proposition: Theorem round_N_opp : forall choice, forall x, round (Znearest choice) (-x) = (- round (Znearest (fun t => negb (choice (- (t + 1))%Z))) x)%R.
proof: Proof. intros choice x. unfold round, F2R. simpl. rewrite cexp_opp. rewrite scaled_mantissa_opp. rewrite Znearest_opp. rewrite opp_IZR. now rewrite Ropp_mult_distr_l_reverse. Qed.
imports: Coq(ZArith Reals Lia) Zaux Raux Defs Round_pred Float_prop