cheat_sheet.tex

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amssymb}
\title{Osztott rendszerek szintézise\\1. zhig használt definíciók}
\begin{document}
\ \\
$P \rightarrow Q \equiv \neg P \lor Q\\\\
P \triangleright_S Q \equiv P \land \neg Q \Rightarrow lf(S,P \lor Q) \equiv lf(s_1, P \lor Q) \land lf(s_2, P \lor Q)\\\\
P \mapsto_S Q  \equiv P \triangleright_S Q \land (((P \land \neg Q \Rightarrow lf(s_1,Q)) \lor (P \land \neg Q \Rightarrow lf(s_2,Q)))\\\\
P \hookrightarrow_S Q$
\begin{enumerate}
\item[]\ \\
$P \hookrightarrow_S Q\ \ ,\  Q \Rightarrow R$\\
-------------------------- Jobb oldal gyengítése\\
\hspace*{0.9cm} $P \hookrightarrow_S R$
\item[]\ \\
$P \hookrightarrow_S Q\ \ ,\  R \Rightarrow P$\\
-------------------------- Bal oldal erősítése\\
\hspace*{0.9cm} $P \hookrightarrow_S Q$
\item[]\ \\
$P \hookrightarrow_S Q\ \ ,\  Q\ \triangleright_S \downarrow$\\
-------------------------- Stabillal metszés\\
\hspace*{0.1cm}$P \land K \hookrightarrow_S Q \land K$
\end{enumerate}
\textbf{masodik ZH-hoz}:\newline\newline
%%Q \in INIT_h \ \ \ \ \ 
$legyen \ K \in inv_s(\land INIT_h)\\\\
P \triangleright_h Q \longrightarrow P \land K \triangleright_s Q \land K\\\\
P \mapsto_h Q \longrightarrow P \land K \mapsto_s Q \land K\\\\
P \hookrightarrow_h Q \longrightarrow P \land K \hookrightarrow_s Q \land K\\\\
P \in inv_h \longrightarrow P \land K \in inv_s(\land INIT_h)\\\\
FP_h \Rightarrow R \longrightarrow \varphi_s \land K \Rightarrow R\\\\
Q \in TERM_h \longrightarrow sp(s_0, Q) \hookrightarrow_s \varphi_s\\\
$
\end{document}