A language L is called slithy if it contains at least two strings and has the following property: For every two strings x,y in L such that Ix) < lyl, the string obtained by taking the first letter of y and inserting it at the start of x is also in L. For example, if L contains aaa and baaba, then it must also contain the string baaa. Prove by contradiction that every slithy language contains two strings of the same length.

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A language L is called slithy if it contains at least two strings and has the following property:
For every two strings x, y in L such that |x|< lyl, the string obtained by taking the first letter of y
and inserting it at the start of x is also in L.
For example, if L contains aaa and baaba, then it must also contain the string baaa.
Prove by contradiction that every slithy language contains two strings of the same length.
Transcribed Image Text:on A language L is called slithy if it contains at least two strings and has the following property: For every two strings x, y in L such that |x|< lyl, the string obtained by taking the first letter of y and inserting it at the start of x is also in L. For example, if L contains aaa and baaba, then it must also contain the string baaa. Prove by contradiction that every slithy language contains two strings of the same length.
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