changeset 31970 | ccaadfcf6941 |
parent 31969 | 09524788a6b9 |
child 32235 | 8f9b8d14fc9f |
--- a/src/HOL/IMP/Machines.thy Thu Jul 09 17:33:22 2009 +0200 +++ b/src/HOL/IMP/Machines.thy Thu Jul 09 17:34:59 2009 +0200 @@ -2,9 +2,6 @@ imports Natural begin -lemma rel_pow_commute: "R O R ^^ n = R ^^ n O R" - by (induct n) (simp, simp add: O_assoc [symmetric]) - lemma converse_in_rel_pow_eq: "((x,z) \<in> R ^^ n) = (n=0 \<and> z=x \<or> (\<exists>m y. n = Suc m \<and> (x,y) \<in> R \<and> (y,z) \<in> R ^^ m))" apply(rule iffI)