  Herbrand's theorem is often presented as a corollary of Gentzen's sharpened
Hauptsatz for the classical sequent calculus. However, the midsequent gives
Herbrand's theorem directly only for formulae in prenex normal form. In the
Handbook of Proof Theory, Buss claims to give a proof of the full statement of
the theorem, using sequent calculus methods to show completeness of a calculus
of Herbrand proofs, but as we demonstrate there is a flaw in the proof. In this
note we give a correct demonstration of Herbrand's theorem in its full
generality, as a corollary of the full cut-elimination theorem for LK. The
major difficulty is to show that, if there is an Herbrand proof of the premiss
of a contraction rule, there is an Herbrand proof of its conclusion. We solve
this problem by showing the admissibility of a deep contraction rule.
