\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{t33\_partit1 (TMd1hPbPVjPN8wysJkhrB6Ew3ApJQD4a1ck)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_partit1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_partit1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_eqrel\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_eqrel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (k4\_tarski~X0~X1 \in \\
k2\_zfmisc\_1~X2~X3){\unicdbdjded}((X0 \in X2){\unicdcdcdhd}(X1 \in X3))\end{array}
\label{hyp:ehidhdpfkhggngjgdhdgpfbd}
\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 .  (v3\_relat\_2~(k1\_eqrel\_1~X0)){\unicdcdcdhd}((v8\_relat\_2~(k1\_eqrel\_1~\\
X0)){\unicdcdcdhd}(v1\_partfun1~(k1\_eqrel\_1~X0)~X0))\end{array}
\label{hyp:ggdgcdpffgbhchfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_eqrel\_1~X1~X0){\unicdbdjdcd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~X0)))\end{array}
\label{hyp:egehpfngbdpffgbhchfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({\preoh{{{v1\_xboole\_0}~{X0}}}})}{\unicdbdjdcd}{({{{m1\_eqrel\_1}~{({{k6\_partit1}~{X0}})}}~{X0}})}}}\label{hyp:egehpflggdpfahbgchehjgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  m1\_subset\_1~(k1\_eqrel\_1~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0))\end{array}
\label{hyp:egehpflgbdpffgbhchfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({\preoh{{{v1\_xboole\_0}~{X0}}}})}{\unicdbdjdcd}{({{{k6\_partit1}~{X0}}={{k1\_tarski}~{X0}}})}}}\label{hyp:egidpfahbgchehjgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_eqrel\_1~X1~X0){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_partfun1~X2~X0){\unicdcdcdhd}((v3\_relat\_2~X2){\unicdcdcdhd}((v8\_relat\_2~\\
X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)))))){\unicdbdjdcd}((\\
X2=k4\_partit1~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (k4\_tarski~X3~X4 \in \\
X2){\unicdbdjded}({\unicdcdaddd} X5 .  (m1\_subset\_1~X5~(k1\_zfmisc\_1~X0)){\unicdcdcdhd}((X5 \in X1){\unicdcdcdhd}\\
((X3 \in X5){\unicdcdcdhd}(X4 \in X5))))))))\end{array}
\label{hyp:eggdpfahbgchehjgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k4\_tarski~X0~X1=k2\_tarski~(k2\_tarski~X0~\\
X1)~(k1\_tarski~X0)\end{array}
\label{hyp:egfdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (X1=k1\_tarski~X0){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X1){\unicdbdjded}\\
(X2=X0))\end{array}
\label{hyp:egbdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k1\_eqrel\_1}~{X0}}={{{k2\_zfmisc\_1}~{X0}}~{X0}}}}\label{hyp:egbdpffgbhchfgmgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddddpfahbgchehjgehbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}(k4\_partit1~X0~(k6\_partit1~X0)=\\
k1\_eqrel\_1~X0)\end{array}$$
\end{theorem}
\end{document}
