X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2Fnat%2Fexp.ma;h=52793cb5a77b21d853ff56cac6868ff4c9e24905;hb=3f5a0152427fd9a89e7239befd259d27b97aaef5;hp=cb64efee23ede4a7b329cfde8cd311178a91465a;hpb=9475bcd66c14f82b84c27d4c759aa94783ec08d3;p=helm.git

diff --git a/helm/software/matita/library/nat/exp.ma b/helm/software/matita/library/nat/exp.ma
index cb64efee2..52793cb5a 100644
--- a/helm/software/matita/library/nat/exp.ma
+++ b/helm/software/matita/library/nat/exp.ma
@@ -186,6 +186,11 @@ apply nat_elim2;intros
   ]
 qed.
 
+theorem le_exp_to_le1 : \forall n,m,p.O < p \to exp n p \leq exp m p \to n \leq m.
+intros;apply not_lt_to_le;intro;apply (lt_to_not_le ? ? ? H1);
+apply lt_exp1;assumption.
+qed.
+     
 theorem lt_exp_to_lt: 
 \forall a,n,m. S O < a \to exp a n < exp a m \to n < m.
 intros.
@@ -202,6 +207,23 @@ elim (le_to_or_lt_eq n m)
     ]
   ]
 qed.
+
+theorem lt_exp_to_lt1: 
+\forall a,n,m. O < a \to exp n a < exp m a \to n < m.
+intros.
+elim (le_to_or_lt_eq n m)
+  [assumption
+  |apply False_ind.
+   apply (lt_to_not_eq ? ? H1).
+   rewrite < H2.
+   reflexivity
+  |apply (le_exp_to_le1 ? ? a)
+    [assumption
+    |apply lt_to_le.
+     assumption
+    ]
+  ]
+qed.
      
 theorem times_exp: 
 \forall n,m,p. exp n p * exp m p = exp (n*m) p.