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\begin{document}
\title{t57\_sincos10 (TMaTRKUdJerDoZWmxZk3qAYhtLTSVTTyYhR)}
\maketitle
Let $ k1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k2\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_sincos10 : {\iota}$ be given.
Let $ k1\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k7\_square\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k1\_fdiff\_9 : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k10\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k32\_sin\_cos : {\iota}$ be given.
Let $ np\_\_4 : {\iota}$ be given.
Let $ k1\_partfun2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ 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.
Assume the following.
\begin{equation}
\begin{array}{c}k3\_relat\_1~(k2\_partfun1~k1\_numbers~k1\_numbers~k1\_sincos10~(k1\_rcomp\_1~\\
np\_\_1~(k7\_square\_1~np\_\_2)))~(k2\_partfun1~k1\_numbers~k1\_numbers~\\
k1\_fdiff\_9~(k1\_rcomp\_1~k6\_numbers~(k10\_real\_1~k32\_sin\_cos~np\_\_4)))=\\
k1\_partfun2~k1\_numbers~(k1\_rcomp\_1~np\_\_1~(k7\_square\_1~np\_\_2))\end{array}
\label{hyp:ehfdddpfdhjgogdgpgdhbdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
(((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1)))){\unicdcdcdhd}((v1\_funct\_1~X5){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X2~X3))))){\unicdbdjdcd}(k1\_partfun1~X0~X1~X2~X3~X4~X5=k3\_relat\_1~X4~X5)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_funct\_1~X2){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}((v1\_funct\_1~\\
(k2\_partfun1~X0~X1~X2~X3)){\unicdcdcdhd}(m1\_subset\_1~(k2\_partfun1~X0~X1~X2~X3)~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))))\end{array}
\label{hyp:egehpflgcdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k1\_sincos10){\unicdcdcdhd}(m1\_subset\_1~k1\_sincos10~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))\end{array}
\label{hyp:egehpflgbdpfdhjgogdgpgdhbdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k1\_fdiff\_9){\unicdcdcdhd}(m1\_subset\_1~k1\_fdiff\_9~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))\end{array}
\label{hyp:egehpflgbdpfggegjgggggpfjd}
\end{equation}
\begin{theorem}\label{thm:ehfdhdpfdhjgogdgpgdhbdad}
$$\begin{array}{c}k1\_partfun1~k1\_numbers~k1\_numbers~k1\_numbers~k1\_numbers~(k2\_partfun1~\\
k1\_numbers~k1\_numbers~k1\_sincos10~(k1\_rcomp\_1~np\_\_1~(k7\_square\_1~\\
np\_\_2)))~(k2\_partfun1~k1\_numbers~k1\_numbers~k1\_fdiff\_9~(k1\_rcomp\_1~\\
k6\_numbers~(k10\_real\_1~k32\_sin\_cos~np\_\_4)))=k1\_partfun2~k1\_numbers~\\
(k1\_rcomp\_1~np\_\_1~(k7\_square\_1~np\_\_2))\end{array}$$
\end{theorem}
\end{document}
