Notation sumV := (\sum_(i <- r0 | P i) Vs i)%VCanonical subvs_subType := Eval hnf in [subType for vsval].by <:].
Canonical subvs_eqType := Eval hnf in EqType subvs_of subvs_eq<:].
Canonical subvs_choiceType := ChoiceType subvs_of subvs_choiceMi

Lemma subvsP w : vsval w \in U. Proof