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\begin{document}
\title{t21\_sin\_cos2 (TMU8jsc1HCCwUgB1fqnmgnCBG8m6fhtR2tw)}
\maketitle
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_sin\_cos2 : {\iota}$ be given.
Let $ k9\_binop\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_sin\_cos2 : {\iota}$ be given.
Let $ k10\_binop\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}(k1\_seq\_1~\\
k1\_sin\_cos2~(k10\_binop\_2~X0~X1)=k9\_real\_1~(k8\_real\_1~(k1\_seq\_1~\\
k1\_sin\_cos2~X0)~(k1\_seq\_1~k4\_sin\_cos2~X1))~(k8\_real\_1~(k1\_seq\_1~\\
k4\_sin\_cos2~X0)~(k1\_seq\_1~k1\_sin\_cos2~X1))))\end{array}
\label{hyp:mgddedpfdhjgogpfdgpgdhcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}(k1\_seq\_1~\\
k1\_sin\_cos2~(k9\_binop\_2~X0~X1)=k7\_real\_1~(k8\_real\_1~(k1\_seq\_1~\\
k1\_sin\_cos2~X0)~(k1\_seq\_1~k4\_sin\_cos2~X1))~(k8\_real\_1~(k1\_seq\_1~\\
k4\_sin\_cos2~X0)~(k1\_seq\_1~k1\_sin\_cos2~X1))))\end{array}
\label{hyp:mgcdddpfdhjgogpfdgpgdhcd}
\end{equation}
\begin{theorem}\label{thm:ehcdbdpfdhjgogpfdgpgdhcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}((k1\_seq\_1~\\
k1\_sin\_cos2~(k9\_binop\_2~X0~X1)=k7\_real\_1~(k8\_real\_1~(k1\_seq\_1~\\
k1\_sin\_cos2~X0)~(k1\_seq\_1~k4\_sin\_cos2~X1))~(k8\_real\_1~(k1\_seq\_1~\\
k4\_sin\_cos2~X0)~(k1\_seq\_1~k1\_sin\_cos2~X1))){\unicdcdcdhd}(k1\_seq\_1~k1\_sin\_cos2~\\
(k10\_binop\_2~X0~X1)=k9\_real\_1~(k8\_real\_1~(k1\_seq\_1~k1\_sin\_cos2~\\
X0)~(k1\_seq\_1~k4\_sin\_cos2~X1))~(k8\_real\_1~(k1\_seq\_1~k4\_sin\_cos2~\\
X0)~(k1\_seq\_1~k1\_sin\_cos2~X1)))))\end{array}$$
\end{theorem}
\end{document}
