Definition Rnd_NG_pt_unicity_prop F P :=
  forall x d u,
  Rnd_DN_pt F x d -> Rnd_N_pt F x d ->
  Rnd_UP_pt F x u -> Rnd_N_pt F x u ->
  P x d -> P x u -> d = u.

Theorem Rnd_NA_NG_pt : forall F : R -> Prop, F 0 -> forall x f, Rnd_NA_pt F x f <-> Rnd_NG_pt F (fun x f => Rabs x <= Rabs f) x f.