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Because is a maximal element of, then.
Therefore, (mathscr{P}) has a maximal element.
From Zorn's lemma, cl ( C ) has a maximal element.
Let (underline {k}) be the maximal element of Λ f.
By Zorn's lemma, ( X, ⪯ ) has a maximal element x ¯.
Hence, by Zorn's Lemma, has a maximal element.
By Zorn's Lemma, admits a maximal element.
It follows from Zorn's lemma that has maximal element.
By Theorem 3.1, we have the following maximal element theorem.
Now, we prove that has a maximal element.
It is clear that if D has a minimal (maximal) element, then the minimal (maximal) element is unique.
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