\documentclass{article}
\newtheorem{axiom}{Axiom}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
\newcommand\unicdcdadad{\forall}
\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
\newcommand\uniddcgcg{\lambda}
\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t8\_altcat\_2 (TMWNQRjWiNKmV9JQrFN7f4naZqigqDzjAzn)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r2\_altcat\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (r1\_tarski~X0~X1){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X0){\unicdbdjdcd}\\
(X2 \in X1))\end{array}
\label{hyp:egddpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~\\
X2~X0){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_partfun1~X2~X0)))){\unicdbdjdcd}({\unicdcdadad} X3 .  (\\
(v1\_relat\_1~X3){\unicdcdcdhd}((v4\_relat\_1~X3~X1){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}(v1\_partfun1~\\
X3~X1)))){\unicdbdjdcd}((r2\_altcat\_2~X0~X1~X2~X3){\unicdbdjded}((r1\_tarski~X0~X1){\unicdcdcdhd}({\unicdcdadad} X4 .  \\
(X4 \in X0){\unicdbdjdcd}(r1\_tarski~(k1\_funct\_1~X2~X4)~(k1\_funct\_1~X3~X4))))))\end{array}
\label{hyp:egcdpfbgmgehdgbgehpfcd}
\end{equation}
\begin{theorem}\label{thm:ehidpfbgmgehdgbgehpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}\\
((v4\_relat\_1~X3~X0){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}(v1\_partfun1~X3~X0)))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  ((v1\_relat\_1~X4){\unicdcdcdhd}((v4\_relat\_1~X4~X1){\unicdcdcdhd}((v1\_funct\_1~\\
X4){\unicdcdcdhd}(v1\_partfun1~X4~X1)))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_relat\_1~X5){\unicdcdcdhd}((v4\_relat\_1~\\
X5~X2){\unicdcdcdhd}((v1\_funct\_1~X5){\unicdcdcdhd}(v1\_partfun1~X5~X2)))){\unicdbdjdcd}(((r2\_altcat\_2~\\
X0~X1~X3~X4){\unicdcdcdhd}(r2\_altcat\_2~X1~X2~X4~X5)){\unicdbdjdcd}(r2\_altcat\_2~X0~X2~X3~X5))))\end{array}$$
\end{theorem}
\end{document}
