\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{t38\_cgames\_1 (TMc4K241WhXoU9QbvappL9VLzcLLfKrXe89)}
\maketitle
Let $ v2\_cgames\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_cgames\_1 : {\iota}$ be given.
Let $ k10\_cgames\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k8\_cgames\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_cgames\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\preoh{{({{X0}{\unicdcdgdad}{k1\_xboole\_0}})}}}{\unicdcdcdhd}{({{\unicdcdadad} X1 .  {\preoh{{{X1} \in {X0}}}}})}}}\label{hyp:ehhdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v2\_cgames\_1~X0){\unicdbdjdcd}((X0=k3\_cgames\_1){\unicdbdjded}(k8\_cgames\_1~\\
X0=k1\_xboole\_0))\end{array}
\label{hyp:ehgdpfdghgbgngfgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v2\_cgames\_1~X1){\unicdbdjdcd}((X0 \in k10\_cgames\_1~X1){\unicdbdjded}\\
(\preoh (X0{\unicdcdgdad}X1){\unicdcdcdhd}({\unicdcdadad} X2 .  (v2\_cgames\_1~X2){\unicdbdjdcd}(\preoh (X2 \in k8\_cgames\_1~X1){\unicdcdcdhd}\\
(X0 \in k10\_cgames\_1~X2)))))\end{array}
\label{hyp:ehcdhdpfdghgbgngfgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v3\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (v2\_cgames\_1~\\
X2){\unicdbdjdcd}(((X2 \in k2\_cgames\_1~X1){\unicdcdcdhd}(X0 \in k8\_cgames\_1~X2)){\unicdbdjdcd}(X0 \in k2\_cgames\_1~\\
X1)))\end{array}
\label{hyp:ehbdadpfdghgbgngfgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 : \iota{\unicdbdjdcd}o .  ({\unicdcdaddd} X1 .  (v2\_cgames\_1~X1){\unicdcdcdhd}(X0~X1)){\unicdbdjdcd}(\\
{\unicdcdaddd} X1 .  (v2\_cgames\_1~X1){\unicdcdcdhd}((X0~X1){\unicdcdcdhd}({\unicdcdadad} X2 .  (v2\_cgames\_1~\\
X2){\unicdbdjdcd}(\preoh (X2 \in k8\_cgames\_1~X1){\unicdcdcdhd}(X0~X2)))))\end{array}
\label{hyp:dhcdpfdghgbgngfgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v2\_cgames\_1~X0){\unicdbdjded}({\unicdcdaddd} X1 .  (v3\_ordinal1~X1){\unicdcdcdhd}(X0 \in \\
k2\_cgames\_1~X1))\end{array}
\label{hyp:egddpfdghgbgngfgdhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddidpfdghgbgngfgdhpfbd}
${{\unicdcdadad} X0 .  {{({{v2\_cgames\_1}~{X0}})}{\unicdbdjdcd}{({{k3\_cgames\_1} \in {{k10\_cgames\_1}~{X0}}})}}}$.
\end{theorem}
\end{document}
