\documentclass{article}
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\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\begin{document}
\title{t14\_valued\_1 (TMVuvZ2hRyexH6xXrV1DqT5qx4VGW4ti4dB)}
\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 $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k45\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
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}(((k9\_xtuple\_0~X0=k9\_xtuple\_0~\\
X1){\unicdcdcdhd}({\unicdcdadad} X2 .  (X2 \in k9\_xtuple\_0~X0){\unicdbdjdcd}(k1\_funct\_1~X0~X2=k1\_funct\_1~\\
X1~X2))){\unicdbdjdcd}(X0=X1)))\end{array}
\label{hyp:ehcdpfggfhogdgehpfbd}
\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}({\unicdcdadad} X2 .  (X2 \in k9\_xtuple\_0~(k45\_valued\_1~X0~X1)){\unicdbdjdcd}(k1\_funct\_1~\\
(k45\_valued\_1~X0~X1)~X2=k6\_xcmplx\_0~(k1\_funct\_1~X0~X2)~(k1\_funct\_1~\\
X1~X2))))\end{array}
\label{hyp:ehbdddpfghbgmgfhfgegpfbd}
\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\_valued\_0~\\
X0))){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_valued\_0~X1)))){\unicdbdjdcd}\\
((v1\_relat\_1~(k45\_valued\_1~X0~X1)){\unicdcdcdhd}((v1\_funct\_1~(k45\_valued\_1~\\
X0~X1)){\unicdcdcdhd}(v1\_valued\_0~(k45\_valued\_1~X0~X1))))\end{array}
\label{hyp:ggdgidbdpfghbgmgfhfgegpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdedpfghbgmgfhfgegpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_valued\_0~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_valued\_0~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~X2)){\unicdbdjdcd}(((k9\_xtuple\_0~\\
X2=k9\_xtuple\_0~(k45\_valued\_1~X0~X1)){\unicdcdcdhd}({\unicdcdadad} X3 .  (X3 \in k9\_xtuple\_0~\\
X2){\unicdbdjdcd}(k1\_funct\_1~X2~X3=k6\_xcmplx\_0~(k1\_funct\_1~X0~X3)~(k1\_funct\_1~\\
X1~X3)))){\unicdbdjdcd}(X2=k45\_valued\_1~X0~X1))))\end{array}$$
\end{theorem}
\end{document}
