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We have the following indirect implication of form equivalence classes:

144 \(\Rightarrow\) 413 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
144 \(\Rightarrow\) 413	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.
413:	Every infinite set \(S\) is the union of a set, well-ordered by inclusion, of subsets which are non-equipollent to \(S\).

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