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.
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.