this is for holding javascript data
Mazdak Farrokhzad edited 4b2.tex
over 9 years ago
Commit id: fdf749d223e7e22c1edacc202fb0cc7fc8984593
deletions | additions
diff --git a/4b2.tex b/4b2.tex
index 0376729..9204892 100644
--- a/4b2.tex
+++ b/4b2.tex
...
\begin{equation}
\begin{split}
& I \a B &\to&
wp{S}{I}\\ \wp{S}{I}\\
& I \a B &\to&
wp{res \wp{res := res * i; i := i + 1}{I}\\
\rule{2} \iff &
\I I \a B &\to&
wp{res \wp{res := res *
i, \wp{i i}{\wp{i := i + 1}{I}}\\
\rule{1} \iff &
\I I \a B &\to&
wp{res \wp{res := res *
i, (i i}{(i + 1 \leq n + 1) \a (res = i!)}\\
\rule{1} \iff &
\I I \a B &\to& (i + 1 \leq n + 1) \a (res * i =
i!)}\\ i!)\\
\end{split}
\end{equation}
Substituting $I, B$ we get:
\begin{equation}
\begin{split}
\iff & (i \leq n + 1) \a (res = (i - 1)!) \a (i \leq n) & \to\\
& (i + 1 \leq n + 1) \a (res * i = i!) &\\
\iff & \T &
\end{split}
\end{equation}