proposition: Lemma xcprodm_cent : gK @* CK \subset 'C(gH @* CH).
proof: Proof. by rewrite !im_ifactm. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div) mathcomp(fintype bigop finset fingroup morphism perm) mathcomp(automorphism quotient action gproduct gfunctor) mathcomp(cyclic)