A Formalization of Properties of Continuous Functions on Closed Intervals

Formal mathematics is getting increasing attention in mathematics and computer science. In particular, the formalization of calculus has important applications in engineering design and analysis. In this paper, we present a formal proof of some fundamental theorems of continuous functions on closed intervals based on the Coq proof assistant. In this formalization, we build a real number system referring to Landau’s Foundations of Analysis. Then we complete the formalization of the basic definitions of interval, function, and limit and formally prove the theorems including completeness theorem, intermediate value theorem, uniform continuity theorem and others in Coq. The proof process is normalized, rigorous and reliable.