proposition: Lemma cfRes_vchar_on A phi : H \subset G -> phi \in 'Z[irr G, A] -> 'Res[H] phi \in 'Z[irr H, A].
proof: Proof. rewrite zchar_split => sHG /andP[Zphi Aphi]; rewrite zchar_split cfRes_vchar //. apply/cfun_onP=> x /(cfun_onP Aphi); rewrite !cfunElock !genGid sHG => ->. exact: mul0rn. 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(frobenius vector ssrnum ssrint archimedean intdiv) mathcomp(algC algnum classfun character integral_char)