]
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.