X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2Fnat%2Frelevant_equations.ma;h=a2ef6e40cdc6ffaba378c058d3a030a6fa9bea9d;hb=e880d6eab5e1700f4a625ddcd7d0fa8f0cce2dcc;hp=f4cf43775058d9cfdd550c68f2cb959f00fba512;hpb=55b82bd235d82ff7f0a40d980effe1efde1f5073;p=helm.git

diff --git a/helm/software/matita/library/nat/relevant_equations.ma b/helm/software/matita/library/nat/relevant_equations.ma
index f4cf43775..a2ef6e40c 100644
--- a/helm/software/matita/library/nat/relevant_equations.ma
+++ b/helm/software/matita/library/nat/relevant_equations.ma
@@ -12,10 +12,10 @@
 (*                                                                        *)
 (**************************************************************************)
 
-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.
@@ -48,3 +48,13 @@ 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.