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We have the following indirect implication of form equivalence classes:

144 \(\Rightarrow\) 416 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
144 \(\Rightarrow\) 416	Constructive order theory, Ern'e, M. 2001, Math. Logic Quart.

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

Howard-Rubin Number	Statement
144:	Every set is almost well orderable.
416:	Every non-compact topological space \(S\) is the union of a set that is well-ordered by inclusion and consists of open proper subsets of \(S\).

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