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

Lemma setI_set_eq_r {A : Type} (s1 s2 s2' : set A) :
s2 <--> s2' ->
(s1 :&: s2) <--> (s1 :&: s2').