proposition: Lemma matrix_eq0 m n (A : 'M_(m, n)) : (A == 0) = [forall i, forall j, A i j == 0].
proof: Proof. apply/eqP/'forall_'forall_eqP => [-> i j|A_eq0]; first by rewrite !mxE. by apply/matrixP => i j; rewrite A_eq0 !mxE. 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 countalg finalg zmodp)