proposition: Lemma Zle_Qle_Qceiling (q : Q) (z : Z) : (Qceiling q <= z)%Z <-> q <= inject_Z z.
proof: Proof. split; intro A. + rewrite Zle_Qle in A. apply Qle_trans with (y := inject_Z (Qceiling q)); [apply Qle_ceiling | trivial]. + apply Z.lt_pred_le. rewrite Zlt_Qlt. now apply Qlt_le_trans with (y := q); [apply Qceiling_lt |]. 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