In this article we show the correctness of integer arithmetic based on Chinese Remainder theorem as described e.g. in : Integers are transformed to finite sequences of modular integers, on which the arithmetic operations are performed. Retransformation of the results to the integers is then accomplished by means of the Chinese Remainder theorem. The method presented is a typical example for computing in homomorphic images.
If the inline PDF is not rendering correctly, you can download the PDF file here.
 Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics 1(1):41-46 1990.
 Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics 1(1):91-96 1990.
 Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics 1(1):107-114 1990.