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

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

diff --git a/helm/software/matita/library/nat/lt_arith.ma b/helm/software/matita/library/nat/lt_arith.ma
index d8422a4dd5ff080a8e8de9eee45ace0f53a10a6f..b4c31c526ca8bb321902661bc89040274349b99a 100644 (file)
--- 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).