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Problem

Asssuming no bird can be both a Lark and a Kestrel, prove that it is impossible for a Lark to be fond of a Kestrel.

Solution

Imagine that L is fond of K:

L(K) === K;

Since both sides of the equation are equal, so is the result of applying both to K again:

L(K)(K) === K(K);

But from the definition of the Lark, we know it's also true that:

L(K)(K) === K(K(K));

...Meaning K(K) and K(K(K)) are the same. Now, we've shown in #18 that, if K is fond of K(x), K is fond of x—therefore, K is fond of K, and is egocentric. And from #19, we know that an egocentric Kestrel must be the only bird in the forest. This contradicts the given fact that L is also present in the forest.

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