X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Flib%2Fbasics%2Fsets.ma;h=8e40b666bfdee2eb318478d2899a3bece809619f;hb=bf816f05ddbe0ded4948dd33490619724dc4f7cf;hp=7c791da41b07eeb308c124706a1901bb565f1141;hpb=fe7d9f4665e92d9c6934988b2b215547ab7ecf3f;p=helm.git diff --git a/matita/matita/lib/basics/sets.ma b/matita/matita/lib/basics/sets.ma index 7c791da41..8e40b666b 100644 --- a/matita/matita/lib/basics/sets.ma +++ b/matita/matita/lib/basics/sets.ma @@ -10,6 +10,8 @@ V_______________________________________________________________ *) include "basics/logic.ma". +include "basics/core_notation/singl_1.ma". +include "basics/core_notation/subseteq_2.ma". (**** a subset of A is just an object of type A→Prop ****) @@ -38,6 +40,7 @@ interpretation "subset" 'subseteq a b = (subset ? a b). (* extensional equality *) definition eqP ≝ λA:Type[0].λP,Q:A → Prop.∀a:A.P a ↔ Q a. +(* ≐ is typed as \doteq *) notation "A ≐ B" non associative with precedence 45 for @{'eqP $A $B}. interpretation "extensional equality" 'eqP a b = (eqP ? a b). @@ -115,4 +118,4 @@ qed. (* substraction *) lemma substract_def:∀U.∀A,B:U→Prop. A-B ≐ A ∩ ¬B. #U #A #B #w normalize /2/ -qed. \ No newline at end of file +qed.