We have the following indirect implication of form equivalence classes:

254 \(\Rightarrow\) 254
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
254 \(\Rightarrow\) 254

Here are the links and statements of the form equivalence classes referenced above:

Howard-Rubin Number Statement
254:

\(Z(D,R,l)\): Every directed relation \((P,R)\) in which ramified subsets have least upper bounds, has a maximal element.

254:

\(Z(D,R,l)\): Every directed relation \((P,R)\) in which ramified subsets have least upper bounds, has a maximal element.

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