\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{t32\_random\_1 (TMKTUMeAspikoSamrKgAVApwAJuRmP8qQtw)}
\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\_random\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_random\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k18\_rvsum\_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 $ 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 $ k1\_mesfunc6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_prob\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\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}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_finset\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m2\_prob\_1~X1~X0~(k1\_random\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_random\_1~X2~\\
X0~(k1\_random\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_finseq\_1~X3~k1\_numbers){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m2\_finseq\_1~X4~X0){\unicdbdjdcd}(((k3\_finseq\_1~X3=k5\_card\_1~\\
X0){\unicdcdcdhd}((v2\_funct\_1~X4){\unicdcdcdhd}((k2\_relset\_1~X0~X4=X0){\unicdcdcdhd}((k3\_finseq\_1~\\
X4=k5\_card\_1~X0){\unicdcdcdhd}({\unicdcdadad} X5 .  (v7\_ordinal1~X5){\unicdbdjdcd}((X5 \in k4\_finseq\_1~\\
X3){\unicdbdjdcd}(k1\_seq\_1~X3~X5=k8\_real\_1~(k1\_seq\_1~X2~(k1\_funct\_1~X4~X5))~\\
(k1\_seq\_1~X1~(k1\_tarski~(k1\_funct\_1~X4~X5)))))))))){\unicdbdjdcd}(k8\_random\_1~\\
X0~(k1\_random\_1~X0)~X1~X2=k18\_rvsum\_1~X3))))))\end{array}
\label{hyp:ehddbdpfchbgogegpgngpfbd}
\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 .  \\
(m2\_prob\_1~X1~X0~(k1\_random\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}\\
((v1\_funct\_2~X2~X0~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(\\
k2\_zfmisc\_1~X0~k1\_numbers))))){\unicdbdjdcd}({\unicdcdaddd} X3 .  (m2\_finseq\_1~X3~k1\_numbers){\unicdcdcdhd}\\
({\unicdcdaddd} X4 .  (m2\_finseq\_1~X4~X0){\unicdcdcdhd}((k3\_finseq\_1~X3=k5\_card\_1~X0){\unicdcdcdhd}\\
((v2\_funct\_1~X4){\unicdcdcdhd}((k2\_relset\_1~X0~X4=X0){\unicdcdcdhd}((k3\_finseq\_1~X4=k5\_card\_1~\\
X0){\unicdcdcdhd}(({\unicdcdadad} X5 .  (v7\_ordinal1~X5){\unicdbdjdcd}((X5 \in k4\_finseq\_1~X3){\unicdbdjdcd}(k1\_seq\_1~\\
X3~X5=k8\_real\_1~(k1\_seq\_1~X2~(k1\_funct\_1~X4~X5))~(k1\_seq\_1~X1~(k1\_tarski~\\
(k1\_funct\_1~X4~X5)))))){\unicdcdcdhd}(k1\_mesfunc6~X0~(k1\_random\_1~X0)~(k2\_prob\_4~\\
X0~(k1\_random\_1~X0)~X1)~X2=k18\_rvsum\_1~X3))))))))))\end{array}
\label{hyp:ehbdddpfchbgogegpgngpfbd}
\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 .  (m1\_random\_1~X2~X0~X1){\unicdbdjdcd}((\\
v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~X0~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k1\_numbers))))))\end{array}
\label{hyp:egehpfngbdpfchbgogegpgngpfbd}
\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}
\begin{theorem}\label{thm:ehddcdpfchbgogegpgngpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_finset\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m2\_prob\_1~X1~X0~(k1\_random\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_random\_1~X2~\\
X0~(k1\_random\_1~X0)){\unicdbdjdcd}({\unicdcdaddd} X3 .  (m2\_finseq\_1~X3~k1\_numbers){\unicdcdcdhd}\\
({\unicdcdaddd} X4 .  (m2\_finseq\_1~X4~X0){\unicdcdcdhd}((k3\_finseq\_1~X3=k5\_card\_1~X0){\unicdcdcdhd}\\
((v2\_funct\_1~X4){\unicdcdcdhd}((k2\_relset\_1~X0~X4=X0){\unicdcdcdhd}((k3\_finseq\_1~X4=k5\_card\_1~\\
X0){\unicdcdcdhd}(({\unicdcdadad} X5 .  (v7\_ordinal1~X5){\unicdbdjdcd}((X5 \in k4\_finseq\_1~X3){\unicdbdjdcd}(k1\_seq\_1~\\
X3~X5=k8\_real\_1~(k1\_seq\_1~X2~(k1\_funct\_1~X4~X5))~(k1\_seq\_1~X1~(k1\_tarski~\\
(k1\_funct\_1~X4~X5)))))){\unicdcdcdhd}(k8\_random\_1~X0~(k1\_random\_1~X0)~X1~X2=\\
k18\_rvsum\_1~X3))))))))))\end{array}$$
\end{theorem}
\end{document}
