\begin{omgroup}[id=sec.functions,creators=miko]{Functions}
\begin{module}[id=functions]
\symdef[assocarg=1]{cart}[1]{\assoc[p=500]{\times}{#1}}
\symdef{fun}[3]{\mixfixiii[p=200]{}{#1}{\colon}{#2}{\rightarrow}{#3}{}}
\symdef{inset}[2]{\infix[p=650]{\in}{#1}{#2}}
\symdef[name=sseteq]{sseteqOp}{\subseteq} 
\symdef{sseteq}[2]{\infix[p=300]\sseteqOp{#1}{#2}} 
\symdef{tup}[1]{\langle#1\rangle}
\symdef{cart}[1]{\assoc\times{#1}}
\symdef[name=setdiff]{setdiffOp}{\backslash}
\symdef{setdiff}[2]{\mixfixii[p=600]{}{#1}\setdiffOp{#2}{}} 
\symdef[assocarg=1]{set}[1]{\mixfixa[nobrackets]{\{}{#1}{\}},}
\symdef{setst}[2]{\mixfixii[nobrackets]{\{}{#1}{\,\mid\,}{#2}{\}}}
\begin{definition}[id=functions.def]
 A {\defi{function}} $\fun{f}AB$ is a left-total, right-unique relation in $\cart{A,B}$
\end{definition}
\end{module}
\end{omgroup}
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