Let eqmx_sum_nop m n (A : 'M_(m, n)) : (addsmx_nop A :=: A)%MS.
Section AddsmxSub.
Variable (m1 m2 n : nat) (A : 'M[F]_(m1, n)) (B : 'M[F]_(m2, n)).

Lemma col_mx_sub m3 (C : 'M_(m3, n)) :
(col_mx A B <= C)%MS = (A <= C)%MS && (B <= C)%MS.