(** The following one is false for x = 0 in FTZ *)

(* Specifications: *)
Theorem pred_pos_plus_ulp :
forall x, (0 < x)%R -> F x ->
(pred_pos x + ulp (pred_pos x) = x)%R.
Theorem pred_pos_plus_ulp :
forall x, (0 < x)%R -> F x ->
(pred_pos x + ulp (pred_pos x) = x)%R.