\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{t6\_recdef\_2 (TMLehyXtH7U2EXomsLN5FkkrixfXzULp4Lz)}
\maketitle
Let $ k4\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k6\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k7\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_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.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  \preoh (X0 \in \\
k4\_zfmisc\_1~X1~X2~X3~X4){\unicdcdcdhd}({\unicdcdadad} X5 .  {\unicdcdadad} X6 .  {\unicdcdadad} X7 .  {\unicdcdadad} X8 .  \\
\preoh (X5 \in X1){\unicdcdcdhd}((X6 \in X2){\unicdcdcdhd}((X7 \in X3){\unicdcdcdhd}((X8 \in X4){\unicdcdcdhd}(X0=k6\_xtuple\_0~X5~X6~\\
X7~X8)))))\end{array}
\label{hyp:ehhdjdpfngdgbgchehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ({\unicdcdaddd} X1 .  {\unicdcdaddd} X2 .  {\unicdcdaddd} X3 .  {\unicdcdaddd} X4 .  X0=k6\_xtuple\_0~\\
X1~X2~X3~X4){\unicdbdjdcd}(X0=k6\_xtuple\_0~(k7\_xtuple\_0~X0)~(k8\_xtuple\_0~X0)~\\
(k5\_xtuple\_0~X0)~(k2\_xtuple\_0~X0))\end{array}
\label{hyp:ehedpfchfgdgegfgggpfcd}
\end{equation}
\begin{theorem}\label{thm:ehgdpfchfgdgegfgggpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (X0 \in k4\_zfmisc\_1~\\
X1~X2~X3~X4){\unicdbdjdcd}(X0=k6\_xtuple\_0~(k7\_xtuple\_0~X0)~(k8\_xtuple\_0~X0)~\\
(k5\_xtuple\_0~X0)~(k2\_xtuple\_0~X0))\end{array}$$
\end{theorem}
\end{document}
