proposition: Lemma capmx_idPr n m1 m2 (A : 'M_(m1, n)) (B : 'M_(m2, n)) : reflect (A :&: B :=: B)%MS (B <= A)%MS.
proof: Proof. have:= @eqmxP _ _ _ (A :&: B)%MS B. by rewrite capmxSr sub_capmx submx_refl !andbT. 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)