\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{t2\_cgames\_1 (TMdh6x88KU1GGBAvfum7faZdHFtmofpDXAS)}
\maketitle
Let $ k2\_cgames\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_cgames\_1 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_cgames\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_cgames\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_cgames\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_cgames\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ g1\_cgames\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{r1\_tarski}~{({{k1\_tarski}~{X0}})}}~{X1}})}{\unicdbdjded}{({{X0} \in {X1}})}}}}\label{hyp:ehddbdpfkhggngjgdhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v3\_ordinal1~X1){\unicdbdjdcd}((X0 \in k2\_cgames\_1~X1){\unicdbdjded}\\
({\unicdcdaddd} X2 .  ((v1\_cgames\_1~X2){\unicdcdcdhd}(l1\_cgames\_1~X2)){\unicdcdcdhd}((X0=X2){\unicdcdcdhd}(\\
{\unicdcdadad} X3 .  \preoh (X3 \in k2\_xboole\_0~(u1\_cgames\_1~X2)~(u2\_cgames\_1~X2)){\unicdcdcdhd}\\
({\unicdcdadad} X4 .  (v3\_ordinal1~X4){\unicdbdjdcd}(\preoh (X4 \in X1){\unicdcdcdhd}(X3 \in k2\_cgames\_1~X4)))))))\end{array}
\label{hyp:ehbdpfdghgbgngfgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{{k2\_xboole\_0}~{X0}}~{k1\_xboole\_0}}={X0}}}\label{hyp:ehbdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (g1\_cgames\_1~X0~X1=\\
g1\_cgames\_1~X2~X3){\unicdbdjdcd}((X0=X2){\unicdcdcdhd}(X1=X3))\end{array}
\label{hyp:ggchfgfgpfhgbdpfdghgbgngfgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}(\preoh v1\_xboole\_0~(k2\_xboole\_0~\\
X1~X0))\end{array}
\label{hyp:ggdgfdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{k1\_xboole\_0}}\label{hyp:ggdgbdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_cgames\_1~(g1\_cgames\_1~X0~X1)){\unicdcdcdhd}(l1\_cgames\_1~\\
(g1\_cgames\_1~X0~X1))\end{array}
\label{hyp:egehpfhgbdpfdghgbgngfgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (r1\_tarski~X0~X1){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X0){\unicdbdjdcd}\\
(X2 \in X1))\end{array}
\label{hyp:egddpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjded}{({{\unicdcdadad} X1 .  {\preoh{{{X1} \in {X0}}}}})}}}\label{hyp:egbdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{k1\_cgames\_1}={{{g1\_cgames\_1}~{k1\_xboole\_0}}~{k1\_xboole\_0}}}\label{hyp:egbdpfdghgbgngfgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0}={X1}})}{\unicdbdjded}{({{({{{r1\_tarski}~{X0}}~{X1}})}{\unicdcdcdhd}{({{{r1\_tarski}~{X1}}~{X0}})}})}}}}\label{hyp:egbdadpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{v3\_ordinal1}~{X0}})}}}\label{hyp:dgdgddpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_cgames\_1~X0){\unicdbdjdcd}((v1\_cgames\_1~X0){\unicdbdjdcd}(X0=g1\_cgames\_1~\\
(u1\_cgames\_1~X0)~(u2\_cgames\_1~X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdpfdghgbgngfgdhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdpfdghgbgngfgdhpfbd}
${{{k2\_cgames\_1}~{k1\_xboole\_0}}={{k1\_tarski}~{k1\_cgames\_1}}}$.
\end{theorem}
\end{document}
