Instance proper_set_incl A :
Morphisms.Proper (set_eq ==> set_eq ==> Basics.impl) (@set_incl A).
Instance eq_setI U : Proper (set_eq ==> set_eq ==> set_eq) (@setI U).

Lemma setI_comm {U} (s1 s2 : set U) :
s1 :&: s2 <--> s2 :&: s1.