\documentclass{article}
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\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\begin{document}
\title{t25\_mesfun9c (TMND3zDRw5HAZhsZnZvpm8ENDRwca41iU43)}
\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 $ v1\_mesfunc8 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k11\_mesfun7c : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k12\_mesfun7c : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_mesfunc5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_comseq\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_mesfun7c : {{\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 .  ((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\_mesfunc8~X1~X0~k2\_numbers){\unicdbdjded}(v1\_mesfunc8~(k11\_mesfun7c~X0~\\
X1)~X0~k1\_numbers)))\end{array}
\label{hyp:ehcdedpfngfgdhggfhogjddg}
\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}((v1\_mesfunc8~\\
X1~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}(v1\_mesfunc8~(k12\_mesfun7c~X0~X1)~X0~k1\_numbers)))\end{array}
\label{hyp:ggdgedpfngfgdhggfhoghddg}
\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~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\_mesfunc8~\\
X2~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  (v7\_ordinal1~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (v7\_ordinal1~\\
X4){\unicdbdjdcd}(k1\_relset\_1~X0~(k4\_mesfunc5~X0~X1~X2~X3)=k1\_relset\_1~X0~(k4\_mesfunc5~\\
X0~X1~X2~X4)))))\end{array}
\label{hyp:egcdpfngfgdhggfhogdgid}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((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}\\
({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~k5\_numbers~(k4\_partfun1~\\
X0~k1\_numbers)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~\\
(k4\_partfun1~X0~k1\_numbers)))))){\unicdbdjdcd}((X2=k12\_mesfun7c~X0~X1){\unicdbdjded}(\\
{\unicdcdadad} X3 .  (v7\_ordinal1~X3){\unicdbdjdcd}((k1\_relset\_1~X0~(k4\_mesfunc5~X0~\\
k1\_numbers~X2~X3)=k1\_relset\_1~X0~(k4\_mesfunc5~X0~k2\_numbers~X1~\\
X3)){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~X0){\unicdbdjdcd}((X4 \in k1\_relset\_1~X0~(k4\_mesfunc5~\\
X0~k1\_numbers~X2~X3)){\unicdbdjdcd}(k1\_seq\_1~(k4\_mesfunc5~X0~k1\_numbers~X2~X3)~\\
X4=k1\_seq\_1~(k8\_comseq\_3~(k9\_mesfun7c~X0~X1~X4))~X3))))))))\end{array}
\label{hyp:egbdcdpfngfgdhggfhoghddg}
\end{equation}
\begin{theorem}\label{thm:ehcdfdpfngfgdhggfhogjddg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~k5\_numbers~(k4\_partfun1~X0~k2\_numbers)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k4\_partfun1~X0~k2\_numbers)))))){\unicdbdjdcd}\\
((v1\_mesfunc8~(k11\_mesfun7c~X0~X1)~X0~k1\_numbers){\unicdbdjded}(v1\_mesfunc8~\\
(k12\_mesfun7c~X0~X1)~X0~k1\_numbers)))\end{array}$$
\end{theorem}
\end{document}
