Section LtmxIdentities.
Variables (m1 m2 n : nat) (A : 'M_(m1, n)) (B : 'M_(m2, n)).
Hint Resolve rank_leq_row rank_leq_col row_ebase_unit col_ebase_unit : core.
Arguments mulmx_max_rank [r m n].
Arguments submxP {m1 m2 n A B}.
Arguments row_subP {m1 m2 n A B}.

Lemma rV_subP m1 m2 n (A : 'M_(m1, n)) (B : 'M_(m2, n)) :
reflect (forall v : 'rV_n, v <= A -> v <= B)%MS (A <= B)%MS.