Formalization of Real Binomial Coefficient in HOL4

The theorem proving is a formal method and plays an important role in the verification of safety-critical system.The fractional calculus is the basis of the complex system's analysis.The real binomial coefficient is an important part of the fractional calculus GL definition.Currently,there is not the formalization of real binomial coefficient in higher-order-logic theorem library.This paper presented the formalization of the real binomial coefficients.The factorial power was firstly formalized in HOL4.And the real binomial coefficient was formalized using the formalization of factorial power.The paper also presented the formal verification of the fractional calculus.At the same time it illustrateed the practical effectiveness and utilization of our approach.