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).
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).