Definition round_sign_UP s l :=
  match l with
  | loc_Exact => false
  | _ => negb s
  end.

Theorem inbetween_int_UP_sign : forall x m l, inbetween_int m (Rabs x) l -> Zceil x = cond_Zopp (Rlt_bool x 0) (cond_incr (round_sign_UP (Rlt_bool x 0) l) m).