Another Fact about Kestrels

Problem

Prove that for any Kestrel K and any bird x, if K is fond of K(x), then K is fond of x.

Solution

Our premise is that K is fond of K(x):

K(K(x)) => K(x);

And our conclusion is that K is fond of x:

K(x) => x;

So how do we get there? Recall that the Kestrel fixates on its first argument. From K(K(x)) => K(x), it's true that 1.) K(K(x)) is fixated on K(x) and 2.) K(x) is fixated on x. But K(K(x)) and K(x) are the same bird, (the first evaluates to the second), which means a single bird is fixated on both K(x) and x. That means K(x) and x are the same bird, or K(x) => x—therefore, K is fond of x.

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