\documentclass{article}
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\newtheorem{lemma}{Lemma}
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\newtheorem{definition}{Definition}
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\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\begin{document}
\title{t44\_exchsort (TMc4i9svEjZ8bchPBcdSdMEzT499Y3Kjivd)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_exchsort : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_exchsort : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k10\_funct\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~\\
X2){\unicdcdcdhd}(v1\_exchsort~X2))){\unicdbdjdcd}(((X0 \in k9\_xtuple\_0~X2){\unicdcdcdhd}(X1 \in k9\_xtuple\_0~\\
X2)){\unicdbdjdcd}((m1\_exchsort~(k10\_funct\_7~X2~X0~X1)~X2){\unicdcdcdhd}(m1\_exchsort~X2~\\
(k10\_funct\_7~X2~X0~X1))))\end{array}
\label{hyp:ehedddpffgihdgigdhpgcheh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_exchsort~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_exchsort~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_exchsort~\\
X2))){\unicdbdjdcd}(((m1\_exchsort~X0~X1){\unicdcdcdhd}(m1\_exchsort~X1~X2)){\unicdbdjdcd}(m1\_exchsort~\\
X0~X2))))\end{array}
\label{hyp:ehedadpffgihdgigdhpgcheh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_exchsort~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_exchsort~\\
X1))){\unicdbdjdcd}((m1\_exchsort~X0~X1){\unicdbdjdcd}(m1\_exchsort~X1~X0)))\end{array}
\label{hyp:ehddjdpffgihdgigdhpgcheh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_exchsort~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_exchsort~X1~X0){\unicdbdjdcd}((k9\_xtuple\_0~X1=k9\_xtuple\_0~\\
X0){\unicdcdcdhd}(k10\_xtuple\_0~X1=k10\_xtuple\_0~X0)))\end{array}
\label{hyp:ehddhdpffgihdgigdhpgcheh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_exchsort~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_exchsort~X1~X0){\unicdbdjdcd}((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~\\
X1){\unicdcdcdhd}(v1\_exchsort~X1))))\end{array}
\label{hyp:egehpfngbdpffgihdgigdhpgcheh}
\end{equation}
\begin{theorem}\label{thm:ehededpffgihdgigdhpgcheh}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~\\
X2){\unicdcdcdhd}(v1\_exchsort~X2))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}((v1\_funct\_1~\\
X3){\unicdcdcdhd}(v1\_exchsort~X3))){\unicdbdjdcd}(((X0 \in k9\_xtuple\_0~X2){\unicdcdcdhd}((X1 \in k9\_xtuple\_0~\\
X2){\unicdcdcdhd}(m1\_exchsort~X2~X3))){\unicdbdjdcd}((m1\_exchsort~(k10\_funct\_7~X2~X0~X1)~\\
X3){\unicdcdcdhd}(m1\_exchsort~X2~(k10\_funct\_7~X3~X0~X1)))))\end{array}$$
\end{theorem}
\end{document}
