proposition: Lemma orderM a b : commute a b -> coprime #[a] #[b] -> #[a * b] = (#[a] * #[b])%N.
proof: Proof. by move=> cab co_ab; rewrite -coprime_cardMg -?cycleM. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice div) mathcomp(fintype bigop prime finset fingroup morphism) mathcomp(perm automorphism quotient gproduct ssralg) mathcomp(finalg zmodp poly)