Definition is_finite f :=
  match f with
  | B754_finite _ _ _ _ => true
  | B754_zero _ => true
  | _ => false
  end.Definition is_finite_FF f :=
  match f with
  | F754_finite _ _ _ => true
  | F754_zero _ => true
  | _ => false
  end.

(* Specifications: *)
Theorem is_finite_FF2B : forall x Hx, is_finite (FF2B x Hx) = is_finite_FF x.
Theorem is_finite_FF_B2FF : forall x, is_finite_FF (B2FF x) = is_finite x.
Theorem B2R_Bsign_inj: forall x y : binary_float, is_finite x = true -> is_finite y = true -> B2R x = B2R y -> Bsign x = Bsign y -> x = y.
Theorem is_finite_FF2B : forall x Hx, is_finite (FF2B x Hx) = is_finite_FF x.
Theorem is_finite_FF_B2FF : forall x, is_finite_FF (B2FF x) = is_finite x.
Theorem B2R_Bsign_inj: forall x y : binary_float, is_finite x = true -> is_finite y = true -> B2R x = B2R y -> Bsign x = Bsign y -> x = y.