Abstract
In this paper we present a contraction-free sequent calculus including inductive definitions for the first-order intuitionistic logic. We show that it is a natural extension to Dyckhoff’s LJT calculus and we prove the contraction- and cut-elimination properties, thus extending Dyckhoff’s result, in order to validate its use as a basis for proof-search procedures. Finally we describe the proof-search strategy used in our implementation as a tactic in the Coq proof assistant [2].
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Corbineau, P. (2004). First-Order Reasoning in the Calculus of Inductive Constructions. In: Berardi, S., Coppo, M., Damiani, F. (eds) Types for Proofs and Programs. TYPES 2003. Lecture Notes in Computer Science, vol 3085. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24849-1_11
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DOI: https://doi.org/10.1007/978-3-540-24849-1_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22164-7
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