proposition: Lemma Archimedes' : forall x : R1, {n : nat | x [<] nring n}.
proof: Proof. intro x. elim (Archimedes (x[+][1])); intros n Hn. exists n. apply less_leEq_trans with (x[+][1]); auto. apply less_plusOne. Qed.
imports: CoRN.model.reals.Cauchy_IR CoRN.model.monoids.Nmonoid CoRN.model.rings.Zring CoRN.algebra.CRing_Homomorphisms CoRN.algebra.Expon Coq.QArith.Qpower CoRN.tactics.CornTac