proposition: Lemma rfix_gen (H : {set gT}) : H \subset G -> (rfix_mx rGA H :=: in_gen (rfix_mx rG H))%MS.
proof: Proof. move/subsetP=> sHG; apply/eqmxP/andP; split; last first. by apply/rfix_mxP=> g Hg; rewrite -in_genJ ?sHG ?rfix_mx_id. rewrite -[rfix_mx rGA H]val_genK; apply: submx_in_gen. by apply/rfix_mxP=> g Hg; rewrite -val_genJ ?rfix_mx_id ?sHG. 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)