the decentralization of core notation continues ...

[helm.git] / matita / matita / lib / basics / sets.ma

diff --git a/matita/matita/lib/basics/sets.ma b/matita/matita/lib/basics/sets.ma
index 43b22bff6900c1a329610a05596c4a37b41346a6..8e40b666bfdee2eb318478d2899a3bece809619f 100644 (file)
--- a/matita/matita/lib/basics/sets.ma
+++ b/matita/matita/lib/basics/sets.ma
@@ -10,10 +10,12 @@
       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 ****)
 
-definition empty_set ≝ λA:Type[0].λa:A.⊥.
+definition empty_set ≝ λA:Type[0].λa:A.False.
 notation "\emptyv" non associative with precedence 90 for @{'empty_set}.
 interpretation "empty set" 'empty_set = (empty_set ?).
 
@@ -116,4 +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.