\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{t16\_domain\_1 (TMWfQJKbyEtQeGoP1ZAujLZAviisZX45c7m)}
\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 $ k7\_mcart\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k5\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ 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 $ k2\_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 .  {\unicdcdadad} X5 .  \\
{\unicdcdadad} X6 .  {\unicdcdadad} X7 .  (k6\_xtuple\_0~X0~X1~X2~X3 \in k4\_zfmisc\_1~X4~X5~\\
X6~X7){\unicdbdjded}((X0 \in X4){\unicdcdcdhd}((X1 \in X5){\unicdcdcdhd}((X2 \in X6){\unicdcdcdhd}(X3 \in X7))))\end{array}
\label{hyp:ehidadpfngdgbgchehpfbd}
\end{equation}
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 .  (\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}(X4=k6\_xtuple\_0~\\
(k4\_mcart\_1~X0~X1~X2~X3~X4)~(k5\_mcart\_1~X0~X1~X2~X3~X4)~(k6\_mcart\_1~\\
X0~X1~X2~X3~X4)~(k7\_mcart\_1~X0~X1~X2~X3~X4))))))\end{array}
\label{hyp:ehfdgdpfngdgbgchehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\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}((X0 \in k4\_zfmisc\_1~X1~X2~X3~X4){\unicdbdjded}({\unicdcdaddd} X5 .  (m1\_subset\_1~X5~\\
X1){\unicdcdcdhd}({\unicdcdaddd} X6 .  (m1\_subset\_1~X6~X2){\unicdcdcdhd}({\unicdcdaddd} X7 .  (m1\_subset\_1~\\
X7~X3){\unicdcdcdhd}({\unicdcdaddd} X8 .  (m1\_subset\_1~X8~X4){\unicdcdcdhd}(X0=k6\_xtuple\_0~X5~X6~X7~\\
X8)))))))))\end{array}
\label{hyp:ehbdadpfegpgngbgjgogpfbd}
\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 .  {\unicdcdadad} X5 .  \\
{\unicdcdadad} X6 .  {\unicdcdadad} X7 .  ((\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~X0){\unicdcdcdhd}\\
((m1\_subset\_1~X5~X1){\unicdcdcdhd}((m1\_subset\_1~X6~X2){\unicdcdcdhd}(m1\_subset\_1~X7~X3)))))))){\unicdbdjdcd}\\
(k5\_domain\_1~X0~X1~X2~X3~X4~X5~X6~X7=k6\_xtuple\_0~X4~X5~X6~X7)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfegpgngbgjgogpfbd}
\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}\\
(\preoh v1\_xboole\_0~(k4\_zfmisc\_1~X0~X1~X2~X3))\end{array}
\label{hyp:ggdgbdcdpfdhfhcgdhfgehpfbd}
\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~(k7\_mcart\_1~\\
X0~X1~X2~X3~X4)~X3)\end{array}
\label{hyp:egehpflghdpfngdgbgchehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdgdpfegpgngbgjgogpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (\preoh v1\_xboole\_0~\\
X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (\preoh v1\_xboole\_0~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (\preoh v1\_xboole\_0~\\
X4){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(k4\_zfmisc\_1~X1~X2~X3~X4)){\unicdbdjdcd}((X0=\\
k7\_mcart\_1~X1~X2~X3~X4~X5){\unicdbdjded}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~X1){\unicdbdjdcd}({\unicdcdadad} X7 .  \\
(m1\_subset\_1~X7~X2){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_subset\_1~X8~X3){\unicdbdjdcd}({\unicdcdadad} X9 .  \\
(m1\_subset\_1~X9~X4){\unicdbdjdcd}((X5=k5\_domain\_1~X1~X2~X3~X4~X6~X7~X8~X9){\unicdbdjdcd}(X0=\\
X9)))))))))))\end{array}$$
\end{theorem}
\end{document}
