We give a short proof-theoretic treatment of a terminating contraction-free calculus G4-LC for the zero-order Gödel-Dummett logic LC. This calculus is a slight variant of a calculus given by Avellone et al, who show its completeness by model-theoretic techniques. In our calculus, all the rules of G4-LC are invertible, thus allowing a deterministic proof-search procedure.