  We present a manuscript of Paul Lorenzen that provides a proof of consistency
for elementary number theory as an application of the construction of the free
countably complete pseudocomplemented semilattice over a preordered set. This
manuscript rests in the Oskar-Becker-Nachlass at the Philosophisches Archiv of
Universit{\"a}t Konstanz, file OB 5-3b-5. It has probably been written between
March and May 1944. We also compare this proof to Gentzen's and Novikov's, and
provide a translation of the manuscript.
