End Submodule.
(* Properties of enveloping algebra as a subspace of 'rV_(n ^ 2). *)

(* Specifications: *)
Lemma envelop_mx_id x : x \in G -> (rG x \in E_G)%MS.
Lemma envelop_mx1 : (1%:M \in E_G)%MS.
Lemma envelop_mxM A B : (A \in E_G -> B \in E_G -> A *m B \in E_G)%MS.
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.