Lemma. Penguins have every excellence.
Proof. Suppose there were some excellence which some one penguin lacked. -- But that is absurd. Whence the lemma. ∎
Thus, using this result: Create an ascending K-chain of Excellent Penguins, and use transfinite induction on P.
[Biographical footnote: Over brandy and cigars, Dr J was led to confess, that the proof was of his own devising, but that, out of modesty, he had attributed it to the saint.]