intuition.
eapply eqRat_ratAdd_same_r.
rewrite ratAdd_comm.
rewrite H.
rewrite <- ratAdd_0_l.
intuition.
Qed.
Definition ratHalf(r : Rat) :=
r * (1 / 2).

Theorem ratHalf_ne_0 : forall r,
~ r == 0 ->
~ (ratHalf r) == 0.