intuition.
rewrite <- ratMult_num_den.
eapply num_dem_same_rat1.
unfold posnatMult, natToPosnat, posnatToNat.
eapply mult_comm.
Qed.

Lemma half_distance_1_le : forall r,
~ 1 <= r ->
~ 1 <= r + (1 / 2) * (ratSubtract 1 r).