proposition: Lemma cprodm_actf : {in H & K, morph_act 'J 'J fH fK}.
proof: Proof. case/cprodP: eqHK_G => _ _ cHK a b Ha Kb /=. by rewrite /conjg -(centsP cHK b) // -(centsP cfHK (fK b)) ?mulKg ?mem_morphim. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div) mathcomp(choice fintype bigop finset fingroup morphism) mathcomp(quotient action)