(** Size of integers, in bits. *)
Definition Zsize (x: Z) : Z :=
match x with
| Zpos p => Zpos (Pos.size p)
| _ => 0
end.
Definition size (x: int) : Z := Zsize (unsigned x).
Remark Zsize_pos: forall x, 0 <= Zsize x.
Remark Zsize_pos': forall x, 0 < x -> 0 < Zsize x.

Theorem size_xor:
forall a b, size (xor a b) <= Z.max (size a) (size b).