\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{t79\_xxreal\_2 (TMTopQNKeDMQDu29Q3xoztfEv4vChgsJ8Cd)}
\maketitle
Let $ v2\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xxreal\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_xxreal\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_xxreal\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_xxreal\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_xxreal\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xxreal\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_xxreal\_0 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  \preoh (v1\_xboole\_0~X0){\unicdcdcdhd}((X0{\unicdcdgdad}X1){\unicdcdcdhd}(v1\_xboole\_0~\\
X1))\end{array}
\label{hyp:ehidpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_membered~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xxreal\_2~\\
X0){\unicdcdcdhd}((\preoh v2\_xxreal\_2~X0){\unicdcdcdhd}(v6\_xxreal\_2~X0))))){\unicdbdjdcd}(X0=k4\_xxreal\_1~\\
(k2\_xxreal\_2~X0)~(k1\_xxreal\_2~X0))\end{array}
\label{hyp:ehhdidpfihihchfgbgmgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v2\_membered~X0){\unicdbdjdcd}((\preoh v1\_xboole\_0~X0){\unicdbdjded}(r1\_xxreal\_0~\\
(k2\_xxreal\_2~X0)~(k1\_xxreal\_2~X0)))\end{array}
\label{hyp:ehedadpfihihchfgbgmgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xxreal\_0~X0){\unicdcdcdhd}(v1\_xxreal\_0~X1)){\unicdbdjdcd}(\\
r1\_xxreal\_0~X0~X0)\end{array}
\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xxreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xboole\_0}~{({{{k4\_xxreal\_1}~{X0}}~{X0}})}})}}}\label{hyp:ggdgidpfihihchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xxreal\_0}~{k2\_xxreal\_0}}\label{hyp:ggdgcdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v2\_membered}~{X0}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{({{k2\_xxreal\_2}~{X0}})}})}}}\label{hyp:egehpflgcdpfihihchfgbgmgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v2\_membered}~{X0}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{({{k1\_xxreal\_2}~{X0}})}})}}}\label{hyp:egehpflgbdpfihihchfgbgmgpfcd}
\end{equation}
\begin{theorem}\label{thm:ehhdjdpfihihchfgbgmgpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_membered~X0){\unicdcdcdhd}((\preoh v1\_xxreal\_2~X0){\unicdcdcdhd}((\preoh v2\_xxreal\_2~\\
X0){\unicdcdcdhd}(v6\_xxreal\_2~X0)))){\unicdbdjdcd}({\unicdcdaddd} X1 .  (v1\_xxreal\_0~X1){\unicdcdcdhd}({\unicdcdaddd} X2 .  \\
(v1\_xxreal\_0~X2){\unicdcdcdhd}((r1\_xxreal\_0~X1~X2){\unicdcdcdhd}(X0=k4\_xxreal\_1~X1~X2))))\end{array}$$
\end{theorem}
\end{document}
