X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2Fnat%2Fnth_prime.ma;h=9d01e99f211e0b3a6e65cc7cb567c732aeff1c6e;hb=cf4088e2cabcbce9b112f1e1fd5cfd38fe16d427;hp=e174266e6884f41cfb4fe256cbe83294790096a4;hpb=b7ed6e0e8e98441ae0688b060196994e9a68cc72;p=helm.git

diff --git a/helm/software/matita/library/nat/nth_prime.ma b/helm/software/matita/library/nat/nth_prime.ma
index e174266e6..9d01e99f2 100644
--- a/helm/software/matita/library/nat/nth_prime.ma
+++ b/helm/software/matita/library/nat/nth_prime.ma
@@ -159,6 +159,17 @@ intros.apply (trans_lt O (S O)).
 unfold lt. apply le_n.apply lt_SO_nth_prime_n.
 qed.
 
+theorem lt_n_nth_prime_n : \forall n:nat. n \lt nth_prime n.
+intro.
+elim n
+  [apply lt_O_nth_prime_n
+  |apply (lt_to_le_to_lt ? (S (nth_prime n1)))
+    [unfold.apply le_S_S.assumption
+    |apply lt_nth_prime_n_nth_prime_Sn
+    ]
+  ]
+qed.
+
 theorem ex_m_le_n_nth_prime_m: 
 \forall n: nat. nth_prime O \le n \to 
 \exists m. nth_prime m \le n \land n < nth_prime (S m).