\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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\newcommand\unicdcdidid{\not\subseteq}
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\begin{document}
\title{t26\_partfun1 (TMLq4Yeya4ZZj6vtQPB8dZZVgMk3Q7M47os)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\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}
\label{hyp:ehcdfdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}\\
(v1\_funct\_1~X3)){\unicdbdjdcd}((X0 \in k1\_relset\_1~X1~(k3\_partfun1~X3~X1~X2)){\unicdbdjded}\\
((X0 \in k9\_xtuple\_0~X3){\unicdcdcdhd}((X0 \in X1){\unicdcdcdhd}(k1\_funct\_1~X3~X0 \in X2))))\end{array}
\label{hyp:ehcdedpfahbgchehggfhogbd}
\end{equation}
\begin{theorem}\label{thm:ehcdgdpfahbgchehggfhogbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}\\
(v1\_funct\_1~X3)){\unicdbdjdcd}((X0 \in k1\_relset\_1~X1~(k3\_partfun1~X3~X1~X2)){\unicdbdjdcd}\\
(k1\_funct\_1~(k3\_partfun1~X3~X1~X2)~X0=k1\_funct\_1~X3~X0))\end{array}$$
\end{theorem}
\end{document}
