proposition: Theorem Zaway_opp : forall x, Zaway (- x) = Z.opp (Zaway x).
proof: Proof. intros x. unfold Zaway at 2. case Rlt_bool_spec ; intro H. rewrite Zaway_ceil. unfold Zceil. now rewrite Ropp_involutive. apply Rlt_le. now apply Ropp_0_gt_lt_contravar. rewrite Zaway_floor. apply sym_eq. apply Z.opp_involutive. rewrite <- Ropp_0. now apply Ropp_le_contravar. Qed.
imports: Coq(Psatz Reals ZArith) Zaux