Qed.
Definition Qinv (x : Q) :=
match x with
| Qpos x => Qpos (Qpositive_inv x)
| Qneg x => Qneg (Qpositive_inv x)
| Zero => Zero
end.

Theorem Qinv_def : forall x : Q, x <> Zero -> Qmult x (Qinv x) = Qpos One.
intros x; case x.