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

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