Title

Theorem Proving in Elementary Analysis

Publication Date

6-2007

Type of Culminating Activity

Thesis

Degree Title

Master of Science in Mathematics

Department

Mathematics

Major Advisor

M. Randall Holmes

Abstract

We describe how the theorem prover Marcel, a program written by Randall Holmes, can be used to prove a result from introductory analysis. We were given the axioms for an ordered field, and we completed a proof of the theorem that every positive real number has a square root. Marcel implements first-order logic via a Gentzen-style sequent calculus, and we first give an outline of the rules for this sequent calculus. We go on to describe how these rules are implemented in Marcel and give example proofs completed using Marcel. This is followed by a brief overview of the axioms for an ordered field and how these axioms were declared in Marcel. We give an outline of an intuitive pencil and paper-style proof of the fact that every positive number has a square root, and we go on to describe a formal proof, completed using Marcel, of the same fact. Finally, we give a few comments regarding the possibilities of using Marcel as an educational tool.

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