Even if the error is not localized, it was not a good idea to make the unification...

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

diff --git a/helm/software/matita/library/nat/exp.ma b/helm/software/matita/library/nat/exp.ma
index 49efe8525504d4f431e81de36ea702f7c9d46f76..74a3be71f63d202ed5118663088ac238688d142d 100644 (file)
--- a/helm/software/matita/library/nat/exp.ma
+++ b/helm/software/matita/library/nat/exp.ma
@@ -187,6 +187,30 @@ elim (le_to_or_lt_eq n m)
   ]
 qed.
      
-   
+theorem times_exp: 
+\forall n,m,p. exp n p * exp m p = exp (n*m) p.
+intros.elim p
+  [simplify.reflexivity
+  |simplify.
+   rewrite > assoc_times.
+   rewrite < assoc_times in ⊢ (? ? (? ? %) ?).
+   rewrite < sym_times in ⊢ (? ? (? ? (? % ?)) ?).
+   rewrite > assoc_times in ⊢ (? ? (? ? %) ?).
+   rewrite < assoc_times.
+   rewrite < H.
+   reflexivity
+  ]
+qed.
+
+theorem monotonic_exp1: \forall n.
+monotonic nat le (\lambda x.(exp x n)).
+unfold monotonic. intros.
+simplify.elim n
+  [apply le_n
+  |simplify.
+   apply le_times;assumption
+  ]
+qed.
+  
    
    
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