\documentclass{article}
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\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t84\_cfunct\_1 (TMcxWMh4ZJAZdDKZ7UbcDExun179TLLDVzr)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\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 $ k2\_numbers : {\iota}$ be given.
Let $ v1\_comseq\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v3\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k46\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k3\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k19\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~\\
X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~k2\_numbers)))){\unicdbdjdcd}\\
((v3\_funct\_1~(k2\_partfun1~X1~k2\_numbers~X2~X0)){\unicdbdjdcd}(v1\_comseq\_2~\\
(k2\_partfun1~X1~k2\_numbers~X2~X0))))\end{array}
\label{hyp:ehidbdpfdgggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (\preoh v1\_xboole\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v1\_funct\_1~X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X2~\\
k2\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~X4~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~X2~k2\_numbers)))){\unicdbdjdcd}(((v1\_comseq\_2~\\
(k2\_partfun1~X2~k2\_numbers~X3~X0)){\unicdcdcdhd}(v1\_comseq\_2~(k2\_partfun1~\\
X2~k2\_numbers~X4~X1))){\unicdbdjdcd}((v1\_comseq\_2~(k2\_partfun1~X2~k2\_numbers~\\
(k19\_valued\_1~X2~k2\_numbers~k2\_numbers~X3~X4)~(k3\_xboole\_0~X0~X1))){\unicdcdcdhd}\\
(v1\_comseq\_2~(k2\_partfun1~X2~k2\_numbers~(k46\_valued\_1~X2~k2\_numbers~\\
k2\_numbers~X3~X4)~(k3\_xboole\_0~X0~X1)))))))\end{array}
\label{hyp:ehhdgdpfdgggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k3\_xboole\_0}~{X0}}~{X1}}={{{k3\_xboole\_0}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgddpfihcgpgpgmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:ehidedpfdgggfhogdgehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (\preoh v1\_xboole\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v1\_funct\_1~X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X2~\\
k2\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~X4~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~X2~k2\_numbers)))){\unicdbdjdcd}(((v1\_comseq\_2~\\
(k2\_partfun1~X2~k2\_numbers~X3~X0)){\unicdcdcdhd}(v3\_funct\_1~(k2\_partfun1~X2~\\
k2\_numbers~X4~X1))){\unicdbdjdcd}((v1\_comseq\_2~(k2\_partfun1~X2~k2\_numbers~\\
(k46\_valued\_1~X2~k2\_numbers~k2\_numbers~X3~X4)~(k3\_xboole\_0~X0~X1))){\unicdcdcdhd}\\
((v1\_comseq\_2~(k2\_partfun1~X2~k2\_numbers~(k46\_valued\_1~X2~k2\_numbers~\\
k2\_numbers~X4~X3)~(k3\_xboole\_0~X0~X1))){\unicdcdcdhd}(v1\_comseq\_2~(k2\_partfun1~\\
X2~k2\_numbers~(k19\_valued\_1~X2~k2\_numbers~k2\_numbers~X3~X4)~(k3\_xboole\_0~\\
X0~X1))))))))\end{array}$$
\end{theorem}
\end{document}
