ s) : s ⊆ insert a t ↔ s ⊆ t :=
+  forall₂_congr fun b hb => or_iff_right <| ne_of_mem_of_not_mem hb ha
 #align set.subset_insert_iff_of_not_mem Set.subset_insert_iff_of_not_mem
 
 /- warning: set.ssubset_iff_insert -> Set.ssubset_iff_insert is a dubious translation:
@@ -4115,7 +4104,7 @@ theorem powerset_univ : 𝒫(univ : Set α) = univ :=
 #align set.powerset_univ Set.powerset_univ
 -/
 
--- The powerset of a singleton contains only `∅` and the singleton itself.
+/-- The powerset of a singleton contains only `∅` and the singleton itself. -/
 theorem powerset_singleton (x : α) : 𝒫({x} : Set α) = {∅, {x}} :=
   by
   ext y

45501380

bump to nightly-2023-02-23-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/3ade05ac9447ae31a22d2ea5423435e054131240

5c91f1b0

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Leonardo de Moura
 
 ! This file was ported from Lean 3 source module data.set.basic
-! leanprover-community/mathlib commit bc7d81beddb3d6c66f71449c5bc76c38cb77cf9e
+! leanprover-community/mathlib commit 4550138052d0a416b700c27056d492e2ef53214e
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -2031,6 +2031,21 @@ theorem insert_subset_insert_iff (ha : a ∉ s) : insert a s ⊆ insert a t ↔
 #align set.insert_subset_insert_iff Set.insert_subset_insert_iff
 -/
 
+theorem subset_insert_iff_of_not_mem {s t : Set α} {a : α} (h : a ∉ s) : s ⊆ insert a t ↔ s ⊆ t :=
+  by
+  constructor
+  · intro g y hy
+    specialize g hy
+    rw [mem_insert_iff] at g
+    rcases g with (g | g)
+    · rw [g] at hy
+      contradiction
+    · assumption
+  · intro g y hy
+    specialize g hy
+    exact mem_insert_of_mem _ g
+#align set.subset_insert_iff_of_not_mem Set.subset_insert_iff_of_not_mem
+
 /- warning: set.ssubset_iff_insert -> Set.ssubset_iff_insert is a dubious translation:
 lean 3 declaration is
   forall {α : Type.{u1}} {s : Set.{u1} α} {t : Set.{u1} α}, Iff (HasSSubset.SSubset.{u1} (Set.{u1} α) (Set.hasSsubset.{u1} α) s t) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s)) (fun (H : Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s)) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a s) t)))
@@ -4100,6 +4115,13 @@ theorem powerset_univ : 𝒫(univ : Set α) = univ :=
 #align set.powerset_univ Set.powerset_univ
 -/
 
+-- The powerset of a singleton contains only `∅` and the singleton itself.
+theorem powerset_singleton (x : α) : 𝒫({x} : Set α) = {∅, {x}} :=
+  by
+  ext y
+  rw [mem_powerset_iff, subset_singleton_iff_eq, mem_insert_iff, mem_singleton_iff]
+#align set.powerset_singleton Set.powerset_singleton
+
 /-! ### Sets defined as an if-then-else -/

bc7d81be

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

chore: split Subsingleton,Nontrivial off of Data.Set.Basic (#11832)

Moves definition of and lemmas related to Set.Subsingleton and Set.Nontrivial to a new file, so that Basic can be shorter.

493a947e

Diff

@@ -44,10 +44,6 @@ Definitions in the file:
 * `Nonempty s : Prop` : the predicate `s ≠ ∅`. Note that this is the preferred way to express the
   fact that `s` has an element (see the Implementation Notes).
 
-* `Subsingleton s : Prop` : the predicate saying that `s` has at most one element.
-
-* `Nontrivial s : Prop` : the predicate saying that `s` has at least two distinct elements.
-
 * `inclusion s₁ s₂ : ↥s₁ → ↥s₂` : the map `↥s₁ → ↥s₂` induced by an inclusion `s₁ ⊆ s₂`.
 
 ## Notation
@@ -2322,319 +2318,6 @@ theorem ite_eq_of_subset_right (t : Set α) {s₁ s₂ : Set α} (h : s₂ ⊆ s
   ext x
   by_cases hx : x ∈ t <;> simp [*, Set.ite, or_iff_left_of_imp (@h x)]
 
-/-! ### Subsingleton -/
-
-
-/-- A set `s` is a `Subsingleton` if it has at most one element. -/
-protected def Subsingleton (s : Set α) : Prop :=
-  ∀ ⦃x⦄ (_ : x ∈ s) ⦃y⦄ (_ : y ∈ s), x = y
-#align set.subsingleton Set.Subsingleton
-
-theorem Subsingleton.anti (ht : t.Subsingleton) (hst : s ⊆ t) : s.Subsingleton := fun _ hx _ hy =>
-  ht (hst hx) (hst hy)
-#align set.subsingleton.anti Set.Subsingleton.anti
-
-theorem Subsingleton.eq_singleton_of_mem (hs : s.Subsingleton) {x : α} (hx : x ∈ s) : s = {x} :=
-  ext fun _ => ⟨fun hy => hs hx hy ▸ mem_singleton _, fun hy => (eq_of_mem_singleton hy).symm ▸ hx⟩
-#align set.subsingleton.eq_singleton_of_mem Set.Subsingleton.eq_singleton_of_mem
-
-@[simp]
-theorem subsingleton_empty : (∅ : Set α).Subsingleton := fun _ => False.elim
-#align set.subsingleton_empty Set.subsingleton_empty
-
-@[simp]
-theorem subsingleton_singleton {a} : ({a} : Set α).Subsingleton := fun _ hx _ hy =>
-  (eq_of_mem_singleton hx).symm ▸ (eq_of_mem_singleton hy).symm ▸ rfl
-#align set.subsingleton_singleton Set.subsingleton_singleton
-
-theorem subsingleton_of_subset_singleton (h : s ⊆ {a}) : s.Subsingleton :=
-  subsingleton_singleton.anti h
-#align set.subsingleton_of_subset_singleton Set.subsingleton_of_subset_singleton
-
-theorem subsingleton_of_forall_eq (a : α) (h : ∀ b ∈ s, b = a) : s.Subsingleton := fun _ hb _ hc =>
-  (h _ hb).trans (h _ hc).symm
-#align set.subsingleton_of_forall_eq Set.subsingleton_of_forall_eq
-
-theorem subsingleton_iff_singleton {x} (hx : x ∈ s) : s.Subsingleton ↔ s = {x} :=
-  ⟨fun h => h.eq_singleton_of_mem hx, fun h => h.symm ▸ subsingleton_singleton⟩
-#align set.subsingleton_iff_singleton Set.subsingleton_iff_singleton
-
-theorem Subsingleton.eq_empty_or_singleton (hs : s.Subsingleton) : s = ∅ ∨ ∃ x, s = {x} :=
-  s.eq_empty_or_nonempty.elim Or.inl fun ⟨x, hx⟩ => Or.inr ⟨x, hs.eq_singleton_of_mem hx⟩
-#align set.subsingleton.eq_empty_or_singleton Set.Subsingleton.eq_empty_or_singleton
-
-theorem Subsingleton.induction_on {p : Set α → Prop} (hs : s.Subsingleton) (he : p ∅)
-    (h₁ : ∀ x, p {x}) : p s := by
-  rcases hs.eq_empty_or_singleton with (rfl | ⟨x, rfl⟩)
-  exacts [he, h₁ _]
-#align set.subsingleton.induction_on Set.Subsingleton.induction_on
-
-theorem subsingleton_univ [Subsingleton α] : (univ : Set α).Subsingleton := fun x _ y _ =>
-  Subsingleton.elim x y
-#align set.subsingleton_univ Set.subsingleton_univ
-
-theorem subsingleton_of_univ_subsingleton (h : (univ : Set α).Subsingleton) : Subsingleton α :=
-  ⟨fun a b => h (mem_univ a) (mem_univ b)⟩
-#align set.subsingleton_of_univ_subsingleton Set.subsingleton_of_univ_subsingleton
-
-@[simp]
-theorem subsingleton_univ_iff : (univ : Set α).Subsingleton ↔ Subsingleton α :=
-  ⟨subsingleton_of_univ_subsingleton, fun h => @subsingleton_univ _ h⟩
-#align set.subsingleton_univ_iff Set.subsingleton_univ_iff
-
-theorem subsingleton_of_subsingleton [Subsingleton α] {s : Set α} : Set.Subsingleton s :=
-  subsingleton_univ.anti (subset_univ s)
-#align set.subsingleton_of_subsingleton Set.subsingleton_of_subsingleton
-
-theorem subsingleton_isTop (α : Type*) [PartialOrder α] : Set.Subsingleton { x : α | IsTop x } :=
-  fun x hx _ hy => hx.isMax.eq_of_le (hy x)
-#align set.subsingleton_is_top Set.subsingleton_isTop
-
-theorem subsingleton_isBot (α : Type*) [PartialOrder α] : Set.Subsingleton { x : α | IsBot x } :=
-  fun x hx _ hy => hx.isMin.eq_of_ge (hy x)
-#align set.subsingleton_is_bot Set.subsingleton_isBot
-
-theorem exists_eq_singleton_iff_nonempty_subsingleton :
-    (∃ a : α, s = {a}) ↔ s.Nonempty ∧ s.Subsingleton := by
-  refine' ⟨_, fun h => _⟩
-  · rintro ⟨a, rfl⟩
-    exact ⟨singleton_nonempty a, subsingleton_singleton⟩
-  · exact h.2.eq_empty_or_singleton.resolve_left h.1.ne_empty
-#align set.exists_eq_singleton_iff_nonempty_subsingleton Set.exists_eq_singleton_iff_nonempty_subsingleton
-
-/-- `s`, coerced to a type, is a subsingleton type if and only if `s` is a subsingleton set. -/
-@[simp, norm_cast]
-theorem subsingleton_coe (s : Set α) : Subsingleton s ↔ s.Subsingleton := by
-  constructor
-  · refine' fun h => fun a ha b hb => _
-    exact SetCoe.ext_iff.2 (@Subsingleton.elim s h ⟨a, ha⟩ ⟨b, hb⟩)
-  · exact fun h => Subsingleton.intro fun a b => SetCoe.ext (h a.property b.property)
-#align set.subsingleton_coe Set.subsingleton_coe
-
-theorem Subsingleton.coe_sort {s : Set α} : s.Subsingleton → Subsingleton s :=
-  s.subsingleton_coe.2
-#align set.subsingleton.coe_sort Set.Subsingleton.coe_sort
-
-/-- The `coe_sort` of a set `s` in a subsingleton type is a subsingleton.
-For the corresponding result for `Subtype`, see `subtype.subsingleton`. -/
-instance subsingleton_coe_of_subsingleton [Subsingleton α] {s : Set α} : Subsingleton s := by
-  rw [s.subsingleton_coe]
-  exact subsingleton_of_subsingleton
-#align set.subsingleton_coe_of_subsingleton Set.subsingleton_coe_of_subsingleton
-
-/-! ### Nontrivial -/
-
-/-- A set `s` is `Set.Nontrivial` if it has at least two distinct elements. -/
-protected def Nontrivial (s : Set α) : Prop :=
-  ∃ x ∈ s, ∃ y ∈ s, x ≠ y
-#align set.nontrivial Set.Nontrivial
-
-theorem nontrivial_of_mem_mem_ne {x y} (hx : x ∈ s) (hy : y ∈ s) (hxy : x ≠ y) : s.Nontrivial :=
-  ⟨x, hx, y, hy, hxy⟩
-#align set.nontrivial_of_mem_mem_ne Set.nontrivial_of_mem_mem_ne
-
--- Porting note: following the pattern for `Exists`, we have renamed `some` to `choose`.
-
-/-- Extract witnesses from s.nontrivial. This function might be used instead of case analysis on the
-argument. Note that it makes a proof depend on the classical.choice axiom. -/
-protected noncomputable def Nontrivial.choose (hs : s.Nontrivial) : α × α :=
-  (Exists.choose hs, hs.choose_spec.right.choose)
-#align set.nontrivial.some Set.Nontrivial.choose
-
-protected theorem Nontrivial.choose_fst_mem (hs : s.Nontrivial) : hs.choose.fst ∈ s :=
-  hs.choose_spec.left
-#align set.nontrivial.some_fst_mem Set.Nontrivial.choose_fst_mem
-
-protected theorem Nontrivial.choose_snd_mem (hs : s.Nontrivial) : hs.choose.snd ∈ s :=
-  hs.choose_spec.right.choose_spec.left
-#align set.nontrivial.some_snd_mem Set.Nontrivial.choose_snd_mem
-
-protected theorem Nontrivial.choose_fst_ne_choose_snd (hs : s.Nontrivial) :
-    hs.choose.fst ≠ hs.choose.snd :=
-  hs.choose_spec.right.choose_spec.right
-#align set.nontrivial.some_fst_ne_some_snd Set.Nontrivial.choose_fst_ne_choose_snd
-
-theorem Nontrivial.mono (hs : s.Nontrivial) (hst : s ⊆ t) : t.Nontrivial :=
-  let ⟨x, hx, y, hy, hxy⟩ := hs
-  ⟨x, hst hx, y, hst hy, hxy⟩
-#align set.nontrivial.mono Set.Nontrivial.mono
-
-theorem nontrivial_pair {x y} (hxy : x ≠ y) : ({x, y} : Set α).Nontrivial :=
-  ⟨x, mem_insert _ _, y, mem_insert_of_mem _ (mem_singleton _), hxy⟩
-#align set.nontrivial_pair Set.nontrivial_pair
-
-theorem nontrivial_of_pair_subset {x y} (hxy : x ≠ y) (h : {x, y} ⊆ s) : s.Nontrivial :=
-  (nontrivial_pair hxy).mono h
-#align set.nontrivial_of_pair_subset Set.nontrivial_of_pair_subset
-
-theorem Nontrivial.pair_subset (hs : s.Nontrivial) : ∃ x y, x ≠ y ∧ {x, y} ⊆ s :=
-  let ⟨x, hx, y, hy, hxy⟩ := hs
-  ⟨x, y, hxy, insert_subset hx <| singleton_subset_iff.2 hy⟩
-#align set.nontrivial.pair_subset Set.Nontrivial.pair_subset
-
-theorem nontrivial_iff_pair_subset : s.Nontrivial ↔ ∃ x y, x ≠ y ∧ {x, y} ⊆ s :=
-  ⟨Nontrivial.pair_subset, fun H =>
-    let ⟨_, _, hxy, h⟩ := H
-    nontrivial_of_pair_subset hxy h⟩
-#align set.nontrivial_iff_pair_subset Set.nontrivial_iff_pair_subset
-
-theorem nontrivial_of_exists_ne {x} (hx : x ∈ s) (h : ∃ y ∈ s, y ≠ x) : s.Nontrivial :=
-  let ⟨y, hy, hyx⟩ := h
-  ⟨y, hy, x, hx, hyx⟩
-#align set.nontrivial_of_exists_ne Set.nontrivial_of_exists_ne
-
-theorem Nontrivial.exists_ne (hs : s.Nontrivial) (z) : ∃ x ∈ s, x ≠ z := by
-  by_contra! H
-  rcases hs with ⟨x, hx, y, hy, hxy⟩
-  rw [H x hx, H y hy] at hxy
-  exact hxy rfl
-#align set.nontrivial.exists_ne Set.Nontrivial.exists_ne
-
-theorem nontrivial_iff_exists_ne {x} (hx : x ∈ s) : s.Nontrivial ↔ ∃ y ∈ s, y ≠ x :=
-  ⟨fun H => H.exists_ne _, nontrivial_of_exists_ne hx⟩
-#align set.nontrivial_iff_exists_ne Set.nontrivial_iff_exists_ne
-
-theorem nontrivial_of_lt [Preorder α] {x y} (hx : x ∈ s) (hy : y ∈ s) (hxy : x < y) :
-    s.Nontrivial :=
-  ⟨x, hx, y, hy, ne_of_lt hxy⟩
-#align set.nontrivial_of_lt Set.nontrivial_of_lt
-
-theorem nontrivial_of_exists_lt [Preorder α]
-    (H : ∃ᵉ (x ∈ s) (y ∈ s), x < y) : s.Nontrivial :=
-  let ⟨_, hx, _, hy, hxy⟩ := H
-  nontrivial_of_lt hx hy hxy
-#align set.nontrivial_of_exists_lt Set.nontrivial_of_exists_lt
-
-theorem Nontrivial.exists_lt [LinearOrder α] (hs : s.Nontrivial) : ∃ᵉ (x ∈ s) (y ∈ s), x < y :=
-  let ⟨x, hx, y, hy, hxy⟩ := hs
-  Or.elim (lt_or_gt_of_ne hxy) (fun H => ⟨x, hx, y, hy, H⟩) fun H => ⟨y, hy, x, hx, H⟩
-#align set.nontrivial.exists_lt Set.Nontrivial.exists_lt
-
-theorem nontrivial_iff_exists_lt [LinearOrder α] :
-    s.Nontrivial ↔ ∃ᵉ (x ∈ s) (y ∈ s), x < y :=
-  ⟨Nontrivial.exists_lt, nontrivial_of_exists_lt⟩
-#align set.nontrivial_iff_exists_lt Set.nontrivial_iff_exists_lt
-
-protected theorem Nontrivial.nonempty (hs : s.Nontrivial) : s.Nonempty :=
-  let ⟨x, hx, _⟩ := hs
-  ⟨x, hx⟩
-#align set.nontrivial.nonempty Set.Nontrivial.nonempty
-
-protected theorem Nontrivial.ne_empty (hs : s.Nontrivial) : s ≠ ∅ :=
-  hs.nonempty.ne_empty
-#align set.nontrivial.ne_empty Set.Nontrivial.ne_empty
-
-theorem Nontrivial.not_subset_empty (hs : s.Nontrivial) : ¬s ⊆ ∅ :=
-  hs.nonempty.not_subset_empty
-#align set.nontrivial.not_subset_empty Set.Nontrivial.not_subset_empty
-
-@[simp]
-theorem not_nontrivial_empty : ¬(∅ : Set α).Nontrivial := fun h => h.ne_empty rfl
-#align set.not_nontrivial_empty Set.not_nontrivial_empty
-
-@[simp]
-theorem not_nontrivial_singleton {x} : ¬({x} : Set α).Nontrivial := fun H => by
-  rw [nontrivial_iff_exists_ne (mem_singleton x)] at H
-  let ⟨y, hy, hya⟩ := H
-  exact hya (mem_singleton_iff.1 hy)
-#align set.not_nontrivial_singleton Set.not_nontrivial_singleton
-
-theorem Nontrivial.ne_singleton {x} (hs : s.Nontrivial) : s ≠ {x} := fun H => by
-  rw [H] at hs
-  exact not_nontrivial_singleton hs
-#align set.nontrivial.ne_singleton Set.Nontrivial.ne_singleton
-
-theorem Nontrivial.not_subset_singleton {x} (hs : s.Nontrivial) : ¬s ⊆ {x} :=
-  (not_congr subset_singleton_iff_eq).2 (not_or_of_not hs.ne_empty hs.ne_singleton)
-#align set.nontrivial.not_subset_singleton Set.Nontrivial.not_subset_singleton
-
-theorem nontrivial_univ [Nontrivial α] : (univ : Set α).Nontrivial :=
-  let ⟨x, y, hxy⟩ := exists_pair_ne α
-  ⟨x, mem_univ _, y, mem_univ _, hxy⟩
-#align set.nontrivial_univ Set.nontrivial_univ
-
-theorem nontrivial_of_univ_nontrivial (h : (univ : Set α).Nontrivial) : Nontrivial α :=
-  let ⟨x, _, y, _, hxy⟩ := h
-  ⟨⟨x, y, hxy⟩⟩
-#align set.nontrivial_of_univ_nontrivial Set.nontrivial_of_univ_nontrivial
-
-@[simp]
-theorem nontrivial_univ_iff : (univ : Set α).Nontrivial ↔ Nontrivial α :=
-  ⟨nontrivial_of_univ_nontrivial, fun h => @nontrivial_univ _ h⟩
-#align set.nontrivial_univ_iff Set.nontrivial_univ_iff
-
-theorem nontrivial_of_nontrivial (hs : s.Nontrivial) : Nontrivial α :=
-  let ⟨x, _, y, _, hxy⟩ := hs
-  ⟨⟨x, y, hxy⟩⟩
-#align set.nontrivial_of_nontrivial Set.nontrivial_of_nontrivial
-
--- Porting note: simp_rw broken here
--- Perhaps review after https://github.com/leanprover/lean4/issues/1937?
-/-- `s`, coerced to a type, is a nontrivial type if and only if `s` is a nontrivial set. -/
-@[simp, norm_cast]
-theorem nontrivial_coe_sort {s : Set α} : Nontrivial s ↔ s.Nontrivial := by
-  -- simp_rw [← nontrivial_univ_iff, Set.Nontrivial, mem_univ, exists_true_left, SetCoe.exists,
-  --   Subtype.mk_eq_mk]
-  rw [← nontrivial_univ_iff, Set.Nontrivial, Set.Nontrivial]
-  apply Iff.intro
-  · rintro ⟨x, _, y, _, hxy⟩
-    exact ⟨x, Subtype.prop x, y, Subtype.prop y, fun h => hxy (Subtype.coe_injective h)⟩
-  · rintro ⟨x, hx, y, hy, hxy⟩
-    exact ⟨⟨x, hx⟩, mem_univ _, ⟨y, hy⟩, mem_univ _, Subtype.mk_eq_mk.not.mpr hxy⟩
-#align set.nontrivial_coe_sort Set.nontrivial_coe_sort
-
-alias ⟨_, Nontrivial.coe_sort⟩ := nontrivial_coe_sort
-#align set.nontrivial.coe_sort Set.Nontrivial.coe_sort
-
-/-- A type with a set `s` whose `coe_sort` is a nontrivial type is nontrivial.
-For the corresponding result for `Subtype`, see `Subtype.nontrivial_iff_exists_ne`. -/
-theorem nontrivial_of_nontrivial_coe (hs : Nontrivial s) : Nontrivial α :=
-  nontrivial_of_nontrivial <| nontrivial_coe_sort.1 hs
-#align set.nontrivial_of_nontrivial_coe Set.nontrivial_of_nontrivial_coe
-
-theorem nontrivial_mono {α : Type*} {s t : Set α} (hst : s ⊆ t) (hs : Nontrivial s) :
-    Nontrivial t :=
-  Nontrivial.coe_sort <| (nontrivial_coe_sort.1 hs).mono hst
-#align set.nontrivial_mono Set.nontrivial_mono
-
-@[simp]
-theorem not_subsingleton_iff : ¬s.Subsingleton ↔ s.Nontrivial := by
-  simp_rw [Set.Subsingleton, Set.Nontrivial, not_forall, exists_prop]
-#align set.not_subsingleton_iff Set.not_subsingleton_iff
-
-@[simp]
-theorem not_nontrivial_iff : ¬s.Nontrivial ↔ s.Subsingleton :=
-  Iff.not_left not_subsingleton_iff.symm
-#align set.not_nontrivial_iff Set.not_nontrivial_iff
-
-alias ⟨_, Subsingleton.not_nontrivial⟩ := not_nontrivial_iff
-#align set.subsingleton.not_nontrivial Set.Subsingleton.not_nontrivial
-
-alias ⟨_, Nontrivial.not_subsingleton⟩ := not_subsingleton_iff
-#align set.nontrivial.not_subsingleton Set.Nontrivial.not_subsingleton
-
-protected lemma subsingleton_or_nontrivial (s : Set α) : s.Subsingleton ∨ s.Nontrivial := by
-  simp [or_iff_not_imp_right]
-#align set.subsingleton_or_nontrivial Set.subsingleton_or_nontrivial
-
-lemma eq_singleton_or_nontrivial (ha : a ∈ s) : s = {a} ∨ s.Nontrivial := by
-  rw [← subsingleton_iff_singleton ha]; exact s.subsingleton_or_nontrivial
-#align set.eq_singleton_or_nontrivial Set.eq_singleton_or_nontrivial
-
-lemma nontrivial_iff_ne_singleton (ha : a ∈ s) : s.Nontrivial ↔ s ≠ {a} :=
-  ⟨Nontrivial.ne_singleton, (eq_singleton_or_nontrivial ha).resolve_left⟩
-#align set.nontrivial_iff_ne_singleton Set.nontrivial_iff_ne_singleton
-
-lemma Nonempty.exists_eq_singleton_or_nontrivial : s.Nonempty → (∃ a, s = {a}) ∨ s.Nontrivial :=
-  fun ⟨a, ha⟩ ↦ (eq_singleton_or_nontrivial ha).imp_left <| Exists.intro a
-#align set.nonempty.exists_eq_singleton_or_nontrivial Set.Nonempty.exists_eq_singleton_or_nontrivial
-
-theorem univ_eq_true_false : univ = ({True, False} : Set Prop) :=
-  Eq.symm <| eq_univ_of_forall fun x => by
-    rw [mem_insert_iff, mem_singleton_iff]
-    exact Classical.propComplete x
-#align set.univ_eq_true_false Set.univ_eq_true_false
-
 section Preorder
 
 variable [Preorder α] [Preorder β] {f : α → β}
@@ -2664,47 +2347,6 @@ theorem strictAntiOn_iff_strictAnti : StrictAntiOn f s ↔
   simp [StrictAnti, StrictAntiOn]
 #align set.strict_anti_on_iff_strict_anti Set.strictAntiOn_iff_strictAnti
 
-variable (f)
-
-/-! ### Monotonicity on singletons -/
-
-
-protected theorem Subsingleton.monotoneOn (h : s.Subsingleton) : MonotoneOn f s :=
-  fun _ ha _ hb _ => (congr_arg _ (h ha hb)).le
-#align set.subsingleton.monotone_on Set.Subsingleton.monotoneOn
-
-protected theorem Subsingleton.antitoneOn (h : s.Subsingleton) : AntitoneOn f s :=
-  fun _ ha _ hb _ => (congr_arg _ (h hb ha)).le
-#align set.subsingleton.antitone_on Set.Subsingleton.antitoneOn
-
-protected theorem Subsingleton.strictMonoOn (h : s.Subsingleton) : StrictMonoOn f s :=
-  fun _ ha _ hb hlt => (hlt.ne (h ha hb)).elim
-#align set.subsingleton.strict_mono_on Set.Subsingleton.strictMonoOn
-
-protected theorem Subsingleton.strictAntiOn (h : s.Subsingleton) : StrictAntiOn f s :=
-  fun _ ha _ hb hlt => (hlt.ne (h ha hb)).elim
-#align set.subsingleton.strict_anti_on Set.Subsingleton.strictAntiOn
-
-@[simp]
-theorem monotoneOn_singleton : MonotoneOn f {a} :=
-  subsingleton_singleton.monotoneOn f
-#align set.monotone_on_singleton Set.monotoneOn_singleton
-
-@[simp]
-theorem antitoneOn_singleton : AntitoneOn f {a} :=
-  subsingleton_singleton.antitoneOn f
-#align set.antitone_on_singleton Set.antitoneOn_singleton
-
-@[simp]
-theorem strictMonoOn_singleton : StrictMonoOn f {a} :=
-  subsingleton_singleton.strictMonoOn f
-#align set.strict_mono_on_singleton Set.strictMonoOn_singleton
-
-@[simp]
-theorem strictAntiOn_singleton : StrictAntiOn f {a} :=
-  subsingleton_singleton.strictAntiOn f
-#align set.strict_anti_on_singleton Set.strictAntiOn_singleton
-
 end Preorder
 
 section LinearOrder

refactor: move disjoint_sdiff_inter (#12021)

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

d1a8af0e

Diff

@@ -1575,6 +1575,11 @@ lemma disjoint_sdiff_left : Disjoint (t \ s) s := disjoint_sdiff_self_left
 lemma disjoint_sdiff_right : Disjoint s (t \ s) := disjoint_sdiff_self_right
 #align set.disjoint_sdiff_right Set.disjoint_sdiff_right
 
+-- TODO: prove this in terms of a lattice lemma
+theorem disjoint_sdiff_inter : Disjoint (s \ t) (s ∩ t) :=
+  disjoint_of_subset_right (inter_subset_right _ _) disjoint_sdiff_left
+#align set.disjoint_sdiff_inter Set.disjoint_sdiff_inter
+
 theorem diff_union_diff_cancel (hts : t ⊆ s) (hut : u ⊆ t) : s \ t ∪ t \ u = s \ u :=
   sdiff_sup_sdiff_cancel hts hut
 #align set.diff_union_diff_cancel Set.diff_union_diff_cancel

chore(*Set): golf (#12117)

Golf Directed.exists_mem_subset_of_finset_subset_biUnion using induction tactic.
Golf Set.fintype.
Reduce abuse of Set α = α → Prop defeq.

02b6c2be

Diff

@@ -1425,12 +1425,12 @@ theorem sep_false : { x ∈ s | False } = ∅ :=
 
 --Porting note (#10618): removed `simp` attribute because `simp` can prove it
 theorem sep_empty (p : α → Prop) : { x ∈ (∅ : Set α) | p x } = ∅ :=
-  empty_inter p
+  empty_inter {x | p x}
 #align set.sep_empty Set.sep_empty
 
 --Porting note (#10618): removed `simp` attribute because `simp` can prove it
 theorem sep_univ : { x ∈ (univ : Set α) | p x } = { x | p x } :=
-  univ_inter p
+  univ_inter {x | p x}
 #align set.sep_univ Set.sep_univ
 
 @[simp]
@@ -1440,12 +1440,12 @@ theorem sep_union : { x | (x ∈ s ∨ x ∈ t) ∧ p x } = { x ∈ s | p x } 
 
 @[simp]
 theorem sep_inter : { x | (x ∈ s ∧ x ∈ t) ∧ p x } = { x ∈ s | p x } ∩ { x ∈ t | p x } :=
-  inter_inter_distrib_right s t p
+  inter_inter_distrib_right s t {x | p x}
 #align set.sep_inter Set.sep_inter
 
 @[simp]
 theorem sep_and : { x ∈ s | p x ∧ q x } = { x ∈ s | p x } ∩ { x ∈ s | q x } :=
-  inter_inter_distrib_left s p q
+  inter_inter_distrib_left s {x | p x} {x | q x}
 #align set.sep_and Set.sep_and
 
 @[simp]

chore: remove more bex and ball from lemma names (#11615)

Follow-up to #10816.

Remaining places containing such lemmas are

Option.bex_ne_none and Option.ball_ne_none: defined in Lean core
Nat.decidableBallLT and Nat.decidableBallLE: defined in Lean core
bef_def is still used in a number of places and could be renamed
BAll.imp_{left,right}, BEx.imp_{left,right}, BEx.intro and BEx.elim

I only audited the first ~150 lemmas mentioning "ball"; too many lemmas named after Metric.ball/openBall/closedBall.

Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

7b7bbd73

Diff

@@ -614,9 +614,10 @@ theorem subset_eq_empty {s t : Set α} (h : t ⊆ s) (e : s = ∅) : t = ∅ :=
   subset_empty_iff.1 <| e ▸ h
 #align set.subset_eq_empty Set.subset_eq_empty
 
-theorem ball_empty_iff {p : α → Prop} : (∀ x ∈ (∅ : Set α), p x) ↔ True :=
+theorem forall_mem_empty {p : α → Prop} : (∀ x ∈ (∅ : Set α), p x) ↔ True :=
   iff_true_intro fun _ => False.elim
-#align set.ball_empty_iff Set.ball_empty_iff
+#align set.ball_empty_iff Set.forall_mem_empty
+@[deprecated] alias ball_empty_iff := forall_mem_empty -- 2024-03-23
 
 instance (α : Type u) : IsEmpty.{u + 1} (↥(∅ : Set α)) :=
   ⟨fun x => x.2⟩
@@ -1206,15 +1207,17 @@ theorem forall_insert_of_forall {P : α → Prop} {a : α} {s : Set α} (H : ∀
 
 /- Porting note: ∃ x ∈ insert a s, P x is parsed as ∃ x, x ∈ insert a s ∧ P x,
  where in Lean3 it was parsed as `∃ x, ∃ (h : x ∈ insert a s), P x` -/
-theorem bex_insert_iff {P : α → Prop} {a : α} {s : Set α} :
+theorem exists_mem_insert {P : α → Prop} {a : α} {s : Set α} :
     (∃ x ∈ insert a s, P x) ↔ (P a ∨ ∃ x ∈ s, P x) := by
   simp [mem_insert_iff, or_and_right, exists_and_left, exists_or]
-#align set.bex_insert_iff Set.bex_insert_iff
+#align set.bex_insert_iff Set.exists_mem_insert
+@[deprecated] alias bex_insert_iff := exists_mem_insert -- 2024-03-23
 
-theorem ball_insert_iff {P : α → Prop} {a : α} {s : Set α} :
+theorem forall_mem_insert {P : α → Prop} {a : α} {s : Set α} :
     (∀ x ∈ insert a s, P x) ↔ P a ∧ ∀ x ∈ s, P x :=
-  ball_or_left.trans <| and_congr_left' forall_eq
-#align set.ball_insert_iff Set.ball_insert_iff
+  forall₂_or_left.trans <| and_congr_left' forall_eq
+#align set.ball_insert_iff Set.forall_mem_insert
+@[deprecated] alias ball_insert_iff := forall_mem_insert -- 2024-03-23
 
 /-! ### Lemmas about singletons -/

chore: avoid Ne.def (adaptation for nightly-2024-03-27) (#11801)

1b40c7bc

Diff

@@ -1533,7 +1533,7 @@ lemma disjoint_or_nonempty_inter (s t : Set α) : Disjoint s t ∨ (s ∩ t).Non
 #align set.disjoint_or_nonempty_inter Set.disjoint_or_nonempty_inter
 
 lemma disjoint_iff_forall_ne : Disjoint s t ↔ ∀ ⦃a⦄, a ∈ s → ∀ ⦃b⦄, b ∈ t → a ≠ b := by
-  simp only [Ne.def, disjoint_left, @imp_not_comm _ (_ = _), forall_eq']
+  simp only [Ne, disjoint_left, @imp_not_comm _ (_ = _), forall_eq']
 #align set.disjoint_iff_forall_ne Set.disjoint_iff_forall_ne
 
 alias ⟨_root_.Disjoint.ne_of_mem, _⟩ := disjoint_iff_forall_ne

chore: Golf Set.pair_eq_pair_iff (#11564)

Resolve a porting note

31bc122d

Diff

@@ -1362,14 +1362,9 @@ theorem pair_comm (a b : α) : ({a, b} : Set α) = {b, a} :=
   union_comm _ _
 #align set.pair_comm Set.pair_comm
 
--- Porting note: first branch after `constructor` used to be by `tauto!`.
 theorem pair_eq_pair_iff {x y z w : α} :
     ({x, y} : Set α) = {z, w} ↔ x = z ∧ y = w ∨ x = w ∧ y = z := by
-  simp only [Set.Subset.antisymm_iff, Set.insert_subset_iff, Set.mem_insert_iff,
-    Set.mem_singleton_iff, Set.singleton_subset_iff]
-  constructor
-  · rintro ⟨⟨rfl | rfl, rfl | rfl⟩, ⟨h₁, h₂⟩⟩ <;> simp [h₁, h₂] at * <;> simp [h₁, h₂]
-  · rintro (⟨rfl, rfl⟩ | ⟨rfl, rfl⟩) <;> simp
+  simp [subset_antisymm_iff, insert_subset_iff]; aesop
 #align set.pair_eq_pair_iff Set.pair_eq_pair_iff
 
 /-! ### Lemmas about sets defined as `{x ∈ s | p x}`. -/

chore(Set/Finset): standardize names of distributivity laws (#11572)

Standardizes the following names for distributivity laws across Finset and Set:

inter_union_distrib_left
inter_union_distrib_right
union_inter_distrib_left
union_inter_distrib_right

Makes arguments explicit in:

Set.union_inter_distrib_right
Set.union_inter_distrib_left
Set.inter_union_distrib_right

Deprecates these theorem names:

Finset.inter_distrib_left
Finset.inter_distrib_right
Finset.union_distrib_right
Finset.union_distrib_left
Set.inter_distrib_left
Set.inter_distrib_right
Set.union_distrib_right
Set.union_distrib_left

Fixes use of deprecated names and implicit arguments in these files:

Topology/Basic
Topology/Connected/Basic
MeasureTheory/MeasurableSpace/Basic
MeasureTheory/Covering/Differentiation
MeasureTheory/Constructions/BorelSpace/Basic
Data/Set/Image
Data/Set/Basic
Data/PFun
Data/Matroid/Dual
Data/Finset/Sups
Data/Finset/Basic
Combinatorics/SetFamily/FourFunctions
Combinatorics/Additive/SalemSpencer
Counterexamples/Phillips.lean
Archive/Imo/Imo2021Q1.lean

b7f0470e

Diff

@@ -1021,38 +1021,27 @@ theorem setOf_inter_eq_sep (p : α → Prop) (s : Set α) : {a | p a} ∩ s = {a
 
 /-! ### Distributivity laws -/
 
-
-theorem inter_distrib_left (s t u : Set α) : s ∩ (t ∪ u) = s ∩ t ∪ s ∩ u :=
-  inf_sup_left _ _ _
-#align set.inter_distrib_left Set.inter_distrib_left
-
-theorem inter_union_distrib_left {s t u : Set α} : s ∩ (t ∪ u) = s ∩ t ∪ s ∩ u :=
+theorem inter_union_distrib_left (s t u : Set α) : s ∩ (t ∪ u) = s ∩ t ∪ s ∩ u :=
   inf_sup_left _ _ _
-#align set.inter_union_distrib_left Set.inter_union_distrib_left
-
-theorem inter_distrib_right (s t u : Set α) : (s ∪ t) ∩ u = s ∩ u ∪ t ∩ u :=
-  inf_sup_right _ _ _
-#align set.inter_distrib_right Set.inter_distrib_right
+#align set.inter_distrib_left Set.inter_union_distrib_left
 
-theorem union_inter_distrib_right {s t u : Set α} : (s ∪ t) ∩ u = s ∩ u ∪ t ∩ u :=
+theorem union_inter_distrib_right (s t u : Set α) : (s ∪ t) ∩ u = s ∩ u ∪ t ∩ u :=
   inf_sup_right _ _ _
-#align set.union_inter_distrib_right Set.union_inter_distrib_right
-
-theorem union_distrib_left (s t u : Set α) : s ∪ t ∩ u = (s ∪ t) ∩ (s ∪ u) :=
-  sup_inf_left _ _ _
-#align set.union_distrib_left Set.union_distrib_left
+#align set.inter_distrib_right Set.union_inter_distrib_right
 
-theorem union_inter_distrib_left {s t u : Set α} : s ∪ t ∩ u = (s ∪ t) ∩ (s ∪ u) :=
+theorem union_inter_distrib_left (s t u : Set α) : s ∪ t ∩ u = (s ∪ t) ∩ (s ∪ u) :=
   sup_inf_left _ _ _
-#align set.union_inter_distrib_left Set.union_inter_distrib_left
+#align set.union_distrib_left Set.union_inter_distrib_left
 
-theorem union_distrib_right (s t u : Set α) : s ∩ t ∪ u = (s ∪ u) ∩ (t ∪ u) :=
+theorem inter_union_distrib_right (s t u : Set α) : s ∩ t ∪ u = (s ∪ u) ∩ (t ∪ u) :=
   sup_inf_right _ _ _
-#align set.union_distrib_right Set.union_distrib_right
+#align set.union_distrib_right Set.inter_union_distrib_right
 
-theorem inter_union_distrib_right {s t u : Set α} : s ∩ t ∪ u = (s ∪ u) ∩ (t ∪ u) :=
-  sup_inf_right _ _ _
-#align set.inter_union_distrib_right Set.inter_union_distrib_right
+-- 2024-03-22
+@[deprecated] alias inter_distrib_left := inter_union_distrib_left
+@[deprecated] alias inter_distrib_right := union_inter_distrib_right
+@[deprecated] alias union_distrib_left := union_inter_distrib_left
+@[deprecated] alias union_distrib_right := inter_union_distrib_right
 
 theorem union_union_distrib_left (s t u : Set α) : s ∪ (t ∪ u) = s ∪ t ∪ (s ∪ u) :=
   sup_sup_distrib_left _ _ _
@@ -1448,7 +1437,7 @@ theorem sep_univ : { x ∈ (univ : Set α) | p x } = { x | p x } :=
 
 @[simp]
 theorem sep_union : { x | (x ∈ s ∨ x ∈ t) ∧ p x } = { x ∈ s | p x } ∪ { x ∈ t | p x } :=
-  union_inter_distrib_right
+  union_inter_distrib_right { x | x ∈ s } { x | x ∈ t } p
 #align set.sep_union Set.sep_union
 
 @[simp]
@@ -1463,7 +1452,7 @@ theorem sep_and : { x ∈ s | p x ∧ q x } = { x ∈ s | p x } ∩ { x ∈ s |
 
 @[simp]
 theorem sep_or : { x ∈ s | p x ∨ q x } = { x ∈ s | p x } ∪ { x ∈ s | q x } :=
-  inter_union_distrib_left
+  inter_union_distrib_left s p q
 #align set.sep_or Set.sep_or
 
 @[simp]

chore: classify "simp can prove" porting notes (#11550)

Classifies by adding issue number #10618 to porting notes claiming "simp can prove it".

5befdcb9

Diff

@@ -162,12 +162,12 @@ theorem Set.coe_setOf (p : α → Prop) : ↥{ x | p x } = { x // p x } :=
   rfl
 #align set.coe_set_of Set.coe_setOf
 
--- Porting note: removed `simp` because `simp` can prove it
+-- Porting note (#10618): removed `simp` because `simp` can prove it
 theorem SetCoe.forall {s : Set α} {p : s → Prop} : (∀ x : s, p x) ↔ ∀ (x) (h : x ∈ s), p ⟨x, h⟩ :=
   Subtype.forall
 #align set_coe.forall SetCoe.forall
 
--- Porting note: removed `simp` because `simp` can prove it
+-- Porting note (#10618): removed `simp` because `simp` can prove it
 theorem SetCoe.exists {s : Set α} {p : s → Prop} :
     (∃ x : s, p x) ↔ ∃ (x : _) (h : x ∈ s), p ⟨x, h⟩ :=
   Subtype.exists
@@ -407,7 +407,7 @@ theorem not_mem_empty (x : α) : ¬x ∈ (∅ : Set α) :=
   id
 #align set.not_mem_empty Set.not_mem_empty
 
--- Porting note: removed `simp` because `simp` can prove it
+-- Porting note (#10618): removed `simp` because `simp` can prove it
 theorem not_not_mem : ¬a ∉ s ↔ a ∈ s :=
   not_not
 #align set.not_not_mem Set.not_not_mem
@@ -1169,7 +1169,7 @@ theorem insert_comm (a b : α) (s : Set α) : insert a (insert b s) = insert b (
   ext fun _ => or_left_comm
 #align set.insert_comm Set.insert_comm
 
--- Porting note: removing `simp` attribute because `simp` can prove it
+-- Porting note (#10618): removing `simp` attribute because `simp` can prove it
 theorem insert_idem (a : α) (s : Set α) : insert a (insert a s) = insert a s :=
   insert_eq_of_mem <| mem_insert _ _
 #align set.insert_idem Set.insert_idem
@@ -1291,7 +1291,7 @@ theorem singleton_ne_empty (a : α) : ({a} : Set α) ≠ ∅ :=
   (singleton_nonempty _).ne_empty
 #align set.singleton_ne_empty Set.singleton_ne_empty
 
---Porting note (#11119): removed `simp` attribute because `simp` can prove it
+--Porting note (#10618): removed `simp` attribute because `simp` can prove it
 theorem empty_ssubset_singleton : (∅ : Set α) ⊂ {a} :=
   (singleton_nonempty _).empty_ssubset
 #align set.empty_ssubset_singleton Set.empty_ssubset_singleton
@@ -1364,7 +1364,7 @@ theorem default_coe_singleton (x : α) : (default : ({x} : Set α)) = ⟨x, rfl
 /-! ### Lemmas about pairs -/
 
 
---Porting note (#11119): removed `simp` attribute because `simp` can prove it
+--Porting note (#10618): removed `simp` attribute because `simp` can prove it
 theorem pair_eq_singleton (a : α) : ({a, a} : Set α) = {a} :=
   union_self _
 #align set.pair_eq_singleton Set.pair_eq_singleton
@@ -1426,22 +1426,22 @@ theorem sep_eq_empty_iff_mem_false : { x ∈ s | p x } = ∅ ↔ ∀ x ∈ s, ¬
   simp_rw [ext_iff, mem_sep_iff, mem_empty_iff_false, iff_false_iff, not_and]
 #align set.sep_eq_empty_iff_mem_false Set.sep_eq_empty_iff_mem_false
 
---Porting note (#11119): removed `simp` attribute because `simp` can prove it
+--Porting note (#10618): removed `simp` attribute because `simp` can prove it
 theorem sep_true : { x ∈ s | True } = s :=
   inter_univ s
 #align set.sep_true Set.sep_true
 
---Porting note (#11119): removed `simp` attribute because `simp` can prove it
+--Porting note (#10618): removed `simp` attribute because `simp` can prove it
 theorem sep_false : { x ∈ s | False } = ∅ :=
   inter_empty s
 #align set.sep_false Set.sep_false
 
---Porting note (#11119): removed `simp` attribute because `simp` can prove it
+--Porting note (#10618): removed `simp` attribute because `simp` can prove it
 theorem sep_empty (p : α → Prop) : { x ∈ (∅ : Set α) | p x } = ∅ :=
   empty_inter p
 #align set.sep_empty Set.sep_empty
 
---Porting note (#11119): removed `simp` attribute because `simp` can prove it
+--Porting note (#10618): removed `simp` attribute because `simp` can prove it
 theorem sep_univ : { x ∈ (univ : Set α) | p x } = { x | p x } :=
   univ_inter p
 #align set.sep_univ Set.sep_univ
@@ -2055,7 +2055,7 @@ theorem insert_diff_singleton_comm (hab : a ≠ b) (s : Set α) :
     diff_singleton_eq_self (mem_singleton_iff.not.2 hab.symm)]
 #align set.insert_diff_singleton_comm Set.insert_diff_singleton_comm
 
---Porting note (#11119): removed `simp` attribute because `simp` can prove it
+--Porting note (#10618): removed `simp` attribute because `simp` can prove it
 theorem diff_self {s : Set α} : s \ s = ∅ :=
   sdiff_self
 #align set.diff_self Set.diff_self

chore(Order): Make more arguments explicit (#11033)

Those lemmas have historically been very annoying to use in rw since all their arguments were implicit. One too many people complained about it on Zulip, so I'm changing them.

Downstream code broken by this change can fix it by adding appropriately many _s.

Also marks CauSeq.ext @[ext].

`Order.BoundedOrder`

top_sup_eq
sup_top_eq
bot_sup_eq
sup_bot_eq
top_inf_eq
inf_top_eq
bot_inf_eq
inf_bot_eq

`Order.Lattice`

sup_idem
sup_comm
sup_assoc
sup_left_idem
sup_right_idem
inf_idem
inf_comm
inf_assoc
inf_left_idem
inf_right_idem
sup_inf_left
sup_inf_right
inf_sup_left
inf_sup_right

`Order.MinMax`

max_min_distrib_left
max_min_distrib_right
min_max_distrib_left
min_max_distrib_right

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

0eaff363

Diff

@@ -859,13 +859,11 @@ theorem union_empty_iff {s t : Set α} : s ∪ t = ∅ ↔ s = ∅ ∧ t = ∅ :
 #align set.union_empty_iff Set.union_empty_iff
 
 @[simp]
-theorem union_univ {s : Set α} : s ∪ univ = univ :=
-  sup_top_eq
+theorem union_univ (s : Set α) : s ∪ univ = univ := sup_top_eq _
 #align set.union_univ Set.union_univ
 
 @[simp]
-theorem univ_union {s : Set α} : univ ∪ s = univ :=
-  top_sup_eq
+theorem univ_union (s : Set α) : univ ∪ s = univ := top_sup_eq _
 #align set.univ_union Set.univ_union
 
 /-! ### Lemmas about intersection -/
@@ -983,13 +981,11 @@ theorem inter_eq_inter_iff_right : s ∩ u = t ∩ u ↔ t ∩ u ⊆ s ∧ s ∩
 #align set.inter_eq_inter_iff_right Set.inter_eq_inter_iff_right
 
 @[simp, mfld_simps]
-theorem inter_univ (a : Set α) : a ∩ univ = a :=
-  inf_top_eq
+theorem inter_univ (a : Set α) : a ∩ univ = a := inf_top_eq _
 #align set.inter_univ Set.inter_univ
 
 @[simp, mfld_simps]
-theorem univ_inter (a : Set α) : univ ∩ a = a :=
-  top_inf_eq
+theorem univ_inter (a : Set α) : univ ∩ a = a := top_inf_eq _
 #align set.univ_inter Set.univ_inter
 
 @[gcongr]
@@ -1027,35 +1023,35 @@ theorem setOf_inter_eq_sep (p : α → Prop) (s : Set α) : {a | p a} ∩ s = {a
 
 
 theorem inter_distrib_left (s t u : Set α) : s ∩ (t ∪ u) = s ∩ t ∪ s ∩ u :=
-  inf_sup_left
+  inf_sup_left _ _ _
 #align set.inter_distrib_left Set.inter_distrib_left
 
 theorem inter_union_distrib_left {s t u : Set α} : s ∩ (t ∪ u) = s ∩ t ∪ s ∩ u :=
-  inf_sup_left
+  inf_sup_left _ _ _
 #align set.inter_union_distrib_left Set.inter_union_distrib_left
 
 theorem inter_distrib_right (s t u : Set α) : (s ∪ t) ∩ u = s ∩ u ∪ t ∩ u :=
-  inf_sup_right
+  inf_sup_right _ _ _
 #align set.inter_distrib_right Set.inter_distrib_right
 
 theorem union_inter_distrib_right {s t u : Set α} : (s ∪ t) ∩ u = s ∩ u ∪ t ∩ u :=
-  inf_sup_right
+  inf_sup_right _ _ _
 #align set.union_inter_distrib_right Set.union_inter_distrib_right
 
 theorem union_distrib_left (s t u : Set α) : s ∪ t ∩ u = (s ∪ t) ∩ (s ∪ u) :=
-  sup_inf_left
+  sup_inf_left _ _ _
 #align set.union_distrib_left Set.union_distrib_left
 
 theorem union_inter_distrib_left {s t u : Set α} : s ∪ t ∩ u = (s ∪ t) ∩ (s ∪ u) :=
-  sup_inf_left
+  sup_inf_left _ _ _
 #align set.union_inter_distrib_left Set.union_inter_distrib_left
 
 theorem union_distrib_right (s t u : Set α) : s ∩ t ∪ u = (s ∪ u) ∩ (t ∪ u) :=
-  sup_inf_right
+  sup_inf_right _ _ _
 #align set.union_distrib_right Set.union_distrib_right
 
 theorem inter_union_distrib_right {s t u : Set α} : s ∩ t ∪ u = (s ∪ u) ∩ (t ∪ u) :=
-  sup_inf_right
+  sup_inf_right _ _ _
 #align set.inter_union_distrib_right Set.inter_union_distrib_right
 
 theorem union_union_distrib_left (s t u : Set α) : s ∪ (t ∪ u) = s ∪ t ∪ (s ∪ u) :=

feat: add simp lemma (#11206)

It is already there for inf/sup, now add it to inter/union. Now simp succeeds in cases where previously symm; simp was necessary

24e73186

Diff

@@ -954,6 +954,10 @@ theorem subset_inter_iff {s t r : Set α} : r ⊆ s ∩ t ↔ r ⊆ s ∧ r ⊆
 @[simp] lemma inter_eq_right : s ∩ t = t ↔ t ⊆ s := inf_eq_right
 #align set.inter_eq_right_iff_subset Set.inter_eq_right
 
+@[simp] lemma left_eq_inter : s = s ∩ t ↔ s ⊆ t := left_eq_inf
+
+@[simp] lemma right_eq_inter : t = s ∩ t ↔ t ⊆ s := right_eq_inf
+
 theorem inter_eq_self_of_subset_left {s t : Set α} : s ⊆ t → s ∩ t = s :=
   inter_eq_left.mpr
 #align set.inter_eq_self_of_subset_left Set.inter_eq_self_of_subset_left

chore: classify @[simp] removed porting notes (#11184)

Classifying by adding issue number #11119 to porting notes claiming anything semantically equivalent to:

"@[simp] removed [...]"
"@[simp] removed [...]"
"removed simp attribute"

28527d30

Diff

@@ -1255,7 +1255,7 @@ theorem setOf_eq_eq_singleton' {a : α} : { x | a = x } = {a} :=
 #align set.set_of_eq_eq_singleton' Set.setOf_eq_eq_singleton'
 
 -- TODO: again, annotation needed
--- Porting note: removed `simp` attribute
+--Porting note (#11119): removed `simp` attribute
 theorem mem_singleton (a : α) : a ∈ ({a} : Set α) :=
   @rfl _ _
 #align set.mem_singleton Set.mem_singleton
@@ -1291,7 +1291,7 @@ theorem singleton_ne_empty (a : α) : ({a} : Set α) ≠ ∅ :=
   (singleton_nonempty _).ne_empty
 #align set.singleton_ne_empty Set.singleton_ne_empty
 
--- Porting note: removed `simp` attribute because `simp` can prove it
+--Porting note (#11119): removed `simp` attribute because `simp` can prove it
 theorem empty_ssubset_singleton : (∅ : Set α) ⊂ {a} :=
   (singleton_nonempty _).empty_ssubset
 #align set.empty_ssubset_singleton Set.empty_ssubset_singleton
@@ -1364,7 +1364,7 @@ theorem default_coe_singleton (x : α) : (default : ({x} : Set α)) = ⟨x, rfl
 /-! ### Lemmas about pairs -/
 
 
--- Porting note: removed `simp` attribute because `simp` can prove it
+--Porting note (#11119): removed `simp` attribute because `simp` can prove it
 theorem pair_eq_singleton (a : α) : ({a, a} : Set α) = {a} :=
   union_self _
 #align set.pair_eq_singleton Set.pair_eq_singleton
@@ -1426,22 +1426,22 @@ theorem sep_eq_empty_iff_mem_false : { x ∈ s | p x } = ∅ ↔ ∀ x ∈ s, ¬
   simp_rw [ext_iff, mem_sep_iff, mem_empty_iff_false, iff_false_iff, not_and]
 #align set.sep_eq_empty_iff_mem_false Set.sep_eq_empty_iff_mem_false
 
--- Porting note: removed `simp` attribute because `simp` can prove it
+--Porting note (#11119): removed `simp` attribute because `simp` can prove it
 theorem sep_true : { x ∈ s | True } = s :=
   inter_univ s
 #align set.sep_true Set.sep_true
 
--- Porting note: removed `simp` attribute because `simp` can prove it
+--Porting note (#11119): removed `simp` attribute because `simp` can prove it
 theorem sep_false : { x ∈ s | False } = ∅ :=
   inter_empty s
 #align set.sep_false Set.sep_false
 
--- Porting note: removed `simp` attribute because `simp` can prove it
+--Porting note (#11119): removed `simp` attribute because `simp` can prove it
 theorem sep_empty (p : α → Prop) : { x ∈ (∅ : Set α) | p x } = ∅ :=
   empty_inter p
 #align set.sep_empty Set.sep_empty
 
--- Porting note: removed `simp` attribute because `simp` can prove it
+--Porting note (#11119): removed `simp` attribute because `simp` can prove it
 theorem sep_univ : { x ∈ (univ : Set α) | p x } = { x | p x } :=
   univ_inter p
 #align set.sep_univ Set.sep_univ
@@ -2055,7 +2055,7 @@ theorem insert_diff_singleton_comm (hab : a ≠ b) (s : Set α) :
     diff_singleton_eq_self (mem_singleton_iff.not.2 hab.symm)]
 #align set.insert_diff_singleton_comm Set.insert_diff_singleton_comm
 
--- Porting note: removed `simp` attribute because `simp` can prove it
+--Porting note (#11119): removed `simp` attribute because `simp` can prove it
 theorem diff_self {s : Set α} : s \ s = ∅ :=
   sdiff_self
 #align set.diff_self Set.diff_self

chore: move Mathlib to v4.7.0-rc1 (#11162)

This is a very large PR, but it has been reviewed piecemeal already in PRs to the bump/v4.7.0 branch as we update to intermediate nightlies.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: damiano <adomani@gmail.com>

fa48894a

Diff

@@ -546,7 +546,7 @@ theorem setOf_false : { _a : α | False } = ∅ :=
 
 @[simp]
 theorem empty_subset (s : Set α) : ∅ ⊆ s :=
-  fun.
+  nofun
 #align set.empty_subset Set.empty_subset
 
 theorem subset_empty_iff {s : Set α} : s ⊆ ∅ ↔ s = ∅ :=

style: homogenise porting notes (#11145)

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

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

8be0b69c

Diff

@@ -1169,7 +1169,7 @@ theorem insert_comm (a b : α) (s : Set α) : insert a (insert b s) = insert b (
   ext fun _ => or_left_comm
 #align set.insert_comm Set.insert_comm
 
---Porting note: removing `simp` attribute because `simp` can prove it
+-- Porting note: removing `simp` attribute because `simp` can prove it
 theorem insert_idem (a : α) (s : Set α) : insert a (insert a s) = insert a s :=
   insert_eq_of_mem <| mem_insert _ _
 #align set.insert_idem Set.insert_idem
@@ -1255,7 +1255,7 @@ theorem setOf_eq_eq_singleton' {a : α} : { x | a = x } = {a} :=
 #align set.set_of_eq_eq_singleton' Set.setOf_eq_eq_singleton'
 
 -- TODO: again, annotation needed
---Porting note: removed `simp` attribute
+-- Porting note: removed `simp` attribute
 theorem mem_singleton (a : α) : a ∈ ({a} : Set α) :=
   @rfl _ _
 #align set.mem_singleton Set.mem_singleton
@@ -1291,7 +1291,7 @@ theorem singleton_ne_empty (a : α) : ({a} : Set α) ≠ ∅ :=
   (singleton_nonempty _).ne_empty
 #align set.singleton_ne_empty Set.singleton_ne_empty
 
---Porting note: removed `simp` attribute because `simp` can prove it
+-- Porting note: removed `simp` attribute because `simp` can prove it
 theorem empty_ssubset_singleton : (∅ : Set α) ⊂ {a} :=
   (singleton_nonempty _).empty_ssubset
 #align set.empty_ssubset_singleton Set.empty_ssubset_singleton
@@ -1364,7 +1364,7 @@ theorem default_coe_singleton (x : α) : (default : ({x} : Set α)) = ⟨x, rfl
 /-! ### Lemmas about pairs -/
 
 
---Porting note: removed `simp` attribute because `simp` can prove it
+-- Porting note: removed `simp` attribute because `simp` can prove it
 theorem pair_eq_singleton (a : α) : ({a, a} : Set α) = {a} :=
   union_self _
 #align set.pair_eq_singleton Set.pair_eq_singleton
@@ -1426,22 +1426,22 @@ theorem sep_eq_empty_iff_mem_false : { x ∈ s | p x } = ∅ ↔ ∀ x ∈ s, ¬
   simp_rw [ext_iff, mem_sep_iff, mem_empty_iff_false, iff_false_iff, not_and]
 #align set.sep_eq_empty_iff_mem_false Set.sep_eq_empty_iff_mem_false
 
---Porting note: removed `simp` attribute because `simp` can prove it
+-- Porting note: removed `simp` attribute because `simp` can prove it
 theorem sep_true : { x ∈ s | True } = s :=
   inter_univ s
 #align set.sep_true Set.sep_true
 
---Porting note: removed `simp` attribute because `simp` can prove it
+-- Porting note: removed `simp` attribute because `simp` can prove it
 theorem sep_false : { x ∈ s | False } = ∅ :=
   inter_empty s
 #align set.sep_false Set.sep_false
 
---Porting note: removed `simp` attribute because `simp` can prove it
+-- Porting note: removed `simp` attribute because `simp` can prove it
 theorem sep_empty (p : α → Prop) : { x ∈ (∅ : Set α) | p x } = ∅ :=
   empty_inter p
 #align set.sep_empty Set.sep_empty
 
---Porting note: removed `simp` attribute because `simp` can prove it
+-- Porting note: removed `simp` attribute because `simp` can prove it
 theorem sep_univ : { x ∈ (univ : Set α) | p x } = { x | p x } :=
   univ_inter p
 #align set.sep_univ Set.sep_univ
@@ -2055,7 +2055,7 @@ theorem insert_diff_singleton_comm (hab : a ≠ b) (s : Set α) :
     diff_singleton_eq_self (mem_singleton_iff.not.2 hab.symm)]
 #align set.insert_diff_singleton_comm Set.insert_diff_singleton_comm
 
---Porting note: removed `simp` attribute because `simp` can prove it
+-- Porting note: removed `simp` attribute because `simp` can prove it
 theorem diff_self {s : Set α} : s \ s = ∅ :=
   sdiff_self
 #align set.diff_self Set.diff_self
@@ -2889,7 +2889,7 @@ instance decidableSetOf (p : α → Prop) [Decidable (p a)] : Decidable (a ∈ {
   assumption
 #align set.decidable_set_of Set.decidableSetOf
 
--- porting note: Lean 3 unfolded `{a}` before finding instances but Lean 4 needs additional help
+-- Porting note: Lean 3 unfolded `{a}` before finding instances but Lean 4 needs additional help
 instance decidableMemSingleton {a b : α} [DecidableEq α] :
     Decidable (a ∈ ({b} : Set α)) := decidableSetOf _ (· = b)

chore(Set,Finset): add gcongr attributes (#11004)

5bd4e663

Diff

@@ -1868,14 +1868,17 @@ theorem inter_union_compl (s t : Set α) : s ∩ t ∪ s ∩ tᶜ = s :=
   inter_union_diff _ _
 #align set.inter_union_compl Set.inter_union_compl
 
+@[gcongr]
 theorem diff_subset_diff {s₁ s₂ t₁ t₂ : Set α} : s₁ ⊆ s₂ → t₂ ⊆ t₁ → s₁ \ t₁ ⊆ s₂ \ t₂ :=
   show s₁ ≤ s₂ → t₂ ≤ t₁ → s₁ \ t₁ ≤ s₂ \ t₂ from sdiff_le_sdiff
 #align set.diff_subset_diff Set.diff_subset_diff
 
+@[gcongr]
 theorem diff_subset_diff_left {s₁ s₂ t : Set α} (h : s₁ ⊆ s₂) : s₁ \ t ⊆ s₂ \ t :=
   sdiff_le_sdiff_right ‹s₁ ≤ s₂›
 #align set.diff_subset_diff_left Set.diff_subset_diff_left
 
+@[gcongr]
 theorem diff_subset_diff_right {s t u : Set α} (h : t ⊆ u) : s \ u ⊆ s \ t :=
   sdiff_le_sdiff_left ‹t ≤ u›
 #align set.diff_subset_diff_right Set.diff_subset_diff_right

feat: Add Set.subset_setOf and Set.setOf_subset lemmas (#10812)

Expressions like s ⊆ setOf p often appear unintentionally; these replace them with clean ∀ statements.

These aren't registered as @[simp], not least because doing so breaks a few things in mathlib, and it's not clear one always wants to do these.

c8bd1526

Diff

@@ -267,6 +267,12 @@ theorem setOf_bijective : Bijective (setOf : (α → Prop) → Set α) :=
   bijective_id
 #align set.set_of_bijective Set.setOf_bijective
 
+theorem subset_setOf {p : α → Prop} {s : Set α} : s ⊆ setOf p ↔ ∀ x, x ∈ s → p x :=
+  Iff.rfl
+
+theorem setOf_subset {p : α → Prop} {s : Set α} : setOf p ⊆ s ↔ ∀ x, p x → x ∈ s :=
+  Iff.rfl
+
 @[simp]
 theorem setOf_subset_setOf {p q : α → Prop} : { a | p a } ⊆ { a | q a } ↔ ∀ a, p a → q a :=
   Iff.rfl

chore: remove terminal, terminal refines (#10762)

I replaced a few "terminal" refine/refine's with exact.

The strategy was very simple-minded: essentially any refine whose following line had smaller indentation got replaced by exact and then I cleaned up the mess.

This PR certainly leaves some further terminal refines, but maybe the current change is beneficial.

ea36aa7d

Diff

@@ -672,7 +672,7 @@ theorem eq_univ_of_forall {s : Set α} : (∀ x, x ∈ s) → s = univ :=
 
 theorem Nonempty.eq_univ [Subsingleton α] : s.Nonempty → s = univ := by
   rintro ⟨x, hx⟩
-  refine' eq_univ_of_forall fun y => by rwa [Subsingleton.elim y x]
+  exact eq_univ_of_forall fun y => by rwa [Subsingleton.elim y x]
 #align set.nonempty.eq_univ Set.Nonempty.eq_univ
 
 theorem eq_univ_of_subset {s t : Set α} (h : s ⊆ t) (hs : s = univ) : t = univ :=

fix(Data/Set/Image): simp confluence issues with image_subset_iff (#8683)

image_subset_iff is a questionable simp lemma because it converts an application of Set.image into an application of Set.preimage unconditionally. This means that if any simp lemma applies to images, there must be a corresponding lemma for preimages. These lemmas are what I found missing after loogling.

I also added machine-checked examples of each confluence issue to a new file tests/simp_confluence.

4841d69d

Diff

@@ -654,6 +654,7 @@ theorem empty_ne_univ [Nonempty α] : (∅ : Set α) ≠ univ := fun e =>
 theorem subset_univ (s : Set α) : s ⊆ univ := fun _ _ => trivial
 #align set.subset_univ Set.subset_univ
 
+@[simp]
 theorem univ_subset_iff {s : Set α} : univ ⊆ s ↔ s = univ :=
   @top_le_iff _ _ _ s
 #align set.univ_subset_iff Set.univ_subset_iff

chore(*): shake imports (#10199)

Remove Data.Set.Basic from scripts/noshake.json.
Remove an exception that was used by examples only, move these examples to a new test file.
Drop an exception for Order.Filter.Basic dependency on Control.Traversable.Instances, as the relevant parts were moved to Order.Filter.ListTraverse.
Run lake exe shake --fix.

c167d468

Diff

@@ -216,9 +216,6 @@ variable {α : Type u} {β : Type v} {γ : Type w} {ι : Sort x} {a b : α} {s s
 instance : Inhabited (Set α) :=
   ⟨∅⟩
 
-attribute [ext] Set.ext
-#align set.ext Set.ext
-
 theorem ext_iff {s t : Set α} : s = t ↔ ∀ x, x ∈ s ↔ x ∈ t :=
   ⟨fun h x => by rw [h], ext⟩
 #align set.ext_iff Set.ext_iff

chore: move to v4.6.0-rc1, merging adaptations from bump/v4.6.0 (#10176)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Joachim Breitner <mail@joachim-breitner.de>

490d2d48

Diff

@@ -757,11 +757,11 @@ theorem union_assoc (a b c : Set α) : a ∪ b ∪ c = a ∪ (b ∪ c) :=
   ext fun _ => or_assoc
 #align set.union_assoc Set.union_assoc
 
-instance union_isAssoc : IsAssociative (Set α) (· ∪ ·) :=
+instance union_isAssoc : Std.Associative (α := Set α) (· ∪ ·) :=
   ⟨union_assoc⟩
 #align set.union_is_assoc Set.union_isAssoc
 
-instance union_isComm : IsCommutative (Set α) (· ∪ ·) :=
+instance union_isComm : Std.Commutative (α := Set α) (· ∪ ·) :=
   ⟨union_comm⟩
 #align set.union_is_comm Set.union_isComm
 
@@ -911,11 +911,11 @@ theorem inter_assoc (a b c : Set α) : a ∩ b ∩ c = a ∩ (b ∩ c) :=
   ext fun _ => and_assoc
 #align set.inter_assoc Set.inter_assoc
 
-instance inter_isAssoc : IsAssociative (Set α) (· ∩ ·) :=
+instance inter_isAssoc : Std.Associative (α := Set α) (· ∩ ·) :=
   ⟨inter_assoc⟩
 #align set.inter_is_assoc Set.inter_isAssoc
 
-instance inter_isComm : IsCommutative (Set α) (· ∩ ·) :=
+instance inter_isComm : Std.Commutative (α := Set α) (· ∩ ·) :=
   ⟨inter_comm⟩
 #align set.inter_is_comm Set.inter_isComm

chore: scope symmDiff notations (#9844)

Those notations are not scoped whereas the file is very low in the import hierarchy.

99f08122

Diff

@@ -2075,6 +2075,9 @@ theorem union_eq_diff_union_diff_union_inter (s t : Set α) : s ∪ t = s \ t 
 
 /-! ### Symmetric difference -/
 
+section
+
+open scoped symmDiff
 
 theorem mem_symmDiff : a ∈ s ∆ t ↔ a ∈ s ∧ a ∉ t ∨ a ∈ t ∧ a ∉ s :=
   Iff.rfl
@@ -2114,6 +2117,8 @@ theorem subset_symmDiff_union_symmDiff_right (h : Disjoint t u) : s ⊆ s ∆ t
   h.le_symmDiff_sup_symmDiff_right
 #align set.subset_symm_diff_union_symm_diff_right Set.subset_symmDiff_union_symmDiff_right
 
+end
+
 /-! ### Powerset -/
 
 #align set.powerset Set.powerset

chore: reduce imports (#9830)

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

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

f4c4ca61

Diff

@@ -3,12 +3,13 @@ Copyright (c) 2014 Jeremy Avigad. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Leonardo de Moura
 -/
+import Mathlib.Init.ZeroOne
+import Mathlib.Data.Set.Defs
+import Mathlib.Order.Basic
 import Mathlib.Order.SymmDiff
 import Mathlib.Tactic.Tauto
 import Mathlib.Tactic.ByContra
 import Mathlib.Util.Delaborators
-import Mathlib.Data.Set.Defs
-import Mathlib.Init.ZeroOne
 
 #align_import data.set.basic from "leanprover-community/mathlib"@"001ffdc42920050657fd45bd2b8bfbec8eaaeb29"

chore(Data/Set): move definitions to a new file (#9737)

This and other similar PRs will help us reduce import dependencies and improve parallel compilation in the future.

9fb36425

Diff

@@ -4,10 +4,10 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Leonardo de Moura
 -/
 import Mathlib.Order.SymmDiff
-import Mathlib.Logic.Function.Iterate
 import Mathlib.Tactic.Tauto
 import Mathlib.Tactic.ByContra
 import Mathlib.Util.Delaborators
+import Mathlib.Data.Set.Defs
 import Mathlib.Init.ZeroOne
 
 #align_import data.set.basic from "leanprover-community/mathlib"@"001ffdc42920050657fd45bd2b8bfbec8eaaeb29"
@@ -66,15 +66,6 @@ set, sets, subset, subsets, union, intersection, insert, singleton, complement,
 
 -/
 
--- https://github.com/leanprover/lean4/issues/2096
-compile_def% Union.union
-compile_def% Inter.inter
-compile_def% SDiff.sdiff
-compile_def% HasCompl.compl
-compile_def% EmptyCollection.emptyCollection
-compile_def% Insert.insert
-compile_def% Singleton.singleton
-
 /-! ### Set coercion to a type -/
 
 open Function
@@ -92,9 +83,9 @@ instance instBooleanAlgebraSet : BooleanAlgebra (Set α) :=
     lt := fun s t => s ⊆ t ∧ ¬t ⊆ s,
     inf := (· ∩ ·),
     bot := ∅,
-    compl := fun s => { x | x ∉ s },
+    compl := (·ᶜ),
     top := univ,
-    sdiff := fun s t => { x | x ∈ s ∧ x ∉ t } }
+    sdiff := (· \ ·) }
 
 instance : HasSSubset (Set α) :=
   ⟨(· < ·)⟩
@@ -143,19 +134,6 @@ alias ⟨_root_.LE.le.subset, _root_.HasSubset.Subset.le⟩ := le_iff_subset
 alias ⟨_root_.LT.lt.ssubset, _root_.HasSSubset.SSubset.lt⟩ := lt_iff_ssubset
 #align has_ssubset.ssubset.lt HasSSubset.SSubset.lt
 
--- Porting note: I've introduced this abbreviation, with the `@[coe]` attribute,
--- so that `norm_cast` has something to index on.
--- It is currently an abbreviation so that instance coming from `Subtype` are available.
--- If you're interested in making it a `def`, as it probably should be,
--- you'll then need to create additional instances (and possibly prove lemmas about them).
--- The first error should appear below at `monotoneOn_iff_monotone`.
-/-- Given the set `s`, `Elem s` is the `Type` of element of `s`. -/
-@[coe, reducible] def Elem (s : Set α) : Type u := { x // x ∈ s }
-
-/-- Coercion from a set to the corresponding subtype. -/
-instance {α : Type u} : CoeSort (Set α) (Type u) :=
-  ⟨Elem⟩
-
 instance PiSetCoe.canLift (ι : Type u) (α : ι → Type v) [∀ i, Nonempty (α i)] (s : Set ι) :
     CanLift (∀ i : s, α i) (∀ i, α i) (fun f i => f i) fun _ => True :=
   PiSubtype.canLift ι α s
@@ -255,9 +233,6 @@ theorem forall_in_swap {p : α → β → Prop} : (∀ a ∈ s, ∀ (b), p a b)
 
 /-! ### Lemmas about `mem` and `setOf` -/
 
-@[simp, mfld_simps] theorem mem_setOf_eq {x : α} {p : α → Prop} : (x ∈ {y | p y}) = p x := rfl
-#align set.mem_set_of_eq Set.mem_setOf_eq
-
 theorem mem_setOf {a : α} {p : α → Prop} : a ∈ { x | p x } ↔ p a :=
   Iff.rfl
 #align set.mem_set_of Set.mem_setOf
@@ -667,11 +642,6 @@ theorem setOf_true : { _x : α | True } = univ :=
 
 @[simp] theorem setOf_top : { _x : α | ⊤ } = univ := rfl
 
-@[simp, mfld_simps]
-theorem mem_univ (x : α) : x ∈ @univ α :=
-  trivial
-#align set.mem_univ Set.mem_univ
-
 @[simp]
 theorem univ_eq_empty_iff : (univ : Set α) = ∅ ↔ IsEmpty α :=
   eq_empty_iff_forall_not_mem.trans
@@ -1649,7 +1619,6 @@ theorem inter_diff_distrib_right (s t u : Set α) : s \ t ∩ u = (s ∩ u) \ (t
 
 /-! ### Lemmas about complement -/
 
-
 theorem compl_def (s : Set α) : sᶜ = { x | x ∉ s } :=
   rfl
 #align set.compl_def Set.compl_def
@@ -1666,11 +1635,6 @@ theorem not_mem_of_mem_compl {s : Set α} {x : α} (h : x ∈ sᶜ) : x ∉ s :=
   h
 #align set.not_mem_of_mem_compl Set.not_mem_of_mem_compl
 
-@[simp]
-theorem mem_compl_iff (s : Set α) (x : α) : x ∈ sᶜ ↔ x ∉ s :=
-  Iff.rfl
-#align set.mem_compl_iff Set.mem_compl_iff
-
 theorem not_mem_compl_iff {x : α} : x ∉ sᶜ ↔ x ∈ s :=
   not_not
 #align set.not_mem_compl_iff Set.not_mem_compl_iff
@@ -1822,20 +1786,6 @@ theorem inter_compl_nonempty_iff {s t : Set α} : (s ∩ tᶜ).Nonempty ↔ ¬s
 
 /-! ### Lemmas about set difference -/
 
-
-theorem diff_eq (s t : Set α) : s \ t = s ∩ tᶜ :=
-  rfl
-#align set.diff_eq Set.diff_eq
-
-@[simp]
-theorem mem_diff {s t : Set α} (x : α) : x ∈ s \ t ↔ x ∈ s ∧ x ∉ t :=
-  Iff.rfl
-#align set.mem_diff Set.mem_diff
-
-theorem mem_diff_of_mem {s t : Set α} {x : α} (h1 : x ∈ s) (h2 : x ∉ t) : x ∈ s \ t :=
-  ⟨h1, h2⟩
-#align set.mem_diff_of_mem Set.mem_diff_of_mem
-
 theorem not_mem_diff_of_mem {s t : Set α} {x : α} (hx : x ∈ t) : x ∉ s \ t := fun h => h.2 hx
 #align set.not_mem_diff_of_mem Set.not_mem_diff_of_mem

fix: shake the import tree (#9749)

cherry-picked from #9347

Co-Authored-By: @digama0

1d3b4790

Diff

@@ -8,6 +8,7 @@ import Mathlib.Logic.Function.Iterate
 import Mathlib.Tactic.Tauto
 import Mathlib.Tactic.ByContra
 import Mathlib.Util.Delaborators
+import Mathlib.Init.ZeroOne
 
 #align_import data.set.basic from "leanprover-community/mathlib"@"001ffdc42920050657fd45bd2b8bfbec8eaaeb29"

chore(*): replace $ with <| (#9319)

See Zulip thread for the discussion.

9f6d3388

Diff

@@ -1559,7 +1559,7 @@ theorem disjoint_right : Disjoint s t ↔ ∀ ⦃a⦄, a ∈ t → a ∉ s := by
 #align set.disjoint_right Set.disjoint_right
 
 lemma not_disjoint_iff : ¬Disjoint s t ↔ ∃ x, x ∈ s ∧ x ∈ t :=
-  Set.disjoint_iff.not.trans $ not_forall.trans $ exists_congr fun _ ↦ not_not
+  Set.disjoint_iff.not.trans <| not_forall.trans <| exists_congr fun _ ↦ not_not
 #align set.not_disjoint_iff Set.not_disjoint_iff
 
 lemma not_disjoint_iff_nonempty_inter : ¬ Disjoint s t ↔ (s ∩ t).Nonempty := not_disjoint_iff
@@ -2077,7 +2077,7 @@ theorem diff_self_inter {s t : Set α} : s \ (s ∩ t) = s \ t :=
 
 @[simp]
 theorem diff_singleton_eq_self {a : α} {s : Set α} (h : a ∉ s) : s \ {a} = s :=
-  sdiff_eq_self_iff_disjoint.2 $ by simp [h]
+  sdiff_eq_self_iff_disjoint.2 <| by simp [h]
 #align set.diff_singleton_eq_self Set.diff_singleton_eq_self
 
 @[simp]
@@ -2670,7 +2670,7 @@ lemma nontrivial_iff_ne_singleton (ha : a ∈ s) : s.Nontrivial ↔ s ≠ {a} :=
 #align set.nontrivial_iff_ne_singleton Set.nontrivial_iff_ne_singleton
 
 lemma Nonempty.exists_eq_singleton_or_nontrivial : s.Nonempty → (∃ a, s = {a}) ∨ s.Nontrivial :=
-  fun ⟨a, ha⟩ ↦ (eq_singleton_or_nontrivial ha).imp_left $ Exists.intro a
+  fun ⟨a, ha⟩ ↦ (eq_singleton_or_nontrivial ha).imp_left <| Exists.intro a
 #align set.nonempty.exists_eq_singleton_or_nontrivial Set.Nonempty.exists_eq_singleton_or_nontrivial
 
 theorem univ_eq_true_false : univ = ({True, False} : Set Prop) :=

chore(*): drop $/<| before fun (#9361)

Subset of #9319

3694e27d

Diff

@@ -1177,7 +1177,7 @@ theorem insert_subset_insert (h : s ⊆ t) : insert a s ⊆ insert a t := fun _
 #align set.insert_subset_insert_iff Set.insert_subset_insert_iff
 
 theorem subset_insert_iff_of_not_mem (ha : a ∉ s) : s ⊆ insert a t ↔ s ⊆ t :=
-  forall₂_congr <| fun _ hb => or_iff_right <| ne_of_mem_of_not_mem hb ha
+  forall₂_congr fun _ hb => or_iff_right <| ne_of_mem_of_not_mem hb ha
 #align set.subset_insert_iff_of_not_mem Set.subset_insert_iff_of_not_mem
 
 theorem ssubset_iff_insert {s t : Set α} : s ⊂ t ↔ ∃ a ∉ s, insert a s ⊆ t := by
@@ -1255,7 +1255,7 @@ theorem ball_insert_iff {P : α → Prop} {a : α} {s : Set α} :
 
 /- porting note: instance was in core in Lean3 -/
 instance : IsLawfulSingleton α (Set α) :=
-  ⟨fun x => Set.ext <| fun a => by
+  ⟨fun x => Set.ext fun a => by
     simp only [mem_empty_iff_false, mem_insert_iff, or_false]
     exact Iff.rfl⟩
 
@@ -2674,7 +2674,7 @@ lemma Nonempty.exists_eq_singleton_or_nontrivial : s.Nonempty → (∃ a, s = {a
 #align set.nonempty.exists_eq_singleton_or_nontrivial Set.Nonempty.exists_eq_singleton_or_nontrivial
 
 theorem univ_eq_true_false : univ = ({True, False} : Set Prop) :=
-  Eq.symm <| eq_univ_of_forall <| fun x => by
+  Eq.symm <| eq_univ_of_forall fun x => by
     rw [mem_insert_iff, mem_singleton_iff]
     exact Classical.propComplete x
 #align set.univ_eq_true_false Set.univ_eq_true_false

refactor(*): change definition of Set.image2 etc (#9275)

Redefine Set.image2 to use ∃ a ∈ s, ∃ b ∈ t, f a b = c instead of ∃ a b, a ∈ s ∧ b ∈ t ∧ f a b = c.
Redefine Set.seq as Set.image2. The new definition is equal to the old one but rw [Set.seq] gives a different result.
Redefine Filter.map₂ to use ∃ u ∈ f, ∃ v ∈ g, image2 m u v ⊆ s instead of ∃ u v, u ∈ f ∧ v ∈ g ∧ ...
Update lemmas like Set.mem_image2, Finset.mem_image₂, Set.mem_mul, Finset.mem_div etc

The two reasons to make the change are:

∃ a ∈ s, ∃ b ∈ t, _ is a simp-normal form, and
it looks a bit nicer.

8f17470f

Diff

@@ -393,8 +393,9 @@ theorem not_subset : ¬s ⊆ t ↔ ∃ a ∈ s, a ∉ t := by
   simp only [subset_def, not_forall, exists_prop]
 #align set.not_subset Set.not_subset
 
-/-! ### Definition of strict subsets `s ⊂ t` and basic properties. -/
+lemma eq_of_forall_subset_iff (h : ∀ u, s ⊆ u ↔ t ⊆ u) : s = t := eq_of_forall_ge_iff h
 
+/-! ### Definition of strict subsets `s ⊂ t` and basic properties. -/
 
 protected theorem eq_or_ssubset_of_subset (h : s ⊆ t) : s = t ∨ s ⊂ t :=
   eq_or_lt_of_le h

chore(*): use ∃ x ∈ s, _ instead of ∃ (x) (_ : x ∈ s), _ (#9184)

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

In some rare cases, golf proofs that needed fixing.

14c72960

Diff

@@ -2510,12 +2510,12 @@ theorem nontrivial_of_pair_subset {x y} (hxy : x ≠ y) (h : {x, y} ⊆ s) : s.N
   (nontrivial_pair hxy).mono h
 #align set.nontrivial_of_pair_subset Set.nontrivial_of_pair_subset
 
-theorem Nontrivial.pair_subset (hs : s.Nontrivial) : ∃ (x y : _) (_ : x ≠ y), {x, y} ⊆ s :=
+theorem Nontrivial.pair_subset (hs : s.Nontrivial) : ∃ x y, x ≠ y ∧ {x, y} ⊆ s :=
   let ⟨x, hx, y, hy, hxy⟩ := hs
-  ⟨x, y, hxy, insert_subset_iff.2 ⟨hx, singleton_subset_iff.2 hy⟩⟩
+  ⟨x, y, hxy, insert_subset hx <| singleton_subset_iff.2 hy⟩
 #align set.nontrivial.pair_subset Set.Nontrivial.pair_subset
 
-theorem nontrivial_iff_pair_subset : s.Nontrivial ↔ ∃ (x y : _) (_ : x ≠ y), {x, y} ⊆ s :=
+theorem nontrivial_iff_pair_subset : s.Nontrivial ↔ ∃ x y, x ≠ y ∧ {x, y} ⊆ s :=
   ⟨Nontrivial.pair_subset, fun H =>
     let ⟨_, _, hxy, h⟩ := H
     nontrivial_of_pair_subset hxy h⟩
@@ -2543,19 +2543,18 @@ theorem nontrivial_of_lt [Preorder α] {x y} (hx : x ∈ s) (hy : y ∈ s) (hxy
 #align set.nontrivial_of_lt Set.nontrivial_of_lt
 
 theorem nontrivial_of_exists_lt [Preorder α]
-    (H : ∃ (x : α) (_ : x ∈ s) (y : α) (_ : y ∈ s), x < y) : s.Nontrivial :=
+    (H : ∃ᵉ (x ∈ s) (y ∈ s), x < y) : s.Nontrivial :=
   let ⟨_, hx, _, hy, hxy⟩ := H
   nontrivial_of_lt hx hy hxy
 #align set.nontrivial_of_exists_lt Set.nontrivial_of_exists_lt
 
-theorem Nontrivial.exists_lt [LinearOrder α] (hs : s.Nontrivial) :
-    ∃ (x : α) (_ : x ∈ s) (y : α) (_ : y ∈ s), x < y :=
+theorem Nontrivial.exists_lt [LinearOrder α] (hs : s.Nontrivial) : ∃ᵉ (x ∈ s) (y ∈ s), x < y :=
   let ⟨x, hx, y, hy, hxy⟩ := hs
   Or.elim (lt_or_gt_of_ne hxy) (fun H => ⟨x, hx, y, hy, H⟩) fun H => ⟨y, hy, x, hx, H⟩
 #align set.nontrivial.exists_lt Set.Nontrivial.exists_lt
 
 theorem nontrivial_iff_exists_lt [LinearOrder α] :
-    s.Nontrivial ↔ ∃ (x : α) (_ : x ∈ s) (y : α) (_ : y ∈ s), x < y :=
+    s.Nontrivial ↔ ∃ᵉ (x ∈ s) (y ∈ s), x < y :=
   ⟨Nontrivial.exists_lt, nontrivial_of_exists_lt⟩
 #align set.nontrivial_iff_exists_lt Set.nontrivial_iff_exists_lt
 
@@ -2759,8 +2758,8 @@ variable [LinearOrder α] [LinearOrder β] {f : α → β}
 downright. -/
 theorem not_monotoneOn_not_antitoneOn_iff_exists_le_le :
     ¬MonotoneOn f s ∧ ¬AntitoneOn f s ↔
-      ∃ (a : α) (_ : a ∈ s) (b : α) (_ : b ∈ s) (c : α) (_ : c ∈ s),
-        a ≤ b ∧ b ≤ c ∧ (f a < f b ∧ f c < f b ∨ f b < f a ∧ f b < f c) := by
+      ∃ᵉ (a ∈ s) (b ∈ s) (c ∈ s), a ≤ b ∧ b ≤ c ∧
+        (f a < f b ∧ f c < f b ∨ f b < f a ∧ f b < f c) := by
   simp [monotoneOn_iff_monotone, antitoneOn_iff_antitone, and_assoc, exists_and_left,
     not_monotone_not_antitone_iff_exists_le_le, @and_left_comm (_ ∈ s)]
 #align set.not_monotone_on_not_antitone_on_iff_exists_le_le Set.not_monotoneOn_not_antitoneOn_iff_exists_le_le
@@ -2769,8 +2768,8 @@ theorem not_monotoneOn_not_antitoneOn_iff_exists_le_le :
 downright. -/
 theorem not_monotoneOn_not_antitoneOn_iff_exists_lt_lt :
     ¬MonotoneOn f s ∧ ¬AntitoneOn f s ↔
-      ∃ (a : α) (_ : a ∈ s) (b : α) (_ : b ∈ s) (c : α) (_ : c ∈ s),
-        a < b ∧ b < c ∧ (f a < f b ∧ f c < f b ∨ f b < f a ∧ f b < f c) := by
+      ∃ᵉ (a ∈ s) (b ∈ s) (c ∈ s), a < b ∧ b < c ∧
+        (f a < f b ∧ f c < f b ∨ f b < f a ∧ f b < f c) := by
   simp [monotoneOn_iff_monotone, antitoneOn_iff_antitone, and_assoc, exists_and_left,
     not_monotone_not_antitone_iff_exists_lt_lt, @and_left_comm (_ ∈ s)]
 #align set.not_monotone_on_not_antitone_on_iff_exists_lt_lt Set.not_monotoneOn_not_antitoneOn_iff_exists_lt_lt

chore: update std4 to b197bd2, catching up to leanprover/std4#427 (#8888)

Co-authored-by: James <jamesgallicchio@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com> Co-authored-by: Siddharth Bhat <siddu.druid@gmail.com>

bacd2ecf

Diff

@@ -1179,7 +1179,7 @@ theorem subset_insert_iff_of_not_mem (ha : a ∉ s) : s ⊆ insert a t ↔ s ⊆
   forall₂_congr <| fun _ hb => or_iff_right <| ne_of_mem_of_not_mem hb ha
 #align set.subset_insert_iff_of_not_mem Set.subset_insert_iff_of_not_mem
 
-theorem ssubset_iff_insert {s t : Set α} : s ⊂ t ↔ ∃ a, a ∉ s ∧ insert a s ⊆ t := by
+theorem ssubset_iff_insert {s t : Set α} : s ⊂ t ↔ ∃ a ∉ s, insert a s ⊆ t := by
   simp only [insert_subset_iff, exists_and_right, ssubset_def, not_subset]
   aesop
 #align set.ssubset_iff_insert Set.ssubset_iff_insert

feat: Finsets and multisets are graded (#8892)

Characterise IsAtom, IsCoatom, Covby in Set α, Multiset α, Finset α and deduce that Multiset α, Finset α are graded orders.

Note I am moving some existing characterisations to here because it makes sense thematically, but I could be convinced otherwise.

818337c6

Diff

@@ -1179,9 +1179,9 @@ theorem subset_insert_iff_of_not_mem (ha : a ∉ s) : s ⊆ insert a t ↔ s ⊆
   forall₂_congr <| fun _ hb => or_iff_right <| ne_of_mem_of_not_mem hb ha
 #align set.subset_insert_iff_of_not_mem Set.subset_insert_iff_of_not_mem
 
-theorem ssubset_iff_insert {s t : Set α} : s ⊂ t ↔ ∃ (a : α) (_ : a ∉ s), insert a s ⊆ t := by
+theorem ssubset_iff_insert {s t : Set α} : s ⊂ t ↔ ∃ a, a ∉ s ∧ insert a s ⊆ t := by
   simp only [insert_subset_iff, exists_and_right, ssubset_def, not_subset]
-  simp only [exists_prop, and_comm]
+  aesop
 #align set.ssubset_iff_insert Set.ssubset_iff_insert
 
 theorem ssubset_insert {s : Set α} {a : α} (h : a ∉ s) : s ⊂ insert a s :=
@@ -1634,6 +1634,9 @@ lemma disjoint_singleton : Disjoint ({a} : Set α) {b} ↔ a ≠ b :=
 lemma subset_diff : s ⊆ t \ u ↔ s ⊆ t ∧ Disjoint s u := le_iff_subset.symm.trans le_sdiff
 #align set.subset_diff Set.subset_diff
 
+lemma ssubset_iff_sdiff_singleton : s ⊂ t ↔ ∃ a ∈ t, s ⊆ t \ {a} := by
+  simp [ssubset_iff_insert, subset_diff, insert_subset_iff]; aesop
+
 theorem inter_diff_distrib_left (s t u : Set α) : s ∩ (t \ u) = (s ∩ t) \ (s ∩ u) :=
   inf_sdiff_distrib_left _ _ _
 #align set.inter_diff_distrib_left Set.inter_diff_distrib_left

chore: rename by_contra' to by_contra! (#8797)

To fit with the "please try harder" convention of ! tactics.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

738b1a97

Diff

@@ -2524,7 +2524,7 @@ theorem nontrivial_of_exists_ne {x} (hx : x ∈ s) (h : ∃ y ∈ s, y ≠ x) :
 #align set.nontrivial_of_exists_ne Set.nontrivial_of_exists_ne
 
 theorem Nontrivial.exists_ne (hs : s.Nontrivial) (z) : ∃ x ∈ s, x ≠ z := by
-  by_contra' H
+  by_contra! H
   rcases hs with ⟨x, hx, y, hy, hxy⟩
   rw [H x hx, H y hy] at hxy
   exact hxy rfl

chore: space after ← (#8178)

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

5fb9beab

Diff

@@ -2659,7 +2659,7 @@ protected lemma subsingleton_or_nontrivial (s : Set α) : s.Subsingleton ∨ s.N
 #align set.subsingleton_or_nontrivial Set.subsingleton_or_nontrivial
 
 lemma eq_singleton_or_nontrivial (ha : a ∈ s) : s = {a} ∨ s.Nontrivial := by
-  rw [←subsingleton_iff_singleton ha]; exact s.subsingleton_or_nontrivial
+  rw [← subsingleton_iff_singleton ha]; exact s.subsingleton_or_nontrivial
 #align set.eq_singleton_or_nontrivial Set.eq_singleton_or_nontrivial
 
 lemma nontrivial_iff_ne_singleton (ha : a ∈ s) : s.Nontrivial ↔ s ≠ {a} :=

feat: Add Set.Nonempty.eq_zero and variations (#8423)

See the Zulip thread

Co-authored-by: Ruben Van de Velde <ruben.vandevelde+github@gmail.com>

Co-authored-by: Junyan Xu <junyanxumath@gmail.com>

414c0c82

Diff

@@ -1521,6 +1521,20 @@ theorem eq_empty_of_ssubset_singleton {s : Set α} {x : α} (hs : s ⊂ {x}) : s
   ssubset_singleton_iff.1 hs
 #align set.eq_empty_of_ssubset_singleton Set.eq_empty_of_ssubset_singleton
 
+theorem eq_of_nonempty_of_subsingleton {α} [Subsingleton α] (s t : Set α) [Nonempty s]
+    [Nonempty t] : s = t :=
+  nonempty_of_nonempty_subtype.eq_univ.trans nonempty_of_nonempty_subtype.eq_univ.symm
+
+theorem eq_of_nonempty_of_subsingleton' {α} [Subsingleton α] {s : Set α} (t : Set α)
+    (hs : s.Nonempty) [Nonempty t] : s = t :=
+  have := hs.to_subtype; eq_of_nonempty_of_subsingleton s t
+
+theorem Nonempty.eq_zero [Subsingleton α] [Zero α] {s : Set α} (h : s.Nonempty) :
+    s = {0} := eq_of_nonempty_of_subsingleton' {0} h
+
+theorem Nonempty.eq_one [Subsingleton α] [One α] {s : Set α} (h : s.Nonempty) :
+    s = {1} := eq_of_nonempty_of_subsingleton' {1} h
+
 /-! ### Disjointness -/

chore: bump Std to Std#340 (#8104)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

92e16069

Diff

@@ -763,7 +763,7 @@ theorem mem_union (x : α) (a b : Set α) : x ∈ a ∪ b ↔ x ∈ a ∨ x ∈
 
 @[simp]
 theorem union_self (a : Set α) : a ∪ a = a :=
-  ext fun _ => or_self_iff _
+  ext fun _ => or_self_iff
 #align set.union_self Set.union_self
 
 @[simp]
@@ -917,7 +917,7 @@ theorem mem_of_mem_inter_right {x : α} {a b : Set α} (h : x ∈ a ∩ b) : x 
 
 @[simp]
 theorem inter_self (a : Set α) : a ∩ a = a :=
-  ext fun _ => and_self_iff _
+  ext fun _ => and_self_iff
 #align set.inter_self Set.inter_self
 
 @[simp]

feat: let push_neg replace not (Set.Nonempty s) with s = emptyset (#8000)

Co-authored-by: Kyle Miller <kmill31415@gmail.com>

43030491

Diff

@@ -433,14 +433,6 @@ theorem not_not_mem : ¬a ∉ s ↔ a ∈ s :=
 
 /-! ### Non-empty sets -/
 
-
-/-- The property `s.Nonempty` expresses the fact that the set `s` is not empty. It should be used
-in theorem assumptions instead of `∃ x, x ∈ s` or `s ≠ ∅` as it gives access to a nice API thanks
-to the dot notation. -/
-protected def Nonempty (s : Set α) : Prop :=
-  ∃ x, x ∈ s
-#align set.nonempty Set.Nonempty
-
 -- Porting note: we seem to need parentheses at `(↥s)`,
 -- even if we increase the right precedence of `↥` in `Mathlib.Tactic.Coe`.
 -- Porting note: removed `simp` as it is competing with `nonempty_subtype`.

chore: bump toolchain to v4.3.0-rc1 (#8051)

This incorporates changes from

#7845
#7847
#7853
#7872 (was never actually made to work, but the diffs in nightly-testing are unexciting: we need to fully qualify a few names)

They can all be closed when this is merged.

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

1ff3bf34

Diff

@@ -2202,19 +2202,15 @@ theorem powerset_singleton (x : α) : 𝒫({x} : Set α) = {∅, {x}} := by
 
 /-! ### Sets defined as an if-then-else -/
 
---Porting note: New theorem to prove `mem_dite` lemmas.
--- `simp [h]` where `h : p` does not simplify `∀ (h : p), x ∈ s h` any more.
--- https://github.com/leanprover/lean4/issues/1926
 theorem mem_dite (p : Prop) [Decidable p] (s : p → Set α) (t : ¬ p → Set α) (x : α) :
     (x ∈ if h : p then s h else t h) ↔ (∀ h : p, x ∈ s h) ∧ ∀ h : ¬p, x ∈ t h := by
   split_ifs with hp
   · exact ⟨fun hx => ⟨fun _ => hx, fun hnp => (hnp hp).elim⟩, fun hx => hx.1 hp⟩
   · exact ⟨fun hx => ⟨fun h => (hp h).elim, fun _ => hx⟩, fun hx => hx.2 hp⟩
 
---Porting note: Old proof was `split_ifs; simp [h]`
 theorem mem_dite_univ_right (p : Prop) [Decidable p] (t : p → Set α) (x : α) :
     (x ∈ if h : p then t h else univ) ↔ ∀ h : p, x ∈ t h := by
-  simp [mem_dite]
+  split_ifs <;> simp_all
 #align set.mem_dite_univ_right Set.mem_dite_univ_right
 
 @[simp]
@@ -2225,7 +2221,7 @@ theorem mem_ite_univ_right (p : Prop) [Decidable p] (t : Set α) (x : α) :
 
 theorem mem_dite_univ_left (p : Prop) [Decidable p] (t : ¬p → Set α) (x : α) :
     (x ∈ if h : p then univ else t h) ↔ ∀ h : ¬p, x ∈ t h := by
-  simp [mem_dite]
+  split_ifs <;> simp_all
 #align set.mem_dite_univ_left Set.mem_dite_univ_left
 
 @[simp]

Misc lemmas about Specializes, Inseparable and path-connectedness (#7970)

Generalizing one of the proofs introduced in #7878

46d7a401

Diff

@@ -2350,6 +2350,16 @@ theorem subset_ite {t s s' u : Set α} : u ⊆ t.ite s s' ↔ u ∩ t ⊆ s ∧
   by_cases hx : x ∈ t <;> simp [*, Set.ite]
 #align set.subset_ite Set.subset_ite
 
+theorem ite_eq_of_subset_left (t : Set α) {s₁ s₂ : Set α} (h : s₁ ⊆ s₂) :
+    t.ite s₁ s₂ = s₁ ∪ (s₂ \ t) := by
+  ext x
+  by_cases hx : x ∈ t <;> simp [*, Set.ite, or_iff_right_of_imp (@h x)]
+
+theorem ite_eq_of_subset_right (t : Set α) {s₁ s₂ : Set α} (h : s₂ ⊆ s₁) :
+    t.ite s₁ s₂ = (s₁ ∩ t) ∪ s₂ := by
+  ext x
+  by_cases hx : x ∈ t <;> simp [*, Set.ite, or_iff_left_of_imp (@h x)]
+
 /-! ### Subsingleton -/

feat: more delaborators (#7964)

Co-authored-by: Kyle Miller <kmill31415@gmail.com>

eeb791d8

Diff

@@ -7,6 +7,7 @@ import Mathlib.Order.SymmDiff
 import Mathlib.Logic.Function.Iterate
 import Mathlib.Tactic.Tauto
 import Mathlib.Tactic.ByContra
+import Mathlib.Util.Delaborators
 
 #align_import data.set.basic from "leanprover-community/mathlib"@"001ffdc42920050657fd45bd2b8bfbec8eaaeb29"

feat: Adjunction between topological spaces and locales (#4593)

We define the contravariant functors between the categories of Frames and Topological Spaces and prove that they form an adjunction. Work started at the BIRS workshop "Formalization of Cohomology Theories", Banff, May 2023.

Co-authored-by: Anne Baanen <vierkantor@vierkantor.com> Co-authored-by: leopoldmayer <leomayer@uw.edu> Co-authored-by: Brendan Seamas Murphy <shamrockfrost@gmail.com>

Co-authored-by: leopoldmayer <leomayer@uw.edu> Co-authored-by: Brendan Murphy <shamrockfrost@gmail.com> Co-authored-by: Vierkantor <vierkantor@vierkantor.com> Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

21c7184c

Diff

@@ -568,6 +568,8 @@ theorem setOf_false : { _a : α | False } = ∅ :=
   rfl
 #align set.set_of_false Set.setOf_false
 
+@[simp] theorem setOf_bot : { _x : α | ⊥ } = ∅ := rfl
+
 @[simp]
 theorem empty_subset (s : Set α) : ∅ ⊆ s :=
   fun.
@@ -668,6 +670,8 @@ theorem setOf_true : { _x : α | True } = univ :=
   rfl
 #align set.set_of_true Set.setOf_true
 
+@[simp] theorem setOf_top : { _x : α | ⊤ } = univ := rfl
+
 @[simp, mfld_simps]
 theorem mem_univ (x : α) : x ∈ @univ α :=
   trivial

chore: remove many Type _ before the colon (#7718)

We have turned to Type* instead of Type _, but many of them remained in mathlib because the straight replacement did not work. In general, having Type _ before the colon is a code smell, though, as it hides which types should be in the same universe and which shouldn't, and is not very robust.

This PR replaces most of the remaining Type _ before the colon (except those in category theory) by Type* or Type u. This has uncovered a few bugs (where declarations were not as polymorphic as they should be).

I had to increase heartbeats at two places when replacing Type _ by Type*, but I think it's worth it as it's really more robust.

fe9572d2

Diff

@@ -81,9 +81,9 @@ universe u v w x
 
 namespace Set
 
-variable {α : Type _} {s t : Set α}
+variable {α : Type u} {s t : Set α}
 
-instance instBooleanAlgebraSet {α : Type _} : BooleanAlgebra (Set α) :=
+instance instBooleanAlgebraSet : BooleanAlgebra (Set α) :=
   { (inferInstance : BooleanAlgebra (α → Prop)) with
     sup := (· ∪ ·),
     le := (· ≤ ·),

feat: Finset family induction (#7522)

Provide an induction principle for finset families: One can increase the support of a finset family one by one.

c98e6b7f

Diff

@@ -1172,7 +1172,7 @@ theorem insert_subset (ha : a ∈ t) (hs : s ⊆ t) : insert a s ⊆ t :=
 theorem insert_subset_insert (h : s ⊆ t) : insert a s ⊆ insert a t := fun _ => Or.imp_right (@h _)
 #align set.insert_subset_insert Set.insert_subset_insert
 
-theorem insert_subset_insert_iff (ha : a ∉ s) : insert a s ⊆ insert a t ↔ s ⊆ t := by
+@[simp] theorem insert_subset_insert_iff (ha : a ∉ s) : insert a s ⊆ insert a t ↔ s ⊆ t := by
   refine' ⟨fun h x hx => _, insert_subset_insert⟩
   rcases h (subset_insert _ _ hx) with (rfl | hxt)
   exacts [(ha hx).elim, hxt]

chore: fix aligns (#7529)

81fa8d9e

Diff

@@ -806,12 +806,12 @@ theorem union_right_comm (s₁ s₂ s₃ : Set α) : s₁ ∪ s₂ ∪ s₃ = s
 @[simp]
 theorem union_eq_left {s t : Set α} : s ∪ t = s ↔ t ⊆ s :=
   sup_eq_left
-#align set.union_eq_left Set.union_eq_left
+#align set.union_eq_left_iff_subset Set.union_eq_left
 
 @[simp]
 theorem union_eq_right {s t : Set α} : s ∪ t = t ↔ s ⊆ t :=
   sup_eq_right
-#align set.union_eq_right Set.union_eq_right
+#align set.union_eq_right_iff_subset Set.union_eq_right
 
 theorem union_eq_self_of_subset_left {s t : Set α} (h : s ⊆ t) : s ∪ t = t :=
   union_eq_right.mpr h

chore: Make Set/Finset lemmas match lattice lemma names (#7378)

Rename union_eq_left_iff_subset to union_eq_left to match sup_eq_left. Similarly for the right and inter versions.

aef04106

Diff

@@ -804,21 +804,21 @@ theorem union_right_comm (s₁ s₂ s₃ : Set α) : s₁ ∪ s₂ ∪ s₃ = s
 #align set.union_right_comm Set.union_right_comm
 
 @[simp]
-theorem union_eq_left_iff_subset {s t : Set α} : s ∪ t = s ↔ t ⊆ s :=
+theorem union_eq_left {s t : Set α} : s ∪ t = s ↔ t ⊆ s :=
   sup_eq_left
-#align set.union_eq_left_iff_subset Set.union_eq_left_iff_subset
+#align set.union_eq_left Set.union_eq_left
 
 @[simp]
-theorem union_eq_right_iff_subset {s t : Set α} : s ∪ t = t ↔ s ⊆ t :=
+theorem union_eq_right {s t : Set α} : s ∪ t = t ↔ s ⊆ t :=
   sup_eq_right
-#align set.union_eq_right_iff_subset Set.union_eq_right_iff_subset
+#align set.union_eq_right Set.union_eq_right
 
 theorem union_eq_self_of_subset_left {s t : Set α} (h : s ⊆ t) : s ∪ t = t :=
-  union_eq_right_iff_subset.mpr h
+  union_eq_right.mpr h
 #align set.union_eq_self_of_subset_left Set.union_eq_self_of_subset_left
 
 theorem union_eq_self_of_subset_right {s t : Set α} (h : t ⊆ s) : s ∪ t = s :=
-  union_eq_left_iff_subset.mpr h
+  union_eq_left.mpr h
 #align set.union_eq_self_of_subset_right Set.union_eq_self_of_subset_right
 
 @[simp]
@@ -974,22 +974,18 @@ theorem subset_inter_iff {s t r : Set α} : r ⊆ s ∩ t ↔ r ⊆ s ∧ r ⊆
   (forall_congr' fun _ => imp_and).trans forall_and
 #align set.subset_inter_iff Set.subset_inter_iff
 
-@[simp]
-theorem inter_eq_left_iff_subset {s t : Set α} : s ∩ t = s ↔ s ⊆ t :=
-  inf_eq_left
-#align set.inter_eq_left_iff_subset Set.inter_eq_left_iff_subset
+@[simp] lemma inter_eq_left : s ∩ t = s ↔ s ⊆ t := inf_eq_left
+#align set.inter_eq_left_iff_subset Set.inter_eq_left
 
-@[simp]
-theorem inter_eq_right_iff_subset {s t : Set α} : s ∩ t = t ↔ t ⊆ s :=
-  inf_eq_right
-#align set.inter_eq_right_iff_subset Set.inter_eq_right_iff_subset
+@[simp] lemma inter_eq_right : s ∩ t = t ↔ t ⊆ s := inf_eq_right
+#align set.inter_eq_right_iff_subset Set.inter_eq_right
 
 theorem inter_eq_self_of_subset_left {s t : Set α} : s ⊆ t → s ∩ t = s :=
-  inter_eq_left_iff_subset.mpr
+  inter_eq_left.mpr
 #align set.inter_eq_self_of_subset_left Set.inter_eq_self_of_subset_left
 
 theorem inter_eq_self_of_subset_right {s t : Set α} : t ⊆ s → s ∩ t = t :=
-  inter_eq_right_iff_subset.mpr
+  inter_eq_right.mpr
 #align set.inter_eq_self_of_subset_right Set.inter_eq_self_of_subset_right
 
 theorem inter_congr_left (ht : s ∩ u ⊆ t) (hu : s ∩ t ⊆ u) : s ∩ t = s ∩ u :=

Match https://github.com/leanprover-community/mathlib/pull/18506

feat: Sigma-algebra generated by a singleton (#2513)

d84c8d2f

Diff

@@ -8,7 +8,7 @@ import Mathlib.Logic.Function.Iterate
 import Mathlib.Tactic.Tauto
 import Mathlib.Tactic.ByContra
 
-#align_import data.set.basic from "leanprover-community/mathlib"@"48fb5b5280e7c81672afc9524185ae994553ebf4"
+#align_import data.set.basic from "leanprover-community/mathlib"@"001ffdc42920050657fd45bd2b8bfbec8eaaeb29"
 
 /-!
 # Basic properties of sets
@@ -3018,3 +3018,7 @@ theorem subset_right_of_subset_union (h : s ⊆ t ∪ u) (hab : Disjoint s t) :
 #align disjoint.subset_right_of_subset_union Disjoint.subset_right_of_subset_union
 
 end Disjoint
+
+@[simp] theorem Prop.compl_singleton (p : Prop) : ({p}ᶜ : Set Prop) = {¬p} :=
+  ext fun q ↦ by simpa [@Iff.comm q] using not_iff
+#align Prop.compl_singleton Prop.compl_singleton

chore: delay import of Tactic.Common (#7000)

I know that this is contrary to what we've done previously, but:

I'm trying to upstream a great many tactics from Mathlib to Std (essentially, everything that non-mathematicians want too).
This makes it much easier for me to see what is going on, and understand the import requirements (particularly for the "big" tactics norm_num / ring / linarith)
It's actually not as bad as it looks here, because as these tactics move up to Std they will start disappearing again from explicit imports, but Mathlib can happily import all of Std.

(Oh

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

4f3418a7

Diff

@@ -5,6 +5,8 @@ Authors: Jeremy Avigad, Leonardo de Moura
 -/
 import Mathlib.Order.SymmDiff
 import Mathlib.Logic.Function.Iterate
+import Mathlib.Tactic.Tauto
+import Mathlib.Tactic.ByContra
 
 #align_import data.set.basic from "leanprover-community/mathlib"@"48fb5b5280e7c81672afc9524185ae994553ebf4"

feat(Data/Set): +3 lemmas about Set.inclusion (#6944)

05474e33

Diff

@@ -2831,6 +2831,10 @@ theorem inclusion_injective (h : s ⊆ t) : Injective (inclusion h)
   | ⟨_, _⟩, ⟨_, _⟩ => Subtype.ext_iff_val.2 ∘ Subtype.ext_iff_val.1
 #align set.inclusion_injective Set.inclusion_injective
 
+@[simp]
+theorem inclusion_inj (h : s ⊆ t) {x y : s} : inclusion h x = inclusion h y ↔ x = y :=
+  (inclusion_injective h).eq_iff
+
 theorem eq_of_inclusion_surjective {s t : Set α} {h : s ⊆ t}
     (h_surj : Function.Surjective (inclusion h)) : s = t := by
   refine' Set.Subset.antisymm h (fun x hx => _)
@@ -2838,6 +2842,14 @@ theorem eq_of_inclusion_surjective {s t : Set α} {h : s ⊆ t}
   exact mem_of_eq_of_mem (congr_arg Subtype.val hy).symm y.prop
 #align set.eq_of_inclusion_surjective Set.eq_of_inclusion_surjective
 
+@[simp]
+theorem inclusion_le_inclusion [Preorder α] {s t : Set α} (h : s ⊆ t) {x y : s} :
+    inclusion h x ≤ inclusion h y ↔ x ≤ y := Iff.rfl
+
+@[simp]
+theorem inclusion_lt_inclusion [Preorder α] {s t : Set α} (h : s ⊆ t) {x y : s} :
+    inclusion h x < inclusion h y ↔ x < y := Iff.rfl
+
 end Inclusion
 
 end Set

refactor(Data/Set): redefine Set.Nontrivial (#6805)

Fixes #4353

0a341a61

Diff

@@ -2451,7 +2451,7 @@ instance subsingleton_coe_of_subsingleton [Subsingleton α] {s : Set α} : Subsi
 
 /-- A set `s` is `Set.Nontrivial` if it has at least two distinct elements. -/
 protected def Nontrivial (s : Set α) : Prop :=
-  ∃ (x : α) (_ : x ∈ s) (y : α) (_ : y ∈ s), x ≠ y
+  ∃ x ∈ s, ∃ y ∈ s, x ≠ y
 #align set.nontrivial Set.Nontrivial
 
 theorem nontrivial_of_mem_mem_ne {x y} (hx : x ∈ s) (hy : y ∈ s) (hxy : x ≠ y) : s.Nontrivial :=
@@ -2463,20 +2463,20 @@ theorem nontrivial_of_mem_mem_ne {x y} (hx : x ∈ s) (hy : y ∈ s) (hxy : x 
 /-- Extract witnesses from s.nontrivial. This function might be used instead of case analysis on the
 argument. Note that it makes a proof depend on the classical.choice axiom. -/
 protected noncomputable def Nontrivial.choose (hs : s.Nontrivial) : α × α :=
-  (Exists.choose hs, hs.choose_spec.choose_spec.choose)
+  (Exists.choose hs, hs.choose_spec.right.choose)
 #align set.nontrivial.some Set.Nontrivial.choose
 
 protected theorem Nontrivial.choose_fst_mem (hs : s.Nontrivial) : hs.choose.fst ∈ s :=
-  hs.choose_spec.choose
+  hs.choose_spec.left
 #align set.nontrivial.some_fst_mem Set.Nontrivial.choose_fst_mem
 
 protected theorem Nontrivial.choose_snd_mem (hs : s.Nontrivial) : hs.choose.snd ∈ s :=
-  hs.choose_spec.choose_spec.choose_spec.choose
+  hs.choose_spec.right.choose_spec.left
 #align set.nontrivial.some_snd_mem Set.Nontrivial.choose_snd_mem
 
 protected theorem Nontrivial.choose_fst_ne_choose_snd (hs : s.Nontrivial) :
     hs.choose.fst ≠ hs.choose.snd :=
-  hs.choose_spec.choose_spec.choose_spec.choose_spec
+  hs.choose_spec.right.choose_spec.right
 #align set.nontrivial.some_fst_ne_some_snd Set.Nontrivial.choose_fst_ne_choose_snd
 
 theorem Nontrivial.mono (hs : s.Nontrivial) (hst : s ⊆ t) : t.Nontrivial :=
@@ -2625,7 +2625,7 @@ theorem nontrivial_mono {α : Type*} {s t : Set α} (hst : s ⊆ t) (hs : Nontri
 
 @[simp]
 theorem not_subsingleton_iff : ¬s.Subsingleton ↔ s.Nontrivial := by
-  simp_rw [Set.Subsingleton, Set.Nontrivial, not_forall]
+  simp_rw [Set.Subsingleton, Set.Nontrivial, not_forall, exists_prop]
 #align set.not_subsingleton_iff Set.not_subsingleton_iff
 
 @[simp]

feat: patch for new alias command (#6172)

19e0ba92

Diff

@@ -133,10 +133,10 @@ theorem lt_iff_ssubset : s < t ↔ s ⊂ t :=
   Iff.rfl
 #align set.lt_iff_ssubset Set.lt_iff_ssubset
 
-alias le_iff_subset ↔ _root_.LE.le.subset _root_.HasSubset.Subset.le
+alias ⟨_root_.LE.le.subset, _root_.HasSubset.Subset.le⟩ := le_iff_subset
 #align has_subset.subset.le HasSubset.Subset.le
 
-alias lt_iff_ssubset ↔ _root_.LT.lt.ssubset _root_.HasSSubset.SSubset.lt
+alias ⟨_root_.LT.lt.ssubset, _root_.HasSSubset.SSubset.lt⟩ := lt_iff_ssubset
 #align has_ssubset.ssubset.lt HasSSubset.SSubset.lt
 
 -- Porting note: I've introduced this abbreviation, with the `@[coe]` attribute,
@@ -446,7 +446,7 @@ theorem nonempty_coe_sort {s : Set α} : Nonempty (↥s) ↔ s.Nonempty :=
   nonempty_subtype
 #align set.nonempty_coe_sort Set.nonempty_coe_sort
 
-alias nonempty_coe_sort ↔ _ Nonempty.coe_sort
+alias ⟨_, Nonempty.coe_sort⟩ := nonempty_coe_sort
 #align set.nonempty.coe_sort Set.Nonempty.coe_sort
 
 theorem nonempty_def : s.Nonempty ↔ ∃ x, x ∈ s :=
@@ -615,7 +615,7 @@ theorem not_nonempty_iff_eq_empty' : ¬Nonempty s ↔ s = ∅ := by
 theorem nonempty_iff_ne_empty' : Nonempty s ↔ s ≠ ∅ :=
   not_nonempty_iff_eq_empty'.not_right
 
-alias nonempty_iff_ne_empty ↔ Nonempty.ne_empty _
+alias ⟨Nonempty.ne_empty, _⟩ := nonempty_iff_ne_empty
 #align set.nonempty.ne_empty Set.Nonempty.ne_empty
 
 @[simp]
@@ -648,7 +648,7 @@ theorem empty_ssubset : ∅ ⊂ s ↔ s.Nonempty :=
   (@bot_lt_iff_ne_bot (Set α) _ _ _).trans nonempty_iff_ne_empty.symm
 #align set.empty_ssubset Set.empty_ssubset
 
-alias empty_ssubset ↔ _ Nonempty.empty_ssubset
+alias ⟨_, Nonempty.empty_ssubset⟩ := empty_ssubset
 #align set.nonempty.empty_ssubset Set.Nonempty.empty_ssubset
 
 /-!
@@ -689,7 +689,7 @@ theorem univ_subset_iff {s : Set α} : univ ⊆ s ↔ s = univ :=
   @top_le_iff _ _ _ s
 #align set.univ_subset_iff Set.univ_subset_iff
 
-alias univ_subset_iff ↔ eq_univ_of_univ_subset _
+alias ⟨eq_univ_of_univ_subset, _⟩ := univ_subset_iff
 #align set.eq_univ_of_univ_subset Set.eq_univ_of_univ_subset
 
 theorem eq_univ_iff_forall {s : Set α} : s = univ ↔ ∀ x, x ∈ s :=
@@ -1555,7 +1555,7 @@ lemma not_disjoint_iff : ¬Disjoint s t ↔ ∃ x, x ∈ s ∧ x ∈ t :=
 lemma not_disjoint_iff_nonempty_inter : ¬ Disjoint s t ↔ (s ∩ t).Nonempty := not_disjoint_iff
 #align set.not_disjoint_iff_nonempty_inter Set.not_disjoint_iff_nonempty_inter
 
-alias not_disjoint_iff_nonempty_inter ↔ _ Nonempty.not_disjoint
+alias ⟨_, Nonempty.not_disjoint⟩ := not_disjoint_iff_nonempty_inter
 #align set.nonempty.not_disjoint Set.Nonempty.not_disjoint
 
 lemma disjoint_or_nonempty_inter (s t : Set α) : Disjoint s t ∨ (s ∩ t).Nonempty :=
@@ -1566,7 +1566,7 @@ lemma disjoint_iff_forall_ne : Disjoint s t ↔ ∀ ⦃a⦄, a ∈ s → ∀ ⦃
   simp only [Ne.def, disjoint_left, @imp_not_comm _ (_ = _), forall_eq']
 #align set.disjoint_iff_forall_ne Set.disjoint_iff_forall_ne
 
-alias disjoint_iff_forall_ne ↔ _root_.Disjoint.ne_of_mem _
+alias ⟨_root_.Disjoint.ne_of_mem, _⟩ := disjoint_iff_forall_ne
 #align disjoint.ne_of_mem Disjoint.ne_of_mem
 
 lemma disjoint_of_subset_left (h : s ⊆ u) (d : Disjoint u t) : Disjoint s t := d.mono_left h
@@ -1773,16 +1773,16 @@ theorem disjoint_compl_right_iff_subset : Disjoint s tᶜ ↔ s ⊆ t :=
   disjoint_compl_right_iff
 #align set.disjoint_compl_right_iff_subset Set.disjoint_compl_right_iff_subset
 
-alias subset_compl_iff_disjoint_right ↔ _ _root_.Disjoint.subset_compl_right
+alias ⟨_, _root_.Disjoint.subset_compl_right⟩ := subset_compl_iff_disjoint_right
 #align disjoint.subset_compl_right Disjoint.subset_compl_right
 
-alias subset_compl_iff_disjoint_left ↔ _ _root_.Disjoint.subset_compl_left
+alias ⟨_, _root_.Disjoint.subset_compl_left⟩ := subset_compl_iff_disjoint_left
 #align disjoint.subset_compl_left Disjoint.subset_compl_left
 
-alias disjoint_compl_left_iff_subset ↔ _ _root_.HasSubset.Subset.disjoint_compl_left
+alias ⟨_, _root_.HasSubset.Subset.disjoint_compl_left⟩ := disjoint_compl_left_iff_subset
 #align has_subset.subset.disjoint_compl_left HasSubset.Subset.disjoint_compl_left
 
-alias disjoint_compl_right_iff_subset ↔ _ _root_.HasSubset.Subset.disjoint_compl_right
+alias ⟨_, _root_.HasSubset.Subset.disjoint_compl_right⟩ := disjoint_compl_right_iff_subset
 #align has_subset.subset.disjoint_compl_right HasSubset.Subset.disjoint_compl_right
 
 theorem subset_union_compl_iff_inter_subset {s t u : Set α} : s ⊆ t ∪ uᶜ ↔ s ∩ u ⊆ t :=
@@ -2609,7 +2609,7 @@ theorem nontrivial_coe_sort {s : Set α} : Nontrivial s ↔ s.Nontrivial := by
     exact ⟨⟨x, hx⟩, mem_univ _, ⟨y, hy⟩, mem_univ _, Subtype.mk_eq_mk.not.mpr hxy⟩
 #align set.nontrivial_coe_sort Set.nontrivial_coe_sort
 
-alias nontrivial_coe_sort ↔ _ Nontrivial.coe_sort
+alias ⟨_, Nontrivial.coe_sort⟩ := nontrivial_coe_sort
 #align set.nontrivial.coe_sort Set.Nontrivial.coe_sort
 
 /-- A type with a set `s` whose `coe_sort` is a nontrivial type is nontrivial.
@@ -2633,10 +2633,10 @@ theorem not_nontrivial_iff : ¬s.Nontrivial ↔ s.Subsingleton :=
   Iff.not_left not_subsingleton_iff.symm
 #align set.not_nontrivial_iff Set.not_nontrivial_iff
 
-alias not_nontrivial_iff ↔ _ Subsingleton.not_nontrivial
+alias ⟨_, Subsingleton.not_nontrivial⟩ := not_nontrivial_iff
 #align set.subsingleton.not_nontrivial Set.Subsingleton.not_nontrivial
 
-alias not_subsingleton_iff ↔ _ Nontrivial.not_subsingleton
+alias ⟨_, Nontrivial.not_subsingleton⟩ := not_subsingleton_iff
 #align set.nontrivial.not_subsingleton Set.Nontrivial.not_subsingleton
 
 protected lemma subsingleton_or_nontrivial (s : Set α) : s.Subsingleton ∨ s.Nontrivial := by

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

@@ -19,7 +19,7 @@ This file provides some basic definitions related to sets and functions not pres
 library, as well as extra lemmas for functions in the core library (empty set, univ, union,
 intersection, insert, singleton, set-theoretic difference, complement, and powerset).
 
-Note that a set is a term, not a type. There is a coercion from `Set α` to `Type _` sending
+Note that a set is a term, not a type. There is a coercion from `Set α` to `Type*` sending
 `s` to the corresponding subtype `↥s`.
 
 See also the file `SetTheory/ZFC.lean`, which contains an encoding of ZFC set theory in Lean.
@@ -54,7 +54,7 @@ Definitions in the file:
 * `s.Nonempty` is to be preferred to `s ≠ ∅` or `∃ x, x ∈ s`. It has the advantage that
 the `s.Nonempty` dot notation can be used.
 
-* For `s : Set α`, do not use `Subtype s`. Instead use `↥s` or `(s : Type _)` or `s`.
+* For `s : Set α`, do not use `Subtype s`. Instead use `↥s` or `(s : Type*)` or `s`.
 
 ## Tags
 
@@ -217,7 +217,7 @@ theorem SetCoe.ext_iff {s : Set α} {a b : s} : (↑a : α) = ↑b ↔ a = b :=
 end SetCoe
 
 /-- See also `Subtype.prop` -/
-theorem Subtype.mem {α : Type _} {s : Set α} (p : s) : (p : α) ∈ s :=
+theorem Subtype.mem {α : Type*} {s : Set α} (p : s) : (p : α) ∈ s :=
   p.prop
 #align subtype.mem Subtype.mem
 
@@ -713,11 +713,11 @@ theorem exists_mem_of_nonempty (α) : ∀ [Nonempty α], ∃ x : α, x ∈ (univ
   | ⟨x⟩ => ⟨x, trivial⟩
 #align set.exists_mem_of_nonempty Set.exists_mem_of_nonempty
 
-theorem ne_univ_iff_exists_not_mem {α : Type _} (s : Set α) : s ≠ univ ↔ ∃ a, a ∉ s := by
+theorem ne_univ_iff_exists_not_mem {α : Type*} (s : Set α) : s ≠ univ ↔ ∃ a, a ∉ s := by
   rw [← not_forall, ← eq_univ_iff_forall]
 #align set.ne_univ_iff_exists_not_mem Set.ne_univ_iff_exists_not_mem
 
-theorem not_subset_iff_exists_mem_not_mem {α : Type _} {s t : Set α} :
+theorem not_subset_iff_exists_mem_not_mem {α : Type*} {s t : Set α} :
     ¬s ⊆ t ↔ ∃ x, x ∈ s ∧ x ∉ t := by simp [subset_def]
 #align set.not_subset_iff_exists_mem_not_mem Set.not_subset_iff_exists_mem_not_mem
 
@@ -1502,7 +1502,7 @@ theorem sep_setOf : { x ∈ { y | p y } | q x } = { x | p x ∧ q x } :=
 end Sep
 
 @[simp]
-theorem subset_singleton_iff {α : Type _} {s : Set α} {x : α} : s ⊆ {x} ↔ ∀ y ∈ s, y = x :=
+theorem subset_singleton_iff {α : Type*} {s : Set α} {x : α} : s ⊆ {x} ↔ ∀ y ∈ s, y = x :=
   Iff.rfl
 #align set.subset_singleton_iff Set.subset_singleton_iff
 
@@ -2411,11 +2411,11 @@ theorem subsingleton_of_subsingleton [Subsingleton α] {s : Set α} : Set.Subsin
   subsingleton_univ.anti (subset_univ s)
 #align set.subsingleton_of_subsingleton Set.subsingleton_of_subsingleton
 
-theorem subsingleton_isTop (α : Type _) [PartialOrder α] : Set.Subsingleton { x : α | IsTop x } :=
+theorem subsingleton_isTop (α : Type*) [PartialOrder α] : Set.Subsingleton { x : α | IsTop x } :=
   fun x hx _ hy => hx.isMax.eq_of_le (hy x)
 #align set.subsingleton_is_top Set.subsingleton_isTop
 
-theorem subsingleton_isBot (α : Type _) [PartialOrder α] : Set.Subsingleton { x : α | IsBot x } :=
+theorem subsingleton_isBot (α : Type*) [PartialOrder α] : Set.Subsingleton { x : α | IsBot x } :=
   fun x hx _ hy => hx.isMin.eq_of_ge (hy x)
 #align set.subsingleton_is_bot Set.subsingleton_isBot
 
@@ -2618,7 +2618,7 @@ theorem nontrivial_of_nontrivial_coe (hs : Nontrivial s) : Nontrivial α :=
   nontrivial_of_nontrivial <| nontrivial_coe_sort.1 hs
 #align set.nontrivial_of_nontrivial_coe Set.nontrivial_of_nontrivial_coe
 
-theorem nontrivial_mono {α : Type _} {s t : Set α} (hst : s ⊆ t) (hs : Nontrivial s) :
+theorem nontrivial_mono {α : Type*} {s t : Set α} (hst : s ⊆ t) (hs : Nontrivial s) :
     Nontrivial t :=
   Nontrivial.coe_sort <| (nontrivial_coe_sort.1 hs).mono hst
 #align set.nontrivial_mono Set.nontrivial_mono
@@ -2765,7 +2765,7 @@ open Set
 
 namespace Function
 
-variable {ι : Sort _} {α : Type _} {β : Type _} {f : α → β}
+variable {ι : Sort*} {α : Type*} {β : Type*} {f : α → β}
 
 theorem Injective.nonempty_apply_iff {f : Set α → Set β} (hf : Injective f) (h2 : f ∅ = ∅)
     {s : Set α} : (f s).Nonempty ↔ s.Nonempty := by
@@ -2783,7 +2783,7 @@ namespace Set
 
 section Inclusion
 
-variable {α : Type _} {s t u : Set α}
+variable {α : Type*} {s t u : Set α}
 
 /-- `inclusion` is the "identity" function between two subsets `s` and `t`, where `s ⊆ t` -/
 def inclusion (h : s ⊆ t) : s → t := fun x : s => (⟨x, h x.2⟩ : t)
@@ -2844,7 +2844,7 @@ end Set
 
 namespace Subsingleton
 
-variable {α : Type _} [Subsingleton α]
+variable {α : Type*} [Subsingleton α]
 
 theorem eq_univ_of_nonempty {s : Set α} : s.Nonempty → s = univ := fun ⟨x, hx⟩ =>
   eq_univ_of_forall fun y => Subsingleton.elim x y ▸ hx
@@ -2855,7 +2855,7 @@ theorem set_cases {p : Set α → Prop} (h0 : p ∅) (h1 : p univ) (s) : p s :=
   (s.eq_empty_or_nonempty.elim fun h => h.symm ▸ h0) fun h => (eq_univ_of_nonempty h).symm ▸ h1
 #align subsingleton.set_cases Subsingleton.set_cases
 
-theorem mem_iff_nonempty {α : Type _} [Subsingleton α] {s : Set α} {x : α} : x ∈ s ↔ s.Nonempty :=
+theorem mem_iff_nonempty {α : Type*} [Subsingleton α] {s : Set α} {x : α} : x ∈ s ↔ s.Nonempty :=
   ⟨fun hx => ⟨x, hx⟩, fun ⟨y, hy⟩ => Subsingleton.elim y x ▸ hy⟩
 #align subsingleton.mem_iff_nonempty Subsingleton.mem_iff_nonempty
 
@@ -2904,7 +2904,7 @@ end Set
 /-! ### Monotone lemmas for sets -/
 
 section Monotone
-variable {α β : Type _}
+variable {α β : Type*}
 
 theorem Monotone.inter [Preorder β] {f g : β → Set α} (hf : Monotone f) (hg : Monotone g) :
     Monotone fun x => f x ∩ g x :=
@@ -2967,7 +2967,7 @@ end Monotone
 
 /-! ### Disjoint sets -/
 
-variable {α β : Type _} {s t u : Set α} {f : α → β}
+variable {α β : Type*} {s t u : Set α} {f : α → β}
 
 namespace Disjoint

chore: ensure all instances referred to directly have explicit names (#6423)

Per https://github.com/leanprover/lean4/issues/2343, we are going to need to change the automatic generation of instance names, as they become too long.

This PR ensures that everywhere in Mathlib that refers to an instance by name, that name is given explicitly, rather than being automatically generated.

There are four exceptions, which are now commented, with links to https://github.com/leanprover/lean4/issues/2343.

This was implemented by running Mathlib against a modified Lean that appended _ᾰ to all automatically generated names, and fixing everything.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

65a35f78

Diff

@@ -81,7 +81,7 @@ namespace Set
 
 variable {α : Type _} {s t : Set α}
 
-instance {α : Type _} : BooleanAlgebra (Set α) :=
+instance instBooleanAlgebraSet {α : Type _} : BooleanAlgebra (Set α) :=
   { (inferInstance : BooleanAlgebra (α → Prop)) with
     sup := (· ∪ ·),
     le := (· ≤ ·),

feat(Topology/ExtremallyDisconnected): prove Gleason's theorem (#5634)

This work was done during the 2023 Copenhagen masterclass on formalisation of condensed mathematics. Numerous participants contributed.

Co-authored-by: Filippo A E Nuccio <filippo.nuccio@univ-st-etienne.fr> Co-authored-by: Dagur Ásgeirsson <dagurtomas@gmail.com> Co-authored-by: Nikolas Kuhn <nikolaskuhn@gmx.de>

a2c34345

Diff

@@ -607,6 +607,14 @@ theorem nonempty_iff_ne_empty : s.Nonempty ↔ s ≠ ∅ :=
   not_nonempty_iff_eq_empty.not_right
 #align set.nonempty_iff_ne_empty Set.nonempty_iff_ne_empty
 
+/-- See also `nonempty_iff_ne_empty'`. -/
+theorem not_nonempty_iff_eq_empty' : ¬Nonempty s ↔ s = ∅ := by
+  rw [nonempty_subtype, not_exists, eq_empty_iff_forall_not_mem]
+
+/-- See also `not_nonempty_iff_eq_empty'`. -/
+theorem nonempty_iff_ne_empty' : Nonempty s ↔ s ≠ ∅ :=
+  not_nonempty_iff_eq_empty'.not_right
+
 alias nonempty_iff_ne_empty ↔ Nonempty.ne_empty _
 #align set.nonempty.ne_empty Set.Nonempty.ne_empty

chore: change 'Porting:' to 'Porting note:' (#6378)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

ffef20af

Diff

@@ -179,12 +179,12 @@ theorem Set.coe_setOf (p : α → Prop) : ↥{ x | p x } = { x // p x } :=
   rfl
 #align set.coe_set_of Set.coe_setOf
 
--- Porting: removed `simp` because `simp` can prove it
+-- Porting note: removed `simp` because `simp` can prove it
 theorem SetCoe.forall {s : Set α} {p : s → Prop} : (∀ x : s, p x) ↔ ∀ (x) (h : x ∈ s), p ⟨x, h⟩ :=
   Subtype.forall
 #align set_coe.forall SetCoe.forall
 
--- Porting: removed `simp` because `simp` can prove it
+-- Porting note: removed `simp` because `simp` can prove it
 theorem SetCoe.exists {s : Set α} {p : s → Prop} :
     (∃ x : s, p x) ↔ ∃ (x : _) (h : x ∈ s), p ⟨x, h⟩ :=
   Subtype.exists
@@ -423,7 +423,7 @@ theorem not_mem_empty (x : α) : ¬x ∈ (∅ : Set α) :=
   id
 #align set.not_mem_empty Set.not_mem_empty
 
--- Porting: removed `simp` because `simp` can prove it
+-- Porting note: removed `simp` because `simp` can prove it
 theorem not_not_mem : ¬a ∉ s ↔ a ∈ s :=
   not_not
 #align set.not_not_mem Set.not_not_mem

chore: use · instead of . (#6085)

898a8e78

Diff

@@ -307,34 +307,34 @@ theorem setOf_or {p q : α → Prop} : { a | p a ∨ q a } = { a | p a } ∪ { a
 
 
 instance : IsRefl (Set α) (· ⊆ ·) :=
-  show IsRefl (Set α) (. ≤ .) by infer_instance
+  show IsRefl (Set α) (· ≤ ·) by infer_instance
 
 instance : IsTrans (Set α) (· ⊆ ·) :=
-  show IsTrans (Set α) (. ≤ .) by infer_instance
+  show IsTrans (Set α) (· ≤ ·) by infer_instance
 
 instance : Trans ((· ⊆ ·) : Set α → Set α → Prop) (· ⊆ ·) (· ⊆ ·) :=
-  show Trans (. ≤ .) (. ≤ .) (. ≤ .) by infer_instance
+  show Trans (· ≤ ·) (· ≤ ·) (· ≤ ·) by infer_instance
 
 instance : IsAntisymm (Set α) (· ⊆ ·) :=
-  show IsAntisymm (Set α) (. ≤ .) by infer_instance
+  show IsAntisymm (Set α) (· ≤ ·) by infer_instance
 
 instance : IsIrrefl (Set α) (· ⊂ ·) :=
-  show IsIrrefl (Set α) (. < .) by infer_instance
+  show IsIrrefl (Set α) (· < ·) by infer_instance
 
 instance : IsTrans (Set α) (· ⊂ ·) :=
-  show IsTrans (Set α) (. < .) by infer_instance
+  show IsTrans (Set α) (· < ·) by infer_instance
 
 instance : Trans ((· ⊂ ·) : Set α → Set α → Prop) (· ⊂ ·) (· ⊂ ·) :=
-  show Trans (. < .) (. < .) (. < .) by infer_instance
+  show Trans (· < ·) (· < ·) (· < ·) by infer_instance
 
 instance : Trans ((· ⊂ ·) : Set α → Set α → Prop) (· ⊆ ·) (· ⊂ ·) :=
-  show Trans (. < .) (. ≤ .) (. < .) by infer_instance
+  show Trans (· < ·) (· ≤ ·) (· < ·) by infer_instance
 
 instance : Trans ((· ⊆ ·) : Set α → Set α → Prop) (· ⊂ ·) (· ⊂ ·) :=
-  show Trans (. ≤ .) (. < .) (. < .) by infer_instance
+  show Trans (· ≤ ·) (· < ·) (· < ·) by infer_instance
 
 instance : IsAsymm (Set α) (· ⊂ ·) :=
-  show IsAsymm (Set α) (. < .) by infer_instance
+  show IsAsymm (Set α) (· < ·) by infer_instance
 
 instance : IsNonstrictStrictOrder (Set α) (· ⊆ ·) (· ⊂ ·) :=
   ⟨fun _ _ => Iff.rfl⟩

feat: basic measure / topology lemmas (#5986)

af306e0a

Diff

@@ -1700,6 +1700,10 @@ theorem nonempty_compl : sᶜ.Nonempty ↔ s ≠ univ :=
   (ne_univ_iff_exists_not_mem s).symm
 #align set.nonempty_compl Set.nonempty_compl
 
+@[simp] lemma nonempty_compl_of_nontrivial [Nontrivial α] (x : α) : Set.Nonempty {x}ᶜ := by
+  obtain ⟨y, hy⟩ := exists_ne x
+  exact ⟨y, by simp [hy]⟩
+
 theorem mem_compl_singleton_iff {a x : α} : x ∈ ({a} : Set α)ᶜ ↔ x ≠ a :=
   Iff.rfl
 #align set.mem_compl_singleton_iff Set.mem_compl_singleton_iff

chore: gcongr attributes for sup/inf, min/max, union/intersection/complement, image/preimage (#6016)

02f74960

Diff

@@ -828,14 +828,17 @@ theorem union_subset_iff {s t u : Set α} : s ∪ t ⊆ u ↔ s ⊆ u ∧ t ⊆
   (forall_congr' fun _ => or_imp).trans forall_and
 #align set.union_subset_iff Set.union_subset_iff
 
+@[gcongr]
 theorem union_subset_union {s₁ s₂ t₁ t₂ : Set α} (h₁ : s₁ ⊆ s₂) (h₂ : t₁ ⊆ t₂) :
     s₁ ∪ t₁ ⊆ s₂ ∪ t₂ := fun _ => Or.imp (@h₁ _) (@h₂ _)
 #align set.union_subset_union Set.union_subset_union
 
+@[gcongr]
 theorem union_subset_union_left {s₁ s₂ : Set α} (t) (h : s₁ ⊆ s₂) : s₁ ∪ t ⊆ s₂ ∪ t :=
   union_subset_union h Subset.rfl
 #align set.union_subset_union_left Set.union_subset_union_left
 
+@[gcongr]
 theorem union_subset_union_right (s) {t₁ t₂ : Set α} (h : t₁ ⊆ t₂) : s ∪ t₁ ⊆ s ∪ t₂ :=
   union_subset_union Subset.rfl h
 #align set.union_subset_union_right Set.union_subset_union_right
@@ -1005,14 +1008,17 @@ theorem univ_inter (a : Set α) : univ ∩ a = a :=
   top_inf_eq
 #align set.univ_inter Set.univ_inter
 
+@[gcongr]
 theorem inter_subset_inter {s₁ s₂ t₁ t₂ : Set α} (h₁ : s₁ ⊆ t₁) (h₂ : s₂ ⊆ t₂) :
     s₁ ∩ s₂ ⊆ t₁ ∩ t₂ := fun _ => And.imp (@h₁ _) (@h₂ _)
 #align set.inter_subset_inter Set.inter_subset_inter
 
+@[gcongr]
 theorem inter_subset_inter_left {s t : Set α} (u : Set α) (H : s ⊆ t) : s ∩ u ⊆ t ∩ u :=
   inter_subset_inter H Subset.rfl
 #align set.inter_subset_inter_left Set.inter_subset_inter_left
 
+@[gcongr]
 theorem inter_subset_inter_right {s t : Set α} (u : Set α) (H : s ⊆ t) : u ∩ s ⊆ u ∩ t :=
   inter_subset_inter Subset.rfl H
 #align set.inter_subset_inter_right Set.inter_subset_inter_right
@@ -1737,6 +1743,8 @@ theorem compl_subset_compl : sᶜ ⊆ tᶜ ↔ t ⊆ s :=
   @compl_le_compl_iff_le (Set α) _ _ _
 #align set.compl_subset_compl Set.compl_subset_compl
 
+@[gcongr] theorem compl_subset_compl_of_subset (h : t ⊆ s) : sᶜ ⊆ tᶜ := compl_subset_compl.2 h
+
 theorem subset_compl_iff_disjoint_left : s ⊆ tᶜ ↔ Disjoint t s :=
   @le_compl_iff_disjoint_left (Set α) _ _ _
 #align set.subset_compl_iff_disjoint_left Set.subset_compl_iff_disjoint_left

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) 2014 Jeremy Avigad. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Leonardo de Moura
-
-! This file was ported from Lean 3 source module data.set.basic
-! leanprover-community/mathlib commit 48fb5b5280e7c81672afc9524185ae994553ebf4
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Order.SymmDiff
 import Mathlib.Logic.Function.Iterate
 
+#align_import data.set.basic from "leanprover-community/mathlib"@"48fb5b5280e7c81672afc9524185ae994553ebf4"
+
 /-!
 # Basic properties of sets

chore: cleanup whitespace (#5988)

Grepping for [^ .:{-] [^ :] and reviewing the results. Once I started I couldn't stop. :-)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

12343aa5

Diff

@@ -316,7 +316,7 @@ instance : IsTrans (Set α) (· ⊆ ·) :=
   show IsTrans (Set α) (. ≤ .) by infer_instance
 
 instance : Trans ((· ⊆ ·) : Set α → Set α → Prop) (· ⊆ ·) (· ⊆ ·) :=
-  show Trans (. ≤ .) (. ≤ .)  (. ≤ .) by infer_instance
+  show Trans (. ≤ .) (. ≤ .) (. ≤ .) by infer_instance
 
 instance : IsAntisymm (Set α) (· ⊆ ·) :=
   show IsAntisymm (Set α) (. ≤ .) by infer_instance
@@ -328,13 +328,13 @@ instance : IsTrans (Set α) (· ⊂ ·) :=
   show IsTrans (Set α) (. < .) by infer_instance
 
 instance : Trans ((· ⊂ ·) : Set α → Set α → Prop) (· ⊂ ·) (· ⊂ ·) :=
-  show Trans (. < .) (. < .)  (. < .) by infer_instance
+  show Trans (. < .) (. < .) (. < .) by infer_instance
 
 instance : Trans ((· ⊂ ·) : Set α → Set α → Prop) (· ⊆ ·) (· ⊂ ·) :=
-  show Trans (. < .) (. ≤ .)  (. < .) by infer_instance
+  show Trans (. < .) (. ≤ .) (. < .) by infer_instance
 
 instance : Trans ((· ⊆ ·) : Set α → Set α → Prop) (· ⊂ ·) (· ⊂ ·) :=
-  show Trans (. ≤ .) (. < .)  (. < .) by infer_instance
+  show Trans (. ≤ .) (. < .) (. < .) by infer_instance
 
 instance : IsAsymm (Set α) (· ⊂ ·) :=
   show IsAsymm (Set α) (. < .) by infer_instance

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

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

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

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

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

c795bd35

Diff

@@ -226,7 +226,7 @@ theorem Subtype.mem {α : Type _} {s : Set α} (p : s) : (p : α) ∈ s :=
 
 /-- Duplicate of `Eq.subset'`, which currently has elaboration problems. -/
 theorem Eq.subset {α} {s t : Set α} : s = t → s ⊆ t :=
-  fun h₁ _ h₂ => by rw [← h₁] ; exact h₂
+  fun h₁ _ h₂ => by rw [← h₁]; exact h₂
 #align eq.subset Eq.subset
 
 namespace Set

chore: fix focusing dots (#5708)

This PR is the result of running

find . -type f -name "*.lean" -exec sed -i -E 's/^( +)\. /\1· /' {} \;
find . -type f -name "*.lean" -exec sed -i -E 'N;s/^( +·)\n +(.*)$/\1 \2/;P;D' {} \;

which firstly replaces . focusing dots with · and secondly removes isolated instances of such dots, unifying them with the following line. A new rule is placed in the style linter to verify this.

cb02d09e

Diff

@@ -2188,8 +2188,8 @@ theorem powerset_singleton (x : α) : 𝒫({x} : Set α) = {∅, {x}} := by
 theorem mem_dite (p : Prop) [Decidable p] (s : p → Set α) (t : ¬ p → Set α) (x : α) :
     (x ∈ if h : p then s h else t h) ↔ (∀ h : p, x ∈ s h) ∧ ∀ h : ¬p, x ∈ t h := by
   split_ifs with hp
-  . exact ⟨fun hx => ⟨fun _ => hx, fun hnp => (hnp hp).elim⟩, fun hx => hx.1 hp⟩
-  . exact ⟨fun hx => ⟨fun h => (hp h).elim, fun _ => hx⟩, fun hx => hx.2 hp⟩
+  · exact ⟨fun hx => ⟨fun _ => hx, fun hnp => (hnp hp).elim⟩, fun hx => hx.1 hp⟩
+  · exact ⟨fun hx => ⟨fun h => (hp h).elim, fun _ => hx⟩, fun hx => hx.2 hp⟩
 
 --Porting note: Old proof was `split_ifs; simp [h]`
 theorem mem_dite_univ_right (p : Prop) [Decidable p] (t : p → Set α) (x : α) :

refactor: move all register_simp_attrs to 1 file (#5681)

There are slight differences between mathlib3 and mathlib4 (different set of attributes, different lemmas are in core/std), so I redid the same refactor instead of forward-porting changes.

mathlib3 PR: leanprover-community/mathlib#19223

ceaa4ecb

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Leonardo de Moura
 
 ! This file was ported from Lean 3 source module data.set.basic
-! leanprover-community/mathlib commit 9ac7c0c8c4d7a535ec3e5b34b8859aab9233b2f4
+! leanprover-community/mathlib commit 48fb5b5280e7c81672afc9524185ae994553ebf4
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -254,7 +254,7 @@ theorem forall_in_swap {p : α → β → Prop} : (∀ a ∈ s, ∀ (b), p a b)
 
 /-! ### Lemmas about `mem` and `setOf` -/
 
-@[simp] theorem mem_setOf_eq {x : α} {p : α → Prop} : (x ∈ {y | p y}) = p x := rfl
+@[simp, mfld_simps] theorem mem_setOf_eq {x : α} {p : α → Prop} : (x ∈ {y | p y}) = p x := rfl
 #align set.mem_set_of_eq Set.mem_setOf_eq
 
 theorem mem_setOf {a : α} {p : α → Prop} : a ∈ { x | p x } ↔ p a :=
@@ -661,7 +661,7 @@ theorem setOf_true : { _x : α | True } = univ :=
   rfl
 #align set.set_of_true Set.setOf_true
 
-@[simp]
+@[simp, mfld_simps]
 theorem mem_univ (x : α) : x ∈ @univ α :=
   trivial
 #align set.mem_univ Set.mem_univ
@@ -891,7 +891,7 @@ theorem inter_def {s₁ s₂ : Set α} : s₁ ∩ s₂ = { a | a ∈ s₁ ∧ a
   rfl
 #align set.inter_def Set.inter_def
 
-@[simp]
+@[simp, mfld_simps]
 theorem mem_inter_iff (x : α) (a b : Set α) : x ∈ a ∩ b ↔ x ∈ a ∧ x ∈ b :=
   Iff.rfl
 #align set.mem_inter_iff Set.mem_inter_iff
@@ -947,7 +947,7 @@ theorem inter_right_comm (s₁ s₂ s₃ : Set α) : s₁ ∩ s₂ ∩ s₃ = s
   ext fun _ => and_right_comm
 #align set.inter_right_comm Set.inter_right_comm
 
-@[simp]
+@[simp, mfld_simps]
 theorem inter_subset_left (s t : Set α) : s ∩ t ⊆ s := fun _ => And.left
 #align set.inter_subset_left Set.inter_subset_left
 
@@ -998,12 +998,12 @@ theorem inter_eq_inter_iff_right : s ∩ u = t ∩ u ↔ t ∩ u ⊆ s ∧ s ∩
   inf_eq_inf_iff_right
 #align set.inter_eq_inter_iff_right Set.inter_eq_inter_iff_right
 
-@[simp]
+@[simp, mfld_simps]
 theorem inter_univ (a : Set α) : a ∩ univ = a :=
   inf_top_eq
 #align set.inter_univ Set.inter_univ
 
-@[simp]
+@[simp, mfld_simps]
 theorem univ_inter (a : Set α) : univ ∩ a = a :=
   top_inf_eq
 #align set.univ_inter Set.univ_inter

fix: change compl precedence (#5586)

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

4d4f0f25

Diff

@@ -1748,11 +1748,11 @@ theorem subset_compl_iff_disjoint_right : s ⊆ tᶜ ↔ Disjoint s t :=
   @le_compl_iff_disjoint_right (Set α) _ _ _
 #align set.subset_compl_iff_disjoint_right Set.subset_compl_iff_disjoint_right
 
-theorem disjoint_compl_left_iff_subset : Disjoint (sᶜ) t ↔ t ⊆ s :=
+theorem disjoint_compl_left_iff_subset : Disjoint sᶜ t ↔ t ⊆ s :=
   disjoint_compl_left_iff
 #align set.disjoint_compl_left_iff_subset Set.disjoint_compl_left_iff_subset
 
-theorem disjoint_compl_right_iff_subset : Disjoint s (tᶜ) ↔ s ⊆ t :=
+theorem disjoint_compl_right_iff_subset : Disjoint s tᶜ ↔ s ⊆ t :=
   disjoint_compl_right_iff
 #align set.disjoint_compl_right_iff_subset Set.disjoint_compl_right_iff_subset

feat(Data.Set.Basic/Data.Finset.Basic): rename insert_subset (#5450)

Currently, (for both Set and Finset) insert_subset is an iff lemma stating that insert a s ⊆ t if and only if a ∈ t and s ⊆ t. For both types, this PR renames this lemma to insert_subset_iff, and adds an insert_subset lemma that gives the implication just in the reverse direction : namely theorem insert_subset (ha : a ∈ t) (hs : s ⊆ t) : insert a s ⊆ t .

This both aligns the naming with union_subset and union_subset_iff, and removes the need for the awkward insert_subset.mpr ⟨_,_⟩ idiom. It touches a lot of files (too many to list), but in a trivial way.

d8b62864

Diff

@@ -1153,9 +1153,12 @@ theorem insert_ne_self : insert a s ≠ s ↔ a ∉ s :=
   insert_eq_self.not
 #align set.insert_ne_self Set.insert_ne_self
 
-theorem insert_subset : insert a s ⊆ t ↔ a ∈ t ∧ s ⊆ t := by
+theorem insert_subset_iff : insert a s ⊆ t ↔ a ∈ t ∧ s ⊆ t := by
   simp only [subset_def, mem_insert_iff, or_imp, forall_and, forall_eq]
-#align set.insert_subset Set.insert_subset
+#align set.insert_subset Set.insert_subset_iff
+
+theorem insert_subset (ha : a ∈ t) (hs : s ⊆ t) : insert a s ⊆ t :=
+  insert_subset_iff.mpr ⟨ha, hs⟩
 
 theorem insert_subset_insert (h : s ⊆ t) : insert a s ⊆ insert a t := fun _ => Or.imp_right (@h _)
 #align set.insert_subset_insert Set.insert_subset_insert
@@ -1171,7 +1174,7 @@ theorem subset_insert_iff_of_not_mem (ha : a ∉ s) : s ⊆ insert a t ↔ s ⊆
 #align set.subset_insert_iff_of_not_mem Set.subset_insert_iff_of_not_mem
 
 theorem ssubset_iff_insert {s t : Set α} : s ⊂ t ↔ ∃ (a : α) (_ : a ∉ s), insert a s ⊆ t := by
-  simp only [insert_subset, exists_and_right, ssubset_def, not_subset]
+  simp only [insert_subset_iff, exists_and_right, ssubset_def, not_subset]
   simp only [exists_prop, and_comm]
 #align set.ssubset_iff_insert Set.ssubset_iff_insert
 
@@ -1390,8 +1393,8 @@ theorem pair_comm (a b : α) : ({a, b} : Set α) = {b, a} :=
 -- Porting note: first branch after `constructor` used to be by `tauto!`.
 theorem pair_eq_pair_iff {x y z w : α} :
     ({x, y} : Set α) = {z, w} ↔ x = z ∧ y = w ∨ x = w ∧ y = z := by
-  simp only [Set.Subset.antisymm_iff, Set.insert_subset, Set.mem_insert_iff, Set.mem_singleton_iff,
-    Set.singleton_subset_iff]
+  simp only [Set.Subset.antisymm_iff, Set.insert_subset_iff, Set.mem_insert_iff,
+    Set.mem_singleton_iff, Set.singleton_subset_iff]
   constructor
   · rintro ⟨⟨rfl | rfl, rfl | rfl⟩, ⟨h₁, h₂⟩⟩ <;> simp [h₁, h₂] at * <;> simp [h₁, h₂]
   · rintro (⟨rfl, rfl⟩ | ⟨rfl, rfl⟩) <;> simp
@@ -2474,7 +2477,7 @@ theorem nontrivial_of_pair_subset {x y} (hxy : x ≠ y) (h : {x, y} ⊆ s) : s.N
 
 theorem Nontrivial.pair_subset (hs : s.Nontrivial) : ∃ (x y : _) (_ : x ≠ y), {x, y} ⊆ s :=
   let ⟨x, hx, y, hy, hxy⟩ := hs
-  ⟨x, y, hxy, insert_subset.2 ⟨hx, singleton_subset_iff.2 hy⟩⟩
+  ⟨x, y, hxy, insert_subset_iff.2 ⟨hx, singleton_subset_iff.2 hy⟩⟩
 #align set.nontrivial.pair_subset Set.Nontrivial.pair_subset
 
 theorem nontrivial_iff_pair_subset : s.Nontrivial ↔ ∃ (x y : _) (_ : x ≠ y), {x, y} ⊆ s :=

chore: tidy various files (#5268)

5f2c0b74

Diff

@@ -1583,9 +1583,10 @@ lemma disjoint_union_right : Disjoint s (t ∪ u) ↔ Disjoint s t ∧ Disjoint
 #align set.disjoint_univ Set.disjoint_univ
 
 lemma disjoint_sdiff_left : Disjoint (t \ s) s := disjoint_sdiff_self_left
+#align set.disjoint_sdiff_left Set.disjoint_sdiff_left
+
 lemma disjoint_sdiff_right : Disjoint s (t \ s) := disjoint_sdiff_self_right
 #align set.disjoint_sdiff_right Set.disjoint_sdiff_right
-#align set.disjoint_sdiff_left Set.disjoint_sdiff_left
 
 theorem diff_union_diff_cancel (hts : t ⊆ s) (hut : u ⊆ t) : s \ t ∪ t \ u = s \ u :=
   sdiff_sup_sdiff_cancel hts hut

feat: port Geometry.Euclidean.Circumcenter (#4446)

Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: qawbecrdtey <qawbecrdtey@naver.com> Co-authored-by: Moritz Firsching <firsching@google.com>

6b93a4a3

Diff

@@ -544,8 +544,9 @@ theorem Nonempty.to_subtype : s.Nonempty → Nonempty (↥s) :=
 theorem Nonempty.to_type : s.Nonempty → Nonempty α := fun ⟨x, _⟩ => ⟨x⟩
 #align set.nonempty.to_type Set.Nonempty.to_type
 
-instance [Nonempty α] : Nonempty (↥(Set.univ : Set α)) :=
+instance univ.nonempty [Nonempty α] : Nonempty (↥(Set.univ : Set α)) :=
   Set.univ_nonempty.to_subtype
+#align set.univ.nonempty Set.univ.nonempty
 
 theorem nonempty_of_nonempty_subtype [Nonempty (↥s)] : s.Nonempty :=
   nonempty_subtype.mp ‹_›

chore: formatting issues (#4947)

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

5068808d

Diff

@@ -189,12 +189,12 @@ theorem SetCoe.forall {s : Set α} {p : s → Prop} : (∀ x : s, p x) ↔ ∀ (
 
 -- Porting: removed `simp` because `simp` can prove it
 theorem SetCoe.exists {s : Set α} {p : s → Prop} :
-    (∃ x : s, p x) ↔ ∃ (x : _)(h : x ∈ s), p ⟨x, h⟩ :=
+    (∃ x : s, p x) ↔ ∃ (x : _) (h : x ∈ s), p ⟨x, h⟩ :=
   Subtype.exists
 #align set_coe.exists SetCoe.exists
 
 theorem SetCoe.exists' {s : Set α} {p : ∀ x, x ∈ s → Prop} :
-    (∃ (x : _)(h : x ∈ s), p x h) ↔ ∃ x : s, p x.1 x.2 :=
+    (∃ (x : _) (h : x ∈ s), p x h) ↔ ∃ x : s, p x.1 x.2 :=
   (@SetCoe.exists _ _ fun x => p x.1 x.2).symm
 #align set_coe.exists' SetCoe.exists'
 
@@ -1560,7 +1560,7 @@ lemma disjoint_of_subset_right (h : t ⊆ u) (d : Disjoint s u) : Disjoint s t :
 #align set.disjoint_of_subset_right Set.disjoint_of_subset_right
 
 lemma disjoint_of_subset (hs : s₁ ⊆ s₂) (ht : t₁ ⊆ t₂) (h : Disjoint s₂ t₂) : Disjoint s₁ t₁ :=
-h.mono hs ht
+  h.mono hs ht
 #align set.disjoint_of_subset Set.disjoint_of_subset
 
 @[simp]
@@ -1599,7 +1599,7 @@ lemma disjoint_singleton_left : Disjoint {a} s ↔ a ∉ s := by simp [Set.disjo
 
 @[simp]
 lemma disjoint_singleton_right : Disjoint s {a} ↔ a ∉ s :=
-disjoint_comm.trans disjoint_singleton_left
+  disjoint_comm.trans disjoint_singleton_left
 #align set.disjoint_singleton_right Set.disjoint_singleton_right
 
 lemma disjoint_singleton : Disjoint ({a} : Set α) {b} ↔ a ≠ b :=
@@ -2042,7 +2042,7 @@ theorem diff_self_inter {s t : Set α} : s \ (s ∩ t) = s \ t :=
 
 @[simp]
 theorem diff_singleton_eq_self {a : α} {s : Set α} (h : a ∉ s) : s \ {a} = s :=
-sdiff_eq_self_iff_disjoint.2 $ by simp [h]
+  sdiff_eq_self_iff_disjoint.2 $ by simp [h]
 #align set.diff_singleton_eq_self Set.diff_singleton_eq_self
 
 @[simp]
@@ -2617,20 +2617,20 @@ alias not_nontrivial_iff ↔ _ Subsingleton.not_nontrivial
 alias not_subsingleton_iff ↔ _ Nontrivial.not_subsingleton
 #align set.nontrivial.not_subsingleton Set.Nontrivial.not_subsingleton
 
-protected lemma subsingleton_or_nontrivial (s : Set α) : s.Subsingleton ∨ s.Nontrivial :=
-by simp [or_iff_not_imp_right]
+protected lemma subsingleton_or_nontrivial (s : Set α) : s.Subsingleton ∨ s.Nontrivial := by
+  simp [or_iff_not_imp_right]
 #align set.subsingleton_or_nontrivial Set.subsingleton_or_nontrivial
 
-lemma eq_singleton_or_nontrivial (ha : a ∈ s) : s = {a} ∨ s.Nontrivial :=
-by rw [←subsingleton_iff_singleton ha]; exact s.subsingleton_or_nontrivial
+lemma eq_singleton_or_nontrivial (ha : a ∈ s) : s = {a} ∨ s.Nontrivial := by
+  rw [←subsingleton_iff_singleton ha]; exact s.subsingleton_or_nontrivial
 #align set.eq_singleton_or_nontrivial Set.eq_singleton_or_nontrivial
 
 lemma nontrivial_iff_ne_singleton (ha : a ∈ s) : s.Nontrivial ↔ s ≠ {a} :=
-⟨Nontrivial.ne_singleton, (eq_singleton_or_nontrivial ha).resolve_left⟩
+  ⟨Nontrivial.ne_singleton, (eq_singleton_or_nontrivial ha).resolve_left⟩
 #align set.nontrivial_iff_ne_singleton Set.nontrivial_iff_ne_singleton
 
 lemma Nonempty.exists_eq_singleton_or_nontrivial : s.Nonempty → (∃ a, s = {a}) ∨ s.Nontrivial :=
-fun ⟨a, ha⟩ ↦ (eq_singleton_or_nontrivial ha).imp_left $ Exists.intro a
+  fun ⟨a, ha⟩ ↦ (eq_singleton_or_nontrivial ha).imp_left $ Exists.intro a
 #align set.nonempty.exists_eq_singleton_or_nontrivial Set.Nonempty.exists_eq_singleton_or_nontrivial
 
 theorem univ_eq_true_false : univ = ({True, False} : Set Prop) :=

chore: add space after exacts (#4945)

Too often tempted to change these during other PRs, so doing a mass edit here.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au>

bf799bb9

Diff

@@ -1162,7 +1162,7 @@ theorem insert_subset_insert (h : s ⊆ t) : insert a s ⊆ insert a t := fun _
 theorem insert_subset_insert_iff (ha : a ∉ s) : insert a s ⊆ insert a t ↔ s ⊆ t := by
   refine' ⟨fun h x hx => _, insert_subset_insert⟩
   rcases h (subset_insert _ _ hx) with (rfl | hxt)
-  exacts[(ha hx).elim, hxt]
+  exacts [(ha hx).elim, hxt]
 #align set.insert_subset_insert_iff Set.insert_subset_insert_iff
 
 theorem subset_insert_iff_of_not_mem (ha : a ∉ s) : s ⊆ insert a t ↔ s ⊆ t :=

chore: remove sup from union_congr_left statement (#4481)

This appears to have been accidental.

Added in https://github.com/leanprover-community/mathlib/pull/15439

3026bb9e

Diff

@@ -850,7 +850,8 @@ theorem subset_union_of_subset_right {s u : Set α} (h : s ⊆ u) (t : Set α) :
   Subset.trans h (subset_union_right t u)
 #align set.subset_union_of_subset_right Set.subset_union_of_subset_right
 
-theorem union_congr_left (ht : t ⊆ s ∪ u) (hu : u ⊆ s ∪ t) : s ∪ t = s ⊔ u :=
+-- Porting note: replaced `⊔` in RHS
+theorem union_congr_left (ht : t ⊆ s ∪ u) (hu : u ⊆ s ∪ t) : s ∪ t = s ∪ u :=
   sup_congr_left ht hu
 #align set.union_congr_left Set.union_congr_left

feat: add compile_inductive% and compile_def% commands (#4097)

Add a #compile inductive command to compile the recursors of an inductive type, which works by creating a recursive definition and using @[csimp].

Co-authored-by: Parth Shastri <31370288+cppio@users.noreply.github.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com>

63c31ccb

Diff

@@ -65,8 +65,16 @@ set, sets, subset, subsets, union, intersection, insert, singleton, complement,
 
 -/
 
-/-! ### Set coercion to a type -/
+-- https://github.com/leanprover/lean4/issues/2096
+compile_def% Union.union
+compile_def% Inter.inter
+compile_def% SDiff.sdiff
+compile_def% HasCompl.compl
+compile_def% EmptyCollection.emptyCollection
+compile_def% Insert.insert
+compile_def% Singleton.singleton
 
+/-! ### Set coercion to a type -/
 
 open Function
 
@@ -225,8 +233,7 @@ namespace Set
 
 variable {α : Type u} {β : Type v} {γ : Type w} {ι : Sort x} {a b : α} {s s₁ s₂ t t₁ t₂ u : Set α}
 
--- Porting note: remove `noncomputable` later
-noncomputable instance : Inhabited (Set α) :=
+instance : Inhabited (Set α) :=
   ⟨∅⟩
 
 attribute [ext] Set.ext

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

@@ -211,12 +211,12 @@ theorem SetCoe.ext_iff {s : Set α} {a b : s} : (↑a : α) = ↑b ↔ a = b :=
 
 end SetCoe
 
-/-- See also `subtype.prop` -/
+/-- See also `Subtype.prop` -/
 theorem Subtype.mem {α : Type _} {s : Set α} (p : s) : (p : α) ∈ s :=
   p.prop
 #align subtype.mem Subtype.mem
 
-/-- Duplicate of `eq.subset'`, which currently has elaboration problems. -/
+/-- Duplicate of `Eq.subset'`, which currently has elaboration problems. -/
 theorem Eq.subset {α} {s t : Set α} : s = t → s ⊆ t :=
   fun h₁ _ h₂ => by rw [← h₁] ; exact h₂
 #align eq.subset Eq.subset
@@ -2411,7 +2411,7 @@ theorem Subsingleton.coe_sort {s : Set α} : s.Subsingleton → Subsingleton s :
 #align set.subsingleton.coe_sort Set.Subsingleton.coe_sort
 
 /-- The `coe_sort` of a set `s` in a subsingleton type is a subsingleton.
-For the corresponding result for `subtype`, see `subtype.subsingleton`. -/
+For the corresponding result for `Subtype`, see `subtype.subsingleton`. -/
 instance subsingleton_coe_of_subsingleton [Subsingleton α] {s : Set α} : Subsingleton s := by
   rw [s.subsingleton_coe]
   exact subsingleton_of_subsingleton
@@ -2419,7 +2419,7 @@ instance subsingleton_coe_of_subsingleton [Subsingleton α] {s : Set α} : Subsi
 
 /-! ### Nontrivial -/
 
-/-- A set `s` is `nontrivial` if it has at least two distinct elements. -/
+/-- A set `s` is `Set.Nontrivial` if it has at least two distinct elements. -/
 protected def Nontrivial (s : Set α) : Prop :=
   ∃ (x : α) (_ : x ∈ s) (y : α) (_ : y ∈ s), x ≠ y
 #align set.nontrivial Set.Nontrivial

feat: add Mathlib.Tactic.Common, and import (#4056)

This makes a mathlib4 version of mathlib3's tactic.basic, now called Mathlib.Tactic.Common, which imports all tactics which do not have significant theory requirements, and then is imported all across the base of the hierarchy.

This ensures that all common tactics are available nearly everywhere in the library, rather than having to be imported one-by-one as you need them.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

a4eaf1c4

Diff

@@ -10,11 +10,6 @@ Authors: Jeremy Avigad, Leonardo de Moura
 -/
 import Mathlib.Order.SymmDiff
 import Mathlib.Logic.Function.Iterate
-import Mathlib.Tactic.Use
-import Mathlib.Tactic.SolveByElim
-import Mathlib.Tactic.Tauto
-import Mathlib.Tactic.ByContra
-import Mathlib.Tactic.Lift
 
 /-!
 # Basic properties of sets

closes #3680, see https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Stepping.20through.20simp_rw/near/326712986

feat: implement intermediate state for simp_rw (#3738)

ff334843

Diff

@@ -523,7 +523,7 @@ theorem inter_nonempty_iff_exists_left : (s ∩ t).Nonempty ↔ ∃ x ∈ s, x 
 #align set.inter_nonempty_iff_exists_left Set.inter_nonempty_iff_exists_left
 
 theorem inter_nonempty_iff_exists_right : (s ∩ t).Nonempty ↔ ∃ x ∈ t, x ∈ s := by
-  simp_rw [inter_nonempty, exists_prop, and_comm]
+  simp_rw [inter_nonempty, and_comm]
 #align set.inter_nonempty_iff_exists_right Set.inter_nonempty_iff_exists_right
 
 theorem nonempty_iff_univ_nonempty : Nonempty α ↔ (univ : Set α).Nonempty :=

chore: fix #align lines (#3640)

This PR fixes two things:

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

2b42dc7c

Diff

@@ -2582,7 +2582,6 @@ theorem nontrivial_coe_sort {s : Set α} : Nontrivial s ↔ s.Nontrivial := by
     exact ⟨x, Subtype.prop x, y, Subtype.prop y, fun h => hxy (Subtype.coe_injective h)⟩
   · rintro ⟨x, hx, y, hy, hxy⟩
     exact ⟨⟨x, hx⟩, mem_univ _, ⟨y, hy⟩, mem_univ _, Subtype.mk_eq_mk.not.mpr hxy⟩
-
 #align set.nontrivial_coe_sort Set.nontrivial_coe_sort
 
 alias nontrivial_coe_sort ↔ _ Nontrivial.coe_sort

Match https://github.com/leanprover-community/mathlib/pull/18729

feat: insert and erase lemmas (#3569)

04370794

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Leonardo de Moura
 
 ! This file was ported from Lean 3 source module data.set.basic
-! leanprover-community/mathlib commit 29cb56a7b35f72758b05a30490e1f10bd62c35c1
+! leanprover-community/mathlib commit 9ac7c0c8c4d7a535ec3e5b34b8859aab9233b2f4
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -1583,6 +1583,13 @@ lemma disjoint_sdiff_right : Disjoint s (t \ s) := disjoint_sdiff_self_right
 #align set.disjoint_sdiff_right Set.disjoint_sdiff_right
 #align set.disjoint_sdiff_left Set.disjoint_sdiff_left
 
+theorem diff_union_diff_cancel (hts : t ⊆ s) (hut : u ⊆ t) : s \ t ∪ t \ u = s \ u :=
+  sdiff_sup_sdiff_cancel hts hut
+#align set.diff_union_diff_cancel Set.diff_union_diff_cancel
+
+theorem diff_diff_eq_sdiff_union (h : u ⊆ s) : s \ (t \ u) = s \ t ∪ u := sdiff_sdiff_eq_sdiff_sup h
+#align set.diff_diff_eq_sdiff_union Set.diff_diff_eq_sdiff_union
+
 @[simp default+1]
 lemma disjoint_singleton_left : Disjoint {a} s ↔ a ∉ s := by simp [Set.disjoint_iff, subset_def]
 #align set.disjoint_singleton_left Set.disjoint_singleton_left

Match https://github.com/leanprover-community/mathlib/pull/18677

chore: Miscellaneous lemmas (#3213)

93bf16ce

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Leonardo de Moura
 
 ! This file was ported from Lean 3 source module data.set.basic
-! leanprover-community/mathlib commit 75608affb24b4f48699fbcd38f227827f7793771
+! leanprover-community/mathlib commit 29cb56a7b35f72758b05a30490e1f10bd62c35c1
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -1024,6 +1024,14 @@ theorem union_inter_cancel_right {s t : Set α} : (s ∪ t) ∩ t = t :=
   inter_eq_self_of_subset_right <| subset_union_right _ _
 #align set.union_inter_cancel_right Set.union_inter_cancel_right
 
+theorem inter_setOf_eq_sep (s : Set α) (p : α → Prop) : s ∩ {a | p a} = {a ∈ s | p a} :=
+  rfl
+#align set.inter_set_of_eq_sep Set.inter_setOf_eq_sep
+
+theorem setOf_inter_eq_sep (p : α → Prop) (s : Set α) : {a | p a} ∩ s = {a ∈ s | p a} :=
+  inter_comm _ _
+#align set.set_of_inter_eq_sep Set.setOf_inter_eq_sep
+
 /-! ### Distributivity laws -/
 
 
@@ -1303,6 +1311,9 @@ theorem singleton_subset_iff {a : α} {s : Set α} : {a} ⊆ s ↔ a ∈ s :=
   forall_eq
 #align set.singleton_subset_iff Set.singleton_subset_iff
 
+theorem singleton_subset_singleton : ({a} : Set α) ⊆ {b} ↔ a = b := by simp
+#align set.singleton_subset_singleton Set.singleton_subset_singleton
+
 theorem set_compr_eq_eq_singleton {a : α} : { b | b = a } = {a} :=
   rfl
 #align set.set_compr_eq_eq_singleton Set.set_compr_eq_eq_singleton
@@ -1588,6 +1599,14 @@ lemma disjoint_singleton : Disjoint ({a} : Set α) {b} ↔ a ≠ b :=
 lemma subset_diff : s ⊆ t \ u ↔ s ⊆ t ∧ Disjoint s u := le_iff_subset.symm.trans le_sdiff
 #align set.subset_diff Set.subset_diff
 
+theorem inter_diff_distrib_left (s t u : Set α) : s ∩ (t \ u) = (s ∩ t) \ (s ∩ u) :=
+  inf_sdiff_distrib_left _ _ _
+#align set.inter_diff_distrib_left Set.inter_diff_distrib_left
+
+theorem inter_diff_distrib_right (s t u : Set α) : s \ t ∩ u = (s ∩ u) \ (t ∩ u) :=
+  inf_sdiff_distrib_right _ _ _
+#align set.inter_diff_distrib_right Set.inter_diff_distrib_right
+
 /-! ### Lemmas about complement -/
 
 
@@ -2016,11 +2035,22 @@ theorem diff_singleton_eq_self {a : α} {s : Set α} (h : a ∉ s) : s \ {a} = s
 sdiff_eq_self_iff_disjoint.2 $ by simp [h]
 #align set.diff_singleton_eq_self Set.diff_singleton_eq_self
 
+@[simp]
+theorem diff_singleton_sSubset {s : Set α} {a : α} : s \ {a} ⊂ s ↔ a ∈ s :=
+  sdiff_le.lt_iff_ne.trans <| sdiff_eq_left.not.trans <| by simp
+#align set.diff_singleton_ssubset Set.diff_singleton_sSubset
+
 @[simp]
 theorem insert_diff_singleton {a : α} {s : Set α} : insert a (s \ {a}) = insert a s := by
   simp [insert_eq, union_diff_self, -union_singleton, -singleton_union]
 #align set.insert_diff_singleton Set.insert_diff_singleton
 
+theorem insert_diff_singleton_comm (hab : a ≠ b) (s : Set α) :
+    insert a (s \ {b}) = insert a s \ {b} := by
+  simp_rw [← union_singleton, union_diff_distrib,
+    diff_singleton_eq_self (mem_singleton_iff.not.2 hab.symm)]
+#align set.insert_diff_singleton_comm Set.insert_diff_singleton_comm
+
 --Porting note: removed `simp` attribute because `simp` can prove it
 theorem diff_self {s : Set α} : s \ s = ∅ :=
   sdiff_self

feat: Port/Combinatorics.Derangements.Basic (#2530)

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: ChrisHughes24 <chrishughes24@gmail.com>

19cc4324

Diff

@@ -2835,8 +2835,8 @@ instance decidableSetOf (p : α → Prop) [Decidable (p a)] : Decidable (a ∈ {
 #align set.decidable_set_of Set.decidableSetOf
 
 -- porting note: Lean 3 unfolded `{a}` before finding instances but Lean 4 needs additional help
-instance singletonDecidableMem {α: Type _} {a j: α} [DecidableEq α] :
-    Decidable (j ∈ ({a} : Set α)) := decidableSetOf j (fun (b : α) => b = a)
+instance decidableMemSingleton {a b : α} [DecidableEq α] :
+    Decidable (a ∈ ({b} : Set α)) := decidableSetOf _ (· = b)
 
 end Set

feat: add decidable instance to ∈ singleton (#2671)

Adds Decidable (j ∈ ({a} : Set α)) to help Lean 4 infer instances that Lean 3 automatically found

1c1520f6

Diff

@@ -2834,6 +2834,10 @@ instance decidableSetOf (p : α → Prop) [Decidable (p a)] : Decidable (a ∈ {
   assumption
 #align set.decidable_set_of Set.decidableSetOf
 
+-- porting note: Lean 3 unfolded `{a}` before finding instances but Lean 4 needs additional help
+instance singletonDecidableMem {α: Type _} {a j: α} [DecidableEq α] :
+    Decidable (j ∈ ({a} : Set α)) := decidableSetOf j (fun (b : α) => b = a)
+
 end Set
 
 /-! ### Monotone lemmas for sets -/

Match https://github.com/leanprover-community/mathlib/pull/18190

feat: forward-port leanprover-community/mathlib#18356 (#2000)

This is the corresponding forward porting PR to https://github.com/leanprover-community/mathlib/pull/18356 and https://github.com/leanprover-community/mathlib/pull/18491

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

daa9ead4

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Leonardo de Moura
 
 ! This file was ported from Lean 3 source module data.set.basic
-! leanprover-community/mathlib commit b875cbb7f2aa2b4c685aaa2f99705689c95322ad
+! leanprover-community/mathlib commit 75608affb24b4f48699fbcd38f227827f7793771
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -1154,6 +1154,10 @@ theorem insert_subset_insert_iff (ha : a ∉ s) : insert a s ⊆ insert a t ↔
   exacts[(ha hx).elim, hxt]
 #align set.insert_subset_insert_iff Set.insert_subset_insert_iff
 
+theorem subset_insert_iff_of_not_mem (ha : a ∉ s) : s ⊆ insert a t ↔ s ⊆ t :=
+  forall₂_congr <| fun _ hb => or_iff_right <| ne_of_mem_of_not_mem hb ha
+#align set.subset_insert_iff_of_not_mem Set.subset_insert_iff_of_not_mem
+
 theorem ssubset_iff_insert {s t : Set α} : s ⊂ t ↔ ∃ (a : α) (_ : a ∉ s), insert a s ⊆ t := by
   simp only [insert_subset, exists_and_right, ssubset_def, not_subset]
   simp only [exists_prop, and_comm]
@@ -2125,6 +2129,12 @@ theorem powerset_univ : 𝒫(univ : Set α) = univ :=
   eq_univ_of_forall subset_univ
 #align set.powerset_univ Set.powerset_univ
 
+/-- The powerset of a singleton contains only `∅` and the singleton itself. -/
+theorem powerset_singleton (x : α) : 𝒫({x} : Set α) = {∅, {x}} := by
+  ext y
+  rw [mem_powerset_iff, subset_singleton_iff_eq, mem_insert_iff, mem_singleton_iff]
+#align set.powerset_singleton Set.powerset_singleton
+
 /-! ### Sets defined as an if-then-else -/
 
 --Porting note: New theorem to prove `mem_dite` lemmas.

b875cbb7

feat: range (f ∘ e) = range f (#1616)

a379de2a

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Leonardo de Moura
 
 ! This file was ported from Lean 3 source module data.set.basic
-! leanprover-community/mathlib commit b86832321b586c6ac23ef8cdef6a7a27e42b13bd
+! leanprover-community/mathlib commit b875cbb7f2aa2b4c685aaa2f99705689c95322ad
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/

chore: add missing #align statements (#1902)

This PR is the result of a slight variant on the following "algorithm"

take all mathlib 3 names, remove _ and make all uppercase letters into lowercase
take all mathlib 4 names, remove _ and make all uppercase letters into lowercase
look for matches, and create pairs (original_lean3_name, OriginalLean4Name)
for pairs that do not have an align statement:
- use Lean 4 to lookup the file + position of the Lean 4 name
- add an #align statement just before the next empty line
manually fix some tiny mistakes (e.g., empty lines in proofs might cause the #align statement to have been inserted too early)

b72bb858

Diff

@@ -134,8 +134,10 @@ theorem lt_iff_ssubset : s < t ↔ s ⊂ t :=
 #align set.lt_iff_ssubset Set.lt_iff_ssubset
 
 alias le_iff_subset ↔ _root_.LE.le.subset _root_.HasSubset.Subset.le
+#align has_subset.subset.le HasSubset.Subset.le
 
 alias lt_iff_ssubset ↔ _root_.LT.lt.ssubset _root_.HasSSubset.SSubset.lt
+#align has_ssubset.ssubset.lt HasSSubset.SSubset.lt
 
 -- Porting note: I've introduced this abbreviation, with the `@[coe]` attribute,
 -- so that `norm_cast` has something to index on.
@@ -446,6 +448,7 @@ theorem nonempty_coe_sort {s : Set α} : Nonempty (↥s) ↔ s.Nonempty :=
 #align set.nonempty_coe_sort Set.nonempty_coe_sort
 
 alias nonempty_coe_sort ↔ _ Nonempty.coe_sort
+#align set.nonempty.coe_sort Set.Nonempty.coe_sort
 
 theorem nonempty_def : s.Nonempty ↔ ∃ x, x ∈ s :=
   Iff.rfl
@@ -605,6 +608,7 @@ theorem nonempty_iff_ne_empty : s.Nonempty ↔ s ≠ ∅ :=
 #align set.nonempty_iff_ne_empty Set.nonempty_iff_ne_empty
 
 alias nonempty_iff_ne_empty ↔ Nonempty.ne_empty _
+#align set.nonempty.ne_empty Set.Nonempty.ne_empty
 
 @[simp]
 theorem not_nonempty_empty : ¬(∅ : Set α).Nonempty := fun ⟨_, hx⟩ => hx
@@ -637,6 +641,7 @@ theorem empty_ssubset : ∅ ⊂ s ↔ s.Nonempty :=
 #align set.empty_ssubset Set.empty_ssubset
 
 alias empty_ssubset ↔ _ Nonempty.empty_ssubset
+#align set.nonempty.empty_ssubset Set.Nonempty.empty_ssubset
 
 /-!
 
@@ -677,6 +682,7 @@ theorem univ_subset_iff {s : Set α} : univ ⊆ s ↔ s = univ :=
 #align set.univ_subset_iff Set.univ_subset_iff
 
 alias univ_subset_iff ↔ eq_univ_of_univ_subset _
+#align set.eq_univ_of_univ_subset Set.eq_univ_of_univ_subset
 
 theorem eq_univ_iff_forall {s : Set α} : s = univ ↔ ∀ x, x ∈ s :=
   univ_subset_iff.symm.trans <| forall_congr' fun _ => imp_iff_right trivial
@@ -1517,6 +1523,7 @@ lemma not_disjoint_iff_nonempty_inter : ¬ Disjoint s t ↔ (s ∩ t).Nonempty :
 #align set.not_disjoint_iff_nonempty_inter Set.not_disjoint_iff_nonempty_inter
 
 alias not_disjoint_iff_nonempty_inter ↔ _ Nonempty.not_disjoint
+#align set.nonempty.not_disjoint Set.Nonempty.not_disjoint
 
 lemma disjoint_or_nonempty_inter (s t : Set α) : Disjoint s t ∨ (s ∩ t).Nonempty :=
   (em _).imp_right not_disjoint_iff_nonempty_inter.1
@@ -1558,6 +1565,8 @@ lemma disjoint_union_right : Disjoint s (t ∪ u) ↔ Disjoint s t ∧ Disjoint
 
 lemma disjoint_sdiff_left : Disjoint (t \ s) s := disjoint_sdiff_self_left
 lemma disjoint_sdiff_right : Disjoint s (t \ s) := disjoint_sdiff_self_right
+#align set.disjoint_sdiff_right Set.disjoint_sdiff_right
+#align set.disjoint_sdiff_left Set.disjoint_sdiff_left
 
 @[simp default+1]
 lemma disjoint_singleton_left : Disjoint {a} s ↔ a ∉ s := by simp [Set.disjoint_iff, subset_def]
@@ -1710,12 +1719,16 @@ theorem disjoint_compl_right_iff_subset : Disjoint s (tᶜ) ↔ s ⊆ t :=
 #align set.disjoint_compl_right_iff_subset Set.disjoint_compl_right_iff_subset
 
 alias subset_compl_iff_disjoint_right ↔ _ _root_.Disjoint.subset_compl_right
+#align disjoint.subset_compl_right Disjoint.subset_compl_right
 
 alias subset_compl_iff_disjoint_left ↔ _ _root_.Disjoint.subset_compl_left
+#align disjoint.subset_compl_left Disjoint.subset_compl_left
 
 alias disjoint_compl_left_iff_subset ↔ _ _root_.HasSubset.Subset.disjoint_compl_left
+#align has_subset.subset.disjoint_compl_left HasSubset.Subset.disjoint_compl_left
 
 alias disjoint_compl_right_iff_subset ↔ _ _root_.HasSubset.Subset.disjoint_compl_right
+#align has_subset.subset.disjoint_compl_right HasSubset.Subset.disjoint_compl_right
 
 theorem subset_union_compl_iff_inter_subset {s t u : Set α} : s ⊆ t ∪ uᶜ ↔ s ∩ u ⊆ t :=
   (@isCompl_compl _ u _).le_sup_right_iff_inf_left_le
@@ -2526,6 +2539,7 @@ theorem nontrivial_coe_sort {s : Set α} : Nontrivial s ↔ s.Nontrivial := by
 #align set.nontrivial_coe_sort Set.nontrivial_coe_sort
 
 alias nontrivial_coe_sort ↔ _ Nontrivial.coe_sort
+#align set.nontrivial.coe_sort Set.Nontrivial.coe_sort
 
 /-- A type with a set `s` whose `coe_sort` is a nontrivial type is nontrivial.
 For the corresponding result for `Subtype`, see `Subtype.nontrivial_iff_exists_ne`. -/
@@ -2549,8 +2563,10 @@ theorem not_nontrivial_iff : ¬s.Nontrivial ↔ s.Subsingleton :=
 #align set.not_nontrivial_iff Set.not_nontrivial_iff
 
 alias not_nontrivial_iff ↔ _ Subsingleton.not_nontrivial
+#align set.subsingleton.not_nontrivial Set.Subsingleton.not_nontrivial
 
 alias not_subsingleton_iff ↔ _ Nontrivial.not_subsingleton
+#align set.nontrivial.not_subsingleton Set.Nontrivial.not_subsingleton
 
 protected lemma subsingleton_or_nontrivial (s : Set α) : s.Subsingleton ∨ s.Nontrivial :=
 by simp [or_iff_not_imp_right]

chore: Rename Type* to Type _ (#1866)

A bunch of docstrings were still mentioning Type*. This changes them to Type _.

50036b41

Diff

@@ -62,7 +62,7 @@ Definitions in the file:
 * `s.Nonempty` is to be preferred to `s ≠ ∅` or `∃ x, x ∈ s`. It has the advantage that
 the `s.Nonempty` dot notation can be used.
 
-* For `s : Set α`, do not use `Subtype s`. Instead use `↥s` or `(s : Type*)` or `s`.
+* For `s : Set α`, do not use `Subtype s`. Instead use `↥s` or `(s : Type _)` or `s`.
 
 ## Tags

Fix: fix case in a dot notation lemma (#1886)

cd8220b7

Diff

@@ -260,9 +260,9 @@ theorem mem_setOf {a : α} {p : α → Prop} : a ∈ { x | p x } ↔ p a :=
 /-- If `h : a ∈ {x | p x}` then `h.out : p x`. These are definitionally equal, but this can
 nevertheless be useful for various reasons, e.g. to apply further projection notation or in an
 argument to `simp`. -/
-theorem _root_.Membership.Mem.out {p : α → Prop} {a : α} (h : a ∈ { x | p x }) : p a :=
+theorem _root_.Membership.mem.out {p : α → Prop} {a : α} (h : a ∈ { x | p x }) : p a :=
   h
-#align has_mem.mem.out Membership.Mem.out
+#align has_mem.mem.out Membership.mem.out
 
 theorem nmem_setOf_iff {a : α} {p : α → Prop} : a ∉ { x | p x } ↔ ¬p a :=
   Iff.rfl

chore: format by line breaks (#1523)

During porting, I usually fix the desired format we seem to want for the line breaks around by with

awk '{do {{if (match($0, "^  by$") && length(p) < 98) {p=p " by";} else {if (NR!=1) {print p}; p=$0}}} while (getline == 1) if (getline==0) print p}' Mathlib/File/Im/Working/On.lean

I noticed there are some more files that slipped through.

This pull request is the result of running this command:

grep -lr "^  by\$" Mathlib | xargs -n 1 awk -i inplace '{do {{if (match($0, "^  by$") && length(p) < 98 && not (match(p, "^[ \t]*--"))) {p=p " by";} else {if (NR!=1) {print p}; p=$0}}} while (getline == 1) if (getline==0) print p}'

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

d6d859a7

Diff

@@ -2655,8 +2655,7 @@ downright. -/
 theorem not_monotoneOn_not_antitoneOn_iff_exists_le_le :
     ¬MonotoneOn f s ∧ ¬AntitoneOn f s ↔
       ∃ (a : α) (_ : a ∈ s) (b : α) (_ : b ∈ s) (c : α) (_ : c ∈ s),
-        a ≤ b ∧ b ≤ c ∧ (f a < f b ∧ f c < f b ∨ f b < f a ∧ f b < f c) :=
-  by
+        a ≤ b ∧ b ≤ c ∧ (f a < f b ∧ f c < f b ∨ f b < f a ∧ f b < f c) := by
   simp [monotoneOn_iff_monotone, antitoneOn_iff_antitone, and_assoc, exists_and_left,
     not_monotone_not_antitone_iff_exists_le_le, @and_left_comm (_ ∈ s)]
 #align set.not_monotone_on_not_antitone_on_iff_exists_le_le Set.not_monotoneOn_not_antitoneOn_iff_exists_le_le
@@ -2666,8 +2665,7 @@ downright. -/
 theorem not_monotoneOn_not_antitoneOn_iff_exists_lt_lt :
     ¬MonotoneOn f s ∧ ¬AntitoneOn f s ↔
       ∃ (a : α) (_ : a ∈ s) (b : α) (_ : b ∈ s) (c : α) (_ : c ∈ s),
-        a < b ∧ b < c ∧ (f a < f b ∧ f c < f b ∨ f b < f a ∧ f b < f c) :=
-  by
+        a < b ∧ b < c ∧ (f a < f b ∧ f c < f b ∨ f b < f a ∧ f b < f c) := by
   simp [monotoneOn_iff_monotone, antitoneOn_iff_antitone, and_assoc, exists_and_left,
     not_monotone_not_antitone_iff_exists_lt_lt, @and_left_comm (_ ∈ s)]
 #align set.not_monotone_on_not_antitone_on_iff_exists_lt_lt Set.not_monotoneOn_not_antitoneOn_iff_exists_lt_lt

chore: the style linter shouldn't complain about long #align lines (#1643)

54af0498

Diff

@@ -2340,9 +2340,7 @@ theorem exists_eq_singleton_iff_nonempty_subsingleton :
   · rintro ⟨a, rfl⟩
     exact ⟨singleton_nonempty a, subsingleton_singleton⟩
   · exact h.2.eq_empty_or_singleton.resolve_left h.1.ne_empty
-#align
-  set.exists_eq_singleton_iff_nonempty_subsingleton
-  Set.exists_eq_singleton_iff_nonempty_subsingleton
+#align set.exists_eq_singleton_iff_nonempty_subsingleton Set.exists_eq_singleton_iff_nonempty_subsingleton
 
 /-- `s`, coerced to a type, is a subsingleton type if and only if `s` is a subsingleton set. -/
 @[simp, norm_cast]
@@ -2661,9 +2659,7 @@ theorem not_monotoneOn_not_antitoneOn_iff_exists_le_le :
   by
   simp [monotoneOn_iff_monotone, antitoneOn_iff_antitone, and_assoc, exists_and_left,
     not_monotone_not_antitone_iff_exists_le_le, @and_left_comm (_ ∈ s)]
-#align
-  set.not_monotone_on_not_antitone_on_iff_exists_le_le
-  Set.not_monotoneOn_not_antitoneOn_iff_exists_le_le
+#align set.not_monotone_on_not_antitone_on_iff_exists_le_le Set.not_monotoneOn_not_antitoneOn_iff_exists_le_le
 
 /-- A function between linear orders which is neither monotone nor antitone makes a dent upright or
 downright. -/
@@ -2674,9 +2670,7 @@ theorem not_monotoneOn_not_antitoneOn_iff_exists_lt_lt :
   by
   simp [monotoneOn_iff_monotone, antitoneOn_iff_antitone, and_assoc, exists_and_left,
     not_monotone_not_antitone_iff_exists_lt_lt, @and_left_comm (_ ∈ s)]
-#align
-  set.not_monotone_on_not_antitone_on_iff_exists_lt_lt
-  Set.not_monotoneOn_not_antitoneOn_iff_exists_lt_lt
+#align set.not_monotone_on_not_antitone_on_iff_exists_lt_lt Set.not_monotoneOn_not_antitoneOn_iff_exists_lt_lt
 
 end LinearOrder

refactor: use semi-implicit brackets for Set.HasSubset; dedup instances (#1550)

Dan Velleman observed that both Mathlib.Init.Set and Mathlib.Data.Set.Basic have definitions of subset, intersection and union, and they are slightly different since in Init.Set the brackets were implicit and in Set.Basic they were semi-implicit. In this PR we make the situation consistent by moving the semi-implicit definition to Init.Set and removing the duplicate definitions from Set.Basic.

~~I don't have much time to do fixes in the coming two days;~~ Feel free to push to this branch!

Closes: #738

Co-authored-by: Anne Baanen <t.baanen@vu.nl>

d1e6d864

Diff

@@ -81,18 +81,12 @@ namespace Set
 
 variable {α : Type _} {s t : Set α}
 
-instance : LE (Set α) :=
-  ⟨fun s t => ∀ ⦃x⦄, x ∈ s → x ∈ t⟩
-
-instance : HasSubset (Set α) :=
-  ⟨(· ≤ ·)⟩
-
 instance {α : Type _} : BooleanAlgebra (Set α) :=
   { (inferInstance : BooleanAlgebra (α → Prop)) with
-    sup := fun s t => { x | x ∈ s ∨ x ∈ t },
+    sup := (· ∪ ·),
     le := (· ≤ ·),
     lt := fun s t => s ⊆ t ∧ ¬t ⊆ s,
-    inf := fun s t => { x | x ∈ s ∧ x ∈ t },
+    inf := (· ∩ ·),
     bot := ∅,
     compl := fun s => { x | x ∉ s },
     top := univ,
@@ -101,12 +95,6 @@ instance {α : Type _} : BooleanAlgebra (Set α) :=
 instance : HasSSubset (Set α) :=
   ⟨(· < ·)⟩
 
-instance : Union (Set α) :=
-  ⟨(· ⊔ ·)⟩
-
-instance : Inter (Set α) :=
-  ⟨(· ⊓ ·)⟩
-
 @[simp]
 theorem top_eq_univ : (⊤ : Set α) = univ :=
   rfl
@@ -2103,7 +2091,7 @@ theorem powerset_inter (s t : Set α) : 𝒫(s ∩ t) = 𝒫 s ∩ 𝒫 t :=
 
 @[simp]
 theorem powerset_mono : 𝒫 s ⊆ 𝒫 t ↔ s ⊆ t :=
-  ⟨fun h => @h _ (fun h => h), fun h _ hu _ ha => h (hu ha)⟩
+  ⟨fun h => @h _ (fun _ h => h), fun h _ hu _ ha => h (hu ha)⟩
 #align set.powerset_mono Set.powerset_mono
 
 theorem monotone_powerset : Monotone (powerset : Set α → Set (Set α)) := fun _ _ => powerset_mono.2
@@ -2111,7 +2099,7 @@ theorem monotone_powerset : Monotone (powerset : Set α → Set (Set α)) := fun
 
 @[simp]
 theorem powerset_nonempty : (𝒫 s).Nonempty :=
-  ⟨∅, fun h => empty_subset s h⟩
+  ⟨∅, fun _ h => empty_subset s h⟩
 #align set.powerset_nonempty Set.powerset_nonempty
 
 @[simp]

Match https://github.com/leanprover-community/mathlib/pull/17901 and https://github.com/leanprover-community/mathlib/pull/17957

feat: A set is either a subsingleton or nontrivial (#1047)

ca98f897

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Leonardo de Moura
 
 ! This file was ported from Lean 3 source module data.set.basic
-! leanprover-community/mathlib commit 3d95492390dc90e34184b13e865f50bc67f30fbb
+! leanprover-community/mathlib commit b86832321b586c6ac23ef8cdef6a7a27e42b13bd
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -238,7 +238,7 @@ theorem Eq.subset {α} {s t : Set α} : s = t → s ⊆ t :=
 
 namespace Set
 
-variable {α : Type u} {β : Type v} {γ : Type w} {ι : Sort x} {a b : α} {s t u : Set α}
+variable {α : Type u} {β : Type v} {γ : Type w} {ι : Sort x} {a b : α} {s s₁ s₂ t t₁ t₂ u : Set α}
 
 -- Porting note: remove `noncomputable` later
 noncomputable instance : Inhabited (Set α) :=
@@ -1518,9 +1518,75 @@ theorem disjoint_left : Disjoint s t ↔ ∀ ⦃a⦄, a ∈ s → a ∉ t :=
   disjoint_iff_inf_le.trans <| forall_congr' fun _ => not_and
 #align set.disjoint_left Set.disjoint_left
 
-theorem disjoint_right : Disjoint s t ↔ ∀ ⦃a⦄, a ∈ t → a ∉ s := by rw [Disjoint.comm, disjoint_left]
+theorem disjoint_right : Disjoint s t ↔ ∀ ⦃a⦄, a ∈ t → a ∉ s := by rw [disjoint_comm, disjoint_left]
 #align set.disjoint_right Set.disjoint_right
 
+lemma not_disjoint_iff : ¬Disjoint s t ↔ ∃ x, x ∈ s ∧ x ∈ t :=
+  Set.disjoint_iff.not.trans $ not_forall.trans $ exists_congr fun _ ↦ not_not
+#align set.not_disjoint_iff Set.not_disjoint_iff
+
+lemma not_disjoint_iff_nonempty_inter : ¬ Disjoint s t ↔ (s ∩ t).Nonempty := not_disjoint_iff
+#align set.not_disjoint_iff_nonempty_inter Set.not_disjoint_iff_nonempty_inter
+
+alias not_disjoint_iff_nonempty_inter ↔ _ Nonempty.not_disjoint
+
+lemma disjoint_or_nonempty_inter (s t : Set α) : Disjoint s t ∨ (s ∩ t).Nonempty :=
+  (em _).imp_right not_disjoint_iff_nonempty_inter.1
+#align set.disjoint_or_nonempty_inter Set.disjoint_or_nonempty_inter
+
+lemma disjoint_iff_forall_ne : Disjoint s t ↔ ∀ ⦃a⦄, a ∈ s → ∀ ⦃b⦄, b ∈ t → a ≠ b := by
+  simp only [Ne.def, disjoint_left, @imp_not_comm _ (_ = _), forall_eq']
+#align set.disjoint_iff_forall_ne Set.disjoint_iff_forall_ne
+
+alias disjoint_iff_forall_ne ↔ _root_.Disjoint.ne_of_mem _
+#align disjoint.ne_of_mem Disjoint.ne_of_mem
+
+lemma disjoint_of_subset_left (h : s ⊆ u) (d : Disjoint u t) : Disjoint s t := d.mono_left h
+#align set.disjoint_of_subset_left Set.disjoint_of_subset_left
+lemma disjoint_of_subset_right (h : t ⊆ u) (d : Disjoint s u) : Disjoint s t := d.mono_right h
+#align set.disjoint_of_subset_right Set.disjoint_of_subset_right
+
+lemma disjoint_of_subset (hs : s₁ ⊆ s₂) (ht : t₁ ⊆ t₂) (h : Disjoint s₂ t₂) : Disjoint s₁ t₁ :=
+h.mono hs ht
+#align set.disjoint_of_subset Set.disjoint_of_subset
+
+@[simp]
+lemma disjoint_union_left : Disjoint (s ∪ t) u ↔ Disjoint s u ∧ Disjoint t u := disjoint_sup_left
+#align set.disjoint_union_left Set.disjoint_union_left
+
+@[simp]
+lemma disjoint_union_right : Disjoint s (t ∪ u) ↔ Disjoint s t ∧ Disjoint s u := disjoint_sup_right
+#align set.disjoint_union_right Set.disjoint_union_right
+
+@[simp] lemma disjoint_empty (s : Set α) : Disjoint s ∅ := disjoint_bot_right
+#align set.disjoint_empty Set.disjoint_empty
+@[simp] lemma empty_disjoint (s : Set α) : Disjoint ∅ s := disjoint_bot_left
+#align set.empty_disjoint Set.empty_disjoint
+
+@[simp] lemma univ_disjoint : Disjoint univ s ↔ s = ∅ := top_disjoint
+#align set.univ_disjoint Set.univ_disjoint
+@[simp] lemma disjoint_univ : Disjoint s univ ↔ s = ∅ := disjoint_top
+#align set.disjoint_univ Set.disjoint_univ
+
+lemma disjoint_sdiff_left : Disjoint (t \ s) s := disjoint_sdiff_self_left
+lemma disjoint_sdiff_right : Disjoint s (t \ s) := disjoint_sdiff_self_right
+
+@[simp default+1]
+lemma disjoint_singleton_left : Disjoint {a} s ↔ a ∉ s := by simp [Set.disjoint_iff, subset_def]
+#align set.disjoint_singleton_left Set.disjoint_singleton_left
+
+@[simp]
+lemma disjoint_singleton_right : Disjoint s {a} ↔ a ∉ s :=
+disjoint_comm.trans disjoint_singleton_left
+#align set.disjoint_singleton_right Set.disjoint_singleton_right
+
+lemma disjoint_singleton : Disjoint ({a} : Set α) {b} ↔ a ≠ b :=
+  by simp
+#align set.disjoint_singleton Set.disjoint_singleton
+
+lemma subset_diff : s ⊆ t \ u ↔ s ⊆ t ∧ Disjoint s u := le_iff_subset.symm.trans le_sdiff
+#align set.subset_diff Set.subset_diff
+
 /-! ### Lemmas about complement -/
 
 
@@ -1940,14 +2006,9 @@ theorem diff_self_inter {s t : Set α} : s \ (s ∩ t) = s \ t :=
   sdiff_inf_self_left _ _
 #align set.diff_self_inter Set.diff_self_inter
 
-@[simp]
-theorem diff_eq_self {s t : Set α} : s \ t = s ↔ t ∩ s ⊆ ∅ :=
-  show s \ t = s ↔ t ⊓ s ≤ ⊥ from sdiff_eq_self_iff_disjoint.trans disjoint_iff_inf_le
-#align set.diff_eq_self Set.diff_eq_self
-
 @[simp]
 theorem diff_singleton_eq_self {a : α} {s : Set α} (h : a ∉ s) : s \ {a} = s :=
-  diff_eq_self.2 <| by simp [singleton_inter_eq_empty.2 h]
+sdiff_eq_self_iff_disjoint.2 $ by simp [h]
 #align set.diff_singleton_eq_self Set.diff_singleton_eq_self
 
 @[simp]
@@ -2505,6 +2566,22 @@ alias not_nontrivial_iff ↔ _ Subsingleton.not_nontrivial
 
 alias not_subsingleton_iff ↔ _ Nontrivial.not_subsingleton
 
+protected lemma subsingleton_or_nontrivial (s : Set α) : s.Subsingleton ∨ s.Nontrivial :=
+by simp [or_iff_not_imp_right]
+#align set.subsingleton_or_nontrivial Set.subsingleton_or_nontrivial
+
+lemma eq_singleton_or_nontrivial (ha : a ∈ s) : s = {a} ∨ s.Nontrivial :=
+by rw [←subsingleton_iff_singleton ha]; exact s.subsingleton_or_nontrivial
+#align set.eq_singleton_or_nontrivial Set.eq_singleton_or_nontrivial
+
+lemma nontrivial_iff_ne_singleton (ha : a ∈ s) : s.Nontrivial ↔ s ≠ {a} :=
+⟨Nontrivial.ne_singleton, (eq_singleton_or_nontrivial ha).resolve_left⟩
+#align set.nontrivial_iff_ne_singleton Set.nontrivial_iff_ne_singleton
+
+lemma Nonempty.exists_eq_singleton_or_nontrivial : s.Nonempty → (∃ a, s = {a}) ∨ s.Nontrivial :=
+fun ⟨a, ha⟩ ↦ (eq_singleton_or_nontrivial ha).imp_left $ Exists.intro a
+#align set.nonempty.exists_eq_singleton_or_nontrivial Set.Nonempty.exists_eq_singleton_or_nontrivial
+
 theorem univ_eq_true_false : univ = ({True, False} : Set Prop) :=
   Eq.symm <| eq_univ_of_forall <| fun x => by
     rw [mem_insert_iff, mem_singleton_iff]
@@ -2819,8 +2896,6 @@ end Monotone
 
 /-! ### Disjoint sets -/
 
-section Disjoint
-
 variable {α β : Type _} {s t u : Set α} {f : α → β}
 
 namespace Disjoint
@@ -2858,97 +2933,3 @@ theorem subset_right_of_subset_union (h : s ⊆ t ∪ u) (hab : Disjoint s t) :
 #align disjoint.subset_right_of_subset_union Disjoint.subset_right_of_subset_union
 
 end Disjoint
-
-namespace Set
-
-theorem not_disjoint_iff : ¬Disjoint s t ↔ ∃ x, x ∈ s ∧ x ∈ t :=
-  Set.disjoint_iff.not.trans <| not_forall.trans <| exists_congr fun _ => not_not
-#align set.not_disjoint_iff Set.not_disjoint_iff
-
-theorem not_disjoint_iff_nonempty_inter : ¬Disjoint s t ↔ (s ∩ t).Nonempty :=
-  not_disjoint_iff
-#align set.not_disjoint_iff_nonempty_inter Set.not_disjoint_iff_nonempty_inter
-
-alias not_disjoint_iff_nonempty_inter ↔ _ Nonempty.not_disjoint
-
-theorem disjoint_or_nonempty_inter (s t : Set α) : Disjoint s t ∨ (s ∩ t).Nonempty :=
-  (em _).imp_right not_disjoint_iff_nonempty_inter.mp
-#align set.disjoint_or_nonempty_inter Set.disjoint_or_nonempty_inter
-
-theorem disjoint_iff_forall_ne : Disjoint s t ↔ ∀ x ∈ s, ∀ y ∈ t, x ≠ y := by
-  simp only [Ne.def, disjoint_left, @imp_not_comm _ (_ = _), forall_eq']
-#align set.disjoint_iff_forall_ne Set.disjoint_iff_forall_ne
-
-theorem _root_.Disjoint.ne_of_mem (h : Disjoint s t) {x y} (hx : x ∈ s) (hy : y ∈ t) : x ≠ y :=
-  disjoint_iff_forall_ne.mp h x hx y hy
-#align disjoint.ne_of_mem Disjoint.ne_of_mem
-
-theorem disjoint_of_subset_left (h : s ⊆ u) (d : Disjoint u t) : Disjoint s t :=
-  d.mono_left h
-#align set.disjoint_of_subset_left Set.disjoint_of_subset_left
-
-theorem disjoint_of_subset_right (h : t ⊆ u) (d : Disjoint s u) : Disjoint s t :=
-  d.mono_right h
-#align set.disjoint_of_subset_right Set.disjoint_of_subset_right
-
-theorem disjoint_of_subset {s t u v : Set α} (h1 : s ⊆ u) (h2 : t ⊆ v) (d : Disjoint u v) :
-    Disjoint s t :=
-  d.mono h1 h2
-#align set.disjoint_of_subset Set.disjoint_of_subset
-
-@[simp]
-theorem disjoint_union_left : Disjoint (s ∪ t) u ↔ Disjoint s u ∧ Disjoint t u :=
-  disjoint_sup_left
-#align set.disjoint_union_left Set.disjoint_union_left
-
-@[simp]
-theorem disjoint_union_right : Disjoint s (t ∪ u) ↔ Disjoint s t ∧ Disjoint s u :=
-  disjoint_sup_right
-#align set.disjoint_union_right Set.disjoint_union_right
-
-theorem disjoint_diff {a b : Set α} : Disjoint a (b \ a) :=
-  disjoint_iff.2 (inter_diff_self _ _)
-#align set.disjoint_diff Set.disjoint_diff
-
-@[simp]
-theorem disjoint_empty (s : Set α) : Disjoint s ∅ :=
-  disjoint_bot_right
-#align set.disjoint_empty Set.disjoint_empty
-
-@[simp]
-theorem empty_disjoint (s : Set α) : Disjoint ∅ s :=
-  disjoint_bot_left
-#align set.empty_disjoint Set.empty_disjoint
-
-@[simp]
-theorem univ_disjoint {s : Set α} : Disjoint univ s ↔ s = ∅ :=
-  top_disjoint
-#align set.univ_disjoint Set.univ_disjoint
-
-@[simp]
-theorem disjoint_univ {s : Set α} : Disjoint s univ ↔ s = ∅ :=
-  disjoint_top
-#align set.disjoint_univ Set.disjoint_univ
-
-@[simp default+1]
-theorem disjoint_singleton_left {a : α} {s : Set α} : Disjoint {a} s ↔ a ∉ s :=
-  by simp [Set.disjoint_iff, subset_def]
-#align set.disjoint_singleton_left Set.disjoint_singleton_left
-
-@[simp]
-theorem disjoint_singleton_right {a : α} {s : Set α} : Disjoint s {a} ↔ a ∉ s :=
-  by rw [Disjoint.comm]; exact disjoint_singleton_left
-#align set.disjoint_singleton_right Set.disjoint_singleton_right
-
-theorem disjoint_singleton {a b : α} : Disjoint ({a} : Set α) {b} ↔ a ≠ b :=
-  by simp
-#align set.disjoint_singleton Set.disjoint_singleton
-
-theorem subset_diff {s t u : Set α} : s ⊆ t \ u ↔ s ⊆ t ∧ Disjoint s u :=
-  ⟨fun h => ⟨fun _ hxs => (h hxs).1, disjoint_iff_inf_le.mpr fun _ ⟨hxs, hxu⟩ => (h hxs).2 hxu⟩,
-    fun ⟨h1, h2⟩ _ hxs => ⟨h1 hxs, fun hxu => h2.le_bot ⟨hxs, hxu⟩⟩⟩
-#align set.subset_diff Set.subset_diff
-
-end Set
-
-end Disjoint

feat: port some CanLift instances, restore lift tactic usage (#1425)

93812b0f

Diff

@@ -14,6 +14,7 @@ import Mathlib.Tactic.Use
 import Mathlib.Tactic.SolveByElim
 import Mathlib.Tactic.Tauto
 import Mathlib.Tactic.ByContra
+import Mathlib.Tactic.Lift
 
 /-!
 # Basic properties of sets
@@ -161,16 +162,15 @@ alias lt_iff_ssubset ↔ _root_.LT.lt.ssubset _root_.HasSSubset.SSubset.lt
 instance {α : Type u} : CoeSort (Set α) (Type u) :=
   ⟨Elem⟩
 
--- Porting note: the `lift` tactic has not been ported.
--- instance PiSetCoe.canLift (ι : Type u) (α : ∀ i : ι, Type v) [ne : ∀ i, Nonempty (α i)]
---     (s : Set ι) : CanLift (∀ i : s, α i) (∀ i, α i) (fun f i => f i) fun _ => True :=
---   PiSubtype.canLift ι α s
--- #align set.pi_set_coe.can_lift Set.PiSetCoe.canLift
+instance PiSetCoe.canLift (ι : Type u) (α : ι → Type v) [∀ i, Nonempty (α i)] (s : Set ι) :
+    CanLift (∀ i : s, α i) (∀ i, α i) (fun f i => f i) fun _ => True :=
+  PiSubtype.canLift ι α s
+#align set.pi_set_coe.can_lift Set.PiSetCoe.canLift
 
--- instance PiSetCoe.canLift' (ι : Type u) (α : Type v) [ne : Nonempty α] (s : Set ι) :
---     CanLift (s → α) (ι → α) (fun f i => f i) fun _ => True :=
---   PiSetCoe.canLift ι (fun _ => α) s
--- #align set.pi_set_coe.can_lift' Set.PiSetCoe.canLift'
+instance PiSetCoe.canLift' (ι : Type u) (α : Type v) [Nonempty α] (s : Set ι) :
+    CanLift (s → α) (ι → α) (fun f i => f i) fun _ => True :=
+  PiSetCoe.canLift ι (fun _ => α) s
+#align set.pi_set_coe.can_lift' Set.PiSetCoe.canLift'
 
 end Set

chore: remove iff_self from simp only after lean4#1933 (#1406)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

72b23bd4

Diff

@@ -398,7 +398,7 @@ theorem not_mem_subset (h : s ⊆ t) : a ∉ t → a ∉ s :=
 #align set.not_mem_subset Set.not_mem_subset
 
 theorem not_subset : ¬s ⊆ t ↔ ∃ a ∈ s, a ∉ t := by
-  simp only [subset_def, not_forall, exists_prop, iff_self]
+  simp only [subset_def, not_forall, exists_prop]
 #align set.not_subset Set.not_subset
 
 /-! ### Definition of strict subsets `s ⊂ t` and basic properties. -/
@@ -608,7 +608,7 @@ instance uniqueEmpty [IsEmpty α] : Unique (Set α) where
 
 /-- See also `Set.nonempty_iff_ne_empty`. -/
 theorem not_nonempty_iff_eq_empty {s : Set α} : ¬s.Nonempty ↔ s = ∅ := by
-  simp only [Set.Nonempty, not_exists, eq_empty_iff_forall_not_mem, iff_self]
+  simp only [Set.Nonempty, not_exists, eq_empty_iff_forall_not_mem]
 #align set.not_nonempty_iff_eq_empty Set.not_nonempty_iff_eq_empty
 
 /-- See also `Set.not_nonempty_iff_eq_empty`. -/
@@ -1148,7 +1148,7 @@ theorem insert_ne_self : insert a s ≠ s ↔ a ∉ s :=
 #align set.insert_ne_self Set.insert_ne_self
 
 theorem insert_subset : insert a s ⊆ t ↔ a ∈ t ∧ s ⊆ t := by
-  simp only [subset_def, mem_insert_iff, or_imp, forall_and, forall_eq, iff_self]
+  simp only [subset_def, mem_insert_iff, or_imp, forall_and, forall_eq]
 #align set.insert_subset Set.insert_subset
 
 theorem insert_subset_insert (h : s ⊆ t) : insert a s ⊆ insert a t := fun _ => Or.imp_right (@h _)
@@ -1321,7 +1321,7 @@ theorem union_singleton : s ∪ {a} = insert a s :=
 
 @[simp]
 theorem singleton_inter_nonempty : ({a} ∩ s).Nonempty ↔ a ∈ s := by
-  simp only [Set.Nonempty, mem_inter_iff, mem_singleton_iff, exists_eq_left, iff_self]
+  simp only [Set.Nonempty, mem_inter_iff, mem_singleton_iff, exists_eq_left]
 #align set.singleton_inter_nonempty Set.singleton_inter_nonempty
 
 @[simp]

chore: deal with some old porting notes (#1405)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

1a8e98c7

Diff

@@ -2326,8 +2326,7 @@ theorem nontrivial_of_mem_mem_ne {x y} (hx : x ∈ s) (hy : y ∈ s) (hxy : x 
   ⟨x, hx, y, hy, hxy⟩
 #align set.nontrivial_of_mem_mem_ne Set.nontrivial_of_mem_mem_ne
 
--- Porting note:
--- following the pattern for `Exists`, we have renamed `some` to `choose`.
+-- Porting note: following the pattern for `Exists`, we have renamed `some` to `choose`.
 
 /-- Extract witnesses from s.nontrivial. This function might be used instead of case analysis on the
 argument. Note that it makes a proof depend on the classical.choice axiom. -/

chore: tidy various files (#1311)

489ab6d0

Diff

@@ -13,6 +13,7 @@ import Mathlib.Logic.Function.Iterate
 import Mathlib.Tactic.Use
 import Mathlib.Tactic.SolveByElim
 import Mathlib.Tactic.Tauto
+import Mathlib.Tactic.ByContra
 
 /-!
 # Basic properties of sets
@@ -600,8 +601,7 @@ theorem eq_empty_of_isEmpty [IsEmpty α] (s : Set α) : s = ∅ :=
 #align set.eq_empty_of_is_empty Set.eq_empty_of_isEmpty
 
 /-- There is exactly one set of a type that is empty. -/
-instance uniqueEmpty [IsEmpty α] :
-    Unique (Set α) where
+instance uniqueEmpty [IsEmpty α] : Unique (Set α) where
   default := ∅
   uniq := eq_empty_of_isEmpty
 #align set.unique_empty Set.uniqueEmpty
@@ -2327,7 +2327,7 @@ theorem nontrivial_of_mem_mem_ne {x y} (hx : x ∈ s) (hy : y ∈ s) (hxy : x 
 #align set.nontrivial_of_mem_mem_ne Set.nontrivial_of_mem_mem_ne
 
 -- Porting note:
--- following the pattern for `Exists`, we have renamed `choose` to `some`.
+-- following the pattern for `Exists`, we have renamed `some` to `choose`.
 
 /-- Extract witnesses from s.nontrivial. This function might be used instead of case analysis on the
 argument. Note that it makes a proof depend on the classical.choice axiom. -/
@@ -2378,7 +2378,7 @@ theorem nontrivial_of_exists_ne {x} (hx : x ∈ s) (h : ∃ y ∈ s, y ≠ x) :
 #align set.nontrivial_of_exists_ne Set.nontrivial_of_exists_ne
 
 theorem Nontrivial.exists_ne (hs : s.Nontrivial) (z) : ∃ x ∈ s, x ≠ z := by
-  by_contra H; push_neg  at H
+  by_contra' H
   rcases hs with ⟨x, hx, y, hy, hxy⟩
   rw [H x hx, H y hy] at hxy
   exact hxy rfl
@@ -2430,9 +2430,8 @@ theorem not_nontrivial_empty : ¬(∅ : Set α).Nontrivial := fun h => h.ne_empt
 @[simp]
 theorem not_nontrivial_singleton {x} : ¬({x} : Set α).Nontrivial := fun H => by
   rw [nontrivial_iff_exists_ne (mem_singleton x)] at H
-  exact
-    let ⟨y, hy, hya⟩ := H
-    hya (mem_singleton_iff.1 hy)
+  let ⟨y, hy, hya⟩ := H
+  exact hya (mem_singleton_iff.1 hy)
 #align set.not_nontrivial_singleton Set.not_nontrivial_singleton
 
 theorem Nontrivial.ne_singleton {x} (hs : s.Nontrivial) : s ≠ {x} := fun H => by
@@ -2483,7 +2482,7 @@ theorem nontrivial_coe_sort {s : Set α} : Nontrivial s ↔ s.Nontrivial := by
 alias nontrivial_coe_sort ↔ _ Nontrivial.coe_sort
 
 /-- A type with a set `s` whose `coe_sort` is a nontrivial type is nontrivial.
-For the corresponding result for `subtype`, see `subtype.nontrivial_iff_exists_ne`. -/
+For the corresponding result for `Subtype`, see `Subtype.nontrivial_iff_exists_ne`. -/
 theorem nontrivial_of_nontrivial_coe (hs : Nontrivial s) : Nontrivial α :=
   nontrivial_of_nontrivial <| nontrivial_coe_sort.1 hs
 #align set.nontrivial_of_nontrivial_coe Set.nontrivial_of_nontrivial_coe

chore: various naming fixes (#1258)

00088a48

Diff

@@ -1664,7 +1664,7 @@ alias disjoint_compl_left_iff_subset ↔ _ _root_.HasSubset.Subset.disjoint_comp
 alias disjoint_compl_right_iff_subset ↔ _ _root_.HasSubset.Subset.disjoint_compl_right
 
 theorem subset_union_compl_iff_inter_subset {s t u : Set α} : s ⊆ t ∪ uᶜ ↔ s ∩ u ⊆ t :=
-  (@is_compl_compl _ u _).le_sup_right_iff_inf_left_le
+  (@isCompl_compl _ u _).le_sup_right_iff_inf_left_le
 #align set.subset_union_compl_iff_inter_subset Set.subset_union_compl_iff_inter_subset
 
 theorem compl_subset_iff_union {s t : Set α} : sᶜ ⊆ t ↔ s ∪ t = univ :=

chore: move basic lemmas to basic files (#1109)

synchronize with https://github.com/leanprover-community/mathlib/pull/17882

~~Make disjoint_singleton @[simp 1100] because the linter complains it is not in simpNF (because of disjoint_singleton_left and disjoint_singleton_right).~~

Removing simp of disjoint_singleton, making disjoint_singleton_left have a greater priority than disjoint_singleton_right, then disjoint_singleton can be proved by simp.

d90ae095

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Leonardo de Moura
 
 ! This file was ported from Lean 3 source module data.set.basic
-! leanprover-community/mathlib commit 1b36dabc50929b36caec16306358a5cc44ab441e
+! leanprover-community/mathlib commit 3d95492390dc90e34184b13e865f50bc67f30fbb
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -2754,3 +2754,203 @@ instance decidableSetOf (p : α → Prop) [Decidable (p a)] : Decidable (a ∈ {
 #align set.decidable_set_of Set.decidableSetOf
 
 end Set
+
+/-! ### Monotone lemmas for sets -/
+
+section Monotone
+variable {α β : Type _}
+
+theorem Monotone.inter [Preorder β] {f g : β → Set α} (hf : Monotone f) (hg : Monotone g) :
+    Monotone fun x => f x ∩ g x :=
+  hf.inf hg
+#align monotone.inter Monotone.inter
+
+theorem MonotoneOn.inter [Preorder β] {f g : β → Set α} {s : Set β} (hf : MonotoneOn f s)
+    (hg : MonotoneOn g s) : MonotoneOn (fun x => f x ∩ g x) s :=
+  hf.inf hg
+#align monotone_on.inter MonotoneOn.inter
+
+theorem Antitone.inter [Preorder β] {f g : β → Set α} (hf : Antitone f) (hg : Antitone g) :
+    Antitone fun x => f x ∩ g x :=
+  hf.inf hg
+#align antitone.inter Antitone.inter
+
+theorem AntitoneOn.inter [Preorder β] {f g : β → Set α} {s : Set β} (hf : AntitoneOn f s)
+    (hg : AntitoneOn g s) : AntitoneOn (fun x => f x ∩ g x) s :=
+  hf.inf hg
+#align antitone_on.inter AntitoneOn.inter
+
+theorem Monotone.union [Preorder β] {f g : β → Set α} (hf : Monotone f) (hg : Monotone g) :
+    Monotone fun x => f x ∪ g x :=
+  hf.sup hg
+#align monotone.union Monotone.union
+
+theorem MonotoneOn.union [Preorder β] {f g : β → Set α} {s : Set β} (hf : MonotoneOn f s)
+    (hg : MonotoneOn g s) : MonotoneOn (fun x => f x ∪ g x) s :=
+  hf.sup hg
+#align monotone_on.union MonotoneOn.union
+
+theorem Antitone.union [Preorder β] {f g : β → Set α} (hf : Antitone f) (hg : Antitone g) :
+    Antitone fun x => f x ∪ g x :=
+  hf.sup hg
+#align antitone.union Antitone.union
+
+theorem AntitoneOn.union [Preorder β] {f g : β → Set α} {s : Set β} (hf : AntitoneOn f s)
+    (hg : AntitoneOn g s) : AntitoneOn (fun x => f x ∪ g x) s :=
+  hf.sup hg
+#align antitone_on.union AntitoneOn.union
+
+namespace Set
+
+theorem monotone_setOf [Preorder α] {p : α → β → Prop} (hp : ∀ b, Monotone fun a => p a b) :
+    Monotone fun a => { b | p a b } := fun _ _ h b => hp b h
+#align set.monotone_set_of Set.monotone_setOf
+
+theorem antitone_setOf [Preorder α] {p : α → β → Prop} (hp : ∀ b, Antitone fun a => p a b) :
+    Antitone fun a => { b | p a b } := fun _ _ h b => hp b h
+#align set.antitone_set_of Set.antitone_setOf
+
+/-- Quantifying over a set is antitone in the set -/
+theorem antitone_bforall {P : α → Prop} : Antitone fun s : Set α => ∀ x ∈ s, P x :=
+  fun _ _ hst h x hx => h x <| hst hx
+#align set.antitone_bforall Set.antitone_bforall
+
+end Set
+
+end Monotone
+
+/-! ### Disjoint sets -/
+
+section Disjoint
+
+variable {α β : Type _} {s t u : Set α} {f : α → β}
+
+namespace Disjoint
+
+theorem union_left (hs : Disjoint s u) (ht : Disjoint t u) : Disjoint (s ∪ t) u :=
+  hs.sup_left ht
+#align disjoint.union_left Disjoint.union_left
+
+theorem union_right (ht : Disjoint s t) (hu : Disjoint s u) : Disjoint s (t ∪ u) :=
+  ht.sup_right hu
+#align disjoint.union_right Disjoint.union_right
+
+theorem inter_left (u : Set α) (h : Disjoint s t) : Disjoint (s ∩ u) t :=
+  h.inf_left _
+#align disjoint.inter_left Disjoint.inter_left
+
+theorem inter_left' (u : Set α) (h : Disjoint s t) : Disjoint (u ∩ s) t :=
+  h.inf_left' _
+#align disjoint.inter_left' Disjoint.inter_left'
+
+theorem inter_right (u : Set α) (h : Disjoint s t) : Disjoint s (t ∩ u) :=
+  h.inf_right _
+#align disjoint.inter_right Disjoint.inter_right
+
+theorem inter_right' (u : Set α) (h : Disjoint s t) : Disjoint s (u ∩ t) :=
+  h.inf_right' _
+#align disjoint.inter_right' Disjoint.inter_right'
+
+theorem subset_left_of_subset_union (h : s ⊆ t ∪ u) (hac : Disjoint s u) : s ⊆ t :=
+  hac.left_le_of_le_sup_right h
+#align disjoint.subset_left_of_subset_union Disjoint.subset_left_of_subset_union
+
+theorem subset_right_of_subset_union (h : s ⊆ t ∪ u) (hab : Disjoint s t) : s ⊆ u :=
+  hab.left_le_of_le_sup_left h
+#align disjoint.subset_right_of_subset_union Disjoint.subset_right_of_subset_union
+
+end Disjoint
+
+namespace Set
+
+theorem not_disjoint_iff : ¬Disjoint s t ↔ ∃ x, x ∈ s ∧ x ∈ t :=
+  Set.disjoint_iff.not.trans <| not_forall.trans <| exists_congr fun _ => not_not
+#align set.not_disjoint_iff Set.not_disjoint_iff
+
+theorem not_disjoint_iff_nonempty_inter : ¬Disjoint s t ↔ (s ∩ t).Nonempty :=
+  not_disjoint_iff
+#align set.not_disjoint_iff_nonempty_inter Set.not_disjoint_iff_nonempty_inter
+
+alias not_disjoint_iff_nonempty_inter ↔ _ Nonempty.not_disjoint
+
+theorem disjoint_or_nonempty_inter (s t : Set α) : Disjoint s t ∨ (s ∩ t).Nonempty :=
+  (em _).imp_right not_disjoint_iff_nonempty_inter.mp
+#align set.disjoint_or_nonempty_inter Set.disjoint_or_nonempty_inter
+
+theorem disjoint_iff_forall_ne : Disjoint s t ↔ ∀ x ∈ s, ∀ y ∈ t, x ≠ y := by
+  simp only [Ne.def, disjoint_left, @imp_not_comm _ (_ = _), forall_eq']
+#align set.disjoint_iff_forall_ne Set.disjoint_iff_forall_ne
+
+theorem _root_.Disjoint.ne_of_mem (h : Disjoint s t) {x y} (hx : x ∈ s) (hy : y ∈ t) : x ≠ y :=
+  disjoint_iff_forall_ne.mp h x hx y hy
+#align disjoint.ne_of_mem Disjoint.ne_of_mem
+
+theorem disjoint_of_subset_left (h : s ⊆ u) (d : Disjoint u t) : Disjoint s t :=
+  d.mono_left h
+#align set.disjoint_of_subset_left Set.disjoint_of_subset_left
+
+theorem disjoint_of_subset_right (h : t ⊆ u) (d : Disjoint s u) : Disjoint s t :=
+  d.mono_right h
+#align set.disjoint_of_subset_right Set.disjoint_of_subset_right
+
+theorem disjoint_of_subset {s t u v : Set α} (h1 : s ⊆ u) (h2 : t ⊆ v) (d : Disjoint u v) :
+    Disjoint s t :=
+  d.mono h1 h2
+#align set.disjoint_of_subset Set.disjoint_of_subset
+
+@[simp]
+theorem disjoint_union_left : Disjoint (s ∪ t) u ↔ Disjoint s u ∧ Disjoint t u :=
+  disjoint_sup_left
+#align set.disjoint_union_left Set.disjoint_union_left
+
+@[simp]
+theorem disjoint_union_right : Disjoint s (t ∪ u) ↔ Disjoint s t ∧ Disjoint s u :=
+  disjoint_sup_right
+#align set.disjoint_union_right Set.disjoint_union_right
+
+theorem disjoint_diff {a b : Set α} : Disjoint a (b \ a) :=
+  disjoint_iff.2 (inter_diff_self _ _)
+#align set.disjoint_diff Set.disjoint_diff
+
+@[simp]
+theorem disjoint_empty (s : Set α) : Disjoint s ∅ :=
+  disjoint_bot_right
+#align set.disjoint_empty Set.disjoint_empty
+
+@[simp]
+theorem empty_disjoint (s : Set α) : Disjoint ∅ s :=
+  disjoint_bot_left
+#align set.empty_disjoint Set.empty_disjoint
+
+@[simp]
+theorem univ_disjoint {s : Set α} : Disjoint univ s ↔ s = ∅ :=
+  top_disjoint
+#align set.univ_disjoint Set.univ_disjoint
+
+@[simp]
+theorem disjoint_univ {s : Set α} : Disjoint s univ ↔ s = ∅ :=
+  disjoint_top
+#align set.disjoint_univ Set.disjoint_univ
+
+@[simp default+1]
+theorem disjoint_singleton_left {a : α} {s : Set α} : Disjoint {a} s ↔ a ∉ s :=
+  by simp [Set.disjoint_iff, subset_def]
+#align set.disjoint_singleton_left Set.disjoint_singleton_left
+
+@[simp]
+theorem disjoint_singleton_right {a : α} {s : Set α} : Disjoint s {a} ↔ a ∉ s :=
+  by rw [Disjoint.comm]; exact disjoint_singleton_left
+#align set.disjoint_singleton_right Set.disjoint_singleton_right
+
+theorem disjoint_singleton {a b : α} : Disjoint ({a} : Set α) {b} ↔ a ≠ b :=
+  by simp
+#align set.disjoint_singleton Set.disjoint_singleton
+
+theorem subset_diff {s t u : Set α} : s ⊆ t \ u ↔ s ⊆ t ∧ Disjoint s u :=
+  ⟨fun h => ⟨fun _ hxs => (h hxs).1, disjoint_iff_inf_le.mpr fun _ ⟨hxs, hxu⟩ => (h hxs).2 hxu⟩,
+    fun ⟨h1, h2⟩ _ hxs => ⟨h1 hxs, fun hxu => h2.le_bot ⟨hxs, hxu⟩⟩⟩
+#align set.subset_diff Set.subset_diff
+
+end Set
+
+end Disjoint

chore: fix casing per naming scheme (#1183)

Fix a lot of wrong casing mostly in the docstrings but also sometimes in def/theorem names. E.g. fin 2 --> Fin 2, add_monoid_hom --> AddMonoidHom

Remove \n from to_additive docstrings that were inserted by mathport.

Move files and directories with Gcd and Smul to GCD and SMul

71723d8b

Diff

@@ -60,7 +60,7 @@ Definitions in the file:
 * `s.Nonempty` is to be preferred to `s ≠ ∅` or `∃ x, x ∈ s`. It has the advantage that
 the `s.Nonempty` dot notation can be used.
 
-* For `s : set α`, do not use `subtype s`. Instead use `↥s` or `(s : Type*)` or `s`.
+* For `s : Set α`, do not use `Subtype s`. Instead use `↥s` or `(s : Type*)` or `s`.
 
 ## Tags
 
@@ -2124,7 +2124,7 @@ theorem mem_ite_empty_left (p : Prop) [Decidable p] (t : Set α) (x : α) :
 /-! ### If-then-else for sets -/
 
 
-/-- `ite` for sets: `set.ite t s s' ∩ t = s ∩ t`, `set.ite t s s' ∩ tᶜ = s' ∩ tᶜ`.
+/-- `ite` for sets: `Set.ite t s s' ∩ t = s ∩ t`, `Set.ite t s s' ∩ tᶜ = s' ∩ tᶜ`.
 Defined as `s ∩ t ∪ s' \ t`. -/
 protected def ite (t s s' : Set α) : Set α :=
   s ∩ t ∪ s' \ t
@@ -2216,7 +2216,7 @@ theorem subset_ite {t s s' u : Set α} : u ⊆ t.ite s s' ↔ u ∩ t ⊆ s ∧
 /-! ### Subsingleton -/
 
 
-/-- A set `s` is a `subsingleton` if it has at most one element. -/
+/-- A set `s` is a `Subsingleton` if it has at most one element. -/
 protected def Subsingleton (s : Set α) : Prop :=
   ∀ ⦃x⦄ (_ : x ∈ s) ⦃y⦄ (_ : y ∈ s), x = y
 #align set.subsingleton Set.Subsingleton

chore: fix names (#1171)

10507fe5

Diff

@@ -143,9 +143,9 @@ theorem lt_iff_ssubset : s < t ↔ s ⊂ t :=
   Iff.rfl
 #align set.lt_iff_ssubset Set.lt_iff_ssubset
 
-alias le_iff_subset ↔ _root_.has_le.le.subset _root_.has_subset.subset.le
+alias le_iff_subset ↔ _root_.LE.le.subset _root_.HasSubset.Subset.le
 
-alias lt_iff_ssubset ↔ _root_.has_lt.lt.ssubset _root_.has_ssubset.ssubset.lt
+alias lt_iff_ssubset ↔ _root_.LT.lt.ssubset _root_.HasSSubset.SSubset.lt
 
 -- Porting note: I've introduced this abbreviation, with the `@[coe]` attribute,
 -- so that `norm_cast` has something to index on.
@@ -456,7 +456,7 @@ theorem nonempty_coe_sort {s : Set α} : Nonempty (↥s) ↔ s.Nonempty :=
   nonempty_subtype
 #align set.nonempty_coe_sort Set.nonempty_coe_sort
 
-alias nonempty_coe_sort ↔ _ nonempty.coe_sort
+alias nonempty_coe_sort ↔ _ Nonempty.coe_sort
 
 theorem nonempty_def : s.Nonempty ↔ ∃ x, x ∈ s :=
   Iff.rfl
@@ -1659,9 +1659,9 @@ alias subset_compl_iff_disjoint_right ↔ _ _root_.Disjoint.subset_compl_right
 
 alias subset_compl_iff_disjoint_left ↔ _ _root_.Disjoint.subset_compl_left
 
-alias disjoint_compl_left_iff_subset ↔ _ _root_.HasSubset.subset.disjoint_compl_left
+alias disjoint_compl_left_iff_subset ↔ _ _root_.HasSubset.Subset.disjoint_compl_left
 
-alias disjoint_compl_right_iff_subset ↔ _ _root_.HasSubset.subset.disjoint_compl_right
+alias disjoint_compl_right_iff_subset ↔ _ _root_.HasSubset.Subset.disjoint_compl_right
 
 theorem subset_union_compl_iff_inter_subset {s t u : Set α} : s ⊆ t ∪ uᶜ ↔ s ∩ u ⊆ t :=
   (@is_compl_compl _ u _).le_sup_right_iff_inf_left_le

feat: implement basic version of tauto tactic (#1081)

Adds a basic version of the tauto tactic, mostly a line-by-line translation of the Lean 3 version.

As per this zulip discussion, makes tauto always-classical and eliminates tauto!.
Does not yet add any symmetry-based logic or the fancy union-find datastructure from https://github.com/leanprover-community/mathlib/pull/180.
Adds a andThenOnSubgoals tactic combinator in Mathlib.Tactic.Basic.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

3f9ce172

Diff

@@ -12,6 +12,8 @@ import Mathlib.Order.SymmDiff
 import Mathlib.Logic.Function.Iterate
 import Mathlib.Tactic.Use
 import Mathlib.Tactic.SolveByElim
+import Mathlib.Tactic.Tauto
+
 /-!
 # Basic properties of sets
 
@@ -253,9 +255,8 @@ theorem mem_of_mem_of_subset {x : α} {s t : Set α} (hx : x ∈ s) (h : s ⊆ t
   h hx
 #align set.mem_of_mem_of_subset Set.mem_of_mem_of_subset
 
--- Porting note: was `by tauto`
-theorem forall_in_swap {p : α → β → Prop} : (∀ a ∈ s, ∀ (b), p a b) ↔ ∀ (b), ∀ a ∈ s, p a b :=
-  ⟨fun h b a ha => h a ha b, fun h a ha b => h b a ha⟩
+theorem forall_in_swap {p : α → β → Prop} : (∀ a ∈ s, ∀ (b), p a b) ↔ ∀ (b), ∀ a ∈ s, p a b := by
+  tauto
 #align set.forall_in_swap Set.forall_in_swap
 
 /-! ### Lemmas about `mem` and `setOf` -/
@@ -2195,24 +2196,7 @@ theorem ite_inter_inter (t s₁ s₂ s₁' s₂' : Set α) :
     t.ite (s₁ ∩ s₂) (s₁' ∩ s₂') = t.ite s₁ s₁' ∩ t.ite s₂ s₂' := by
   ext x
   simp only [Set.ite, Set.mem_inter_iff, Set.mem_diff, Set.mem_union]
-  -- Porting note: this use to be `itauto`:
-  exact
-  { mp := λ (h0 : (x ∈ s₁ ∧ x ∈ s₂) ∧ x ∈ t ∨ (x ∈ s₁' ∧ x ∈ s₂') ∧ x ∉ t) =>
-      ⟨h0.elim (λ (h1 : (x ∈ s₁ ∧ x ∈ s₂) ∧ x ∈ t) => Or.inl ⟨h1.left.left, h1.right⟩)
-        (λ (h1 : (x ∈ s₁' ∧ x ∈ s₂') ∧ x ∉ t) =>
-            Or.inr ⟨h1.left.left, λ (h2 : x ∈ t) => h1.right h2⟩),
-      h0.elim (λ (h3 : (x ∈ s₁ ∧ x ∈ s₂) ∧ x ∈ t) => Or.inl ⟨h3.left.right, h3.right⟩)
-        (λ (h3 : (x ∈ s₁' ∧ x ∈ s₂') ∧ x ∉ t) =>
-            Or.inr ⟨h3.left.right, λ (h4 : x ∈ t) => h3.right h4⟩)⟩,
-    mpr := λ (h5 : (x ∈ s₁ ∧ x ∈ t ∨ x ∈ s₁' ∧ x ∉ t) ∧ (x ∈ s₂ ∧ x ∈ t ∨ x ∈ s₂' ∧ x ∉ t)) =>
-      h5.right.elim
-        (λ (h6 : x ∈ s₂ ∧ x ∈ t) =>
-            h5.left.elim (λ (h7 : x ∈ s₁ ∧ x ∈ t) => Or.inl ⟨⟨h7.left, h6.left⟩, h7.right⟩)
-              (λ (h7 : x ∈ s₁' ∧ x ∉ t) => (h7.right h6.right).elim))
-        (λ (h6 : x ∈ s₂' ∧ x ∉ t) =>
-            h5.left.elim (λ (h8 : x ∈ s₁ ∧ x ∈ t) => (h6.right h8.right).elim)
-              (λ (h8 : x ∈ s₁' ∧ x ∉ t) =>
-                Or.inr ⟨⟨h8.left, h6.left⟩, λ (h9 : x ∈ t) => h8.right h9⟩)) }
+  tauto
 #align set.ite_inter_inter Set.ite_inter_inter
 
 theorem ite_inter (t s₁ s₂ s : Set α) : t.ite (s₁ ∩ s) (s₂ ∩ s) = t.ite s₁ s₂ ∩ s := by

chore: update lean4/std4 (#1096)

a9a1f7d7

Diff

@@ -526,11 +526,11 @@ theorem inter_nonempty : (s ∩ t).Nonempty ↔ ∃ x, x ∈ s ∧ x ∈ t :=
 #align set.inter_nonempty Set.inter_nonempty
 
 theorem inter_nonempty_iff_exists_left : (s ∩ t).Nonempty ↔ ∃ x ∈ s, x ∈ t := by
-  simp_rw [inter_nonempty, exists_prop]; rfl
+  simp_rw [inter_nonempty]
 #align set.inter_nonempty_iff_exists_left Set.inter_nonempty_iff_exists_left
 
 theorem inter_nonempty_iff_exists_right : (s ∩ t).Nonempty ↔ ∃ x ∈ t, x ∈ s := by
-  simp_rw [inter_nonempty, exists_prop, and_comm]; rfl
+  simp_rw [inter_nonempty, exists_prop, and_comm]
 #align set.inter_nonempty_iff_exists_right Set.inter_nonempty_iff_exists_right
 
 theorem nonempty_iff_univ_nonempty : Nonempty α ↔ (univ : Set α).Nonempty :=
@@ -1162,7 +1162,6 @@ theorem insert_subset_insert_iff (ha : a ∉ s) : insert a s ⊆ insert a t ↔
 theorem ssubset_iff_insert {s t : Set α} : s ⊂ t ↔ ∃ (a : α) (_ : a ∉ s), insert a s ⊆ t := by
   simp only [insert_subset, exists_and_right, ssubset_def, not_subset]
   simp only [exists_prop, and_comm]
-  rfl
 #align set.ssubset_iff_insert Set.ssubset_iff_insert
 
 theorem ssubset_insert {s : Set α} {a : α} (h : a ∉ s) : s ⊂ insert a s :=
@@ -1406,7 +1405,7 @@ theorem mem_sep_iff : x ∈ { x ∈ s | p x } ↔ x ∈ s ∧ p x :=
 #align set.mem_sep_iff Set.mem_sep_iff
 
 theorem sep_ext_iff : { x ∈ s | p x } = { x ∈ s | q x } ↔ ∀ x ∈ s, p x ↔ q x := by
-  simp_rw [ext_iff, mem_sep_iff, and_congr_right_iff]; rfl
+  simp_rw [ext_iff, mem_sep_iff, and_congr_right_iff]
 #align set.sep_ext_iff Set.sep_ext_iff
 
 theorem sep_eq_of_subset (h : s ⊆ t) : { x ∈ t | x ∈ s } = s :=
@@ -1419,12 +1418,12 @@ theorem sep_subset (s : Set α) (p : α → Prop) : { x ∈ s | p x } ⊆ s := f
 
 @[simp]
 theorem sep_eq_self_iff_mem_true : { x ∈ s | p x } = s ↔ ∀ x ∈ s, p x := by
-  simp_rw [ext_iff, mem_sep_iff, and_iff_left_iff_imp]; rfl
+  simp_rw [ext_iff, mem_sep_iff, and_iff_left_iff_imp]
 #align set.sep_eq_self_iff_mem_true Set.sep_eq_self_iff_mem_true
 
 @[simp]
 theorem sep_eq_empty_iff_mem_false : { x ∈ s | p x } = ∅ ↔ ∀ x ∈ s, ¬p x := by
-  simp_rw [ext_iff, mem_sep_iff, mem_empty_iff_false, iff_false_iff, not_and]; rfl
+  simp_rw [ext_iff, mem_sep_iff, mem_empty_iff_false, iff_false_iff, not_and]
 #align set.sep_eq_empty_iff_mem_false Set.sep_eq_empty_iff_mem_false
 
 --Porting note: removed `simp` attribute because `simp` can prove it
@@ -2512,7 +2511,7 @@ theorem nontrivial_mono {α : Type _} {s t : Set α} (hst : s ⊆ t) (hs : Nontr
 
 @[simp]
 theorem not_subsingleton_iff : ¬s.Subsingleton ↔ s.Nontrivial := by
-  simp_rw [Set.Subsingleton, Set.Nontrivial, not_forall]; rfl
+  simp_rw [Set.Subsingleton, Set.Nontrivial, not_forall]
 #align set.not_subsingleton_iff Set.not_subsingleton_iff
 
 @[simp]