proposition: Lemma norm_sub_rstabs_rfix_mx (H : {set gT}) : H \subset G -> 'N_G(H) \subset rstabs (rfix_mx H).
proof: Proof. move=> sHG; apply/subsetP=> x /setIP[Gx nHx]; rewrite inE Gx. apply/rfix_mxP=> y Hy; have Gy := subsetP sHG y Hy. have Hyx: (y ^ x^-1)%g \in H by rewrite memJ_norm ?groupV. rewrite -mulmxA -repr_mxM // conjgCV repr_mxM ?(subsetP sHG _ Hyx) // mulmxA. by rewrite (rfix_mx_id Hyx). 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)