(* Parity and bits. *)

Coercion nat_of_bool (b : bool) := if b then 1 else 0.

(* Specifications: *)
Lemma leq_b1 (b : bool) : b <= 1.
Lemma addn_negb (b : bool) : ~~ b + b = 1.
Lemma lt0b (b : bool) : (b > 0) = b.
Lemma sub1b (b : bool) : 1 - b = ~~ b.
Lemma mulnb (b1 b2 : bool) : b1 * b2 = b1 && b2.
Lemma mulnbl (b : bool) n : b * n = (if b then n else 0).
Lemma mulnbr (b : bool) n : n * b = (if b then n else 0).