We give a short proof-theoretic treatment of a terminating 
contraction-free calculus G4-LC for the zero-order
Goedel-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.