proposition: Lemma sub_cfker_Res A phi : A \subset H -> A \subset cfker phi -> A \subset cfker ('Res[H, G] phi).
proof: Proof. move=> sAH kerA; apply/subsetP=> x Ax; have Hx := subsetP sAH x Ax. rewrite inE Hx; apply/forallP=> y; rewrite !cfunElock !genGid groupMl //. by rewrite !(fun_if phi) cfkerMl // (subsetP kerA). 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)