Implications

We have the following indirect implication of form equivalence classes:

430-p \(\Rightarrow\) 0
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
430-p \(\Rightarrow\) 0

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

Howard-Rubin Number Statement
430-p:

(Where \(p\) is a prime) \(AL21\)\((p)\): Every vector space over \(\mathbb Z_p\) has the property that for every subspace \(S\) of \(V\), there is a subspace \(S'\) of \(V\) such that \(S \cap S' = \{ 0 \}\) and \(S \cup S'\) generates \(V\) in other words such that \(V = S \oplus S'\).   Rubin, H./Rubin, J [1985], p.119, AL21.

0:  \(0 = 0\).

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