
This folder contains a formal proof of the following statement: given an
infinite tape labeled by zeros and ones there are two cells with the same value.
The proof proceeds by a lemma stating that - on a such a tape - there are either
infinitely many zeros or infinitely many ones. This is a subcase of the proof of
the unbounded pigeonhole principle from the infinite pigeonhole principle.

For more information about this proof, please see Section 4.2 of:

C. Urban: Classical Logic and Computation, PhD thesis,
University of Cambridge, 2000

as well as Section 3 of:

M. Baaz, S. Hetzl, A. Leitsch, C. Richter, H. Spohr: Cut-Elimination:
Experiments with CERES. LPAR 2004, Springer LNCS 3452, pg. 481-495

