proposition: Lemma cfker_mul phi psi : cfker phi :&: cfker psi \subset cfker (phi * psi).
proof: Proof. apply/subsetP=> x /setIP[Kphi_x Kpsi_x]; have [Gx _] := setIdP Kphi_x. by rewrite inE Gx; apply/forallP=> y; rewrite !cfunE !cfkerMl. 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)