Definition shl_align_fexp mx ex :=
  shl_align mx ex (fexp (Zpos (digits2_pos mx) + ex)).

Theorem shl_align_fexp_correct : forall mx ex, let (mx', ex') := shl_align_fexp mx ex in F2R (Float radix2 (Zpos mx) ex) = F2R (Float radix2 (Zpos mx') ex') /\ (ex' <= fexp (Zdigits radix2 (Zpos mx') + ex'))%Z.