Bertrand's conjecture (weak), some work in progress

[helm.git] / helm / software / matita / library / nat / relevant_equations.ma

diff --git a/helm/software/matita/library/nat/relevant_equations.ma b/helm/software/matita/library/nat/relevant_equations.ma
index f4cf43775058d9cfdd550c68f2cb959f00fba512..6e641708021d79d36c81b67283f889949e1fe43c 100644 (file)
--- a/helm/software/matita/library/nat/relevant_equations.ma
+++ b/helm/software/matita/library/nat/relevant_equations.ma
@@ -12,10 +12,12 @@
 (*                                                                        *)
 (**************************************************************************)
 
-set "baseuri" "cic:/matita/nat/relevant_equations.ma".
+set "baseuri" "cic:/matita/nat/relevant_equations".
 
 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 +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.