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.