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 round_pred_ge_0 :
forall P : R -> R -> Prop,
round_pred_monotone P ->
P 0 0 ->
forall x f, P x f -> 0 <= x -> 0 <= f.