\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{t37\_cgames\_1 (TMT1StkoXbNSg4L18NyhFWLkTJY2Fm6eN2E)}
\maketitle
Let $ k12\_cgames\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k3\_cgames\_1 : {\iota}$ be given.
Let $ k1\_tarski : {{\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 $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_cgames\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_cgames\_1 : {\iota}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k10\_cgames\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_cgames\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
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 .  (r1\_tarski~X0~(k1\_tarski~X1)){\unicdbdjded}((X0=k1\_xboole\_0){\unicdcdcdid}\\
(X0=k1\_tarski~X1))\end{array}
\label{hyp:ehddddpfkhggngjgdhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{{k2\_cgames\_1}~{k1\_xboole\_0}}={{k1\_tarski}~{k1\_cgames\_1}}}\label{hyp:ehcdpfdghgbgngfgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k3\_cgames\_1}={k1\_cgames\_1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfdghgbgngfgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v3\_ordinal1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k2\_cgames\_1~\\
X0))){\unicdbdjdcd}(k12\_cgames\_1~X0~X1=k10\_cgames\_1~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdcdpfdghgbgngfgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v2\_cgames\_1}~{X0}})}{\unicdbdjdcd}{({\preoh{{{v1\_xboole\_0}~{({{k10\_cgames\_1}~{X0}})}}}})}}}\label{hyp:ggdgjdpfdghgbgngfgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{v2\_cgames\_1}~{k1\_cgames\_1}}\label{hyp:ggdgcdpfdghgbgngfgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{k1\_xboole\_0}}\label{hyp:ggdgbdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k3\_cgames\_1}}~{({{k2\_cgames\_1}~{k1\_xboole\_0}})}}\label{hyp:egehpflgddpfdghgbgngfgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v3\_ordinal1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k2\_cgames\_1~\\
X0))){\unicdbdjdcd}(m1\_subset\_1~(k12\_cgames\_1~X0~X1)~(k1\_zfmisc\_1~(k2\_cgames\_1~\\
X0)))\end{array}
\label{hyp:egehpflgbdcdpfdghgbgngfgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{v3\_ordinal1}~{X0}})}}}\label{hyp:dgdgddpfpgchegjgogbgmgbd}
\end{equation}
\begin{theorem}\label{thm:ehddhdpfdghgbgngfgdhpfbd}
${{{{k12\_cgames\_1}~{k1\_xboole\_0}}~{k3\_cgames\_1}}={{k1\_tarski}~{k3\_cgames\_1}}}$.
\end{theorem}
\end{document}
