\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=}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t30\_prob\_1 (TMNZXiDv5HymhjbWQA2J9n7EpVMmNMS9xnP)}
\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 $ m2\_prob\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_prob\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_prob\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ r1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_prob\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k7\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k9\_setfam\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_prob\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_comseq\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k8\_prob\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_seq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_prob\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
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 .  (\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}((v1\_funct\_2~\\
X2~X1~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~\\
k1\_numbers))))){\unicdbdjdcd}((m2\_prob\_1~X2~X0~X1){\unicdbdjded}(({\unicdcdadad} X3 .  (m1\_prob\_1~\\
X3~X0~X1){\unicdbdjdcd}(r1\_xxreal\_0~k6\_numbers~(k1\_seq\_1~X2~X3))){\unicdcdcdhd}((k1\_seq\_1~\\
X2~X0=np\_\_1){\unicdcdcdhd}(({\unicdcdadad} X3 .  (m1\_prob\_1~X3~X0~X1){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_prob\_1~\\
X4~X0~X1){\unicdbdjdcd}((r1\_xboole\_0~X3~X4){\unicdbdjdcd}(k1\_seq\_1~X2~(k6\_prob\_1~X0~X1~X3~X4)=\\
k7\_real\_1~(k1\_seq\_1~X2~X3)~(k1\_seq\_1~X2~X4))))){\unicdcdcdhd}({\unicdcdadad} X3 .  ((\\
v5\_relat\_1~X3~X1){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~k5\_numbers~\\
(k9\_setfam\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k5\_numbers~(k9\_setfam\_1~X0))))))){\unicdbdjdcd}((v2\_prob\_1~X3){\unicdbdjdcd}((v2\_comseq\_2~\\
(k8\_prob\_1~X0~X1~X3~X2)){\unicdcdcdhd}(k2\_seq\_2~(k8\_prob\_1~X0~X1~X3~X2)=k1\_seq\_1~\\
X2~(k3\_prob\_1~X0~X3)))))))))))\end{array}
\label{hyp:egidpfahchpgcgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\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}(k4\_prob\_1~X0~X1=X0)\end{array}
\label{hyp:eghdpfahchpgcgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddadpfahchpgcgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
((v1\_prob\_1~X1~X0){\unicdcdcdhd}((v4\_prob\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_prob\_1~X2~X0~X1){\unicdbdjdcd}(k1\_seq\_1~\\
X2~(k4\_prob\_1~X0~X1)=np\_\_1)))\end{array}$$
\end{theorem}
\end{document}
