\documentclass{article}
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\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}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t54\_rfunct\_3 (TMcbsYsEomoXUwF5Y8811wiLAhoUwXgiXra)}
\maketitle
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ r2\_rfunct\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k7\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((r1\_tarski~X0~X1){\unicdcdcdhd}(r1\_tarski~\\
X1~X2)){\unicdbdjdcd}(r1\_tarski~X0~X2)\end{array}
\label{hyp:ehbdpfihcgpgpgmgfgpfbd}
\end{equation}
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 .  ((v1\_funct\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (r2\_rfunct\_3~X0~X1){\unicdbdjded}(\\
(r1\_tarski~X1~(k1\_relset\_1~k1\_numbers~X0)){\unicdcdcdhd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~k1\_numbers){\unicdbdjdcd}(((r1\_xxreal\_0~k6\_numbers~X2){\unicdcdcdhd}(r1\_xxreal\_0~X2~\\
np\_\_1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~k1\_numbers){\unicdbdjdcd}(((X3 \in X1){\unicdcdcdhd}((X4 \in X1){\unicdcdcdhd}(k7\_real\_1~\\
(k8\_real\_1~X2~X3)~(k8\_real\_1~(k9\_real\_1~np\_\_1~X2)~X4) \in X1))){\unicdbdjdcd}(r1\_xxreal\_0~\\
(k1\_seq\_1~X0~(k7\_real\_1~(k8\_real\_1~X2~X3)~(k8\_real\_1~(k9\_real\_1~\\
np\_\_1~X2)~X4)))~(k7\_real\_1~(k8\_real\_1~X2~(k1\_seq\_1~X0~X3))~(k8\_real\_1~\\
(k9\_real\_1~np\_\_1~X2)~(k1\_seq\_1~X0~X4)))))))))))\end{array}
\label{hyp:egbdcdpfchggfhogdgehpfdd}
\end{equation}
\begin{theorem}\label{thm:ehfdedpfchggfhogdgehpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((r2\_rfunct\_3~\\
X0~X1){\unicdcdcdhd}(r1\_tarski~X2~X1)){\unicdbdjdcd}(r2\_rfunct\_3~X0~X2))\end{array}$$
\end{theorem}
\end{document}
