intuition.
assert (ratSubtract (r1 + r2) r2 == ratSubtract (r3 + r2) r2).
eapply ratSubtract_eqRat_compat; intuition.
rewrite ratSubtract_ratAdd_assoc in H0.
setoid_rewrite ratAdd_0_r.
eapply eqRat_trans.
eapply ratAdd_eqRat_compat.
eapply eqRat_refl.
eapply eqRat_symm.
apply (@ratSubtract_0 r2 r2).
eapply leRat_refl.
rewrite H0.
rewrite ratSubtract_ratAdd_assoc.
eapply ratAdd_eqRat_compat.
intuition.
apply ratSubtract_0.
eapply leRat_refl.
apply leRat_refl.
apply leRat_refl.
Qed.

Lemma ratAdd_add_same_l : forall r1 r2 r3,
r2 + r1 == r2 + r3 ->
r1 == r3.