proposition: Lemma BZ_lcm_prop3 a b u: BZcoprime a b -> a %|z u -> b %|z u -> (a *z b) %|z u.
proof: Proof. move => g1 au bu. move: (au) (bu) => [uz az _] [_ bz _]. move: (proj33 (BZlcm_prop2 az bz) _ au bu). by rewrite /BZlcm g1 (BZquo_one (ZSp az bz)). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)