The Pigeonhole Principle
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  Suppose that f: A -> B, where A and B are finite,
  and |A| > |B|.  Then f is not injective.


Stronger form -

  Suppose that f: A -> B, where A and B are finite.
  Then there exists b \in B such that 
     | f^{-1}(b) |  >=   \ceiling{ |A| / |B| }