proposition: Lemma le_Qle_Qceiling_to_nat (q : Q) (n : nat) : (Z.to_nat (Qceiling q) <= n)%nat <-> q <= inject_Z (Z.of_nat n).
proof: Proof. rewrite Z.le_Zle_to_nat; apply Zle_Qle_Qceiling. 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