Formalizing Calculus while not Limit Theory in Coq

The rationalisation of the basic theory can contribute to the event of huge comes. During this paper, we tend to gift the rationalisation in Coq of calculus while not limit theory. The idea aims to found a replacement variety of calculus additional simply however strictly. This theory as Associate in Nursing innovation differs from ancient calculus however is equivalent and additional clear. First, the definition of the difference-quotient operation is given intuitively from the physical facts. Further, conditions area unit other to that to urge the spinoff, and outline the integral by the axiomatization. Then some vital conclusions in calculus like the Newton–Leibniz formula and therefore the Taylor formula will be formally verified. This shows that this theory will be freelance of limit theory, and any proof doesn't involve imaginary number completeness. This work will facilitate learners to review calculus and lay the muse for several applications.