\documentclass{article}
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\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t25\_mesfunc8 (TMJRPZ8PqBFcPYSuvT2A1t6Svw6g3jBesip)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_prob\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_prob\_1 : {{\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 $ 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 $ k7\_numbers : {\iota}$ be given.
Let $ v1\_mesfunc8 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ k6\_numbers : {\iota}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_mesfunc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v10\_mesfunc5 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_mesfunc5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k7\_mesfunc8 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_mesfunc8 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k12\_supinf\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_mesfunc8 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_mesfunc5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_rinfsup2 : {{\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){\unicdcdcdhd}\\
((v1\_prob\_1~X1~X0){\unicdcdcdhd}((v4\_prob\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~k5\_numbers~(k4\_partfun1~X0~k7\_numbers)){\unicdcdcdhd}((v1\_mesfunc8~X2~X0~\\
k7\_numbers){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~\\
(k4\_partfun1~X0~k7\_numbers))))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_subset\_1~\\
X3~(k1\_zfmisc\_1~X0)~X1){\unicdbdjdcd}(((k1\_relset\_1~X0~(k4\_mesfunc5~X0~k7\_numbers~\\
X2~k6\_numbers)=X3){\unicdcdcdhd}({\unicdcdadad} X4 .  (v7\_ordinal1~X4){\unicdbdjdcd}(r1\_mesfunc1~\\
X0~X1~(k4\_mesfunc5~X0~k7\_numbers~X2~X4)~X3))){\unicdbdjdcd}(r1\_mesfunc1~X0~X1~\\
(k5\_mesfunc8~X0~X2)~X3)))))\end{array}
\label{hyp:ehcdedpfngfgdhggfhogdgid}
\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~k7\_numbers)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k4\_partfun1~X0~k7\_numbers)))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~X0){\unicdbdjdcd}(((X2 \in k1\_relset\_1~X0~(k7\_mesfunc8~\\
X0~X1)){\unicdcdcdhd}(v10\_mesfunc5~(k3\_mesfunc5~X0~X1~X2))){\unicdbdjdcd}((k12\_supinf\_2~\\
(k7\_mesfunc8~X0~X1)~X2=k12\_supinf\_2~(k6\_mesfunc8~X0~X1)~X2){\unicdcdcdhd}(k12\_supinf\_2~\\
(k7\_mesfunc8~X0~X1)~X2=k12\_supinf\_2~(k5\_mesfunc8~X0~X1)~X2)))))\end{array}
\label{hyp:ehbdedpfngfgdhggfhogdgid}
\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~k7\_numbers)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k4\_partfun1~X0~k7\_numbers))))))){\unicdbdjdcd}\\
((v1\_funct\_1~(k7\_mesfunc8~X0~X1)){\unicdcdcdhd}(m1\_subset\_1~(k7\_mesfunc8~\\
X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k7\_numbers))))\end{array}
\label{hyp:egehpflghdpfngfgdhggfhogdgid}
\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~k7\_numbers)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k4\_partfun1~X0~k7\_numbers))))))){\unicdbdjdcd}\\
((v1\_funct\_1~(k5\_mesfunc8~X0~X1)){\unicdcdcdhd}(m1\_subset\_1~(k5\_mesfunc8~\\
X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k7\_numbers))))\end{array}
\label{hyp:egehpflgfdpfngfgdhggfhogdgid}
\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~k7\_numbers)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k4\_partfun1~X0~k7\_numbers)))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~k7\_numbers)))){\unicdbdjdcd}((X2=k7\_mesfunc8~X0~X1){\unicdbdjded}((k1\_relset\_1~X0~X2=\\
k1\_relset\_1~X0~(k4\_mesfunc5~X0~k7\_numbers~X1~k6\_numbers)){\unicdcdcdhd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~X0){\unicdbdjdcd}((X3 \in k1\_relset\_1~X0~X2){\unicdbdjdcd}(k12\_supinf\_2~X2~\\
X3=k2\_mesfunc5~(k3\_mesfunc5~X0~X1~X3))))))))\end{array}
\label{hyp:egjdpfngfgdhggfhogdgid}
\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~k7\_numbers)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k4\_partfun1~X0~k7\_numbers)))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~k7\_numbers)))){\unicdbdjdcd}((X2=k5\_mesfunc8~X0~X1){\unicdbdjded}((k1\_relset\_1~X0~X2=\\
k1\_relset\_1~X0~(k4\_mesfunc5~X0~k7\_numbers~X1~k6\_numbers)){\unicdcdcdhd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~X0){\unicdbdjdcd}((X3 \in k1\_relset\_1~X0~X2){\unicdbdjdcd}(k12\_supinf\_2~X2~\\
X3=k6\_rinfsup2~(k3\_mesfunc5~X0~X1~X3))))))))\end{array}
\label{hyp:eghdpfngfgdhggfhogdgid}
\end{equation}
\begin{theorem}\label{thm:ehcdfdpfngfgdhggfhogdgid}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
((v1\_prob\_1~X1~X0){\unicdcdcdhd}((v4\_prob\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~k5\_numbers~(k4\_partfun1~X0~k7\_numbers)){\unicdcdcdhd}((v1\_mesfunc8~X2~X0~\\
k7\_numbers){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~\\
(k4\_partfun1~X0~k7\_numbers))))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_subset\_1~\\
X3~(k1\_zfmisc\_1~X0)~X1){\unicdbdjdcd}(((k1\_relset\_1~X0~(k4\_mesfunc5~X0~k7\_numbers~\\
X2~k6\_numbers)=X3){\unicdcdcdhd}(({\unicdcdadad} X4 .  (v7\_ordinal1~X4){\unicdbdjdcd}(r1\_mesfunc1~\\
X0~X1~(k4\_mesfunc5~X0~k7\_numbers~X2~X4)~X3)){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~X0){\unicdbdjdcd}((X4 \in X3){\unicdbdjdcd}(v10\_mesfunc5~(k3\_mesfunc5~X0~X2~X4)))))){\unicdbdjdcd}(r1\_mesfunc1~\\
X0~X1~(k7\_mesfunc8~X0~X2)~X3)))))\end{array}$$
\end{theorem}
\end{document}
