sentences:  Levi's lemma
  
  In theoretical computer science and mathematics, especially in the area of combinatorics on words, the Levi lemma states that, for all strings "u", "v", "x" and "y", if "uv" = "xy", then there exists a string "w" such that either
  
  or
  
  That is, there is a string "w" that is "in the middle", and can be grouped to one side or the other.Levi's lemma is named after Friedrich Wilhelm Levi, who published it in 1944.