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.

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Lemma tech_fp_alp_irr :
forall n m : nat, frac_part_n_alpha n = frac_part_n_alpha m -> n = m.