X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2Fnat%2Forders.ma;h=42454393ca45cc08676ef8205d878a437a1266f2;hb=683978a2627cf1ce15673360f26806593d22f7b5;hp=8053d50de55bfe8afc7d434243b17ceca34b9536;hpb=a9f72dea3b74e3c0c33daf5be8f4d5d75611492c;p=helm.git

diff --git a/helm/software/matita/library/nat/orders.ma b/helm/software/matita/library/nat/orders.ma
index 8053d50de..42454393c 100644
--- a/helm/software/matita/library/nat/orders.ma
+++ b/helm/software/matita/library/nat/orders.ma
@@ -100,6 +100,12 @@ theorem lt_S_S_to_lt: \forall n,m.
 intros. apply le_S_S_to_le. assumption.
 qed.
 
+theorem lt_to_lt_S_S: ∀n,m. n < m → S n < S m.
+intros;
+unfold lt in H;
+apply (le_S_S ? ? H).
+qed.
+
 theorem leS_to_not_zero : \forall n,m:nat. S n \leq m \to not_zero m.
 intros.elim H.exact I.exact I.
 qed.