proposition: Lemma capmx_diff m1 m2 n (A : 'M_(m1, n)) (B : 'M_(m2, n)) : ((A :\: B) :&: B)%MS = 0.
proof: Proof. apply/eqP; pose C := capmx_gen A B; rewrite -submx0 -(capmx_compl C). by rewrite sub_capmx -capmxE sub_capmx andbAC -sub_capmx -diffmxE -sub_capmx. 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)