(** 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).