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\usepackage{xepersian}



\begin{document}


\begin{equation}\tag{\(P_0\)}
 \mathscr{L}_{DEDL}  \text{\rl{ همه اصول موضوعه و قواعد }}
\end{equation}
\begin{description}
\item[\((P_1)\)]
$\displaystyle
\vdash BehComp\leftrightarrow\quad\bigwedge_{\chi=\mathnormal{i}\to\mathcal{O}_s\alpha\in\mathscr{EN}}((\chi\in\mathscr{P})\to(\mathnormal{i}_{\chi}\to\alpha_{\chi}))\qquad\qquad\qquad\qquad\quad
$
\item[\((P_2)\)]
\begin{equation*}
\vdash RegComp\leftrightarrow\quad\bigwedge_{\chi=\mathnormal{i}\to\mathcal{O}_s\alpha\in\mathscr{EN}}((\chi\in\mathscr{P})\to\mathcal{O}_{s}\alpha)\wedge\bigwedge_{\chi=\mathnormal{i}\to\mathcal{P}_s\alpha\in\mathscr{EN}}
((\chi\in\mathscr{P})\to\mathcal{P}_{s}\alpha)
\end{equation*}
\end{description}
راه دیگر:
\begin{align}\tag{\(P_3\)}
\vdash Comp\leftrightarrow  (RegComp\ \wedge\  BehComp)\\
\vdash\mathcal{P}_{s}(Send\psi)\ \leftrightarrow\ (\psi\wedge[Send\psi]Comp)\tag{\(P_4\)}
\end{align}

\begin{equation*} 
(P_{5})\qquad\vdash\Box(\chi\in\mathscr{P})\leftrightarrow (\chi\in\mathscr{P})\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad
\end{equation*}

\begin{equation*}
(P_{6})\qquad\vdash\Box\neg\phi\ \leftrightarrow \ \neg\Box\phi\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad\ 
\end{equation*}



\end{document}