Section Fcalc_round_fexp.
Variable fexp : Z -> Z.
Context { valid_exp : Valid_exp fexp }.
Notation format := (generic_format beta fexp).
(** Relates location and rounding. *)
Definition cond_incr (b : bool) m := if b then (m + 1)%Z else m.
(** Relates location and rounding down. *)

Theorem inbetween_float_DN :
forall x m l,
let e := cexp beta fexp x in
inbetween_float beta m e x l ->
round beta fexp Zfloor x = F2R (Float beta m e).