proposition: Lemma cfResQuo H K phi : K \subset cfker phi -> K \subset H -> H \subset G -> ('Res[H / K] (phi / K) = 'Res[H] phi / K)%CF.
proof: Proof. move=> kerK sKH sHG; apply/cfun_inP=> xb Hxb; rewrite cfResE ?quotientS //. have{xb Hxb} [x nKx Hx ->] := morphimP Hxb. by rewrite !cfQuoEnorm ?cfResE ?sub_cfker_Res // inE ?Hx ?(subsetP sHG). Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path) mathcomp(div choice fintype tuple finfun bigop prime order) mathcomp(ssralg poly finset fingroup morphism perm) mathcomp(automorphism quotient finalg action gproduct) mathcomp(zmodp commutator cyclic center pgroup sylow) mathcomp(matrix vector falgebra ssrnum algC algnum) mathcomp(archimedean)