Section Float_prop.
Variable beta : radix.
Notation bpow e := (bpow beta e).

(** Floats and mag *)
Theorem mag_F2R_bounds :
forall x m e, (0 < m)%Z ->
(F2R (Float beta m e) <= x < F2R (Float beta (m + 1) e))%R ->
mag beta x = mag beta (F2R (Float beta m e)) :> Z.