Instance eq_bigcap T U : Proper (set_eq ==> pointwise_relation T (@set_eq U) ==> set_eq) bigcap.

Lemma bigcup_nil_setI {A B} (f : A -> set B)
(l : seq A) s :
\bigcup_(x in [] :&: s) (f x) \subset
\bigcup_(x in (l :&: s)) (f x).