End Pick.
Section MultiQuant.
Variable f : formula R.
Implicit Types (I : seq nat) (e : seq R).

(* Specifications: *)
Lemma foldExistsP I e :
(exists2 e', {in [predC I], same_env e e'} & holds e' f)
<-> holds e (foldr Exists f I).
Lemma foldForallP I e :
(forall e', {in [predC I], same_env e e'} -> holds e' f)
<-> holds e (foldr Forall f I).