Parallel Postulates and Continuity Axioms: A Mechanized Study in Intuitionistic Logic Using Coq

@article{Boutry2017ParallelPA,
  title={Parallel Postulates and Continuity Axioms: A Mechanized Study in Intuitionistic Logic Using Coq},
  author={Pierre Boutry and Charly Gries and Julien Narboux and Pascal Schreck},
  journal={Journal of Automated Reasoning},
  year={2017},
  volume={62},
  pages={1-68}
}
In this paper we focus on the formalization of the proofs of equivalence between different versions of Euclid’s 5th postulate. Our study is performed in the context of Tarski’s neutral geometry, or equivalently in Hilbert’s geometry defined by the first three groups of axioms, and uses an intuitionistic logic, assuming excluded-middle only for point equality. Our formalization provides a clarification of the conditions under which different versions of the postulates are equivalent. Following… 
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