Definition shr_fexp m e l :=
  shr (shr_record_of_loc m l) e (fexp (Zdigits2 m + e) - e).

Theorem shr_truncate : forall m e l, (0 <= m)%Z -> shr_fexp m e l = let '(m', e', l') := truncate radix2 fexp (m, e, l) in (shr_record_of_loc m' l', e').