This paper examines the possibility of using computers interactively to prove theorems in analysis. For this purpose two pre-existing pieces of software have been harnessed together. VERIFY was designed for set-theoretic proofs, and REDUCE was designed for algebraic manipulation and simplification. The authors demonstrate the success of the combination on a large set of elementary theorems. At present the system is useful for teaching, but the authors envision that additional work will make it useful for research.