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.