Proof of Choice Coherence in Kreps (2013)
If there is no $z \in A$ such that
$u(z) &gt; u(y)$ (perhaps because no other $z$ exists, perhaps for other reasons)
then by definition of $c_u$ we know that $y \in c_u(A)$. This would contradict the assumption of the third sentence, that $y \notin c_u(A)$.


  If, moreover, $y \notin c_u(A)$...