(** Specialization of inbetween for two consecutive integers. *)
Definition inbetween_int m x l :=
inbetween (Z2R m) (Z2R (m + 1)) x l.

Theorem inbetween_float_new_location_single :
forall x m e l,
inbetween_float m e x l ->
inbetween_float (Zdiv m beta) (e + 1) x (new_location beta (Zmod m beta) l).