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_pt_idempotent : forall F : R -> Prop, forall x f : R, Rnd_NA_pt F x f -> F x -> f = x.