intuition.
unfold ratHalf.
eapply eqRat_trans.
apply eqRat_symm.
apply ratMult_distrib.
eapply eqRat_trans.
apply ratMult_eqRat_compat.
apply eqRat_refl.
apply ratOneHalf_add.
rewrite ratMult_1_r.
intuition.
Qed.

Theorem le_ratHalf_0 : forall r,
r <= (ratHalf r) -> r == 0.