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.

Theorem inbetween_float_bounds :
forall x m e l,
inbetween_float m e x l ->
(F2R (Float beta m e) <= x < F2R (Float beta (m + 1) e))%R.