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_single :
forall x m e l,
inbetween_float m e x l ->
inbetween_float (Z.div m beta) (e + 1) x (new_location beta (Zmod m beta) l).