A Constructive Formalization of the Fundamental Theorem of Calculus

  • Luís Cruz-Filipe
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2646)


We have finished a constructive formalization in the theorem prover Coq of the Fundamental Theorem of Calculus, which states that differentiation and integration are inverse processes. In this formalization, we have closely followed Bishop’s work [4]. In this paper, we describe the formalization in some detail, focusing on how some of Bishop’s original proofs had to be refined, adapted or redone from scratch.


Cauchy Sequence Fundamental Theorem Theorem Prove Computer Algebra System Real Analysis 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Luís Cruz-Filipe
    • 1
    • 2
  1. 1.Department of Computer ScienceUniversity of NijmegenThe Netherlands
  2. 2.Center for Logic and ComputationIST, UTLPortugal

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