\documentclass{article}
\newtheorem{axiom}{Axiom}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
\newcommand\unicdcdadad{\forall}
\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
\newcommand\uniddcgcg{\lambda}
\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t16\_random\_2 (TMHxM2UKJpms7V3wV3R7uEJEGt9Tz5fL2Z1)}
\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 $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k11\_binop\_2 : {{\iota}{\unicdbdjdcd}{{\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 $ k1\_numbers : {\iota}$ be given.
Let $ k1\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_bhsp\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k33\_binop\_2 : {\iota}$ be given.
Let $ v1\_prob\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_prob\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({\preoh{{{v1\_xboole\_0}~{X0}}}})}{\unicdbdjdcd}{({{{k1\_random\_1}~{X0}}={{k1\_zfmisc\_1}~{X0}}})}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfchbgogegpgngpfbd}
\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 .  ((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~(k2\_zfmisc\_1~\\
X0~X1)~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1)~k1\_numbers))))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_funct\_1~\\
X5){\unicdcdcdhd}((v1\_funct\_2~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1))~k1\_numbers))))){\unicdbdjdcd}({\unicdcdadad} X6 .  ((\preoh v1\_xboole\_0~X6){\unicdcdcdhd}((v1\_finset\_1~\\
X6){\unicdcdcdhd}(m1\_subset\_1~X6~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X7 .  ((\preoh v1\_xboole\_0~\\
X7){\unicdcdcdhd}((v1\_finset\_1~X7){\unicdcdcdhd}(m1\_subset\_1~X7~(k1\_zfmisc\_1~X1)))){\unicdbdjdcd}(\\
(({\unicdcdadad} X8 .  {\unicdcdadad} X9 .  ((X8 \in X0){\unicdcdcdhd}(X9 \in X1)){\unicdbdjdcd}(k1\_binop\_1~X4~X8~\\
X9=k11\_binop\_2~(k1\_seq\_1~X2~(k1\_tarski~X8))~(k1\_seq\_1~X3~(k1\_tarski~\\
X9)))){\unicdcdcdhd}({\unicdcdadad} X8 .  ((v1\_finset\_1~X8){\unicdcdcdhd}(m1\_subset\_1~X8~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}(k1\_seq\_1~X5~X8=k5\_bhsp\_5~k1\_numbers~(\\
k2\_zfmisc\_1~X0~X1)~k33\_binop\_2~X8~X4))){\unicdbdjdcd}(k1\_seq\_1~X5~(k2\_zfmisc\_1~\\
X6~X7)=k11\_binop\_2~(k1\_seq\_1~X2~X6)~(k1\_seq\_1~X3~X7))))))))))\end{array}
\label{hyp:mgcdddpfchbgogegpgngpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(\preoh v1\_xboole\_0~X1)){\unicdbdjdcd}\\
(\preoh v1\_xboole\_0~(k2\_zfmisc\_1~X0~X1))\end{array}
\label{hyp:ggdgbdadpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\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 .  (m2\_prob\_1~X2~X0~X1){\unicdbdjdcd}((v1\_funct\_1~\\
X2){\unicdcdcdhd}((v1\_funct\_2~X2~X1~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X1~k1\_numbers))))))\end{array}
\label{hyp:egehpfngcdpfahchpgcgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}(v1\_finset\_1~X0)){\unicdcdcdhd}(((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(v1\_finset\_1~X1)){\unicdcdcdhd}\\
((m2\_prob\_1~X2~X0~(k1\_random\_1~X0)){\unicdcdcdhd}(m2\_prob\_1~X3~X1~(k1\_random\_1~\\
X1))))){\unicdbdjdcd}(m2\_prob\_1~(k2\_random\_2~X0~X1~X2~X3)~(k2\_zfmisc\_1~X0~X1)~\\
(k1\_random\_1~(k2\_zfmisc\_1~X0~X1)))\end{array}
\label{hyp:egehpflgcdpfchbgogegpgngpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((\preoh v1\_xboole\_0~(k1\_random\_1~X0)){\unicdcdcdhd}\\
((v1\_prob\_1~(k1\_random\_1~X0)~X0){\unicdcdcdhd}((v4\_prob\_1~(k1\_random\_1~X0)~\\
X0){\unicdcdcdhd}(m1\_subset\_1~(k1\_random\_1~X0)~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
X0))))))\end{array}
\label{hyp:egehpflgbdpfchbgogegpgngpfbd}
\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 .  (m2\_prob\_1~X4~(k2\_zfmisc\_1~X0~X1)~(k1\_random\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}((X4=k2\_random\_2~X0~X1~X2~X3){\unicdbdjded}({\unicdcdaddd} X5 .  \\
((v1\_funct\_1~X5){\unicdcdcdhd}((v1\_funct\_2~X5~(k2\_zfmisc\_1~X0~X1)~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)~\\
k1\_numbers))))){\unicdcdcdhd}(({\unicdcdadad} X6 .  {\unicdcdadad} X7 .  ((X6 \in X0){\unicdcdcdhd}(X7 \in X1)){\unicdbdjdcd}\\
(k1\_binop\_1~X5~X6~X7=k11\_binop\_2~(k1\_seq\_1~X2~(k1\_tarski~X6))~(\\
k1\_seq\_1~X3~(k1\_tarski~X7)))){\unicdcdcdhd}({\unicdcdadad} X6 .  ((v1\_finset\_1~X6){\unicdcdcdhd}\\
(m1\_subset\_1~X6~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}(k1\_seq\_1~\\
X4~X6=k5\_bhsp\_5~k1\_numbers~(k2\_zfmisc\_1~X0~X1)~k33\_binop\_2~X6~X5)))))))))\end{array}
\label{hyp:egcdpfchbgogegpgngpfcd}
\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:ehbdgdpfchbgogegpgngpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_finset\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(v1\_finset\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_prob\_1~\\
X2~X0~(k1\_random\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_prob\_1~X3~X1~(k1\_random\_1~\\
X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~X4){\unicdcdcdhd}((v1\_finset\_1~X4){\unicdcdcdhd}(m1\_subset\_1~\\
X4~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((\preoh v1\_xboole\_0~X5){\unicdcdcdhd}((v1\_finset\_1~\\
X5){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~X1)))){\unicdbdjdcd}(k1\_seq\_1~(k2\_random\_2~\\
X0~X1~X2~X3)~(k2\_zfmisc\_1~X4~X5)=k11\_binop\_2~(k1\_seq\_1~X2~X4)~(k1\_seq\_1~\\
X3~X5)))))))\end{array}$$
\end{theorem}
\end{document}
