proposition: Lemma cprodEY G H : H \subset 'C(G) -> G \* H = G <*> H.
proof: Proof. by move=> cGH; rewrite cprodE ?cent_joinEr. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div) mathcomp(choice fintype bigop finset fingroup morphism) mathcomp(quotient action)