(** Relates location and rounding to nearest. *)

Definition round_N (p : bool) l :=
  match l with
  | loc_Exact => false
  | loc_Inexact Lt => false
  | loc_Inexact Eq => p
  | loc_Inexact Gt => true
  end.

Theorem inbetween_float_NE : forall x m l, let e := canonic_exp beta fexp x in inbetween_float beta m e x l -> round beta fexp ZnearestE x = F2R (Float beta (cond_incr (round_N (negb (Zeven m)) l) m) e).