rattac.
Qed.
(* Definition eqRat_setoid : Setoid_Theory Rat eqRat. econstructor; red. eapply eqRat_refl. eapply eqRat_symm. eapply eqRat_trans. Defined. *)
Add Parametric Relation : Rat leRat
reflexivity proved by leRat_refl
transitivity proved by leRat_trans
as leRat_rel.
Add Parametric Relation : Rat eqRat
reflexivity proved by eqRat_refl
symmetry proved by eqRat_symm
transitivity proved by eqRat_trans
as eqRat_rel.
Global Instance Subrelation_eq_le : subrelation eqRat leRat.
repeat red.
intuition.
eapply eqRat_impl_leRat.
trivial.
Qed.
Global Instance eqRat_resp_leRat :
forall x,
Proper (eqRat ==> Basics.flip Basics.impl)
(leRat x).
intuition.
repeat red; intuition.
simpl.
unfold respectful.
intuition.
eapply leRat_trans.
eapply H0.
eapply eqRat_impl_leRat.
symmetry.
trivial.
Qed.
Local Open Scope rat_scope.

Theorem rat0_le_all : forall r,
0 <= r.