Definition up_Q q:= proj1_sig (Q_Archimedean_inf q).Definition up_Q_property q := proj2_sig (Q_Archimedean_inf q):  q <= (up_Q q) /\ (up_Q q) - q <= Qone.

Lemma Q_Archimedean_nat_inf:forall q:Q, {n:nat | q<=n }.