Abstract
In this paper, we describe how we captured and investigated incidence reasoning in Hilbert’s Foundations of Geometry by using a new discovery tool integrated into an interactive proof assistant. Our tool exploits concurrency, inferring facts independently of the user with the incomplete proof as a guide. It explores the proof space, contributes tedious lemmas and discovers alternative proofs. We show how this tool allowed us to write readable formalised proof-scripts that correspond very closely to Hilbert’s prose arguments.
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Scott, P., Fleuriot, J. (2011). An Investigation of Hilbert’s Implicit Reasoning through Proof Discovery in Idle-Time. In: Schreck, P., Narboux, J., Richter-Gebert, J. (eds) Automated Deduction in Geometry. ADG 2010. Lecture Notes in Computer Science(), vol 6877. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25070-5_11
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DOI: https://doi.org/10.1007/978-3-642-25070-5_11
Publisher Name: Springer, Berlin, Heidelberg
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