Formalizing Constructive Real Analysis

This paper arises from a project with the Nuprl Proof Development System which involved formalizing parts of real analysis, up through the intermediate value theorem. Extensive development of the rational library was required as the real library was being built, resulting in the addition of about 125 rational theorems. The real library now contains about 150 theorems and includes enough basic results that further extensions of the library should be quite feasible. This paper aims to illustrate how higher mathematics can be implemented in a system like Nuprl, and also to introduce system users to the library. 1 Introduction The first part of this paper is a guided tour through the real library with emphasis on the definitions, a handful of useful theorems, and the proof of the intermediate value theorem. Afterwards is a section giving detailed descriptions of the special-purpose tactics that were written in conjunction with the rationals and the reals. Users interested in developing th..