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This paper reports on a six-year collaborative effort that culminated in a complete formalization of a proof of the Feit-Thompson Odd Order Theorem in the Coq proof assistant. The formalized proof is constructive , and relies on nothing but the axioms and rules of the founda-tional framework implemented by Coq. To support the formalization, we developed a(More)
Ventrolateral respiratory column (VRC) circuits that modulate breathing in response to changes in central chemoreceptor drive are incompletely understood. We employed multielectrode arrays and spike train correlation methods to test predictions of the hypothesis that pre-Bötzinger complex (pre-BötC) and retrotrapezoid nucleus/parafacial (RTN-pF) circuits(More)
Large scale real number computation is an essential ingredient in several modern mathematical proofs. Because such lengthy computations cannot be verified by hand, some mathematicians want to use software proof assistants to verify the correctness of these proofs. This paper develops a new implementation of the constructive real numbers and elementary(More)
The following full text is a preprint version which may differ from the publisher's version. Abstract We provide a computer verified exact monadic functional implementation of the Riemann integral in type theory. Together with previous work by O'Connor, this may be seen as the beginning of the realization of Bishop's vision to use constructive mathematics(More)
Compact sets in constructive mathematics capture our intuition of what computable subsets of the plane (or any other complete metric space) ought to be. A good representation of compact sets provides an efficient means of creating and displaying images with a computer. In this paper, I build upon existing work about complete metric spaces to define compact(More)
We present some of the experiments we have performed to best test our design for a library for MathScheme, the mechanized mathematics software system we are building. We wish for our library design to use and reflect, as much as possible, the mathematical structure present in the objects which populate the library.