proposition: Lemma map_capmx m1 m2 n (A : 'M_(m1, n)) (B : 'M_(m2, n)) : ((A :&: B)^f :=: A^f :&: B^f)%MS.
proof: Proof. by apply/eqmxP; rewrite !capmxE -map_capmx_gen !map_submx -!capmxE andbb. 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)