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

Lemma isSome_set_eq {A} (s : set (option A)) (s' : set A) :
s \subset (Some @: s') :|: [set None] ->
Some @: s' \subset s ->
isSome :&: s <--> Some @: s'.