\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{l34\_int\_4 (TMJzudkexHnaaw3cjbUDLophmHJjZfn5RdM)}
\maketitle
Let $ v1\_int\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_int\_4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_numbers : {\iota}$ be given.
Let $ v3\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_relat\_2 : {{\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 $ r2\_int\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_relat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r8\_relat\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r3\_relat\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_int\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_int\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_int\_1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_int\_1~X3){\unicdbdjdcd}(((r2\_int\_1~X0~X1~X2){\unicdcdcdhd}\\
(r2\_int\_1~X1~X3~X2)){\unicdbdjdcd}(r2\_int\_1~X0~X3~X2)))))\end{array}
\label{hyp:ehbdfdpfjgogehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_int\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_int\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_int\_1~X2){\unicdbdjdcd}((r2\_int\_1~X0~X1~X2){\unicdbdjdcd}(r2\_int\_1~X1~X0~X2))))\end{array}
\label{hyp:ehbdedpfjgogehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_partfun1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0)))){\unicdbdjdcd}(k1\_relat\_1~X1=X0)\end{array}
\label{hyp:ehbdcdpfpgchegfgchdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_int\_1}~{X0}})}{\unicdbdjdcd}{({{{v1\_partfun1}~{({{k1\_int\_4}~{X0}})}}~{k4\_numbers}})}}}\label{hyp:ggdgddpfjgogehpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_int\_1~X0){\unicdbdjdcd}(m1\_subset\_1~(k1\_int\_4~X0)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k4\_numbers~k4\_numbers)))\end{array}
\label{hyp:egehpflgbdpfjgogehpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (r8\_relat\_2~X0~X1){\unicdbdjded}({\unicdcdadad} X2 .  \\
{\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((X2 \in X1){\unicdcdcdhd}((X3 \in X1){\unicdcdcdhd}((X4 \in X1){\unicdcdcdhd}((k4\_tarski~\\
X2~X3 \in X0){\unicdcdcdhd}(k4\_tarski~X3~X4 \in X0))))){\unicdbdjdcd}(k4\_tarski~X2~X4 \in X0)))\end{array}
\label{hyp:egidpfchfgmgbgehpfcd}
\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 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (r3\_relat\_2~X0~X1){\unicdbdjded}({\unicdcdadad} X2 .  \\
{\unicdcdadad} X3 .  ((X2 \in X1){\unicdcdcdhd}((X3 \in X1){\unicdcdcdhd}(k4\_tarski~X2~X3 \in X0))){\unicdbdjdcd}(k4\_tarski~\\
X3~X2 \in X0)))\end{array}
\label{hyp:egddpfchfgmgbgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_int\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k4\_numbers~k4\_numbers))){\unicdbdjdcd}((X1=k1\_int\_4~X0){\unicdbdjded}({\unicdcdadad} X2 .  \\
(v1\_int\_1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_int\_1~X3){\unicdbdjdcd}((k4\_tarski~X2~X3 \in X1){\unicdbdjded}\\
(r2\_int\_1~X2~X3~X0))))))\end{array}
\label{hyp:egbdpfjgogehpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}((v8\_relat\_2~X0){\unicdbdjded}(r8\_relat\_2~X0~(\\
k1\_relat\_1~X0)))\end{array}
\label{hyp:egbdgdpfchfgmgbgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}((v3\_relat\_2~X0){\unicdbdjded}(r3\_relat\_2~X0~(\\
k1\_relat\_1~X0)))\end{array}
\label{hyp:egbdbdpfchfgmgbgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k2\_tarski}~{X0}}~{X1}}={{{k2\_tarski}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(v1\_relat\_1~X2)\end{array}
\label{hyp:dgdgbdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_numbers}})}{\unicdbdjdcd}{({{v1\_int\_1}~{X0}})}}}\label{hyp:dgdgbdpfjgogehpfbd}
\end{equation}
\begin{theorem}\label{thm:mgddedpfjgogehpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_int\_1~X0){\unicdbdjdcd}((v1\_partfun1~(k1\_int\_4~X0)~k4\_numbers){\unicdcdcdhd}\\
((v3\_relat\_2~(k1\_int\_4~X0)){\unicdcdcdhd}((v8\_relat\_2~(k1\_int\_4~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
(k1\_int\_4~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k4\_numbers~k4\_numbers))))))\end{array}$$
\end{theorem}
\end{document}
