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_NG_unicity :
forall (F : R -> Prop) (P : R -> R -> Prop),
Rnd_NG_pt_unicity_prop F P ->
forall rnd1 rnd2 : R -> R,
Rnd_NG F P rnd1 -> Rnd_NG F P rnd2 ->
forall x, rnd1 x = rnd2 x.