Implications

We have the following indirect implication of form equivalence classes:

314 \(\Rightarrow\) 314
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
314 \(\Rightarrow\) 314

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

Howard-Rubin Number Statement
314:

For every set \(X\) and every permutation \(\pi\) on \(X\) there are two reflections \(\rho\) and \(\sigma\) on \(X\) such that \(\pi =\rho\circ\sigma\) and for every \(Y\subseteq X\) if \(\pi[Y]=Y\) then \(\rho[Y]=Y\) and \(\sigma[Y]=Y\).  (A reflection is a permutation \(\phi\) such that \(\phi^2\) is the identity.) \ac{Degen} \cite{1988}, \cite{2000}.

314:

For every set \(X\) and every permutation \(\pi\) on \(X\) there are two reflections \(\rho\) and \(\sigma\) on \(X\) such that \(\pi =\rho\circ\sigma\) and for every \(Y\subseteq X\) if \(\pi[Y]=Y\) then \(\rho[Y]=Y\) and \(\sigma[Y]=Y\).  (A reflection is a permutation \(\phi\) such that \(\phi^2\) is the identity.) \ac{Degen} \cite{1988}, \cite{2000}.

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