\documentclass{article}
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\newtheorem{conjecture}{Conjecture}
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\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t31\_seqfunc (TMdqqzBKEpF11Uzz8jqRY3yGL8onz3xYc13)}
\maketitle
Let $ v1\_xboole\_0 : {{\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 $ k4\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_numbers : {\iota}$ 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 $ r1\_seqfunc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ r2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k3\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k10\_seqfunc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_seqfunc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k47\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k7\_seqfunc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k20\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k8\_seqfunc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~k5\_numbers~(k4\_partfun1~X0~k1\_numbers)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k4\_partfun1~X0~k1\_numbers)))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~k5\_numbers~(k4\_partfun1~\\
X0~k1\_numbers)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~\\
(k4\_partfun1~X0~k1\_numbers)))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
X0){\unicdbdjdcd}(((r1\_seqfunc~X0~k1\_numbers~X1~(k1\_tarski~X3)){\unicdcdcdhd}(r1\_seqfunc~\\
X0~k1\_numbers~X2~(k1\_tarski~X3))){\unicdbdjdcd}((r2\_relset\_1~k5\_numbers~k1\_numbers~\\
(k3\_valued\_1~k5\_numbers~k1\_numbers~k1\_numbers~(k10\_seqfunc~X0~\\
X1~X3)~(k10\_seqfunc~X0~X2~X3))~(k10\_seqfunc~X0~(k6\_seqfunc~X0~X1~X2)~\\
X3)){\unicdcdcdhd}((r2\_relset\_1~k5\_numbers~k1\_numbers~(k47\_valued\_1~k5\_numbers~\\
k1\_numbers~k1\_numbers~(k10\_seqfunc~X0~X1~X3)~(k10\_seqfunc~X0~X2~\\
X3))~(k10\_seqfunc~X0~(k7\_seqfunc~X0~X1~X2)~X3)){\unicdcdcdhd}(r2\_relset\_1~k5\_numbers~\\
k1\_numbers~(k20\_valued\_1~k5\_numbers~k1\_numbers~k1\_numbers~(k10\_seqfunc~\\
X0~X1~X3)~(k10\_seqfunc~X0~X2~X3))~(k10\_seqfunc~X0~(k8\_seqfunc~X0~X1~\\
X2)~X3))))))))\end{array}
\label{hyp:ehcdidpfdhfgbhggfhogdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~k5\_numbers~(k4\_partfun1~X0~k1\_numbers)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k4\_partfun1~X0~k1\_numbers)))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (r1\_seqfunc~X0~k1\_numbers~X1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~X0){\unicdbdjdcd}((X3 \in X2){\unicdbdjdcd}(r1\_seqfunc~X0~k1\_numbers~X1~(k1\_tarski~X3))))))\end{array}
\label{hyp:ehcdgdpfdhfgbhggfhogdg}
\end{equation}
\begin{theorem}\label{thm:ehddbdpfdhfgbhggfhogdg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~k5\_numbers~(k4\_partfun1~X0~k1\_numbers)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k4\_partfun1~X0~k1\_numbers)))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~k5\_numbers~(k4\_partfun1~\\
X0~k1\_numbers)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~\\
(k4\_partfun1~X0~k1\_numbers)))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((r1\_seqfunc~X0~\\
k1\_numbers~X1~X3){\unicdcdcdhd}(r1\_seqfunc~X0~k1\_numbers~X2~X3)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~X0){\unicdbdjdcd}((X4 \in X3){\unicdbdjdcd}((r2\_relset\_1~k5\_numbers~k1\_numbers~\\
(k3\_valued\_1~k5\_numbers~k1\_numbers~k1\_numbers~(k10\_seqfunc~X0~\\
X1~X4)~(k10\_seqfunc~X0~X2~X4))~(k10\_seqfunc~X0~(k6\_seqfunc~X0~X1~X2)~\\
X4)){\unicdcdcdhd}((r2\_relset\_1~k5\_numbers~k1\_numbers~(k47\_valued\_1~k5\_numbers~\\
k1\_numbers~k1\_numbers~(k10\_seqfunc~X0~X1~X4)~(k10\_seqfunc~X0~X2~\\
X4))~(k10\_seqfunc~X0~(k7\_seqfunc~X0~X1~X2)~X4)){\unicdcdcdhd}(r2\_relset\_1~k5\_numbers~\\
k1\_numbers~(k20\_valued\_1~k5\_numbers~k1\_numbers~k1\_numbers~(k10\_seqfunc~\\
X0~X1~X4)~(k10\_seqfunc~X0~X2~X4))~(k10\_seqfunc~X0~(k8\_seqfunc~X0~X1~\\
X2)~X4)))))))))\end{array}$$
\end{theorem}
\end{document}
