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|

Let's imagine there's a slithy language L that has two strings x and y with differing lengths, say Ixl Iyl. Let's also claim that L has both of these strings. According to the definition of a slithy language, the string that is formed by taking the first letter of y and putting it at the beginning of x is also in L. This is because the first letter of y is inserted at the beginning of x. However, the length of this new string, Iyl, is greater than the length of the previous string, Ixl, which contradicts the premise that x and y have distinct lengths. Because of this, each and every slithy language has to have two strings that are exactly the same length.