Section MatrixAlgebra.
Variables F : fieldType.
Local Notation "A \in R" := (@submx F _ _ _ (mxvec A) R).

Lemma memmx_subP m1 m2 n (R1 : 'A_(m1, n)) (R2 : 'A_(m2, n)) :
reflect (forall A, A \in R1 -> A \in R2) (R1 <= R2)%MS.