This ProofPower-HOL script contains definitions and proofs concerning some of the basics of analysis. The material covered includes: polynomial functions on the real numbers, limits of sequences, continuity of functions of real variables, differentiation, limits of function values, uniform convergence of limits of functions, series and power series and their use in defining the exponential,
... [Show full abstract] logarithm and sine and cosine functions; the other circular trigonometric functions and the hyperbolic trigonometric functions and a selection of the inverse functions; definition and basic properties of the Henstock-Kurzweil gauge integral including the fundamental theorem of the calculus; calculation of the areas of some simple plane sets.