intuition.
unfold ratSubtract.
rattac.
inversion e0; clear e0; subst.
inversion e; clear e; subst.
arithNormalize.
apply minus_eq_compat.
arithSimplify.
rewrite <- (mult_assoc n1).
rewrite (mult_comm x2).
rewrite mult_assoc.
arithSimplify.
trivial.
rewrite <- (mult_assoc (n2 * x1)).
rewrite (mult_comm x).
rewrite mult_assoc.
arithSimplify.
rewrite <- (mult_assoc n2).
rewrite (mult_comm x1 x0).
rewrite mult_assoc.
arithSimplify.
rewrite mult_comm.
trivial.
Qed.
Add Parametric Morphism : ratSubtract
with signature (eqRat ==> eqRat ==> eqRat)
as ratSubtract_eqRat_mor.
intuition.
eapply ratSubtract_eqRat_compat; trivial.
Qed.

Theorem leRat_antisymm : forall r1 r2,
r1 <= r2 ->
r2 <= r1 ->
r1 == r2.