(** Relates location and rounding down. *)

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