proposition: Lemma rfix_conj (H : {set gT}) : (rfix_mx rGB H :=: B *m rfix_mx rG H *m invmx B)%MS.
proof: Proof. apply/eqmxP/andP; split. rewrite -mulmxA (eqmxMfull (_ *m _)) ?row_full_unit //. rewrite -[rfix_mx rGB H](mulmxK uB) submxMr //; apply/rfix_mxP=> x Hx. apply: (canRL (mulmxKV uB)); rewrite -(rconj_mxJ _ uB) mulmxK //. by rewrite rfix_mx_id. apply/rfix_mxP=> x Gx; rewrite -3!mulmxA; congr (_ *m _). by rewrite !mulmxA mulmxKV // 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)