(** 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.

Theorem Bopp_involutive :
forall opp_nan x,
is_nan x = false ->
Bopp opp_nan (Bopp opp_nan x) = x.