\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{l24\_normform (TMFWQEPo7ijtp8jmRZhx2UrETZUvCCm93sG)}
\maketitle
Let $ v1\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_normform : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_finsub\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ k5\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_finsub\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_normform : {{\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 .  {\unicdcdadad} X3 .  (((v1\_funct\_1~X1){\unicdcdcdhd}\\
((v1\_funct\_2~X1~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~X0))))){\unicdcdcdhd}((m1\_subset\_1~X2~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X3~X0))){\unicdbdjdcd}(k5\_binop\_1~X0~X1~X2~X3=k1\_binop\_1~X1~X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfcgjgogpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((v1\_funct\_1~X1){\unicdcdcdhd}\\
((v1\_funct\_2~X1~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~X0))))){\unicdcdcdhd}((m1\_subset\_1~X2~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X3~X0))){\unicdbdjdcd}(k3\_binop\_1~X0~X1~X2~X3=k1\_binop\_1~X1~X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfcgjgogpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~(k5\_finsub\_1~X0)){\unicdcdcdhd}(v4\_finsub\_1~(k5\_finsub\_1~\\
X0))\end{array}
\label{hyp:ggdgcdpfggjgogdhfhcgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_funct\_1~(k5\_normform~X0)){\unicdcdcdhd}((v1\_funct\_2~(k5\_normform~\\
X0)~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k5\_finsub\_1~X0)~(k5\_finsub\_1~X0))~\\
(k2\_zfmisc\_1~(k5\_finsub\_1~X0)~(k5\_finsub\_1~X0)))~(k2\_zfmisc\_1~\\
(k5\_finsub\_1~X0)~(k5\_finsub\_1~X0))){\unicdcdcdhd}(m1\_subset\_1~(k5\_normform~\\
X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k5\_finsub\_1~\\
X0)~(k5\_finsub\_1~X0))~(k2\_zfmisc\_1~(k5\_finsub\_1~X0)~(k5\_finsub\_1~\\
X0)))~(k2\_zfmisc\_1~(k5\_finsub\_1~X0)~(k5\_finsub\_1~X0))))))\end{array}
\label{hyp:egehpflgfdpfogpgchngggpgchng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k5\_finsub\_1~X0)~(k5\_finsub\_1~X0))~(k2\_zfmisc\_1~\\
(k5\_finsub\_1~X0)~(k5\_finsub\_1~X0)))~(k2\_zfmisc\_1~(k5\_finsub\_1~\\
X0)~(k5\_finsub\_1~X0))){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k5\_finsub\_1~X0)~(k5\_finsub\_1~X0))~\\
(k2\_zfmisc\_1~(k5\_finsub\_1~X0)~(k5\_finsub\_1~X0)))~(k2\_zfmisc\_1~\\
(k5\_finsub\_1~X0)~(k5\_finsub\_1~X0))))))){\unicdbdjdcd}((X1=k5\_normform~X0){\unicdbdjded}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k2\_zfmisc\_1~(k5\_finsub\_1~X0)~(k5\_finsub\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k2\_zfmisc\_1~(k5\_finsub\_1~\\
X0)~(k5\_finsub\_1~X0))){\unicdbdjdcd}(k5\_binop\_1~(k2\_zfmisc\_1~(k5\_finsub\_1~\\
X0)~(k5\_finsub\_1~X0))~X1~X2~X3=k1\_normform~(k5\_finsub\_1~X0)~(k5\_finsub\_1~\\
X0)~X2~X3))))\end{array}
\label{hyp:eggdpfogpgchngggpgchng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k2\_zfmisc\_1~\\
X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0)~X0))))){\unicdbdjdcd}((v1\_binop\_1~X1~X0){\unicdbdjded}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
X0){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~X0){\unicdbdjdcd}(k3\_binop\_1~X0~X1~X2~X3=k3\_binop\_1~\\
X0~X1~X3~X2))))\end{array}
\label{hyp:egcdpfcgjgogpgahpfbd}
\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}
\begin{theorem}\label{thm:mgcdedpfogpgchngggpgchng}
$$\begin{array}{c}{\unicdcdadad} X0 .  v1\_binop\_1~(k5\_normform~X0)~(k2\_zfmisc\_1~(k5\_finsub\_1~\\
X0)~(k5\_finsub\_1~X0))\end{array}$$
\end{theorem}
\end{document}
