proposition: Lemma bigcapmx_inf i0 P m n (A_ : I -> 'M_n) (B : 'M_(m, n)) : P i0 -> (A_ i0 <= B -> \bigcap_(i | P i) A_ i <= B)%MS.
proof: Proof. by move=> Pi0; apply: submx_trans; rewrite (bigD1 i0) // capmxSl. 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)