Implications

We have the following indirect implication of form equivalence classes:

109 \(\Rightarrow\) 236
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
109 \(\Rightarrow\) 236 clear

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

Howard-Rubin Number Statement
109:

Every field \(F\) and every vector space \(V\) over \(F\) has the property that each linearly independent set \(A\subseteq V\) can be extended to a basis. H.Rubin/J.~Rubin [1985], pp 119ff.

236:

If \(V\) is a vector space with a basis and \(S\) is a linearly independent subset of \(V\) such that no proper extension of \(S\) is a basis for \(V\), then \(S\) is a basis for \(V\).

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