proposition: Lemma rker_norm : G \subset 'N(rker).
proof: Proof. apply/subsetP=> x Gx; rewrite inE sub_conjg; apply/subsetP=> y. case/rkerP=> Gy ry1; rewrite mem_conjgV !inE groupJ //=. by rewrite !repr_mxM ?groupM ?groupV // ry1 !mulmxA mulmx1 repr_mxKV. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path) mathcomp(div choice fintype tuple finfun bigop prime) mathcomp(ssralg poly polydiv finset fingroup morphism) mathcomp(perm automorphism quotient finalg action zmodp) mathcomp(commutator cyclic center pgroup matrix mxalgebra) mathcomp(mxpoly)