proposition: Fact scale_is_groupAction : is_groupAction setT scale_action.
proof: Proof. move=> a _ /[1!inE]; apply/andP; split; first by apply/subsetP=> A /[!inE]. by apply/morphicP=> u A _ _ /=; rewrite !actpermE /= /scale_act scalerDr. 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)