Instance RatRel_trans : 
  forall (R : Rat -> Rat -> Prop),
    RatRel R -> Transitive R.Instance RatRel_flip : 
  forall R,
    RatRel R ->
    RatRel (Basics.flip R).(* The class includes equality and inequality. *)

Instance eqRat_RatRel : RatRel eqRat.Instance leRat_RatRel : RatRel leRat.

Lemma rel_sumList_compat : forall (A : Set)(f1 f2 : A -> Rat) ls rel, RatRel rel -> (forall a, In a ls -> rel (f1 a) (f2 a)) -> rel (sumList ls f1) (sumList ls f2).