(* *)
(**************************************************************************)
-set "baseuri" "cic:/matita/nat/plus".
-
include "nat/nat.ma".
let rec plus n m \def
[ O \Rightarrow m
| (S p) \Rightarrow S (plus p m) ].
-(*CSC: the URI must disappear: there is a bug now *)
-interpretation "natural plus" 'plus x y = (cic:/matita/nat/plus/plus.con x y).
+interpretation "natural plus" 'plus x y = (plus x y).
theorem plus_n_O: \forall n:nat. n = n+O.
intros.elim n.
simplify.apply eq_f.assumption.
qed.
+theorem plus_n_SO : \forall n:nat. S n = n+(S O).
+intro.rewrite > plus_n_O.
+apply plus_n_Sm.
+qed.
+
theorem sym_plus: \forall n,m:nat. n+m = m+n.
intros.elim n.
simplify.apply plus_n_O.