proposition: Lemma astab1_scale_act A : A != 0 -> 'C[A | scale_action] = 1%g.
proof: Proof. rewrite -mxrank_eq0=> nzA; apply/trivgP/subsetP=> a; apply: contraLR. rewrite !inE -val_eqE -subr_eq0 sub1set !inE => nz_a1. by rewrite -subr_eq0 -scaleN1r -scalerDl -mxrank_eq0 eqmx_scale. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path) mathcomp(div choice fintype tuple finfun bigop prime) mathcomp(ssralg poly finset fingroup morphism perm) mathcomp(automorphism quotient gproduct action finalg) mathcomp(zmodp commutator cyclic center pgroup gseries) mathcomp(nilpotent sylow maximal abelian matrix) mathcomp(mxalgebra mxrepresentation)