(** Results about the injection [b2n] *)

(* Specifications: *)
Lemma b2n_inj : forall (a0 b0:bool), a0 == b0 -> a0 = b0.
Lemma add_b2n_double_div2 : forall (a0:bool) a, (a0+2*a)/2 == a.
Lemma add_b2n_double_bit0 : forall (a0:bool) a, (a0+2*a).[0] = a0.
Lemma b2n_div2 : forall (a0:bool), a0/2 == 0.
Lemma b2n_bit0 : forall (a0:bool), a0.[0] = a0.
(** The specification of testbit by low and high parts is complete *)
Lemma testbit_unique : forall a n (a0:bool) l h,
l<2^n -> a == l + (a0 + 2*h)*2^n -> a.[n] = a0.