Open Access
2018 Negation-Free and Contradiction-Free Proof of the Steiner–Lehmus Theorem
Victor Pambuccian
Notre Dame J. Formal Logic 59(1): 75-90 (2018). DOI: 10.1215/00294527-2017-0019


By rephrasing quantifier-free axioms as rules of derivation in sequent calculus, we show that the generalized Steiner–Lehmus theorem admits a direct proof in classical logic. This provides a partial answer to a question raised by Sylvester in 1852. We also present some comments on possible intuitionistic approaches.


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Victor Pambuccian. "Negation-Free and Contradiction-Free Proof of the Steiner–Lehmus Theorem." Notre Dame J. Formal Logic 59 (1) 75 - 90, 2018.


Received: 22 March 2014; Accepted: 1 June 2015; Published: 2018
First available in Project Euclid: 1 September 2017

zbMATH: 06848192
MathSciNet: MR3744352
Digital Object Identifier: 10.1215/00294527-2017-0019

Primary: 03F07
Secondary: 03B30 , 51F05

Keywords: absolute geometry , direct proof , indirect proof , sequent calculus , Steiner–Lehmus theorem

Rights: Copyright © 2018 University of Notre Dame

Vol.59 • No. 1 • 2018
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