proposition: Lemma rfix_morphpre (H : {set aT}) : H \subset D -> (rfix_mx rGf H :=: rfix_mx rG (f @* H))%MS.
proof: Proof. move=> sHD; apply/eqmxP/andP; split. by apply/rfix_mxP=> _ /morphimP[x _ Hx ->]; rewrite rfix_mx_id. by apply/rfix_mxP=> x Hx; rewrite rfix_mx_id ?mem_morphim ?(subsetP sHD). 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)