\documentclass{article}
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\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\begin{document}
\title{t33\_sin\_cos2 (TMUkHvVYRcGTct4nxSA2h1MGyX5YYUborFr)}
\maketitle
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_fdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k7\_sin\_cos2 : {\iota}$ be given.
Let $ k1\_fdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k5\_square\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_sin\_cos2 : {\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 $ r2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k3\_rfunct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_sin\_cos2 : {\iota}$ be given.
Let $ v3\_membered : {{\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.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}((r2\_relset\_1~X0~X1~X2~X3){\unicdbdjded}(X2=X3))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchcdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}r2\_relset\_1~k1\_numbers~k1\_numbers~k7\_sin\_cos2~(k3\_rfunct\_1~k1\_numbers~\\
k1\_numbers~k1\_sin\_cos2~k4\_sin\_cos2)\end{array}
\label{hyp:mggdbdpfdhjgogpfdgpgdhcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}((r1\_fdiff\_1~(k3\_rfunct\_1~k1\_numbers~\\
k1\_numbers~k1\_sin\_cos2~k4\_sin\_cos2)~X0){\unicdcdcdhd}(k1\_fdiff\_1~(k3\_rfunct\_1~\\
k1\_numbers~k1\_numbers~k1\_sin\_cos2~k4\_sin\_cos2)~X0=k10\_real\_1~\\
np\_\_1~(k5\_square\_1~(k1\_seq\_1~k4\_sin\_cos2~X0))))\end{array}
\label{hyp:mggdadpfdhjgogpfdgpgdhcd}
\end{equation}
Assume the following.
\begin{equation}
{{v3\_membered}~{k1\_numbers}}\label{hyp:ggdgddpfngfgngcgfgchfgeg}
\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}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v3\_membered~X1){\unicdcdcdhd}\\
(((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1)))){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1)))))){\unicdbdjdcd}((v1\_funct\_1~(k3\_rfunct\_1~X0~X1~X2~X3)){\unicdcdcdhd}(m1\_subset\_1~\\
(k3\_rfunct\_1~X0~X1~X2~X3)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k1\_numbers))))\end{array}
\label{hyp:egehpflgddpfchggfhogdgehpfbd}
\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:ehddddpfdhjgogpfdgpgdhcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}((r1\_fdiff\_1~k7\_sin\_cos2~X0){\unicdcdcdhd}(k1\_fdiff\_1~\\
k7\_sin\_cos2~X0=k10\_real\_1~np\_\_1~(k5\_square\_1~(k1\_seq\_1~k4\_sin\_cos2~\\
X0))))\end{array}$$
\end{theorem}
\end{document}
