If I understand correctly, for two orthonormal states
$\left|\psi\_1\right\rangle$ and $\left|\psi\_2\right\rangle$
in the Hilbert space ***H***, there must exist a unitary
transformation $U$, such that:

$$U\left|\psi\_1\right\rangle\left|\alpha\right\rangle =
\left|\psi\_1\right\rangle\left|\psi\_1\right\rangle$$

$$U\left|\psi\_2\right\rangle\left|\alpha\right\rangle =
\left|\psi\_2\right\rangle\left|\psi\_2\right\rangle$$

where $\left|\alpha\right\rangle$ is the initial state
of the second subsystem, on which orthonormal states
are cloned.

My question is: where can I find the reference for the
formal proof of this folklore lemma?