\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{t17\_random\_2 (TMXJW7oQM6Vp8zGTkt6pZSsEoekDqkPYhLW)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_prob\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_random\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_random\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k11\_binop\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\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.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (X0 \in X1){\unicdbdjdcd}(m1\_subset\_1~(k1\_tarski~X0)~(k1\_zfmisc\_1~\\
X1))\end{array}
\label{hyp:ehedbdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k2\_zfmisc\_1~(k1\_tarski~X0)~(k1\_tarski~X1)=\\
k1\_tarski~(k4\_tarski~X0~X1)\end{array}
\label{hyp:ehcdjdpfkhggngjgdhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_finset\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(v1\_finset\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_prob\_1~\\
X2~X0~(k1\_random\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_prob\_1~X3~X1~(k1\_random\_1~\\
X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~X4){\unicdcdcdhd}((v1\_finset\_1~X4){\unicdcdcdhd}(m1\_subset\_1~\\
X4~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((\preoh v1\_xboole\_0~X5){\unicdcdcdhd}((v1\_finset\_1~\\
X5){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~X1)))){\unicdbdjdcd}(k1\_seq\_1~(k2\_random\_2~\\
X0~X1~X2~X3)~(k2\_zfmisc\_1~X4~X5)=k11\_binop\_2~(k1\_seq\_1~X2~X4)~(k1\_seq\_1~\\
X3~X5)))))))\end{array}
\label{hyp:ehbdgdpfchbgogegpgngpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {\preoh{{{v1\_xboole\_0}~{({{k1\_tarski}~{X0}})}}}}}\label{hyp:ggdgcdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_finset\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v1\_finset\_1~X1))\end{array}
\label{hyp:dgdgcdpfggjgogdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v1\_xboole\_0~X1))\end{array}
\label{hyp:dgdgbdpfdhfhcgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdhdpfchbgogegpgngpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_finset\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(v1\_finset\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_prob\_1~\\
X2~X0~(k1\_random\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_prob\_1~X3~X1~(k1\_random\_1~\\
X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  {\unicdcdadad} X5 .  ((X4 \in X0){\unicdcdcdhd}(X5 \in X1)){\unicdbdjdcd}(k1\_seq\_1~(k2\_random\_2~\\
X0~X1~X2~X3)~(k1\_tarski~(k4\_tarski~X4~X5))=k11\_binop\_2~(k1\_seq\_1~\\
X2~(k1\_tarski~X4))~(k1\_seq\_1~X3~(k1\_tarski~X5)))))))\end{array}$$
\end{theorem}
\end{document}
