Arguments submxP {m1 m2 n A B}.

(* Specifications: *)
Lemma submx_refl m n (A : 'M_(m, n)) : (A <= A)%MS.
Lemma sub_ltmx_trans m1 m2 m3 n
(A : 'M_(m1, n)) (B : 'M_(m2, n)) (C : 'M_(m3, n)) :
(A <= B)%MS -> (B < C)%MS -> (A < C)%MS.
Lemma ltmx_trans m n : transitive (@ltmx m m n).
Lemma summx_sub m1 m2 n (B : 'M_(m2, n))
I (r : seq I) (P : pred I) (A_ : I -> 'M_(m1, n)) :
(forall i, P i -> A_ i <= B)%MS -> ((\sum_(i <- r | P i) A_ i)%R <= B)%MS.
Lemma scalemx_sub m1 m2 n a (A : 'M_(m1, n)) (B : 'M_(m2, n)) :
(A <= B)%MS -> (a *: A <= B)%MS.