(** 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_int_N :
forall choice x m l,
inbetween_int m x l ->
Znearest choice x = cond_incr (round_N (choice m) l) m.