Section Fcalc_bracket_generic.
Variable beta : radix.
Notation bpow e := (bpow beta e).
(** Specialization of inbetween for two consecutive floating-point numbers. *)
Definition inbetween_float m e x l :=
inbetween (F2R (Float beta m e)) (F2R (Float beta (m + 1) e)) x l.
(** Specialization of inbetween for two consecutive integers. *)
Definition inbetween_int m x l :=
inbetween (IZR m) (IZR (m + 1)) x l.

Theorem inbetween_float_new_location :
forall x m e l k,
(0 < k)%Z ->
inbetween_float m e x l ->
inbetween_float (Z.div m (Zpower beta k)) (e + k) x (new_location (Zpower beta k) (Zmod m (Zpower beta k)) l).