\documentclass{article}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t8\_funct\_9 (TMGcJPBsShh7VJvh1fg89yBzsPhZNgzTnZP)}
\maketitle
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k7\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_valued\_0~\\
X0))){\unicdcdcdhd}(v1\_xcmplx\_0~X1)){\unicdbdjdcd}((v1\_relat\_1~(k7\_valued\_1~X0~X1)){\unicdcdcdhd}(\\
v1\_funct\_1~(k7\_valued\_1~X0~X1)))\end{array}
\label{hyp:egehpflghdpfghbgmgfhfgegpfbd}
\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\_xcmplx\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}(\\
v1\_funct\_1~X2)){\unicdbdjdcd}((X2=k7\_valued\_1~X0~X1){\unicdbdjded}((k9\_xtuple\_0~X2=k9\_xtuple\_0~\\
X0){\unicdcdcdhd}({\unicdcdadad} X3 .  (X3 \in k9\_xtuple\_0~X2){\unicdbdjdcd}(k1\_funct\_1~X2~X3=k2\_xcmplx\_0~\\
X1~(k1\_funct\_1~X0~X3)))))))\end{array}
\label{hyp:egcdpfghbgmgfhfgegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~\\
X1)){\unicdbdjdcd}((v1\_funct\_9~X1~X0){\unicdbdjded}((X0{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}({\unicdcdadad} X2 .  (v1\_xreal\_0~\\
X2){\unicdbdjdcd}(((X2 \in k9\_xtuple\_0~X1){\unicdbdjdcd}(k2\_xcmplx\_0~X2~X0 \in k9\_xtuple\_0~X1)){\unicdcdcdhd}\\
(((k2\_xcmplx\_0~X2~X0 \in k9\_xtuple\_0~X1){\unicdbdjdcd}(X2 \in k9\_xtuple\_0~X1)){\unicdcdcdhd}(\\
(X2 \in k9\_xtuple\_0~X1){\unicdbdjdcd}(k1\_funct\_1~X1~X2=k1\_funct\_1~X1~(k2\_xcmplx\_0~\\
X2~X0)))))))))\end{array}
\label{hyp:egbdpfggfhogdgehpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v3\_valued\_0~X0)){\unicdbdjdcd}((v1\_relat\_1~\\
X0){\unicdcdcdhd}(v1\_valued\_0~X0))\end{array}
\label{hyp:dgdggdpfghbgmgfhfgegpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xcmplx\_0}~{X0}})}}}\label{hyp:dgdgddpfihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehidpfggfhogdgehpfjd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v3\_valued\_0~X2))){\unicdbdjdcd}((v1\_funct\_9~\\
X2~X0){\unicdbdjdcd}(v1\_funct\_9~(k7\_valued\_1~X2~X1)~X0))))\end{array}$$
\end{theorem}
\end{document}
