Definition is_nan f :=
  match f with
  | B754_nan _ _ => true
  | _ => false
  end.Definition is_nan_FF f :=
  match f with
  | F754_nan _ _ => true
  | _ => false
  end.

(* Specifications: *)
Theorem is_nan_FF2B : forall x Hx, is_nan (FF2B x Hx) = is_nan_FF x.
Theorem is_nan_FF_B2FF : forall x, is_nan_FF (B2FF x) = is_nan x.
Theorem is_nan_FF2B : forall x Hx, is_nan (FF2B x Hx) = is_nan_FF x.
Theorem is_nan_FF_B2FF : forall x, is_nan_FF (B2FF x) = is_nan x.