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].

Lemma mxrank_add m n (A B : 'M_(m, n)) : \rank (A + B)%R <= \rank A + \rank B.