This paper describes a formalization of the first book of the series ``Elements of Mathematics'' by Nicolas Bourbaki, using the Coq proof assistant. In a first paper published in this journal, we presented the axioms and basic constructions (corresponding to a part of the first two chapters of book I, theory of sets). We discuss here the set of integers (third chapter of book I, theory of set), the sets Z and Q (first chapter of book II, Algebra) and the set of real numbers (Chapter 4 of book III, General topology). We start with a comparison of the Bourbaki approach, the Coq standard library, and the Ssreflect library, then present our implementation.
@article{4771,
title = {Implementation of Bourbaki's Elements of Mathematics in Coq: Part Two, From Natural Numbers to Real Numbers},
journal = {Journal of Formalized Reasoning},
volume = {9},
year = {2016},
doi = {10.6092/issn.1972-5787/4771},
language = {EN},
url = {http://dml.mathdoc.fr/item/4771}
}
Grimm, José. Implementation of Bourbaki's Elements of Mathematics in Coq: Part Two, From Natural Numbers to Real Numbers. Journal of Formalized Reasoning, Tome 9 (2016) . doi : 10.6092/issn.1972-5787/4771. http://gdmltest.u-ga.fr/item/4771/