diff --git a/library/data/set/basic.lean b/library/data/set/basic.lean index e245898742..0c4cd96517 100644 --- a/library/data/set/basic.lean +++ b/library/data/set/basic.lean @@ -53,18 +53,18 @@ assume h, absurd rfl (and.elim_right h) /- bounded quantification -/ abbreviation bounded_forall (a : set X) (P : X → Prop) := ∀⦃x⦄, x ∈ a → P x -notation `forallb` binders `∈` a `, ` r:(scoped:1 P, P) := bounded_forall a r -notation `∀₀` binders `∈` a `, ` r:(scoped:1 P, P) := bounded_forall a r +notation `forallb` binders ` ∈ ` a `, ` r:(scoped:1 P, P) := bounded_forall a r +notation `∀₀` binders ` ∈ ` a `, ` r:(scoped:1 P, P) := bounded_forall a r abbreviation bounded_exists (a : set X) (P : X → Prop) := ∃⦃x⦄, x ∈ a ∧ P x -notation `existsb` binders `∈` a `, ` r:(scoped:1 P, P) := bounded_exists a r -notation `∃₀` binders `∈` a `, ` r:(scoped:1 P, P) := bounded_exists a r +notation `existsb` binders ` ∈ ` a `, ` r:(scoped:1 P, P) := bounded_exists a r +notation `∃₀` binders ` ∈ ` a `, ` r:(scoped:1 P, P) := bounded_exists a r theorem bounded_exists.intro {P : X → Prop} {s : set X} {x : X} (xs : x ∈ s) (Px : P x) : ∃₀ x ∈ s, P x := exists.intro x (and.intro xs Px) -lemma bounded_forall_congr {A : Type} {S : set A} {P Q : A → Prop} (H : ∀₀ x∈S, P x ↔ Q x) : +lemma bounded_forall_congr {A : Type} {S : set A} {P Q : A → Prop} (H : ∀₀ x ∈ S, P x ↔ Q x) : (∀₀ x ∈ S, P x) = (∀₀ x ∈ S, Q x) := begin apply propext, @@ -74,7 +74,7 @@ begin apply H end -lemma bounded_exists_congr {A : Type} {S : set A} {P Q : A → Prop} (H : ∀₀ x∈S, P x ↔ Q x) : +lemma bounded_exists_congr {A : Type} {S : set A} {P Q : A → Prop} (H : ∀₀ x ∈ S, P x ↔ Q x) : (∃₀ x ∈ S, P x) = (∃₀ x ∈ S, Q x) := begin apply propext,