- If $C$ and $C'$ are indistinguishable, then $C = C'$.
Then $\mathcal C$ has the unique readability property for $\mathcal A$.
It is clear that any word in natural language is uniquely readable: we are able to distinguish words precisely when they have a different letter at some position.
Some non-examples can help to illustrate the concept and its usefulness.
Non-examples come in two sorts: Ones where two placeholders cannot be distinguished, and ones where two symbols substituted for a placeholder cannot be distinguished.
As to the first, consider a coin with two identical sides. We consider a placeholder on each side, suitable for one letter.
Then if we write $A$ on one side and $B$ on the other, this cannot be distinguished from writing $B$ on the one side and $A$ on the other.
So since we cannot distinguish the two placeholders, there is no way of knowing whether we tried to express $AB$ or $BA$.
As to the second, consider writing down words of natural language without spaces.
Then we would have to guess whether $\sf Iamnowhere$ should be read as $\sf I\,am\,now\,here$ or as $\sf I\,am\,nowhere$.