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.