X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2Fnat%2Fexp.ma;h=c6e2a008ba565a043360d1bad656b1fe037b7141;hb=442f3a15d7c6afc480da02602d4d4c8db4f44c10;hp=25c81c0697bdd167b48883261e1fa5af5c62c0aa;hpb=7180662b4d33015e3cbc12a381f0cfc8839de697;p=helm.git

diff --git a/helm/software/matita/library/nat/exp.ma b/helm/software/matita/library/nat/exp.ma
index 25c81c069..c6e2a008b 100644
--- a/helm/software/matita/library/nat/exp.ma
+++ b/helm/software/matita/library/nat/exp.ma
@@ -12,8 +12,6 @@
 (*                                                                        *)
 (**************************************************************************)
 
-set "baseuri" "cic:/matita/nat/exp".
-
 include "nat/div_and_mod.ma".
 include "nat/lt_arith.ma".
 
@@ -22,7 +20,7 @@ let rec exp n m on m\def
  [ O \Rightarrow (S O)
  | (S p) \Rightarrow (times n (exp n p)) ].
 
-interpretation "natural exponent" 'exp a b = (cic:/matita/nat/exp/exp.con a b).
+interpretation "natural exponent" 'exp a b = (exp a b).
 
 theorem exp_plus_times : \forall n,p,q:nat. 
 n \sup (p + q) = (n \sup p) * (n \sup q).
@@ -207,6 +205,23 @@ 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.