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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                                 *)
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(* Specifications: *)
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Lemma not_symt_et :
forall P Q R S : Prop, ~ (P /\ Q /\ R /\ S) -> ~ ((P /\ Q) /\ R /\ S).