Qed. Hint Resolve half_adder_carry_true.
(****************************************************************)

Theorem half_adder_ok :
forall a b : bool,
bool_to_nat (half_adder_sum a b) +
(bool_to_nat (half_adder_carry a b) + bool_to_nat (half_adder_carry a b)) =
bool_to_nat a + bool_to_nat b.