proposition: Lemma xcprodmE : {in H & K, forall x y, xcprodm (cpairg1 x * cpair1g y) = fH x * fK y}.
proof: Proof. by move=> x y Hx Ky; rewrite /xcprodm cprodmE ?mem_morphim ?ifactmE. 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)