X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2Fnat%2Frelevant_equations.ma;h=6e641708021d79d36c81b67283f889949e1fe43c;hb=10f29fdd78ee089a9a94446207b543d33d6c851c;hp=9e275aa9ca8a6e8828af7fab7c7073b502cd26b7;hpb=18a895438260a82a83608c14f1ab99870962ba26;p=helm.git

diff --git a/helm/software/matita/library/nat/relevant_equations.ma b/helm/software/matita/library/nat/relevant_equations.ma
index 9e275aa9c..6e6417080 100644
--- a/helm/software/matita/library/nat/relevant_equations.ma
+++ b/helm/software/matita/library/nat/relevant_equations.ma
@@ -50,3 +50,13 @@ rewrite > distr_times_plus.
 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.