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{همه اصول موضوعه و قواعد $\mathscr{L}_{DEDL}$}
{$(\mathnormal{P}_{0})$}

\begin{equation*}
(P_{1})\qquad \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
\end{equation*}

\begin{equation*}
(P_{2})\qquad \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*}

\begin{equation*}
(P_{3})\qquad\vdash Comp\leftrightarrow  (RegComp\ \wedge\  BehComp)\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad
\end{equation*}

\begin{equation*}
(P_{4})\qquad\vdash\mathcal{P}_{s}(Send\psi\)\ \leftrightarrow\ (\psi\wedge[Send\psi]Comp)\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad
\end{equation*}

\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*}



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