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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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(*                               prop_fl.v                                  *)
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(*              Properties first last after              *)
(*                                                       *)
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Require Export prop_elem.
Require Export Classical_Prop.
Unset Standard Proposition Elimination Names.
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Section theoreme.
Hypothesis alpha_irr : forall n p : Z, (alpha * IZR p)%R <> IZR n.
Hypothesis prop_alpha : (0 < alpha)%R /\ (alpha < 1)%R.
Hypothesis prop_N : forall N : nat, N >= 2.

(* Specifications: *)
(**********)
Lemma tech_fp_alp_irr :
forall n m : nat, frac_part_n_alpha n = frac_part_n_alpha m -> n = m.