\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{t7\_domain\_1 (TMJWj1uWXdusrQk12ZUFFG4KfWnhadJ1Pme)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_mcart\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k4\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k3\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_mcart\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k3\_mcart\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\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 .  (m1\_subset\_1~X3~(k3\_zfmisc\_1~\\
X0~X1~X2)){\unicdbdjdcd}(X3=k3\_xtuple\_0~(k1\_mcart\_1~X0~X1~X2~X3)~(k2\_mcart\_1~\\
X0~X1~X2~X3)~(k3\_mcart\_1~X0~X1~X2~X3)))))\end{array}
\label{hyp:ehededpfngdgbgchehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
(k3\_xtuple\_0~X0~X1~X2=k3\_xtuple\_0~X3~X4~X5){\unicdbdjdcd}((X0=X3){\unicdcdcdhd}((X1=X4){\unicdcdcdhd}\\
(X2=X5)))\end{array}
\label{hyp:ehddpfihehfhahmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(\\
(m1\_subset\_1~X3~X0){\unicdcdcdhd}((m1\_subset\_1~X4~X1){\unicdcdcdhd}(m1\_subset\_1~X5~X2)))))){\unicdbdjdcd}\\
(k4\_domain\_1~X0~X1~X2~X3~X4~X5=k3\_xtuple\_0~X3~X4~X5)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfegpgngbgjgogpfbd}
\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}(m1\_subset\_1~X3~(k3\_zfmisc\_1~\\
X0~X1~X2))))){\unicdbdjdcd}(m1\_subset\_1~(k3\_mcart\_1~X0~X1~X2~X3)~X2)\end{array}
\label{hyp:egehpflgddpfngdgbgchehpfbd}
\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}(m1\_subset\_1~X3~(k3\_zfmisc\_1~\\
X0~X1~X2))))){\unicdbdjdcd}(m1\_subset\_1~(k2\_mcart\_1~X0~X1~X2~X3)~X1)\end{array}
\label{hyp:egehpflgcdpfngdgbgchehpfbd}
\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}(m1\_subset\_1~X3~(k3\_zfmisc\_1~\\
X0~X1~X2))))){\unicdbdjdcd}(m1\_subset\_1~(k1\_mcart\_1~X0~X1~X2~X3)~X0)\end{array}
\label{hyp:egehpflgbdpfngdgbgchehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehhdpfegpgngbgjgogpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (\preoh v1\_xboole\_0~\\
X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (\preoh v1\_xboole\_0~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(k3\_zfmisc\_1~X1~X2~X3)){\unicdbdjdcd}((X0=k2\_mcart\_1~X1~X2~X3~X4){\unicdbdjded}({\unicdcdadad} X5 .  \\
(m1\_subset\_1~X5~X1){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~X2){\unicdbdjdcd}({\unicdcdadad} X7 .  \\
(m1\_subset\_1~X7~X3){\unicdbdjdcd}((X4=k4\_domain\_1~X1~X2~X3~X5~X6~X7){\unicdbdjdcd}(X0=X6)))))))))\end{array}$$
\end{theorem}
\end{document}
