Abstract: Integral is one of the most important foundations in many subjects, such as real analysis, the differential equa- lions in signals and systems and so on. Gauge integral is a generalization of the Riemann integral in which some situa- lions are more useful than the Lebesgue integral. This paper formalized the operational properties which contain the fin- rarity, ordering properties, integration by parts, the integral split theorem, integrability on a subinterval, integrability of special functions and limit theorem, cauchy-type integrability criterion of gauge integral in higher-order-logic 4 (HOL4) , and then used them to verify an inverting integrator.

Key words: Formal verification, Thcorcm proving, Gauge integral, HOL4, Integrator