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_subset_compat :
forall (T : Type) (s1 s2 s1' s2' : set T),
s1 \subset s1' -> s2 \subset s2' -> s1 :|: s2 \subset s1' :|: s2'.