### Abstract

We formalize how a natural number can be expanded into its digits in
some base and prove properties about functions that operate on digit
expansions. This includes the formalization of concepts such as digit
shifts and carries. For a base that is a power of 2 we formalize the
binary AND, binary orthogonality and binary masking of two natural
numbers. This library on digit expansions builds the basis for the
formalization of the DPRM theorem.