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* doc/tl/tl.tex: Fix trivial identities for AndNLM.

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Alexandre Duret-Lutz 2011-12-05 19:42:17 +01:00
parent 72609185b8
commit dc5a0620b7
1 changed files with 6 additions and 6 deletions
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doc/tl/tl.tex
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@ -752,29 +752,29 @@ The following rules are all valid with the two arguments swapped, except the one
%\samp{$\FUSION$}.) %\samp{$\FUSION$}.)
\begin{align*} \begin{align*}
f\AND f &\equiv \0& f\AND f &\equiv f&
f\ANDALT f &\equiv f & f\ANDALT f &\equiv f &
f\OR f &\equiv f \\ f\OR f &\equiv f \\
\0\AND f &\equiv f & \0\AND f &\equiv \0 &
\0\ANDALT f &\equiv \0 & \0\ANDALT f &\equiv \0 &
\0\OR f &\equiv f & \0\OR f &\equiv f &
\0 \FUSION f &\equiv \0 & \0 \FUSION f &\equiv \0 &
\0 \CONCAT f &\equiv \0 \\ \0 \CONCAT f &\equiv \0 \\
\1\AND f &\equiv \NOT f& \1\AND f &\equiv f&
\1\ANDALT f &\equiv f & \1\ANDALT f &\equiv f &
\1\OR f &\equiv \1 & \1\OR f &\equiv \1 &
\1 \FUSION f & \equiv f\\ \1 \FUSION f & \equiv f\\
\eword\AND f &\equiv f & \eword\AND f &\equiv f &
\eword\ANDALT f &\equiv \eword\ANDALT f &\equiv
\begin{cases} \begin{cases}
\eword \mathrlap{\text{~if~} \varepsilon\VDash f} \\ \eword &\mathrlap{\text{if~} \varepsilon\VDash f} \\
\0 \mathrlap{\text{~if~} \varepsilon\nVDash f} \\ \0 &\mathrlap{\text{if~} \varepsilon\nVDash f} \\
\end{cases} & \end{cases} &
&& &&
\eword \FUSION f &\equiv \0 & \eword \FUSION f &\equiv \0 &
\eword \CONCAT f &\equiv f\\ \eword \CONCAT f &\equiv f\\
b_1 \AND b_2 &\equiv b_1\ANDALT b_2 &
&& &&
b_1 \ANDALT b_2 &\equiv b_1\AND b_2 &
&& &&
b:f &\stackrel{\dag}{\equiv} b\AND f\\ b:f &\stackrel{\dag}{\equiv} b\AND f\\
\end{align*} \end{align*}