proposition: Lemma subv_bigcapP {P U Vs} : reflect (forall i, P i -> U <= Vs i)%VS (U <= \bigcap_(i | P i) Vs i)%VS.
proof: Proof. apply: (iffP idP) => [sUV i Pi | sUV]. by rewrite (subv_trans sUV) ?(bigcapv_inf Pi). by elim/big_rec: _ => [|i W Pi]; rewrite ?subvf // subv_cap sUV. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype bigop finfun tuple) mathcomp(ssralg matrix mxalgebra zmodp)