%--------------------------------------------------
\newcommand{\step}[1]{گام #1:}
\newcommand{\case}[1]{حالت #1:}
\newcommand{\claim}[1]{ادعا #1:}

\newcommand{\stepi}[1]{\textit{گام #1:}}
\newcommand{\casei}[1]{\textit{حالت #1:}}
\newcommand{\claimi}[1]{\textit{ادعا #1:}}

\newcommand{\stepb}[1]{\textbf{گام #1:}}
\newcommand{\caseb}[1]{\textbf{حالت #1:}}
\newcommand{\claimb}[1]{\textbf{ادعا #1:}}

\newcommand{\stepbi}[1]{\textbf{\textit{گام #1:}}}
\newcommand{\casebi}[1]{\textbf{\textit{حالت #1:}}}
\newcommand{\claimbi}[1]{\textbf{\textit{ادعا #1:}}}
%--------------------------------------------------
\newcommand{\Hom}{\mathrm{Hom}}
\newcommand{\End}{\mathrm{End}}
\newcommand{\Ker}{\mathrm{Ker}}
\newcommand{\Coker}{\mathrm{Coker}}
\newcommand{\Ima}{\mathrm{Im}}
\newcommand{\Aut}{\mathrm{Aut}}
\newcommand{\Out}{\mathrm{Out}}
\newcommand{\Autcent}{\mathrm{Autcent}}
\newcommand{\Inn}{\mathrm{Inn}}
\newcommand{\Rank}{\mathrm{Rank}}
\newcommand{\Fit}{\mathrm{Fit}}
\newcommand{\Rad}{\mathrm{Rad}}
\newcommand{\Supp}{\mathrm{Supp}}
%--------------------------------------------------
\newcommand{\normal}{\trianglelefteq}
\newcommand{\La}{\Leftarrow}
\newcommand{\Ra}{\Rightarrow}
\newcommand{\Lra}{\Leftrightarrow}
\newcommand{\lra}{\longrightarrow}
\newcommand{\lmt}{\longmapsto}
\newcommand{\lcm}{\mathrm{lcm}}
\newcommand{\ol}{\overline}
\newcommand{\ord}{\mathrm{ord}}
\newcommand{\subeq}{\subseteq}
\newcommand{\supeq}{\supseteq}
\newcommand{\join}{~\hspace{-2mm}}
%--------------------------------------------------
\newcommand{\bino}[2]{{#1\choose#2}}
\newcommand{\gen}[1]{\langle#1\rangle}
\newcommand{\wgen}[1]{\left\langle#1\right\rangle}
\newcommand{\ts}{\langle1\rangle}
\newcommand{\es}{\emptyset}
\newcommand{\setm}{\setminus}
\newcommand{\parn}[1]{\left(#1\right)}
\newcommand{\orde}[1]{\left|#1\right|}
\newcommand{\stackunder}[2]{\mathrel{\mathop{#1}\limits_{#2}}}
\newcommand{\arr}[2]{\begin{array}{#1}#2\end{array}}
\newcommand{\dhom}[5]{\begin{array}{rcl}#1:#2&\longrightarrow&#3\\#4&\longmapsto&#5\end{array}}
\newcommand{\ddhom}[7]{\begin{array}{rcl}#1:#2&\longrightarrow&#3\\#4&\longmapsto&#5\\#6&\longmapsto&#7\end{array}}
\newcommand{\functwo}[5]{\left\{\begin{array}{ll}#1,&#2,\\#3,&#4#5\end{array}\right.}
\newcommand{\functhree}[7]{\left\{\begin{array}{ll}#1,&#2,\\#3,&#4,\\#5,&#6#7\end{array}\right.}
\newcommand{\funcfour}[9]{\left\{\begin{array}{ll}#1,&#2,\\#3,&#4,\\#5,&#6,\\#7,&#8#9\end{array}\right.}
%--------------------------------------------------
\newcommand{\N}{\mathbb{N}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\Q}{\mathbb{Q}}
\newcommand{\R}{\mathbb{R}}
%\newcommand{\C}{\mathbb{C}}
%--------------------------------------------------
\newcommand{\al}{\alpha}
\newcommand{\Al}{\Alpha}
\newcommand{\be}{\beta}
\newcommand{\ga}{\gamma}
\newcommand{\Ga}{\Gamma}
\newcommand{\del}{\delta}
\newcommand{\Del}{\Delta}
\newcommand{\ep}{\epsilon}
\newcommand{\vep}{\varepsilon}
\newcommand{\ze}{\zeta}
\newcommand{\et}{\eta}
\newcommand{\thet}{\theta}
\newcommand{\Thet}{\Theta}
\newcommand{\vth}{\vartheta}
\newcommand{\io}{\iota}
\newcommand{\ka}{\kappa}
\newcommand{\lam}{\lambda}
\newcommand{\Lam}{\Lambda}
%\newcommand{\mu}{\mu}
%\newcommand{\nu}{\nu}
%\newcommand{\xi}{\xi}
%\newcommand{\Xi}{\Xi}
%\newcommand{\pi}{\pi}
%\newcommand{\Pi}{\Pi}
\newcommand{\vpi}{\varpi}
%\newcommand{\rho}{\rho}
\newcommand{\vrho}{\varrho}
\newcommand{\si}{\sigma}
\newcommand{\Si}{\Sigma}
\newcommand{\vsi}{\varsigma}
%\newcommand{\tau}{\tau}
\newcommand{\ups}{\upsilon}
\newcommand{\Ups}{\Upsilon}
%\newcommand{\phi}{\phi}
%\newcommand{\Phi}{\Phi}
\newcommand{\vphi}{\varphi}
%\newcommand{\chi}{\chi}
%\newcommand{\psi}{\psi}
%\newcommand{\Psi}{\Psi}
\newcommand{\om}{\omega}
\newcommand{\Om}{\Omega}