proposition: Lemma rfix_quo (K : {group gT}) : K \subset G -> (rfix_mx rGH (K / H)%g :=: rfix_mx rG K)%MS.
proof: Proof. move=> sKG; apply/eqmxP/andP; (split; apply/rfix_mxP) => [x Kx | Hx]. have Gx := subsetP sKG x Kx; rewrite -(quo_mx_coset krH nHG) // rfix_mx_id //. by rewrite mem_morphim ?(subsetP nHG). case/morphimP=> x _ Kx ->; have Gx := subsetP sKG x Kx. by rewrite quo_repr_coset ?rfix_mx_id. 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)