X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2Fnat%2Fcompare.ma;h=b002d78cccdedd6ad690ffeea67aaa0402c14288;hb=947ee89dec9e60561dfac3ce7e1842f35f178cb8;hp=78dc50318197c3dbc449c50d3e757e868aec527d;hpb=af130d273b6be7fbcc2fb2504f3b28ef8fa2344f;p=helm.git

diff --git a/helm/software/matita/library/nat/compare.ma b/helm/software/matita/library/nat/compare.ma
index 78dc50318..b002d78cc 100644
--- a/helm/software/matita/library/nat/compare.ma
+++ b/helm/software/matita/library/nat/compare.ma
@@ -126,6 +126,23 @@ apply nat_elim2; intros; simplify
   ]
 qed.
 
+theorem leb_true_to_le:\forall n,m.
+leb n m = true \to (n \le m).
+intros 2.
+apply leb_elim
+  [intros.assumption
+  |intros.destruct H1.
+  ]
+qed.
+
+theorem leb_false_to_not_le:\forall n,m.
+leb n m = false \to \lnot (n \le m).
+intros 2.
+apply leb_elim
+  [intros.destruct H1
+  |intros.assumption
+  ]
+qed.
 (*
 theorem decidable_le: \forall n,m. n \leq m \lor n \nleq m. 
 intros.