Journal of Automated Reasoning

, Volume 50, Issue 2, pp 217–228

Methods of Lemma Extraction in Natural Deduction Proofs

Open Access

DOI: 10.1007/s10817-012-9267-0

Cite this article as:
Pąk, K. J Autom Reasoning (2013) 50: 217. doi:10.1007/s10817-012-9267-0


The existing examples of natural deduction proofs, either declarative or procedural, indicate that often the legibility of proof scripts is of secondary importance to the authors. As soon as the computer accepts the proof script, many authors do not work on improving the parts that could be shortened and do not avoid repetitions of technical sub-deductions, which often could be replaced by a single lemma. This article presents selected properties of reasoning passages that may be used to determine if a reasoning passage can be extracted from a proof script, transformed into a lemma and replaced by a reference to the newly created lemma. Additionally, we present methods for improving the legibility of the reasoning that remains after the extraction of the lemmas.


Lemma Extraction Natural Deduction Legibility 

Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.Institute of InformaticsUniversity of BiałystokBiałystokPoland

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