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(* 02110-1301 USA                                                     *)
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(*                                                                          *)
(*  Proof of the three gap theorem.                                         *)
(*                                                                          *)
(*  Micaela Mayero (INRIA-Rocquencourt)                                     *)
(*  September 1998                                                          *)
(*                                                                          *)
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(*                               Nat_compl.v                                *)
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(*********************************************************)
(*             Complements for the natural numbers       *)
(*                                                       *)
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Global Set Asymmetric Patterns.
Require Export Arith.
Require Export Compare_dec.
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Definition decidable (P : Prop) := P \/ ~ P.
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(*       Technical lemmas                                 *)
(**********************************************************)
tauto.
Qed.

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Lemma tech_not_exist_pt :
forall P Q R S : nat -> Prop,
((exists k : nat, P k /\ Q k /\ R k /\ S k) -> False) ->
forall k : nat, P k -> Q k -> ~ R k \/ ~ S k.