proposition: Lemma sub_bigcapmxP P m n (A : 'M_(m, n)) (B_ : I -> 'M_n) : reflect (forall i, P i -> A <= B_ i)%MS (A <= \bigcap_(i | P i) B_ i)%MS.
proof: Proof. apply: (iffP idP) => [sAB i Pi | sAB]. by apply: (submx_trans sAB); rewrite (bigcapmx_inf Pi). by elim/big_rec: _ => [|i Pi C sAC]; rewrite ?submx1 // sub_capmx sAB. 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)