intuition.
eapply H.
eapply (leRat_ratAdd_same_r 1).
rewrite <- (@ratSubtract_sum_1 1 r) at 3; trivial.
eapply leRat_trans.
2:{
eapply eqRat_impl_leRat.
eapply ratAdd_assoc.
}
repeat rewrite ratMult_2.
rewrite ratMult_comm.
rewrite (ratMult_comm (2/1)).
eapply (@leRat_ratMult_same_r (1/2)).
intuition.
rewrite ratMult_1_l.
rewrite ratMult_eq_rat1.
eapply leRat_trans.
2:{
eapply eqRat_impl_leRat.
symmetry.
eapply ratMult_distrib_r.
}
rewrite ratMult_assoc.
rewrite ratMult_eq_rat1.
rewrite ratMult_1_r.
rewrite ratMult_comm.
trivial.
Qed.

(* Specifications: *)
Lemma leRat_terms : forall n1 n2 (d1 d2 : posnat),
(n1 <= n2)%nat ->
(d2 <= d1)%nat ->
RatIntro n1 d1 <= RatIntro n2 d2.