proposition: Lemma mxrank_cap_compl m1 m2 n (A : 'M_(m1, n)) (B : 'M_(m2, n)) : (\rank (A :&: B) + \rank (A :\: B))%N = \rank A.
proof: Proof. rewrite addnC -mxrank_disjoint_sum ?addsmx_diff_cap_eq //. by rewrite (capmxC A) capmxA capmx_diff cap0mx. 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)