Qed. Hint Resolve xorb_b_true.
(****************************************************************)
Definition bool_to_nat (b : bool) :=
match b with
| true => 1
| false => 0
end.

(* Specifications: *)
Lemma bool_to_nat_all :
forall b : bool, bool_to_nat b = 0 \/ bool_to_nat b = 1.