proposition: Lemma cdivides_trans a b a': a %|c a'-> b %|c a -> b %|c a'.
proof: Proof. move=> d1 d2. rewrite (cdivides_pr d1) {1} (cdivides_pr d2) - cprodA. move: d1 d2 => [p1 p2 _] [p3 p4 _]. apply: cdivides_pr1 =>//; fprops. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat) mathcomp(binomial div)