\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{t59\_mcart\_1 (TMc24wum8VQb9CHAAnAkE2Z41c3RisBP5mQ)}
\maketitle
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ k6\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k5\_mcart\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k8\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_mcart\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k7\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_xtuple\_0 : {{\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}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((X0{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}\\
((X1{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}((X2{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}(X3{\unicdcdgdad}k1\_xboole\_0)))){\unicdbdjded}\\
(k4\_zfmisc\_1~X0~X1~X2~X3{\unicdcdgdad}k1\_xboole\_0)\end{array}
\label{hyp:ehfdbdpfngdgbgchehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  k3\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1)~X2~X3=k4\_zfmisc\_1~X0~X1~X2~X3\end{array}
\label{hyp:ehfdadpfngdgbgchehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X0 \in X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X2))){\unicdbdjdcd}(m1\_subset\_1~X0~X2)\end{array}
\label{hyp:ehedpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (\preoh (\preoh r1\_tarski~X0~(k3\_zfmisc\_1~\\
X0~X1~X2)){\unicdcdcdhd}((\preoh r1\_tarski~X0~(k3\_zfmisc\_1~X1~X2~X0)){\unicdcdcdhd}(\preoh r1\_tarski~\\
X0~(k3\_zfmisc\_1~X2~X0~X1)))){\unicdbdjdcd}(X0=k1\_xboole\_0)\end{array}
\label{hyp:ehedfdpfngdgbgchehpfbd}
\end{equation}
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 .  \preoh (X0{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}({\unicdcdadad} X1 .  \preoh (X1 \in X0){\unicdcdcdhd}({\unicdcdadad} X2 .  \\
{\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \preoh ((X2 \in X0){\unicdcdcdid}(X3 \in X0)){\unicdcdcdhd}(X1=k6\_xtuple\_0~\\
X2~X3~X4~X5)))\end{array}
\label{hyp:ehddadpfngdgbgchehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~X1){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}\\
(X0 \in X1))\end{array}
\label{hyp:ehcdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}\\
(m1\_subset\_1~X4~(k4\_zfmisc\_1~X0~X1~X2~X3)))))){\unicdbdjdcd}(k5\_mcart\_1~X0~X1~\\
X2~X3~X4=k8\_xtuple\_0~X4)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfngdgbgchehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}\\
(m1\_subset\_1~X4~(k4\_zfmisc\_1~X0~X1~X2~X3)))))){\unicdbdjdcd}(k4\_mcart\_1~X0~X1~\\
X2~X3~X4=k7\_xtuple\_0~X4)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfngdgbgchehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_xtuple\_0~X0){\unicdbdjdcd}(k6\_xtuple\_0~(k7\_xtuple\_0~X0)~(k8\_xtuple\_0~\\
X0)~(k5\_xtuple\_0~X0)~(k2\_xtuple\_0~X0)=X0)\end{array}
\label{hyp:chegbdcdpfihehfhahmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}\\
(m1\_subset\_1~X4~(k4\_zfmisc\_1~X0~X1~X2~X3)))))){\unicdbdjdcd}(m1\_subset\_1~(k5\_mcart\_1~\\
X0~X1~X2~X3~X4)~X1)\end{array}
\label{hyp:egehpflgfdpfngdgbgchehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}\\
(m1\_subset\_1~X4~(k4\_zfmisc\_1~X0~X1~X2~X3)))))){\unicdbdjdcd}(m1\_subset\_1~(k4\_mcart\_1~\\
X0~X1~X2~X3~X4)~X0)\end{array}
\label{hyp:egehpflgedpfngdgbgchehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(\preoh v1\_xboole\_0~X3)))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k4\_zfmisc\_1~X0~X1~X2~X3)){\unicdbdjdcd}(v3\_xtuple\_0~\\
X4))\end{array}
\label{hyp:dgdgcdpfngdgbgchehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehfdjdpfngdgbgchehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (\preoh (\preoh r1\_tarski~X0~\\
(k4\_zfmisc\_1~X0~X1~X2~X3)){\unicdcdcdhd}((\preoh r1\_tarski~X0~(k4\_zfmisc\_1~X1~X2~X3~\\
X0)){\unicdcdcdhd}((\preoh r1\_tarski~X0~(k4\_zfmisc\_1~X2~X3~X0~X1)){\unicdcdcdhd}(\preoh r1\_tarski~X0~\\
(k4\_zfmisc\_1~X3~X0~X1~X2))))){\unicdbdjdcd}(X0=k1\_xboole\_0)\end{array}$$
\end{theorem}
\end{document}
