Hint Extern 0 (RExists _ subrel _ (_ \/ _)%rel) =>
eapply rel_union_subrel_rexists_r : typeclass_instances.

Lemma rel_union_lub {A B} (R1 R2 R: rel A B):
RIntro (subrel R1 R /\ subrel R2 R) subrel (R1 \/ R2)%rel R.