The library grows...

[helm.git] / helm / matita / library / higher_order_defs / functions.ma

diff --git a/helm/matita/library/higher_order_defs/functions.ma b/helm/matita/library/higher_order_defs/functions.ma
index e8fbb6dd9b4b63beee7d9cba581f325e368d6cbf..71b6d84599df20cfcd223a7565e4c83bb85f03e5 100644 (file)
--- a/helm/matita/library/higher_order_defs/functions.ma
+++ b/helm/matita/library/higher_order_defs/functions.ma
@@ -29,6 +29,9 @@ definition surjective: \forall A,B:Type.\forall f:A \to B.Prop
 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 +44,6 @@ 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).