\documentclass{article}
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\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
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\begin{document}
\title{t12\_mesfunc3 (TMNjCEt5SySTbJuakZB4gR5EWs7hJiGw9ev)}
\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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_numbers : {\iota}$ be given.
Let $ r1\_mesfunc2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_prob\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_mesfunc3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k12\_supinf\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_extreal1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_mesfunc2 : {{\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 .  ((\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}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k7\_numbers)))){\unicdbdjdcd}(\preoh (r1\_mesfunc2~\\
X0~X1~X2){\unicdcdcdhd}({\unicdcdadad} X3 .  ((v1\_prob\_2~X3){\unicdcdcdhd}(m2\_finseq\_1~X3~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m2\_finseq\_1~X4~k7\_numbers){\unicdbdjdcd}(\preoh (k1\_relset\_1~X0~X2=k3\_tarski~(\\
k2\_relset\_1~X1~X3)){\unicdcdcdhd}((k4\_finseq\_1~X3=k4\_finseq\_1~X4){\unicdcdcdhd}(({\unicdcdadad} X5 .  \\
(v7\_ordinal1~X5){\unicdbdjdcd}((X5 \in k4\_finseq\_1~X3){\unicdbdjdcd}({\unicdcdadad} X6 .  (X6 \in k1\_funct\_1~\\
X3~X5){\unicdbdjdcd}(k12\_supinf\_2~X2~X6=k12\_supinf\_2~X4~X5)))){\unicdcdcdhd}({\unicdcdadad} X5 .  \\
\preoh (X5 \in k1\_relset\_1~X0~X2){\unicdcdcdhd}({\unicdcdadad} X6 .  (m2\_finseq\_1~X6~k7\_numbers){\unicdbdjdcd}\\
(\preoh (k4\_finseq\_1~X6=k4\_finseq\_1~X4){\unicdcdcdhd}({\unicdcdadad} X7 .  (v7\_ordinal1~\\
X7){\unicdbdjdcd}((X7 \in k4\_finseq\_1~X6){\unicdbdjdcd}(k12\_supinf\_2~X6~X7=k1\_extreal1~(k12\_supinf\_2~\\
X4~X7)~(k12\_supinf\_2~(k3\_mesfunc2~(k1\_funct\_1~X3~X7)~X0)~X5)))))))))))))))\end{array}
\label{hyp:ehddpfngfgdhggfhogdgdd}
\end{equation}
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}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k7\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X3 .  (\\
(v1\_prob\_2~X3){\unicdcdcdhd}(m2\_finseq\_1~X3~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_finseq\_1~\\
X4~k7\_numbers){\unicdbdjdcd}((r1\_mesfunc3~X0~X1~X2~X3~X4){\unicdbdjded}((k1\_relset\_1~X0~X2=\\
k3\_tarski~(k2\_relset\_1~X1~X3)){\unicdcdcdhd}((k4\_finseq\_1~X3=k4\_finseq\_1~\\
X4){\unicdcdcdhd}({\unicdcdadad} X5 .  (v7\_ordinal1~X5){\unicdbdjdcd}((X5 \in k4\_finseq\_1~X3){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
(X6 \in k1\_funct\_1~X3~X5){\unicdbdjdcd}(k12\_supinf\_2~X2~X6=k12\_supinf\_2~X4~X5)))))))))))\end{array}
\label{hyp:egbdpfngfgdhggfhogdgdd}
\end{equation}
\begin{theorem}\label{thm:ehbdcdpfngfgdhggfhogdgdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
((v1\_prob\_1~X1~X0){\unicdcdcdhd}((v4\_prob\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k7\_numbers)))){\unicdbdjdcd}(\preoh (r1\_mesfunc2~\\
X0~X1~X2){\unicdcdcdhd}({\unicdcdadad} X3 .  ((v1\_prob\_2~X3){\unicdcdcdhd}(m2\_finseq\_1~X3~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m2\_finseq\_1~X4~k7\_numbers){\unicdbdjdcd}(\preoh r1\_mesfunc3~X0~X1~X2~X3~X4))))))\end{array}$$
\end{theorem}
\end{document}
