\documentclass{article}
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\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\unicdbdjded{\Leftrightarrow}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t54\_funct\_4 (TMMaBXe7zUJcvUGPffHNrVvGXK8pPXyfs5X)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_funct\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_binop\_1 : {{\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 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
{\unicdcdadad} X6 .  {\unicdcdadad} X7 .  (k4\_tarski~(k4\_tarski~X0~X1)~(k4\_tarski~\\
X2~X3)=k4\_tarski~(k4\_tarski~X4~X5)~(k4\_tarski~X6~X7)){\unicdbdjdcd}((X0=X4){\unicdcdcdhd}\\
((X2=X6){\unicdcdcdhd}((X1=X5){\unicdcdcdhd}(X3=X7))))\end{array}
\label{hyp:mgbdpfggfhogdgehpfed}
\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~(k3\_funct\_4~X0~\\
X1)){\unicdcdcdhd}(v1\_funct\_1~(k3\_funct\_4~X0~X1)))\end{array}
\label{hyp:egehpflgddpfggfhogdgehpfed}
\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=k3\_funct\_4~X0~X1){\unicdbdjded}(({\unicdcdadad} X3 .  (X3 \in k9\_xtuple\_0~\\
X2){\unicdbdjded}({\unicdcdaddd} X4 .  {\unicdcdaddd} X5 .  {\unicdcdaddd} X6 .  {\unicdcdaddd} X7 .  (X3=k4\_tarski~\\
(k4\_tarski~X4~X6)~(k4\_tarski~X5~X7)){\unicdcdcdhd}((k4\_tarski~X4~X5 \in k9\_xtuple\_0~\\
X0){\unicdcdcdhd}(k4\_tarski~X6~X7 \in k9\_xtuple\_0~X1)))){\unicdcdcdhd}({\unicdcdadad} X3 .  {\unicdcdadad} X4 .  \\
{\unicdcdadad} X5 .  {\unicdcdadad} X6 .  ((k4\_tarski~X3~X4 \in k9\_xtuple\_0~X0){\unicdcdcdhd}(k4\_tarski~\\
X5~X6 \in k9\_xtuple\_0~X1)){\unicdbdjdcd}(k1\_binop\_1~X2~(k4\_tarski~X3~X5)~(k4\_tarski~\\
X4~X6)=k4\_tarski~(k1\_binop\_1~X0~X3~X4)~(k1\_binop\_1~X1~X5~X6)))))))\end{array}
\label{hyp:egddpfggfhogdgehpfed}
\end{equation}
\begin{theorem}\label{thm:ehfdedpfggfhogdgehpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((v1\_relat\_1~\\
X4){\unicdcdcdhd}(v1\_funct\_1~X4)){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_relat\_1~X5){\unicdcdcdhd}(v1\_funct\_1~\\
X5)){\unicdbdjdcd}((k4\_tarski~(k4\_tarski~X0~X1)~(k4\_tarski~X2~X3) \in k9\_xtuple\_0~\\
(k3\_funct\_4~X4~X5)){\unicdbdjded}((k4\_tarski~X0~X2 \in k9\_xtuple\_0~X4){\unicdcdcdhd}(k4\_tarski~\\
X1~X3 \in k9\_xtuple\_0~X5))))\end{array}$$
\end{theorem}
\end{document}
