# HG changeset patch # User nipkow # Date 1245455619 -7200 # Node ID b9299916d618f07cc50e01a913938edad4afba16 # Parent 60317e5211a2602050ca38b4b35498ef512baa6d new lemmas and tuning diff -r 60317e5211a2 -r b9299916d618 src/HOL/GCD.thy --- a/src/HOL/GCD.thy Fri Jun 19 22:49:38 2009 +0200 +++ b/src/HOL/GCD.thy Sat Jun 20 01:53:39 2009 +0200 @@ -1421,6 +1421,18 @@ lemma int_lcm_dvd2 [iff]: "(n::int) dvd lcm m n" by (subst int_lcm_commute, rule int_lcm_dvd1) +lemma dvd_lcm_if_dvd1_nat: "(k::nat) dvd m \ k dvd lcm m n" +by(metis nat_lcm_dvd1 dvd_trans) + +lemma dvd_lcm_if_dvd2_nat: "(k::nat) dvd n \ k dvd lcm m n" +by(metis nat_lcm_dvd2 dvd_trans) + +lemma dvd_lcm_if_dvd1_int: "(i::int) dvd m \ i dvd lcm m n" +by(metis int_lcm_dvd1 dvd_trans) + +lemma dvd_lcm_if_dvd2_int: "(i::int) dvd n \ i dvd lcm m n" +by(metis int_lcm_dvd2 dvd_trans) + lemma nat_lcm_unique: "(a::nat) dvd d \ b dvd d \ (\e. a dvd e \ b dvd e \ d dvd e) \ d = lcm a b" by (auto intro: dvd_anti_sym nat_lcm_least)