(** Opposite *)

Definition Bopp opp_nan x :=
  match x with
  | B754_nan sx plx =>
    let '(sres, plres) := opp_nan sx plx in B754_nan sres plres
  | B754_infinity sx => B754_infinity (negb sx)
  | B754_finite sx mx ex Hx => B754_finite (negb sx) mx ex Hx
  | B754_zero sx => B754_zero (negb sx)
  end.

(* Specifications: *)
Theorem Bopp_involutive : forall opp_nan x, is_nan x = false -> Bopp opp_nan (Bopp opp_nan x) = x.
Theorem B2R_Bopp : forall opp_nan x, B2R (Bopp opp_nan x) = (- B2R x)%R.
Theorem is_finite_Bopp : forall opp_nan x, is_finite (Bopp opp_nan x) = is_finite x.
Theorem Bopp_involutive : forall opp_nan x, is_nan x = false -> Bopp opp_nan (Bopp opp_nan x) = x.
Theorem B2R_Bopp : forall opp_nan x, B2R (Bopp opp_nan x) = (- B2R x)%R.
Theorem is_finite_Bopp : forall opp_nan x, is_finite (Bopp opp_nan x) = is_finite x.