Formal Proof of the Mean Value Theorem Based on Coq

This paper introduces the formal proof of the three mean value theorems of differentiation in detail. The differential mean value theorem is the core theorem of differential calculus, an important tool for studying functions, and a bridge between functions and derivatives. Based on the formalization of function, limit, function continuity, and function derivation, etc. We strictly formalized the three median value theorems of differentiation: Rolle's theorem, Lagrange's median value theorem, and Cauchy's median value theorem. This work lays a solid foundation for our subsequent proofs of important theorems in mathematical analysis, not only promoting advancements in the field of education but also contributing to the progress of mathematical mechanization. All the codes involved in this article have been verified in Coq, which fully reflects the high reliability of Coq.