proposition: Lemma row_subP m1 m2 n (A : 'M_(m1, n)) (B : 'M_(m2, n)) : reflect (forall i, row i A <= B)%MS (A <= B)%MS.
proof: Proof. apply: (iffP idP) => [sAB i|sAB]. by apply: submx_trans sAB; apply: row_sub. rewrite submxE; apply/eqP/row_matrixP=> i; apply/eqP. by rewrite row_mul row0 -submxE. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype finfun bigop finset fingroup perm order) mathcomp(div prime binomial ssralg finalg zmodp matrix)