(** Relates location and rounding toward zero. *)
Definition round_ZR (s : bool) l :=
match l with
| loc_Exact => false
| _ => s
end.

Theorem inbetween_int_ZR :
forall x m l,
inbetween_int m x l ->
Ztrunc x = cond_incr (round_ZR (Zlt_bool m 0) l) m.