Section OneMatrix.
Variables (m n : nat) (A : 'M[aT]_(m, n)).
Definition nz_row m n (A : 'M_(m, n)) :=
oapp (fun i => row i A) 0 [pick i | row i A != 0].
Definition is_diag_mx m n (A : 'M[V]_(m, n)) :=
[forall i : 'I__, forall j : 'I__, (i != j :> nat) ==> (A i j == 0)].

Lemma dlsubmx_diag m1 m2 n1 n2 (A : 'M[V]_(m1 + m2, n1 + n2)) :
n1 <= m1 -> is_diag_mx A -> dlsubmx A = 0.