\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{t24\_cgames\_1 (TMGN4ynGPY3deh5TR1T6bDvb37X2S9nZ73i)}
\maketitle
Let $ v2\_cgames\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k10\_cgames\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_cgames\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_cgames\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v2\_cgames\_1~X0){\unicdbdjdcd}({\unicdcdaddd} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((\\
v1\_funct\_1~X1){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_finseq\_1~X1){\unicdcdcdhd}((v3\_cgames\_1~\\
X1){\unicdcdcdhd}(v4\_cgames\_1~X1)))))){\unicdcdcdhd}((k1\_funct\_1~X1~np\_\_1=X0){\unicdcdcdhd}(k1\_funct\_1~\\
X1~(k3\_finseq\_1~X1)=X0)))\end{array}
\label{hyp:mgddgdpfdghgbgngfgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v2\_cgames\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (X1=k10\_cgames\_1~X0){\unicdbdjded}\\
({\unicdcdadad} X2 .  (X2 \in X1){\unicdbdjded}({\unicdcdaddd} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}((v1\_funct\_1~\\
X3){\unicdcdcdhd}((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}((v1\_finseq\_1~X3){\unicdcdcdhd}((v3\_cgames\_1~X3){\unicdcdcdhd}\\
(v4\_cgames\_1~X3)))))){\unicdcdcdhd}((k1\_funct\_1~X3~np\_\_1=X2){\unicdcdcdhd}(k1\_funct\_1~\\
X3~(k3\_finseq\_1~X3)=X0)))))\end{array}
\label{hyp:egbdcdpfdghgbgngfgdhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdedpfdghgbgngfgdhpfbd}
${{\unicdcdadad} X0 .  {{({{v2\_cgames\_1}~{X0}})}{\unicdbdjdcd}{({{X0} \in {{k10\_cgames\_1}~{X0}}})}}}$.
\end{theorem}
\end{document}
