proposition: Lemma mxmodule_envelop m1 m2 (U : 'M_(m1, n)) (W : 'M_(m2, n)) A : (mxmodule U -> mxvec A <= E_G -> W <= U -> W *m A <= U)%MS.
proof: Proof. move=> modU /envelop_mxP[a ->] sWU; rewrite linear_sum summx_sub // => x Gx. by rewrite linearZ scalemx_sub ?mxmodule_trans. 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)