\documentclass{article}
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\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\begin{document}
\title{t25\_partfun1 (TMdh3mjkNPagrCsFBn3DDWJHxacRLjYP5fQ)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\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 $ k3\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\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)){\unicdbdjdcd}((X0 \in k9\_xtuple\_0~(k6\_relat\_1~X1~X2)){\unicdbdjdcd}(k1\_funct\_1~(k6\_relat\_1~\\
X1~X2)~X0=k1\_funct\_1~X2~X0))\end{array}
\label{hyp:ehfdfdpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~\\
X2)){\unicdbdjdcd}((X0 \in k9\_xtuple\_0~(k6\_relat\_1~X1~X2)){\unicdbdjded}((X0 \in k9\_xtuple\_0~\\
X2){\unicdcdcdhd}(k1\_funct\_1~X2~X0 \in X1)))\end{array}
\label{hyp:ehfdedpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~\\
X2)){\unicdbdjdcd}((X0 \in X1){\unicdbdjdcd}(k1\_funct\_1~(k5\_relat\_1~X2~X1)~X0=k1\_funct\_1~X2~\\
X0))\end{array}
\label{hyp:ehedjdpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}((v1\_relat\_1~\\
(k6\_relat\_1~X0~X1)){\unicdcdcdhd}(v1\_funct\_1~(k6\_relat\_1~X0~X1)))\end{array}
\label{hyp:ggdgjdpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \\
k3\_partfun1~X0~X1~X2=k5\_relat\_1~(k6\_relat\_1~X2~X0)~X1)\end{array}
\label{hyp:egbdpfahbgchehggfhogbd}
\end{equation}
\begin{theorem}\label{thm:ehcdfdpfahbgchehggfhogbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}\\
(v1\_funct\_1~X3)){\unicdbdjdcd}(((X0 \in k9\_xtuple\_0~X3){\unicdcdcdhd}((X0 \in X1){\unicdcdcdhd}(k1\_funct\_1~\\
X3~X0 \in X2))){\unicdbdjdcd}(k1\_funct\_1~(k3\_partfun1~X3~X1~X2)~X0=k1\_funct\_1~X3~\\
X0))\end{array}$$
\end{theorem}
\end{document}
