X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2Fnat%2Flt_arith.ma;h=b4c31c526ca8bb321902661bc89040274349b99a;hb=018a168b0ca16c5951106162e515d7949366d754;hp=d8422a4dd5ff080a8e8de9eee45ace0f53a10a6f;hpb=32d926732ac785220007f1999d8ee868efd12e8c;p=helm.git

diff --git a/helm/software/matita/library/nat/lt_arith.ma b/helm/software/matita/library/nat/lt_arith.ma
index d8422a4dd..b4c31c526 100644
--- a/helm/software/matita/library/nat/lt_arith.ma
+++ b/helm/software/matita/library/nat/lt_arith.ma
@@ -118,6 +118,17 @@ apply (nat_case1 a)
 ]
 qed.
 
+lemma lt_times_to_lt_O: \forall i,n,m:nat. i < n*m \to O < m.
+intros.
+elim (le_to_or_lt_eq O ? (le_O_n m))
+  [assumption
+  |apply False_ind.
+   rewrite < H1 in H.
+   rewrite < times_n_O in H.
+   apply (not_le_Sn_O ? H)
+  ]
+qed.
+
 (* times *)
 theorem monotonic_lt_times_r: 
 \forall n:nat.monotonic nat lt (\lambda m.(S n)*m).