\documentclass{article}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t22\_mesfun9c (TMM6qPq5qPGkN8ZTmYTJBKWGNTk71f4BEiX)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ k5\_numbers : {\iota}$ be given.
Let $ k4\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_numbers : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k12\_mesfun7c : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_mesfun9c : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k4\_mesfunc5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k11\_mesfun7c : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_funct\_1 : {{\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 .  {\unicdcdadad} X2 .  ((v1\_funct\_1~\\
X2){\unicdcdcdhd}((v1\_funct\_2~X2~k5\_numbers~(k4\_partfun1~X0~k2\_numbers)){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k4\_partfun1~\\
X0~k2\_numbers)))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (v7\_ordinal1~X3){\unicdbdjdcd}((r2\_relset\_1~\\
X0~k1\_numbers~(k4\_mesfunc5~X0~k1\_numbers~(k11\_mesfun7c~X0~(k1\_mesfun9c~\\
X0~k2\_numbers~X2~X1))~X3)~(k2\_partfun1~X0~k1\_numbers~(k4\_mesfunc5~\\
X0~k1\_numbers~(k11\_mesfun7c~X0~X2)~X3)~X1)){\unicdcdcdhd}(r2\_relset\_1~X0~k1\_numbers~\\
(k4\_mesfunc5~X0~k1\_numbers~(k12\_mesfun7c~X0~(k1\_mesfun9c~X0~k2\_numbers~\\
X2~X1))~X3)~(k2\_partfun1~X0~k1\_numbers~(k4\_mesfunc5~X0~k1\_numbers~\\
(k12\_mesfun7c~X0~X2)~X3)~X1)))))\end{array}
\label{hyp:mgcdddpfngfgdhggfhogjddg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_funct\_1~X2){\unicdcdcdhd}\\
((v1\_funct\_2~X2~k5\_numbers~(k4\_partfun1~X0~X1)){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k4\_partfun1~X0~X1)))))){\unicdbdjdcd}\\
((v1\_funct\_1~(k1\_mesfun9c~X0~X1~X2~X3)){\unicdcdcdhd}((v1\_funct\_2~(k1\_mesfun9c~\\
X0~X1~X2~X3)~k5\_numbers~(k4\_partfun1~X0~X1)){\unicdcdcdhd}(m1\_subset\_1~(k1\_mesfun9c~\\
X0~X1~X2~X3)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k4\_partfun1~\\
X0~X1))))))\end{array}
\label{hyp:egehpflgbdpfngfgdhggfhogjddg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~k5\_numbers~(k4\_partfun1~X0~k2\_numbers)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k4\_partfun1~X0~k2\_numbers))))))){\unicdbdjdcd}\\
((v1\_funct\_1~(k12\_mesfun7c~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(k12\_mesfun7c~\\
X0~X1)~k5\_numbers~(k4\_partfun1~X0~k1\_numbers)){\unicdcdcdhd}(m1\_subset\_1~(\\
k12\_mesfun7c~X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k4\_partfun1~\\
X0~k1\_numbers))))))\end{array}
\label{hyp:egehpflgbdcdpfngfgdhggfhoghddg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~X0~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))))){\unicdbdjdcd}((r2\_funct\_2~X0~X1~X2~X3){\unicdbdjded}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~X0){\unicdbdjdcd}(k1\_funct\_1~X2~X4=k1\_funct\_1~\\
X3~X4))))\end{array}
\label{hyp:egidpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~k5\_numbers~(k4\_partfun1~X0~X1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k5\_numbers~(k4\_partfun1~X0~X1)))))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
{\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~k5\_numbers~(k4\_partfun1~\\
X0~X1)){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~\\
(k4\_partfun1~X0~X1)))))){\unicdbdjdcd}((X4=k1\_mesfun9c~X0~X1~X2~X3){\unicdbdjded}({\unicdcdadad} X5 .  \\
(v7\_ordinal1~X5){\unicdbdjdcd}(r2\_relset\_1~X0~X1~(k4\_mesfunc5~X0~X1~X4~X5)~(k2\_partfun1~\\
X0~X1~(k4\_mesfunc5~X0~X1~X2~X5)~X3)))))\end{array}
\label{hyp:egbdpfngfgdhggfhogjddg}
\end{equation}
\begin{theorem}\label{thm:ehcdcdpfngfgdhggfhogjddg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_funct\_1~\\
X2){\unicdcdcdhd}((v1\_funct\_2~X2~k5\_numbers~(k4\_partfun1~X0~k2\_numbers)){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k4\_partfun1~\\
X0~k2\_numbers)))))){\unicdbdjdcd}(r2\_funct\_2~k5\_numbers~(k4\_partfun1~X0~k1\_numbers)~\\
(k12\_mesfun7c~X0~(k1\_mesfun9c~X0~k2\_numbers~X2~X1))~(k1\_mesfun9c~\\
X0~k1\_numbers~(k12\_mesfun7c~X0~X2)~X1)))\end{array}$$
\end{theorem}
\end{document}
