\documentclass{article}
\newtheorem{axiom}{Axiom}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
\newcommand\unicdcdadad{\forall}
\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
\newcommand\uniddcgcg{\lambda}
\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t10\_recdef\_2 (TMVQ699DuW5HwRhNnU9c7NeQhy2eRQQoDSH)}
\maketitle
Let $ k4\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (X0 \in k3\_zfmisc\_1~\\
X1~X2~X3){\unicdbdjdcd}(X0=k3\_xtuple\_0~(k4\_xtuple\_0~X0)~(k5\_xtuple\_0~X0)~(k2\_xtuple\_0~\\
X0))\end{array}
\label{hyp:ehddpfchfgdgegfgggpfcd}
\end{equation}
\begin{theorem}\label{thm:ehbdadpfchfgdgegfgggpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((k4\_xtuple\_0~\\
X0=k4\_xtuple\_0~X1){\unicdcdcdhd}((k5\_xtuple\_0~X0=k5\_xtuple\_0~X1){\unicdcdcdhd}((k2\_xtuple\_0~\\
X0=k2\_xtuple\_0~X1){\unicdcdcdhd}((X1 \in k3\_zfmisc\_1~X2~X3~X4){\unicdcdcdhd}(X0 \in k3\_zfmisc\_1~\\
X2~X3~X4))))){\unicdbdjdcd}(X0=X1)\end{array}$$
\end{theorem}
\end{document}
