proposition: Lemma cfunM_onI A B phi psi : phi \in 'CF(G, A) -> psi \in 'CF(G, B) -> phi * psi \in 'CF(G, A :&: B).
proof: Proof. rewrite !cfun_onE => Aphi Bpsi; apply/subsetP=> x; rewrite !inE cfunE mulf_eq0. by case/norP=> /(subsetP Aphi)-> /(subsetP Bpsi). 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)