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_set_eq_compat {T} (s1 s2 s1' s2' : set T) :
s1 <--> s1' ->
s2 <--> s2' ->
s1 :|: s2 <--> s1' :|: s2'.