| (neg n) \Rightarrow (neg (pred ((S m)+(S n))))] ].
interpretation "integer plus" 'plus x y = (Zplus x y).
-
+
+theorem eq_plus_Zplus: \forall n,m:nat. Z_of_nat (n+m) =
+Z_of_nat n + Z_of_nat m.
+intro.cases n;intro
+ [reflexivity
+ |cases m
+ [simplify.rewrite < plus_n_O.reflexivity
+ |simplify.reflexivity.
+ ]]
+qed.
+
theorem Zplus_z_OZ: \forall z:Z. z+OZ = z.
intro.elim z.
simplify.reflexivity.