(** Relates location and rounding up. *)

Definition round_UP l :=
  match l with
  | loc_Exact => false
  | _ => true
  end.

(* Specifications: *)
Theorem inbetween_int_UP : forall x m l, inbetween_int m x l -> Zceil x = cond_incr (round_UP l) m.
Theorem inbetween_float_UP : forall x m l, let e := canonic_exp beta fexp x in inbetween_float beta m e x l -> round beta fexp Zceil x = F2R (Float beta (cond_incr (round_UP l) m) e).
Theorem inbetween_int_UP : forall x m l, inbetween_int m x l -> Zceil x = cond_incr (round_UP l) m.
Theorem inbetween_float_UP : forall x m l, let e := canonic_exp beta fexp x in inbetween_float beta m e x l -> round beta fexp Zceil x = F2R (Float beta (cond_incr (round_UP l) m) e).