Ltac apply_Rcompare :=
    match goal with
      | [ |- Some Lt = Some (Rcompare _ _) ] => f_equal; symmetry; apply Rcompare_Lt
      | [ |- Some Eq = Some (Rcompare _ _) ] => f_equal; symmetry; apply Rcompare_Eq
      | [ |- Some Gt = Some (Rcompare _ _) ] => f_equal; symmetry; apply Rcompare_Gt
    end.

Theorem bounded_lt_emax : forall mx ex, bounded mx ex = true -> (F2R (Float radix2 (Zpos mx) ex) < bpow radix2 emax)%R.