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.