Description: There is a unique word having the length of a given word increased by 1
with the given word as prefix if there is a unique symbol which extends
the given word. (Contributed by Alexander van der Vekens, 6-Oct-2018)(Revised by AV, 21-Jan-2022)(Revised by AV, 10-May-2022)(Proof
shortened by AV, 13-Oct-2022)