(* *)
(**************************************************************************)
-set "baseuri" "cic:/matita/Z/times".
-
include "nat/lt_arith.ma".
include "Z/plus.ma".
variant distr_Ztimes_Zplus: \forall x,y,z.
x * (y + z) = x*y + x*z \def
distributive_Ztimes_Zplus.
+
+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.