isProperPrefix on bitstrings of length ≤ 3. See Example 8.5, but here we are considering proper prefixes only. A string x is prefix, but not a proper prefix, of itself: more formally, x is a proper prefix of y if x starts with precisely the symbols of y, followed by one or more other symbols.
For two strings x and y, we say that x is a substring of y if the symbols of x appear consecutively somewhere in y. We say that x is a subsequence of y if the symbols of x appear in order, but not necessarily consecutively, in y. (For example, 001 is a substring of 1001 but not of 0101. But 001 is a subsequence of 1001 and also of 0101.) A string x is called a proper substring/subsequence of y if x is a substring/subsequence of y but x 6= y. Again, write out (by exhaustive enumeration) the full set of pairs in these relations:
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