intuition.
destruct (expRat_half_le_exp_exists H0).
destruct (expRat_le_half_exists H).
exists (x0 * x)%nat.
rewrite expRat_exp_prod.
eapply leRat_trans.
eapply expRat_leRat_compat.
eapply H2.
intuition.
Qed.

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