\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\unicdcdadjd{\notin}
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\newcommand\unicdcdcdid{\lor}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t18\_bor\_cant (TMcgSjMbpdKqY4Gd1NJ4wnR9Zktq4c3Z2Bf)}
\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 $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ 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 $ k5\_numbers : {\iota}$ be given.
Let $ k9\_setfam\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_bor\_cant : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_kurato\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_prob\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k4\_kurato\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_comseq\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_series\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_prob\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v1\_limfunc1 : {{\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}\\
((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}({\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}((r1\_bor\_cant~X0~X1~X2~X3){\unicdbdjdcd}\\
((v2\_comseq\_2~(k3\_series\_1~(k8\_prob\_1~X0~X1~X3~X2))){\unicdcdcdid}((k1\_funct\_1~\\
X2~(k3\_kurato\_0~X0~(k2\_prob\_1~X0~X3))=k6\_numbers){\unicdcdcdhd}(k1\_funct\_1~\\
X2~(k4\_kurato\_0~X0~X3)=np\_\_1)))))))\end{array}
\label{hyp:ehbdhdpfcgpgchpfdgbgogeh}
\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 .  (m2\_prob\_1~X2~X0~X1){\unicdbdjdcd}({\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\_comseq\_2~(k3\_series\_1~\\
(k8\_prob\_1~X0~X1~X3~X2))){\unicdbdjdcd}((k1\_funct\_1~X2~(k4\_kurato\_0~X0~X3)=k6\_numbers){\unicdcdcdhd}\\
(k1\_funct\_1~X2~(k3\_kurato\_0~X0~(k2\_prob\_1~X0~X3))=np\_\_1))){\unicdcdcdhd}((\\
(r1\_bor\_cant~X0~X1~X2~X3){\unicdcdcdhd}(v1\_limfunc1~(k3\_series\_1~(k8\_prob\_1~\\
X0~X1~X3~X2)))){\unicdbdjdcd}((k1\_funct\_1~X2~(k3\_kurato\_0~X0~(k2\_prob\_1~X0~X3))=\\
k6\_numbers){\unicdcdcdhd}(k1\_funct\_1~X2~(k4\_kurato\_0~X0~X3)=np\_\_1)))))))\end{array}
\label{hyp:ehbdgdpfcgpgchpfdgbgogeh}
\end{equation}
\begin{theorem}\label{thm:ehbdidpfcgpgchpfdgbgogeh}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
((v1\_prob\_1~X1~X0){\unicdcdcdhd}((v4\_prob\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_prob\_1~X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v5\_relat\_1~X3~X1){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~k5\_numbers~\\
(k9\_setfam\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k5\_numbers~(k9\_setfam\_1~X0))))))){\unicdbdjdcd}((r1\_bor\_cant~X0~X1~X2~X3){\unicdbdjdcd}\\
(((k1\_funct\_1~X2~(k3\_kurato\_0~X0~(k2\_prob\_1~X0~X3))=k6\_numbers){\unicdcdcdid}\\
(k1\_funct\_1~X2~(k3\_kurato\_0~X0~(k2\_prob\_1~X0~X3))=np\_\_1)){\unicdcdcdhd}((k1\_funct\_1~\\
X2~(k4\_kurato\_0~X0~X3)=k6\_numbers){\unicdcdcdid}(k1\_funct\_1~X2~(k4\_kurato\_0~\\
X0~X3)=np\_\_1)))))))\end{array}$$
\end{theorem}
\end{document}
