\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{t83\_mcart\_1 (TMHRLYzgq3MbtUzByBuQqw5zLRgBuQiSKrq)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k4\_mcart\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ k6\_mcart\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k7\_mcart\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k6\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  \preoh (X0 \in \\
k4\_zfmisc\_1~X1~X2~X3~X4){\unicdcdcdhd}({\unicdcdadad} X5 .  {\unicdcdadad} X6 .  {\unicdcdadad} X7 .  {\unicdcdadad} X8 .  \\
\preoh (X5 \in X1){\unicdcdcdhd}((X6 \in X2){\unicdcdcdhd}((X7 \in X3){\unicdcdcdhd}((X8 \in X4){\unicdcdcdhd}(X0=k6\_xtuple\_0~X5~X6~\\
X7~X8)))))\end{array}
\label{hyp:ehhdjdpfngdgbgchehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (\preoh v1\_xboole\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (\preoh v1\_xboole\_0~X3){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k4\_zfmisc\_1~X0~X1~X2~X3)){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
{\unicdcdadad} X6 .  {\unicdcdadad} X7 .  {\unicdcdadad} X8 .  (X4=k6\_xtuple\_0~X5~X6~X7~X8){\unicdbdjdcd}\\
((k4\_mcart\_1~X0~X1~X2~X3~X4=X5){\unicdcdcdhd}((k5\_mcart\_1~X0~X1~X2~X3~X4=X6){\unicdcdcdhd}(\\
(k6\_mcart\_1~X0~X1~X2~X3~X4=X7){\unicdcdcdhd}(k7\_mcart\_1~X0~X1~X2~X3~X4=X8)))))))))\end{array}
\label{hyp:ehhdedpfngdgbgchehpfbd}
\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}(k7\_mcart\_1~X0~X1~\\
X2~X3~X4=k2\_xtuple\_0~X4)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflghdpfngdgbgchehpfbd}
\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}(k6\_mcart\_1~X0~X1~\\
X2~X3~X4=k5\_xtuple\_0~X4)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfngdgbgchehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  k2\_xtuple\_0~(k6\_xtuple\_0~\\
X0~X1~X2~X3)=X3\end{array}
\label{hyp:chegbdbdpfihehfhahmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  k5\_xtuple\_0~(k6\_xtuple\_0~\\
X0~X1~X2~X3)=X2\end{array}
\label{hyp:chegbdadpfihehfhahmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k5\_xtuple\_0}~{X0}}={{k2\_xtuple\_0}~{({{k1\_xtuple\_0}~{X0}})}}}}\label{hyp:eghdpfihehfhahmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:ehidddpfngdgbgchehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (\preoh v1\_xboole\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (\preoh v1\_xboole\_0~X3){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((\preoh v1\_xboole\_0~X5){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X6 .  ((\preoh v1\_xboole\_0~X6){\unicdcdcdhd}(m1\_subset\_1~X6~(k1\_zfmisc\_1~\\
X2))){\unicdbdjdcd}({\unicdcdadad} X7 .  ((\preoh v1\_xboole\_0~X7){\unicdcdcdhd}(m1\_subset\_1~X7~(k1\_zfmisc\_1~\\
X3))){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_subset\_1~X8~(k4\_zfmisc\_1~X0~X1~X2~X3)){\unicdbdjdcd}(\\
(X8 \in k4\_zfmisc\_1~X4~X5~X6~X7){\unicdbdjdcd}((k4\_mcart\_1~X0~X1~X2~X3~X8 \in X4){\unicdcdcdhd}((k5\_mcart\_1~\\
X0~X1~X2~X3~X8 \in X5){\unicdcdcdhd}((k6\_mcart\_1~X0~X1~X2~X3~X8 \in X6){\unicdcdcdhd}(k7\_mcart\_1~X0~\\
X1~X2~X3~X8 \in X7)))))))))))))\end{array}$$
\end{theorem}
\end{document}
