proposition: Lemma im_cprodm : cprodm @* G = fH @* H * fK @* K.
proof: Proof. by have [_ defHK _] := cprodP eqHK_G; rewrite -{2}defHK morphim_cprodm. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div) mathcomp(choice fintype bigop finset fingroup morphism) mathcomp(quotient action)