new theorem one_le_power
authorpaulson
Fri, 12 May 2000 15:02:57 +0200
changeset 8861 8341f24e09b5
parent 8860 6bbb93189de6
child 8862 78643f8449c6
new theorem one_le_power
src/HOL/Power.ML
--- a/src/HOL/Power.ML	Fri May 12 15:00:45 2000 +0200
+++ b/src/HOL/Power.ML	Fri May 12 15:02:57 2000 +0200
@@ -23,6 +23,13 @@
 by (induct_tac "n" 1);
 by (ALLGOALS (asm_simp_tac (simpset() addsimps [zero_less_mult_iff])));
 qed "zero_less_power";
+Addsimps [zero_less_power];
+
+Goal "!!i::nat. 1 <= i ==> 1 <= i^n";
+by (induct_tac "n" 1);
+by Auto_tac;
+qed "one_le_power";
+Addsimps [one_le_power];
 
 Goalw [dvd_def] "!!(m::nat) (i::nat). m<=n ==> i^m dvd i^n";
 by (etac (not_less_iff_le RS iffD2 RS add_diff_inverse RS subst) 1);