(* *)
(**************************************************************************)
-set "baseuri" "cic:/matita/nat/relevant_equations.ma".
-
include "nat/times.ma".
include "nat/minus.ma".
+include "nat/gcd.ma".
+(* if gcd is compiled before this, the applys will take too much *)
theorem times_plus_l: \forall n,m,p:nat. (n+m)*p = n*p + m*p.
intros.
rewrite > distr_times_plus.
rewrite < assoc_plus.reflexivity.
qed.
+
+theorem eq_pred_to_eq:
+ ∀n,m. O < n → O < m → pred n = pred m → n = m.
+intros;
+generalize in match (eq_f ? ? S ? ? H2);
+intro;
+rewrite < S_pred in H3;
+rewrite < S_pred in H3;
+assumption.
+qed.