Notation true_xorb := xorb_true_l (only parsing).
(** Nilpotency (alternatively: identity is a inverse for [xorb]) *)

(* Specifications: *)
Lemma xorb_nilpotent : forall b:bool, xorb b b = false.
(** Commutativity *)
Lemma xorb_comm : forall b b':bool, xorb b b' = xorb b' b.
(** Associativity *)
Lemma xorb_assoc_reverse :
forall b b' b'':bool, xorb (xorb b b') b'' = xorb b (xorb b' b'').