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 setU_set0_l {A} (s1 s2 s3 : set A) :
s1 <--> set0 ->
s2 <--> s3 ->
(s1 :|: s2) <--> s3.