\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\_realset2 (TMJSSqjqgBBwSm3JUoPfHrc3HWEbvEFhRSM)}
\maketitle
Let $ m3\_realset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_realset2 : {\iota}$ be given.
Let $ c4\_\_realset2 : {\iota}$ be given.
Let $ c5\_\_realset2 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{np\_\_2}}}}\label{hyp:dhahdgcdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~X0)){\unicdbdjdcd}\\
(k6\_domain\_1~X0~X1=k1\_tarski~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfegpgngbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (X0 \in k2\_zfmisc\_1~(k6\_subset\_1~c4\_\_realset2~(k6\_domain\_1~\\
np\_\_2~(k1\_funct\_7~k6\_numbers~np\_\_2)))~(k6\_subset\_1~c4\_\_realset2~\\
(k6\_domain\_1~np\_\_2~(k1\_funct\_7~k6\_numbers~np\_\_2)))){\unicdbdjdcd}(k1\_funct\_1~\\
k2\_realset2~X0 \in k6\_subset\_1~c4\_\_realset2~(k6\_domain\_1~np\_\_2~(\\
k1\_funct\_7~k6\_numbers~np\_\_2)))\end{array}
\label{hyp:mgcdfdpfchfgbgmgdhfgehcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k2\_realset2){\unicdcdcdhd}((v1\_funct\_2~k2\_realset2~(k2\_zfmisc\_1~\\
np\_\_2~np\_\_2)~np\_\_2){\unicdcdcdhd}(m1\_subset\_1~k2\_realset2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~np\_\_2~np\_\_2)~np\_\_2))))\end{array}
\label{hyp:egehpflgcdpfchfgbgmgdhfgehcd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{c5\_\_realset2}}~{c4\_\_realset2}}\label{hyp:egehpfdgfdpfpfchfgbgmgdhfgehcd}
\end{equation}
Assume the following.
\begin{equation}
{{c5\_\_realset2}={{{k1\_funct\_7}~{k6\_numbers}}~{np\_\_2}}}\label{hyp:egfgpfdgfdpfpfchfgbgmgdhfgehcd}
\end{equation}
Assume the following.
\begin{equation}
{{c4\_\_realset2}={np\_\_2}}\label{hyp:egfgpfdgedpfpfchfgbgmgdhfgehcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~\\
X2){\unicdcdcdhd}((v1\_funct\_2~X2~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~X0))))){\unicdbdjdcd}((m3\_realset1~X2~X0~X1){\unicdbdjded}\\
({\unicdcdadad} X3 .  (X3 \in k2\_zfmisc\_1~(k6\_subset\_1~X0~(k1\_tarski~X1))~(\\
k6\_subset\_1~X0~(k1\_tarski~X1))){\unicdbdjdcd}(k1\_funct\_1~X2~X3 \in k6\_subset\_1~\\
X0~(k1\_tarski~X1)))))\end{array}
\label{hyp:eggdpfchfgbgmgdhfgehbd}
\end{equation}
\begin{theorem}\label{thm:mgddedpfchfgbgmgdhfgehcd}
${{{{m3\_realset1}~{k2\_realset2}}~{c4\_\_realset2}}~{c5\_\_realset2}}$.
\end{theorem}
\end{document}
