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.

Theorem oc_comp_wf : forall (A B C : Set)(c : OracleComp A B C), well_formed_oc c -> forall (S : Set)(eqds : EqDec S)(o : S -> A -> Comp (B * S))(s : S), (forall a b, well_formed_comp (o a b)) -> well_formed_comp (c _ _ o s).