proposition: Lemma capmxMr m1 m2 n p (A : 'M_(m1, n)) (B : 'M_(m2, n)) (C : 'M_(n, p)) : ((A :&: B) *m C <= A *m C :&: B *m C)%MS.
proof: Proof. by rewrite sub_capmx !submxMr ?capmxSl ?capmxSr. 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)