proposition: Lemma cfRepr_sim n1 n2 rG1 rG2 : mx_rsim rG1 rG2 -> @cfRepr n1 rG1 = @cfRepr n2 rG2.
proof: Proof. case/mx_rsim_def=> f12 [f21] fK def_rG1; apply/cfun_inP=> x Gx. by rewrite !cfunE def_rG1 // mxtrace_mulC mulmxA fK mul1mx. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype choice ssrnat seq) mathcomp(path div fintype tuple finfun bigop prime order) mathcomp(ssralg poly finset gproduct fingroup morphism) mathcomp(perm automorphism quotient finalg action zmodp) mathcomp(commutator cyclic center pgroup nilpotent sylow) mathcomp(abelian matrix mxalgebra mxpoly mxrepresentation) mathcomp(vector ssrnum algC classfun archimedean)