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_subset_r {U} (s1 s2 s3 : set U) :
s1 \subset s3 ->
s1 \subset (s2 :|: s3).