- E5
[239]Prerequisites:[01R],[(3.171)],[24V].Let \(x,y\) be elements (generic, not necessarily natural numbers), such that
\begin{equation} x⊆ y⊆ S(x) \label{eq:x_ y_ Sx} \end{equation}6prove that
\[ x=y∨ y = S(x)\quad ; \]where the above two are mutually exclusive, and (in the hypothesis ?? above) the second one holds if and only if \(x\in y\); summarizing
\[ \ref{eq:x_ y_ Sx} ⇒ (x=y\iff y ≠ S(x)\iff x∉ y )\quad . \]Note the analogy with [22H].
EDB — 239
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Authors:
"Mennucci , Andrea C. G."
.
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