Lower bound on comparison-based sorting algorithms

This article contains a formal proof of the well-known fact that number of comparisons that a comparison-based sorting algorithm needs to perform to sort a list of length n is at least log₂ (n!) in the worst case, i. e. Ω(n log n).

For this purpose, a shallow embedding for comparison-based sorting algorithms is defined: a sorting algorithm is a recursive datatype containing either a HOL function or a query of a comparison oracle with a continuation containing the remaining computation. This makes it possible to force the algorithm to use only comparisons and to track the number of comparisons made.