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

Lemma bigcap_setI_l {U T} (s1 s2 : set U) (f : U -> set T) :
bigcap (s1 :|: s2) f <-->
bigcap s1 f :&: bigcap s2 f.