Arguments genmxP {m1 m2 n A B}.

(* Specifications: *)
Lemma genmx0 m n : <<0 : 'M_(m, n)>>%MS = 0.
Lemma genmx_id m n (A : 'M_(m, n)) : (<<<<A>>>> = <<A>>)%MS.
Hint Resolve row_base_free col_base_full : core.
Lemma mxrank_leqif_sup m1 m2 n (A : 'M_(m1, n)) (B : 'M_(m2, n)) :
(A <= B)%MS -> \rank A <= \rank B ?= iff (B <= A)%MS.
Lemma mxrank_leqif_eq m1 m2 n (A : 'M_(m1, n)) (B : 'M_(m2, n)) :
(A <= B)%MS -> \rank A <= \rank B ?= iff (A == B)%MS.
Lemma rank_ltmx m1 m2 n (A : 'M_(m1, n)) (B : 'M_(m2, n)) :
(A < B)%MS -> \rank A < \rank B.