In general, it is not true that if A(x) === A(y), x === y. However, it is true if A is a Kestrel. Show that if K(x) === K(y), then x === y.
Given that K(x) === K(y), it's also the case that K(x)(z) === K(y)(z), where z is any arbitrary bird. But K(x)(z) is equal to x, and K(y)(z) is equal to y, so x === y.