proposition: Lemma Qlt_lt_of_nat_inject_Z (q : Q) (n : nat) : inject_Z (Z.of_nat n) < q <-> (n < Z.to_nat (Qceiling q))%nat.
proof: Proof. rewrite (Qlt_Zlt_inject_Z q (Z.of_nat n)); apply Z.lt_Zlt_to_nat. Qed.
imports: Coq.QArith.QArith Coq.ZArith.ZArith Coq.NArith.NArith Coq.QArith.Qpower Coq.QArith.Qround Coq.QArith.Qround Coq.QArith.Qabs CoRN.stdlib_omissions.List