Prove that for any Kestrel K
and any bird x
, if K(x)
is egocentric, then K
must be fond of x
.
We start with a K(x)
that is egocentric:
K(x)(K(x)) => K(x);
But because the Kestrel fixates on its first argument, that same expression must also return x
:
K(x)(K(x)) => x;
Therefore, K(x)
and x
are the same bird, and if K(x) === x
, K
is fond of x
.