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(* 02110-1301 USA                                                     *)
(** lemmas. Some nice lemmas, mostly about le, lt, and mult.  @author Olga Caprotti and Martijn Oostdijk @version $Revision$ *)
Global Set Asymmetric Patterns.

Lemma lt_witness :
forall x y : nat, x < y -> exists q : nat, x + q = y /\ 0 < q.