(Proving Regularity) I want to see if a given string is "contained" within in a much longer string (perhaps for searching a keyword within a large body of text). Certainly, this is true if the given string is a substring. However, it is intuitive that we want to also check if the string is a subsequence of the text as well (perhaps that this word is broken up into several parts throughout the body of text in order).^1 Formally, let L be any language over sigma. Then, consider the language S(L) = {x: wxy elementof L, w, y elementof sigma*} Union {a;: w elementof L, and it: is a subsequence of a: }. Prove that if L is regular, then S(L) is also regular