\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\unicdcdcdjd{\cap}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t73\_prob\_3 (TMKPr2zMKBW2qLX5iTTdBNc7TvbeDd7bgK1)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_finsub\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_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 $ k9\_prob\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_prob\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v4\_prob\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_prob\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_prob\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ 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}\\
((v2\_finsub\_1~X1){\unicdcdcdhd}((v1\_prob\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~X0)))))){\unicdbdjdcd}((\preoh v1\_xboole\_0~(k10\_prob\_3~X0~X1)){\unicdcdcdhd}((\\
v2\_finsub\_1~(k10\_prob\_3~X0~X1)){\unicdcdcdhd}((v1\_prob\_1~(k10\_prob\_3~X0~X1)~\\
X0){\unicdcdcdhd}(m1\_subset\_1~(k10\_prob\_3~X0~X1)~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
X0)))))))\end{array}
\label{hyp:ehhdcdpfahchpgcgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v2\_finsub\_1~X1){\unicdcdcdhd}\\
((v1\_prob\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
X0)))))){\unicdbdjdcd}(((\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)))))){\unicdbdjded}((\\
v2\_prob\_3~X1~X0){\unicdcdcdhd}((v3\_prob\_3~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~X0))))))\end{array}
\label{hyp:ehhdadpfahchpgcgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}((v2\_prob\_3~(k10\_prob\_3~X0~X1)~X0){\unicdcdcdhd}((v3\_prob\_3~\\
(k10\_prob\_3~X0~X1)~X0){\unicdcdcdhd}(m1\_subset\_1~(k10\_prob\_3~X0~X1)~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~X0)))))\end{array}
\label{hyp:egehpflgbdadpfahchpgcgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((v1\_prob\_1~\\
X2~X0){\unicdcdcdhd}((v4\_prob\_1~X2~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
X0)))))){\unicdbdjdcd}((X2=k9\_prob\_1~X0~X1){\unicdbdjded}((r1\_tarski~X1~X2){\unicdcdcdhd}({\unicdcdadad} X3 .  \\
((r1\_tarski~X1~X3){\unicdcdcdhd}((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}((v1\_prob\_1~X3~X0){\unicdcdcdhd}((v4\_prob\_1~\\
X3~X0){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k1\_zfmisc\_1~X0))))))){\unicdbdjdcd}(\\
r1\_tarski~X2~X3))))))\end{array}
\label{hyp:egjdpfahchpgcgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v2\_prob\_3~X2~X0){\unicdcdcdhd}((v3\_prob\_3~\\
X2~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k1\_zfmisc\_1~X0))))){\unicdbdjdcd}((X2=\\
k10\_prob\_3~X0~X1){\unicdbdjded}((r1\_tarski~X1~X2){\unicdcdcdhd}({\unicdcdadad} X3 .  ((r1\_tarski~\\
X1~X3){\unicdcdcdhd}((v2\_prob\_3~X3~X0){\unicdcdcdhd}((v3\_prob\_3~X3~X0){\unicdcdcdhd}(m1\_subset\_1~X3~(\\
k1\_zfmisc\_1~(k1\_zfmisc\_1~X0)))))){\unicdbdjdcd}(r1\_tarski~X2~X3))))))\end{array}
\label{hyp:egbdbdpfahchpgcgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
X0))){\unicdbdjdcd}(((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_prob\_1~X1~X0){\unicdcdcdhd}(v4\_prob\_1~X1~X0))){\unicdbdjdcd}\\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v2\_finsub\_1~X1){\unicdcdcdhd}((v1\_prob\_1~X1~X0){\unicdcdcdhd}(v4\_prob\_1~\\
X1~X0)))))\end{array}
\label{hyp:dgdgbdpfahchpgcgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehhdddpfahchpgcgpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
((v2\_finsub\_1~X1){\unicdcdcdhd}((v1\_prob\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~X0)))))){\unicdbdjdcd}(k9\_prob\_1~X0~X1=k10\_prob\_3~X0~X1))\end{array}$$
\end{theorem}
\end{document}
