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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def _potential_cross_partial_w(moment_index: int, op: ops.Operation, state: _OptimizerState) -> None: """Cross the held W over a partial W gate. [Where W(a) is shorthand for PhasedX(phase_exponent=a).] Uses the following identity: ───W(a)───W(b)^t─── ≡ ───Z^-a───X───Z^a───W(b)^t────── (expand W(a)) ≡ ───Z^-a───X───W(b-a)^t───Z^a──── (move Z^a across, phasing axis) ≡ ───Z^-a───W(a-b)^t───X───Z^a──── (move X across, negating axis angle) ≡ ───W(2a-b)^t───Z^-a───X───Z^a─── (move Z^-a across, phasing axis) ≡ ───W(2a-b)^t───W(a)─── """

    a = state.held_w_phases.get(op.qubits[0])
    if a is None:
        return
    exponent, phase_exponent = cast(Tuple[float, float],
                                    _try_get_known_phased_pauli(op))
    new_op = ops.PhasedXPowGate(
        exponent=exponent,
        phase_exponent=2 * a - phase_exponent).on(op.qubits[0])
    state.deletions.append((moment_index, op))
    state.inline_intos.append((moment_index, new_op))