proposition: Lemma central_central_factor H K : (K / H) \subset 'Z(G / H) -> H <| K -> H <| G -> central_factor G H K.
proof: Proof. case/subsetIP=> sKGb cGKb /andP[sHK nHK] /andP[sHG nHG]. by rewrite /central_factor -quotient_cents2 // cGKb sHK -(quotientSGK nHK). Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path) mathcomp(fintype bigop finset fingroup morphism) mathcomp(automorphism quotient action commutator center)