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

Lemma bigcup_setU_r:
forall (U T : Type) (s : set U) (f g : U -> set T),
\bigcup_(i in s) (f i :|: g i) <-->
\bigcup_(i in s) f i :|: \bigcup_(i in s) g i.