Hint Extern 1 (RExists _ (_ !! fst) _ _) =>
eapply rel_push_fst_rexists : typeclass_instances.

Lemma rel_push_snd_rexists {A1 A2 B1 B2} (x1:A1) (x2:A2) (y1:B1) (y2:B2) R:
RExists (R (x1, y1) (x2, y2)) (R !! snd) y1 y2.