Variable I : finType.
Implicit Type P : pred I.

(* Specifications: *)
Lemma sumv_sup i0 P U Vs :
P i0 -> (U <= Vs i0)%VS -> (U <= \sum_(i | P i) Vs i)%VS.
Lemma memv_sumr P vs (Us : I -> {vspace vT}) :
(forall i, P i -> vs i \in Us i) ->
\sum_(i | P i) vs i \in (\sum_(i | P i) Us i)%VS.