\documentclass{article}
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\newtheorem{lemma}{Lemma}
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\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\begin{document}
\title{t30\_sin\_cos2 (TMZXYAfwYdf4VzdrAQLKYQgrvHrp5JjW1kT)}
\maketitle
Let $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k1\_sin\_cos2 : {\iota}$ be given.
Let $ k4\_sin\_cos2 : {\iota}$ be given.
Let $ k7\_sin\_cos2 : {\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 $ 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.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~X0~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0))))){\unicdbdjdcd}(k1\_relset\_1~\\
X0~X1=X0)\end{array}
\label{hyp:ehfdcdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k7\_sin\_cos2){\unicdcdcdhd}((v1\_funct\_2~k7\_sin\_cos2~k1\_numbers~\\
k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~k7\_sin\_cos2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers))))\end{array}
\label{hyp:egehpflghdpfdhjgogpfdgpgdhcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k4\_sin\_cos2){\unicdcdcdhd}((v1\_funct\_2~k4\_sin\_cos2~k1\_numbers~\\
k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~k4\_sin\_cos2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers))))\end{array}
\label{hyp:egehpflgedpfdhjgogpfdgpgdhcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k1\_sin\_cos2){\unicdcdcdhd}((v1\_funct\_2~k1\_sin\_cos2~k1\_numbers~\\
k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~k1\_sin\_cos2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers))))\end{array}
\label{hyp:egehpflgbdpfdhjgogpfdgpgdhcd}
\end{equation}
\begin{theorem}\label{thm:ehddadpfdhjgogpfdgpgdhcd}
$$\begin{array}{c}(k1\_relset\_1~k1\_numbers~k1\_sin\_cos2=k1\_numbers){\unicdcdcdhd}((k1\_relset\_1~\\
k1\_numbers~k4\_sin\_cos2=k1\_numbers){\unicdcdcdhd}(k1\_relset\_1~k1\_numbers~\\
k7\_sin\_cos2=k1\_numbers))\end{array}$$
\end{theorem}
\end{document}
