Karatsuba Multiplication on Integers

We give a verified implementation of the Karatsuba Multiplication on Integers as well as verified runtime bounds. Integers are represented as LSBF (least significant bit first) boolean lists, on which the algorithm by Karatsuba is implemented. The running time of $O\left(n^{\log_2 3}\right)$ is verified using the Time Monad defined in Root-Balanced Trees by Nipkow.