proposition: Lemma rfix_factmod (H : {set gT}) : H \subset G -> (in_factmod U (rfix_mx rG H) <= rfix_mx rU' H)%MS.
proof: Proof. move=> sHG; apply/rfix_mxP=> x Hx. by rewrite -(in_factmodJ Umod) ?(subsetP sHG) ?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)