coercion nat2int.
definition fst \def \lambda x,y:int.x.
-alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
theorem a: fst O one = fst (positive O) (next one).
reflexivity.
qed.
+
+definition double:
+ \forall f:int \to int. pos \to int
+\def
+ \lambda f:int \to int. \lambda x : pos .f (nat2int x).
+
+definition double1:
+ \forall f:int \to int. pos \to int
+\def
+ \lambda f:int \to int. \lambda x : pos .f (pos2nat x).
+
+definition double2:
+ \forall f:int \to int. pos \to int
+\def
+ \lambda f:int \to int. \lambda x : pos .f (nat2int (pos2nat x)).
+
+
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