proposition: Lemma cfRes_sub_ker phi : H \subset cfker phi -> 'Res[H, G] phi = (phi 1%g)%:A.
proof: Proof. move=> kerHphi; have sHG := subset_trans kerHphi (cfker_sub phi). apply/cfun_inP=> x Hx; have ker_x := subsetP kerHphi x Hx. by rewrite cfResE // cfunE cfun1E Hx mulr1 cfker1. 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)