Section MatrixAlgebra.
Variables F : fieldType.
Local Notation "A \in R" := (@submx F _ _ _ (mxvec A) R).
Arguments memmx_subP {m1 m2 n R1 R2}.
Arguments memmx_eqP {m1 m2 n R1 R2}.

Lemma memmx_addsP m1 m2 n A (R1 : 'A_(m1, n)) (R2 : 'A_(m2, n)) :
reflect (exists D, [/\ D.1 \in R1, D.2 \in R2 & A = D.1 + D.2])
(A \in R1 + R2)%MS.