 This is because, if strings of length "m" + "n" are broken into substrings of lengths "m" and "n", and the longest common subsequences of those substrings are found, they can be concatenated together to get a common substring of the whole strings.It follows from a lemma of Michael Fekete that the limit
exists, and equals the supremum of the values formula_9.These limiting values formula_1 are the Chvátal–Sankoff constants.