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

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