Module Wordsize_8.
Definition wordsize := 8%nat.
Remark wordsize_not_zero: wordsize <> 0%nat.
Remark int_ltu_2_inv:
forall y z,
Int.ltu y iwordsize' = true ->
Int.ltu z iwordsize' = true ->
Int.unsigned (Int.add y z) <= Int.unsigned iwordsize' ->
let y' := repr (Int.unsigned y) in
let z' := repr (Int.unsigned z) in
Int.unsigned y = unsigned y'
/\ Int.unsigned z = unsigned z'
/\ ltu y' iwordsize = true
/\ ltu z' iwordsize = true
/\ Int.unsigned (Int.add y z) = unsigned (add y' z')
/\ add y' z' = repr (Int.unsigned (Int.add y z)).
(** Powers of two with exponents given as 32-bit ints *)
Definition one_bits' (x: int) : list Int.int :=
List.map Int.repr (Z_one_bits wordsize (unsigned x) 0).
Definition is_power2' (x: int) : option Int.int :=
match Z_one_bits wordsize (unsigned x) 0 with
| i :: nil => Some (Int.repr i)
| _ => None
end.
Fixpoint int_of_one_bits' (l: list Int.int) : int :=
match l with
| nil => zero
| a :: b => add (shl' one a) (int_of_one_bits' b)
end.

Theorem mul_pow2':
forall x n logn,
is_power2' n = Some logn ->
mul x n = shl' x logn.