X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=helm%2Fmatita%2Flibrary%2Fhigher_order_defs%2Ffunctions.ma;h=321ae46b7502c1578975b24ccdc25c4351065788;hb=28ac70d3f475442cda4ef30e0e9c0e6d012b2527;hp=e8fbb6dd9b4b63beee7d9cba581f325e368d6cbf;hpb=633474751ddf1074947ff0d324fb1aca2293eff8;p=helm.git

diff --git a/helm/matita/library/higher_order_defs/functions.ma b/helm/matita/library/higher_order_defs/functions.ma
index e8fbb6dd9..321ae46b7 100644
--- a/helm/matita/library/higher_order_defs/functions.ma
+++ b/helm/matita/library/higher_order_defs/functions.ma
@@ -15,20 +15,21 @@
 set "baseuri" "cic:/matita/higher_order_defs/functions/".
 
 include "logic/equality.ma".
-include "logic/connectives.ma".
 
 definition injective: \forall A,B:Type.\forall f:A \to B.Prop
 \def \lambda A,B.\lambda f.
   \forall x,y:A.f x = f y \to x=y.
 
-(* we have still to attach exists *)
 definition surjective: \forall A,B:Type.\forall f:A \to B.Prop
 \def \lambda A,B.\lambda f.
-  \forall z:B.ex A (\lambda x:A.z=f x).
+  \forall z:B. \exists x:A.z=f x.
 
 definition symmetric: \forall A:Type.\forall f:A \to A\to A.Prop
 \def \lambda A.\lambda f.\forall x,y.f x y = f y x.
 
+definition symmetric2: \forall A,B:Type.\forall f:A \to A\to B.Prop
+\def \lambda A,B.\lambda f.\forall x,y.f x y = f y x.
+
 definition associative: \forall A:Type.\forall f:A \to A\to A.Prop
 \def \lambda A.\lambda f.\forall x,y,z.f (f x y) z = f x (f y z).
 
@@ -41,4 +42,6 @@ definition monotonic : \forall A:Type.\forall R:A \to A \to Prop.
 definition distributive: \forall A:Type.\forall f,g:A \to A \to A.Prop
 \def \lambda A.\lambda f,g.\forall x,y,z:A. f x (g y z) = g (f x y) (f x z).
 
-
+definition distributive2: \forall A,B:Type.\forall f:A \to B \to B.
+\forall g: B\to B\to B. Prop
+\def \lambda A,B.\lambda f,g.\forall x:A.\forall y,z:B. f x (g y z) = g (f x y) (f x z).