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_factor_r : forall (A : Set) (f : A -> Rat) (ls : list A) c rel, RatRel rel -> rel (sumList ls (fun a => (f a) * c)) ((sumList ls f) * c).