\documentclass{article}
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\newtheorem{lemma}{Lemma}
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\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\begin{document}
\title{t48\_rfunct\_1 (TMWfA8Ei8wA5wMNmDwUaj4wCwNBkmWohUsS)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_rfunct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k30\_valued\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_rfunct\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k54\_valued\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k18\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_valued\_0~\\
X1))){\unicdbdjdcd}((k5\_relat\_1~(k30\_valued\_1~X1)~X0=k30\_valued\_1~(k5\_relat\_1~\\
X1~X0)){\unicdcdcdhd}((k5\_relat\_1~(k4\_rfunct\_1~X1)~X0=k4\_rfunct\_1~(k5\_relat\_1~\\
X1~X0)){\unicdcdcdhd}(k5\_relat\_1~(k54\_valued\_1~X1)~X0=k54\_valued\_1~(k5\_relat\_1~\\
X1~X0))))\end{array}
\label{hyp:ehedgdpfchggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_valued\_0~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_valued\_0~\\
X2))){\unicdbdjdcd}((k5\_relat\_1~(k18\_valued\_1~X1~X2)~X0=k18\_valued\_1~(k5\_relat\_1~\\
X1~X0)~(k5\_relat\_1~X2~X0)){\unicdcdcdhd}((k5\_relat\_1~(k18\_valued\_1~X1~X2)~X0=\\
k18\_valued\_1~(k5\_relat\_1~X1~X0)~X2){\unicdcdcdhd}(k5\_relat\_1~(k18\_valued\_1~\\
X1~X2)~X0=k18\_valued\_1~X1~(k5\_relat\_1~X2~X0)))))\end{array}
\label{hyp:ehedfdpfchggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_valued\_0~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_valued\_0~\\
X1))){\unicdbdjdcd}(k1\_rfunct\_1~X0~X1=k18\_valued\_1~X0~(k4\_rfunct\_1~X1)))\end{array}
\label{hyp:ehddbdpfchggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}((v1\_relat\_1~\\
(k5\_relat\_1~X0~X1)){\unicdcdcdhd}(v1\_funct\_1~(k5\_relat\_1~X0~X1)))\end{array}
\label{hyp:ggdgidpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_valued\_0~X0)){\unicdbdjdcd}((\\
v1\_relat\_1~(k5\_relat\_1~X0~X1)){\unicdcdcdhd}(v1\_valued\_0~(k5\_relat\_1~X0~X1)))\end{array}
\label{hyp:ggdgedddpfghbgmgfhfgegpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_valued\_0~X0))){\unicdbdjdcd}\\
((v1\_relat\_1~(k4\_rfunct\_1~X0)){\unicdcdcdhd}((v1\_funct\_1~(k4\_rfunct\_1~X0)){\unicdcdcdhd}\\
(v1\_valued\_0~(k4\_rfunct\_1~X0))))\end{array}
\label{hyp:ggdgddpfchggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_valued\_0~X0))){\unicdbdjdcd}\\
((v1\_relat\_1~(k4\_rfunct\_1~X0)){\unicdcdcdhd}(v1\_funct\_1~(k4\_rfunct\_1~X0)))\end{array}
\label{hyp:egehpflgedpfchggfhogdgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedidpfchggfhogdgehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_valued\_0~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_valued\_0~\\
X2))){\unicdbdjdcd}((k5\_relat\_1~(k1\_rfunct\_1~X1~X2)~X0=k1\_rfunct\_1~(k5\_relat\_1~\\
X1~X0)~(k5\_relat\_1~X2~X0)){\unicdcdcdhd}((k5\_relat\_1~(k1\_rfunct\_1~X1~X2)~X0=\\
k1\_rfunct\_1~(k5\_relat\_1~X1~X0)~X2){\unicdcdcdhd}(k5\_relat\_1~(k1\_rfunct\_1~X1~\\
X2)~X0=k1\_rfunct\_1~X1~(k5\_relat\_1~X2~X0)))))\end{array}$$
\end{theorem}
\end{document}
