\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{t75\_mcart\_1 (TMTm2koFsd1Gcrko67RvJGgeXqSFyUuWtgK)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_zfmisc\_1 : {{\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 $ 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 $ k1\_xboole\_0 : {\iota}$ be given.
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 .  \preoh (X0{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}\\
((X1{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}((X2{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}((X3{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}(\\
{\unicdcdaddd} X4 .  (m1\_subset\_1~X4~(k4\_zfmisc\_1~X0~X1~X2~X3)){\unicdcdcdhd}({\unicdcdadad} X5 .  \\
(m1\_subset\_1~X5~X0){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~X1){\unicdbdjdcd}({\unicdcdadad} X7 .  \\
(m1\_subset\_1~X7~X2){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_subset\_1~X8~X3){\unicdbdjdcd}(X4{\unicdcdgdad}k6\_xtuple\_0~\\
X5~X6~X7~X8)))))))))\end{array}
\label{hyp:mggdedpfngdgbgchehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{k1\_xboole\_0}}\label{hyp:ggdgbdpfihcgpgpgmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:ehhdfdpfngdgbgchehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (\preoh v1\_xboole\_0~\\
X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (\preoh v1\_xboole\_0~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (\preoh v1\_xboole\_0~\\
X4){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(k4\_zfmisc\_1~X1~X2~X3~X4)){\unicdbdjdcd}(({\unicdcdadad} X6 .  \\
(m1\_subset\_1~X6~X1){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~X2){\unicdbdjdcd}({\unicdcdadad} X8 .  \\
(m1\_subset\_1~X8~X3){\unicdbdjdcd}({\unicdcdadad} X9 .  (m1\_subset\_1~X9~X4){\unicdbdjdcd}((X5=k6\_xtuple\_0~\\
X6~X7~X8~X9){\unicdbdjdcd}(X0=X6)))))){\unicdbdjdcd}(X0=k4\_mcart\_1~X1~X2~X3~X4~X5))))))\end{array}$$
\end{theorem}
\end{document}
