\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=}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
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\newcommand\unicdcdidid{\not\subseteq}
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\begin{document}
\title{t82\_scmyciel (TMGwAjq7BUhqDsTTFK4hSjD7JNgnf2c8WBM)}
\maketitle
Let $ v4\_scmyciel : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_scmyciel : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k10\_scmyciel : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_scmyciel : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_scmyciel : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v10\_scmyciel : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_eqrel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v7\_scmyciel : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v8\_scmyciel : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v4\_scmyciel~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v10\_scmyciel~X1~X0){\unicdcdcdhd}\\
(m1\_eqrel\_1~X1~(k3\_tarski~X0))){\unicdbdjdcd}((v7\_scmyciel~X1~(k6\_scmyciel~\\
X0)){\unicdcdcdhd}(m1\_eqrel\_1~X1~(k3\_tarski~(k6\_scmyciel~X0)))))\end{array}
\label{hyp:ehidadpfdhdgngjhdgjgfgmg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v4\_scmyciel~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v7\_scmyciel~X1~(k6\_scmyciel~\\
X0)){\unicdcdcdhd}(m1\_eqrel\_1~X1~(k3\_tarski~(k6\_scmyciel~X0)))){\unicdbdjdcd}((v10\_scmyciel~\\
X1~X0){\unicdcdcdhd}(m1\_eqrel\_1~X1~(k3\_tarski~X0))))\end{array}
\label{hyp:ehhdidpfdhdgngjhdgjgfgmg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v4\_scmyciel~X0){\unicdcdcdhd}(v11\_scmyciel~X0)){\unicdbdjdcd}((v4\_scmyciel~\\
(k6\_scmyciel~X0)){\unicdcdcdhd}(v8\_scmyciel~(k6\_scmyciel~X0)))\end{array}
\label{hyp:ggdgcdadpfdhdgngjhdgjgfgmg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v4\_scmyciel}~{X0}})}{\unicdbdjdcd}{({{v4\_scmyciel}~{({{k6\_scmyciel}~{X0}})}})}}}\label{hyp:egehpflggdpfdhdgngjhdgjgfgmg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v4\_scmyciel~X0){\unicdcdcdhd}(v11\_scmyciel~X0)){\unicdbdjdcd}(v7\_ordinal1~\\
(k10\_scmyciel~X0))\end{array}
\label{hyp:egehpflgbdadpfdhdgngjhdgjgfgmg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v4\_scmyciel~X0){\unicdcdcdhd}(v11\_scmyciel~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(v7\_ordinal1~X1){\unicdbdjdcd}((X1=k10\_scmyciel~X0){\unicdbdjded}(({\unicdcdaddd} X2 .  ((v1\_finset\_1~\\
X2){\unicdcdcdhd}((v10\_scmyciel~X2~X0){\unicdcdcdhd}(m1\_eqrel\_1~X2~(k3\_tarski~X0)))){\unicdcdcdhd}(\\
k5\_card\_1~X2=X1)){\unicdcdcdhd}({\unicdcdadad} X2 .  ((v1\_finset\_1~X2){\unicdcdcdhd}((v10\_scmyciel~\\
X2~X0){\unicdcdcdhd}(m1\_eqrel\_1~X2~(k3\_tarski~X0)))){\unicdbdjdcd}(r1\_xxreal\_0~X1~(k5\_card\_1~\\
X2))))))\end{array}
\label{hyp:egcdcdpfdhdgngjhdgjgfgmg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v4\_scmyciel~X0){\unicdcdcdhd}(v8\_scmyciel~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(v7\_ordinal1~X1){\unicdbdjdcd}((X1=k9\_scmyciel~X0){\unicdbdjded}(({\unicdcdaddd} X2 .  ((v1\_finset\_1~\\
X2){\unicdcdcdhd}((v7\_scmyciel~X2~X0){\unicdcdcdhd}(m1\_eqrel\_1~X2~(k3\_tarski~X0)))){\unicdcdcdhd}(k5\_card\_1~\\
X2=X1)){\unicdcdcdhd}({\unicdcdadad} X2 .  ((v1\_finset\_1~X2){\unicdcdcdhd}((v7\_scmyciel~X2~X0){\unicdcdcdhd}\\
(m1\_eqrel\_1~X2~(k3\_tarski~X0)))){\unicdbdjdcd}(r1\_xxreal\_0~X1~(k5\_card\_1~X2))))))\end{array}
\label{hyp:egbdidpfdhdgngjhdgjgfgmg}
\end{equation}
\begin{theorem}\label{thm:ehidcdpfdhdgngjhdgjgfgmg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v4\_scmyciel~X0){\unicdcdcdhd}(v11\_scmyciel~X0)){\unicdbdjdcd}(k10\_scmyciel~\\
X0=k9\_scmyciel~(k6\_scmyciel~X0))\end{array}$$
\end{theorem}
\end{document}
