\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=}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
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\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t8\_topalg\_4 (TMP3rpDdsxsypAtnP7vEk5WTG3pHXcRb1Q7)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k12\_mcart\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k13\_funct\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{k2\_xtuple\_0}~{({{{k4\_tarski}~{X0}}~{X1}})}}={X1}}}}\label{hyp:chegcdpfihehfhahmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k3\_xboole\_0}~{X0}}~{X0}}={X0}}}}\label{hyp:jgegfgngahpgehfgogdgfgpflgddpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdcdcdhd}((\\
v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1))){\unicdbdjdcd}((v1\_relat\_1~(k13\_funct\_3~\\
X0~X1)){\unicdcdcdhd}(v1\_funct\_1~(k13\_funct\_3~X0~X1)))\end{array}
\label{hyp:egehpflgbdddpfggfhogdgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}\\
(v1\_funct\_1~X2)){\unicdbdjdcd}((X2=k13\_funct\_3~X0~X1){\unicdbdjded}((k9\_xtuple\_0~X2=k3\_xboole\_0~\\
(k9\_xtuple\_0~X0)~(k9\_xtuple\_0~X1)){\unicdcdcdhd}({\unicdcdadad} X3 .  (X3 \in k9\_xtuple\_0~\\
X2){\unicdbdjdcd}(k1\_funct\_1~X2~X3=k4\_tarski~(k1\_funct\_1~X0~X3)~(k1\_funct\_1~\\
X1~X3)))))))\end{array}
\label{hyp:eghdpfggfhogdgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}((X1=k12\_mcart\_1~X0){\unicdbdjded}((k9\_xtuple\_0~\\
X1=k9\_xtuple\_0~X0){\unicdcdcdhd}({\unicdcdadad} X2 .  (X2 \in k9\_xtuple\_0~X0){\unicdbdjdcd}(k1\_funct\_1~\\
X1~X2=k2\_xtuple\_0~(k1\_funct\_1~X0~X2))))))\end{array}
\label{hyp:egbdddpfngdgbgchehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehidpfehpgahbgmghgpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}((k9\_xtuple\_0~X0=k9\_xtuple\_0~\\
X1){\unicdbdjdcd}(k12\_mcart\_1~(k13\_funct\_3~X0~X1)=X1)))\end{array}$$
\end{theorem}
\end{document}
