well my question is: Is the following problem trivial enough not to be proved and if not then would you suggest proveing it by cases or induction.
let be a string and its size. Let be a substring of S. Let be the alphabet and its size. Let . Then
so waht i want to prove is that no matter how large the string is the number of different k size substrings cannot be larger then the number of possible k size substrings. To me this looks obvious enough to be assumed. but if think it is not then would you proceede by proving cases <,>,= or ....?