Hint Extern 2 (Symmetric (_ /\ _)) =>
eapply rel_inter_sym : typeclass_instances.
Global Instance rel_inter_flip_sym {A} (R: rel A A):
Symmetric (R /\ flip R).
(** On a related note, a symmetric subrelation of [R] is also a subrelation of its inverse. *)

Lemma subrel_sym_flip {A} (R R': relation A):
Symmetric R ->
RStep (subrel R R') (subrel R (flip R')).