proposition: Lemma subv_sumP {P Us V} : reflect (forall i, P i -> Us i <= V)%VS (\sum_(i | P i) Us i <= V)%VS.
proof: Proof. apply: (iffP idP) => [sUV i Pi | sUV]. by apply: subv_trans sUV; apply: sumv_sup Pi _. by elim/big_rec: _ => [|i W Pi sWV]; rewrite ?sub0v // subv_add sUV. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype bigop finfun tuple) mathcomp(ssralg matrix mxalgebra zmodp)