proposition: Lemma diffmxE m1 m2 n (A : 'M_(m1, n)) (B : 'M_(m2, n)) : (A :\: B :=: A :&: (capmx_gen A B)^C)%MS.
proof: Proof. by rewrite unlock; apply/eqmxP; rewrite !genmxE !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)