\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{t3\_kurato\_1 (TMabHpaybRuHxhJRCNoEdkDiH9SERmDY71u)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_kurato\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_enumset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{r1\_tarski}~{X0}}~{({{{k2\_xboole\_0}~{X0}}~{X1}})}}}}\label{hyp:ehhdpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \preoh (X0 \in X1){\unicdcdcdhd}((m1\_subset\_1~X1~(\\
k1\_zfmisc\_1~X2)){\unicdcdcdhd}(v1\_xboole\_0~X2))\end{array}
\label{hyp:ehfdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X0 \in X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X2))){\unicdbdjdcd}(m1\_subset\_1~X0~X2)\end{array}
\label{hyp:ehedpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~X1)){\unicdbdjded}(r1\_tarski~\\
X0~X1)\end{array}
\label{hyp:ehddpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~X1){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}\\
(X0 \in X1))\end{array}
\label{hyp:ehcdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
{\unicdcdadad} X6 .  {\unicdcdadad} X7 .  (X7=k5\_enumset1~X0~X1~X2~X3~X4~X5~X6){\unicdbdjded}({\unicdcdadad} X8 .  \\
(X8 \in X7){\unicdbdjded}(\preoh (X8{\unicdcdgdad}X0){\unicdcdcdhd}((X8{\unicdcdgdad}X1){\unicdcdcdhd}((X8{\unicdcdgdad}X2){\unicdcdcdhd}((X8{\unicdcdgdad}X3){\unicdcdcdhd}((X8{\unicdcdgdad}X4){\unicdcdcdhd}(\\
(X8{\unicdcdgdad}X5){\unicdcdcdhd}(X8{\unicdcdgdad}X6))))))))\end{array}
\label{hyp:egfdpffgogfhngdhfgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))){\unicdbdjdcd}(k2\_kurato\_1~X0~X1=k2\_xboole\_0~(k5\_enumset1~X1~(k2\_pre\_topc~\\
X0~X1)~(k3\_subset\_1~(u1\_struct\_0~X0)~(k2\_pre\_topc~X0~X1))~(k2\_pre\_topc~\\
X0~(k3\_subset\_1~(u1\_struct\_0~X0)~(k2\_pre\_topc~X0~X1)))~(k3\_subset\_1~\\
(u1\_struct\_0~X0)~(k2\_pre\_topc~X0~(k3\_subset\_1~(u1\_struct\_0~X0)~\\
(k2\_pre\_topc~X0~X1))))~(k2\_pre\_topc~X0~(k3\_subset\_1~(u1\_struct\_0~\\
X0)~(k2\_pre\_topc~X0~(k3\_subset\_1~(u1\_struct\_0~X0)~(k2\_pre\_topc~\\
X0~X1)))))~(k3\_subset\_1~(u1\_struct\_0~X0)~(k2\_pre\_topc~X0~(k3\_subset\_1~\\
(u1\_struct\_0~X0)~(k2\_pre\_topc~X0~(k3\_subset\_1~(u1\_struct\_0~X0)~\\
(k2\_pre\_topc~X0~X1)))))))~(k5\_enumset1~(k3\_subset\_1~(u1\_struct\_0~\\
X0)~X1)~(k2\_pre\_topc~X0~(k3\_subset\_1~(u1\_struct\_0~X0)~X1))~(k3\_subset\_1~\\
(u1\_struct\_0~X0)~(k2\_pre\_topc~X0~(k3\_subset\_1~(u1\_struct\_0~X0)~\\
X1)))~(k2\_pre\_topc~X0~(k3\_subset\_1~(u1\_struct\_0~X0)~(k2\_pre\_topc~\\
X0~(k3\_subset\_1~(u1\_struct\_0~X0)~X1))))~(k3\_subset\_1~(u1\_struct\_0~\\
X0)~(k2\_pre\_topc~X0~(k3\_subset\_1~(u1\_struct\_0~X0)~(k2\_pre\_topc~\\
X0~(k3\_subset\_1~(u1\_struct\_0~X0)~X1)))))~(k2\_pre\_topc~X0~(k3\_subset\_1~\\
(u1\_struct\_0~X0)~(k2\_pre\_topc~X0~(k3\_subset\_1~(u1\_struct\_0~X0)~\\
(k2\_pre\_topc~X0~(k3\_subset\_1~(u1\_struct\_0~X0)~X1))))))~(k3\_subset\_1~\\
(u1\_struct\_0~X0)~(k2\_pre\_topc~X0~(k3\_subset\_1~(u1\_struct\_0~X0)~\\
(k2\_pre\_topc~X0~(k3\_subset\_1~(u1\_struct\_0~X0)~(k2\_pre\_topc~X0~\\
(k3\_subset\_1~(u1\_struct\_0~X0)~X1))))))))))\end{array}
\label{hyp:egcdpflgfhchbgehpgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddpflgfhchbgehpgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))){\unicdbdjdcd}((X1 \in k2\_kurato\_1~X0~X1){\unicdcdcdhd}((k2\_pre\_topc~X0~X1 \in k2\_kurato\_1~\\
X0~X1){\unicdcdcdhd}((k3\_subset\_1~(u1\_struct\_0~X0)~(k2\_pre\_topc~X0~X1) \in k2\_kurato\_1~\\
X0~X1){\unicdcdcdhd}((k2\_pre\_topc~X0~(k3\_subset\_1~(u1\_struct\_0~X0)~(k2\_pre\_topc~\\
X0~X1)) \in k2\_kurato\_1~X0~X1){\unicdcdcdhd}((k3\_subset\_1~(u1\_struct\_0~X0)~(k2\_pre\_topc~\\
X0~(k3\_subset\_1~(u1\_struct\_0~X0)~(k2\_pre\_topc~X0~X1))) \in k2\_kurato\_1~\\
X0~X1){\unicdcdcdhd}((k2\_pre\_topc~X0~(k3\_subset\_1~(u1\_struct\_0~X0)~(k2\_pre\_topc~\\
X0~(k3\_subset\_1~(u1\_struct\_0~X0)~(k2\_pre\_topc~X0~X1)))) \in k2\_kurato\_1~\\
X0~X1){\unicdcdcdhd}(k3\_subset\_1~(u1\_struct\_0~X0)~(k2\_pre\_topc~X0~(k3\_subset\_1~\\
(u1\_struct\_0~X0)~(k2\_pre\_topc~X0~(k3\_subset\_1~(u1\_struct\_0~X0)~\\
(k2\_pre\_topc~X0~X1))))) \in k2\_kurato\_1~X0~X1))))))))\end{array}$$
\end{theorem}
\end{document}
