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_DN_pt_equiv_format :
forall F1 F2 : R -> Prop,
forall a b : R,
F1 a ->
( forall x, a <= x <= b -> (F1 x <-> F2 x) ) ->
forall x f, a <= x <= b -> Rnd_DN_pt F1 x f -> Rnd_DN_pt F2 x f.