proposition: Lemma max_cfRepr_mx1 n (rG : mx_representation algC G n) x : x \in G -> cfRepr rG x = cfRepr rG 1%g -> rG x = 1%:M.
proof: Proof. move=> Gx kerGx; have [|c _ def_x] := @max_cfRepr_norm_scalar n rG x Gx. by rewrite kerGx cfRepr1 normr_nat. move/eqP: kerGx; rewrite cfRepr1 cfunE Gx {rG}def_x mxtrace_scalar. case: n => [_|n]; first by rewrite ![_%:M]flatmx0. rewrite mulrb -subr_eq0 -mulrnBl -mulr_natl mulf_eq0 pnatr_eq0 /=. by rewrite subr_eq0 => /eqP->. 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)