\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{t9\_normform (TMcaDkggFzJ4xbbW6T7FXy7v1sMWarD9Tm4)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_finsub\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_normform : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k1\_normform : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_finsub\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((r1\_tarski~X0~X1){\unicdcdcdhd}(r1\_tarski~\\
X2~X1)){\unicdbdjdcd}(r1\_tarski~(k2\_xboole\_0~X0~X2)~X1)\end{array}
\label{hyp:ehidpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (k1\_xtuple\_0~(k4\_tarski~X0~X1)=X0){\unicdcdcdhd}(k2\_xtuple\_0~\\
(k4\_tarski~X0~X1)=X1)\end{array}
\label{hyp:ehhdpfngdgbgchehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}(k3\_domain\_1~X0~X1~\\
X2=k2\_xtuple\_0~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfegpgngbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}(k2\_domain\_1~X0~X1~\\
X2=k1\_xtuple\_0~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfegpgngbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v4\_finsub\_1~\\
X0)){\unicdcdcdhd}((m1\_subset\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X2~X0))){\unicdbdjdcd}(k1\_finsub\_1~\\
X0~X1~X2=k2\_xboole\_0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfggjgogdhfhcgpfbd}
\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}((m1\_subset\_1~X2~X0){\unicdcdcdhd}(m1\_subset\_1~X3~X1)))){\unicdbdjdcd}\\
(k1\_domain\_1~X0~X1~X2~X3=k4\_tarski~X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfegpgngbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}(m1\_subset\_1~(k3\_domain\_1~\\
X0~X1~X2)~X1)\end{array}
\label{hyp:egehpflgddpfegpgngbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}(m1\_subset\_1~(k2\_domain\_1~\\
X0~X1~X2)~X0)\end{array}
\label{hyp:egehpflgcdpfegpgngbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}(v4\_finsub\_1~X0)){\unicdcdcdhd}(((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(v4\_finsub\_1~X1)){\unicdcdcdhd}\\
((m1\_subset\_1~X2~(k2\_zfmisc\_1~X0~X1)){\unicdcdcdhd}(m1\_subset\_1~X3~(k2\_zfmisc\_1~\\
X0~X1))))){\unicdbdjdcd}(m1\_subset\_1~(k1\_normform~X0~X1~X2~X3)~(k2\_zfmisc\_1~\\
X0~X1))\end{array}
\label{hyp:egehpflgbdpfogpgchngggpgchng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v4\_finsub\_1~\\
X0)){\unicdcdcdhd}((m1\_subset\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X2~X0))){\unicdbdjdcd}(m1\_subset\_1~\\
(k1\_finsub\_1~X0~X1~X2)~X0)\end{array}
\label{hyp:egehpflgbdpfggjgogdhfhcgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v4\_finsub\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(v4\_finsub\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k2\_zfmisc\_1~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k2\_zfmisc\_1~\\
X0~X1)){\unicdbdjdcd}(k1\_normform~X0~X1~X2~X3=k1\_domain\_1~X0~X1~(k1\_finsub\_1~\\
X0~(k2\_domain\_1~X0~X1~X2)~(k2\_domain\_1~X0~X1~X3))~(k1\_finsub\_1~X1~\\
(k3\_domain\_1~X0~X1~X2)~(k3\_domain\_1~X0~X1~X3))))))\end{array}
\label{hyp:egcdpfogpgchngggpgchng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v4\_finsub\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(v4\_finsub\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k2\_zfmisc\_1~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k2\_zfmisc\_1~\\
X0~X1)){\unicdbdjdcd}((r1\_normform~X0~X1~X2~X3){\unicdbdjded}((r1\_tarski~(k2\_domain\_1~X0~\\
X1~X2)~(k2\_domain\_1~X0~X1~X3)){\unicdcdcdhd}(r1\_tarski~(k3\_domain\_1~X0~X1~X2)~\\
(k3\_domain\_1~X0~X1~X3)))))))\end{array}
\label{hyp:egbdpfogpgchngggpgchng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}(v4\_finsub\_1~X0)){\unicdcdcdhd}(((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(v4\_finsub\_1~X1)){\unicdcdcdhd}\\
((m1\_subset\_1~X2~(k2\_zfmisc\_1~X0~X1)){\unicdcdcdhd}(m1\_subset\_1~X3~(k2\_zfmisc\_1~\\
X0~X1))))){\unicdbdjdcd}(k1\_normform~X0~X1~X2~X3=k1\_normform~X0~X1~X3~X2)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgbdpfogpgchngggpgchng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v4\_finsub\_1~\\
X0)){\unicdcdcdhd}((m1\_subset\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X2~X0))){\unicdbdjdcd}(k1\_finsub\_1~\\
X0~X1~X2=k1\_finsub\_1~X0~X2~X1)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgbdpfggjgogdhfhcgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehjdpfogpgchngggpgchng}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v4\_finsub\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(v4\_finsub\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k2\_zfmisc\_1~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k2\_zfmisc\_1~\\
X0~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k2\_zfmisc\_1~X0~X1)){\unicdbdjdcd}(((r1\_normform~\\
X0~X1~X2~X3){\unicdcdcdhd}(r1\_normform~X0~X1~X4~X3)){\unicdbdjdcd}(r1\_normform~X0~X1~(k1\_normform~\\
X0~X1~X2~X4)~X3))))))\end{array}$$
\end{theorem}
\end{document}
