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\begin{document}
\title{t49\_sin\_cos4 (TMGAUC2qbSVCffE4tza3GcJzBDZQs6HXWoE)}
\maketitle
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k17\_sin\_cos : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k20\_sin\_cos : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_sin\_cos4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k21\_sin\_cos : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k18\_sin\_cos : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}((k17\_sin\_cos~\\
(k7\_xcmplx\_0~(k2\_xcmplx\_0~X0~X1)~np\_\_2){\unicdcdgdad}k6\_numbers){\unicdbdjdcd}(k7\_xcmplx\_0~\\
(k2\_xcmplx\_0~(k17\_sin\_cos~X0)~(k17\_sin\_cos~X1))~(k6\_xcmplx\_0~\\
(k20\_sin\_cos~X1)~(k20\_sin\_cos~X0))=k2\_sin\_cos4~(k7\_xcmplx\_0~\\
(k6\_xcmplx\_0~X0~X1)~np\_\_2))))\end{array}
\label{hyp:ehedidpfdhjgogpfdgpgdhed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}((k21\_sin\_cos~k6\_numbers=np\_\_1){\unicdcdcdhd}\\
((k18\_sin\_cos~k6\_numbers=k6\_numbers){\unicdcdcdhd}((k20\_sin\_cos~(k4\_xcmplx\_0~\\
X0)=k20\_sin\_cos~X0){\unicdcdcdhd}(k17\_sin\_cos~(k4\_xcmplx\_0~X0)=k4\_xcmplx\_0~\\
(k17\_sin\_cos~X0)))))\end{array}
\label{hyp:ehddbdpfdhjgogpfdgpgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}(k6\_xcmplx\_0~\\
(k17\_sin\_cos~X0)~(k17\_sin\_cos~X1)=k3\_xcmplx\_0~np\_\_2~(k3\_xcmplx\_0~\\
(k20\_sin\_cos~(k7\_xcmplx\_0~(k2\_xcmplx\_0~X0~X1)~np\_\_2))~(k17\_sin\_cos~\\
(k7\_xcmplx\_0~(k6\_xcmplx\_0~X0~X1)~np\_\_2)))))\end{array}
\label{hyp:ehbdgdpfdhjgogpfdgpgdhed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}(k2\_xcmplx\_0~\\
(k17\_sin\_cos~X0)~(k17\_sin\_cos~X1)=k3\_xcmplx\_0~np\_\_2~(k3\_xcmplx\_0~\\
(k20\_sin\_cos~(k7\_xcmplx\_0~(k6\_xcmplx\_0~X0~X1)~np\_\_2))~(k17\_sin\_cos~\\
(k7\_xcmplx\_0~(k2\_xcmplx\_0~X0~X1)~np\_\_2)))))\end{array}
\label{hyp:ehbdfdpfdhjgogpfdgpgdhed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xcmplx\_0~X0){\unicdcdcdhd}(v1\_xcmplx\_0~X1)){\unicdbdjdcd}(\\
k6\_xcmplx\_0~(k4\_xcmplx\_0~X0)~(k4\_xcmplx\_0~X1)=k6\_xcmplx\_0~X1~\\
X0)\end{array}
\label{hyp:dhahdgjdpfbgchjgehigng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xcmplx\_0~X0){\unicdcdcdhd}(v1\_xcmplx\_0~X1)){\unicdbdjdcd}(\\
k2\_xcmplx\_0~X0~(k4\_xcmplx\_0~X1)=k6\_xcmplx\_0~X0~X1)\end{array}
\label{hyp:dhahdgbdpfbgchjgehigng}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xcmplx\_0}~{X0}})}{\unicdbdjdcd}{({{{k4\_xcmplx\_0}~{({{k4\_xcmplx\_0}~{X0}})}}={X0}})}}}\label{hyp:jgogghpgmgfhehjgghfgogfgdhdhpflgedpfihdgngahmgihpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}((v1\_xcmplx\_0~(k4\_xcmplx\_0~X0)){\unicdcdcdhd}\\
(v1\_xreal\_0~(k4\_xcmplx\_0~X0)))\end{array}
\label{hyp:ggdgddpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xcmplx\_0~X0){\unicdcdcdhd}(v1\_xcmplx\_0~X1)){\unicdbdjdcd}(\\
k2\_xcmplx\_0~X0~X1=k2\_xcmplx\_0~X1~X0)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfihdgngahmgihpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xcmplx\_0}~{X0}})}}}\label{hyp:dgdgddpfihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehedjdpfdhjgogpfdgpgdhed}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}((k17\_sin\_cos~\\
(k7\_xcmplx\_0~(k6\_xcmplx\_0~X0~X1)~np\_\_2){\unicdcdgdad}k6\_numbers){\unicdbdjdcd}(k7\_xcmplx\_0~\\
(k6\_xcmplx\_0~(k17\_sin\_cos~X0)~(k17\_sin\_cos~X1))~(k6\_xcmplx\_0~\\
(k20\_sin\_cos~X1)~(k20\_sin\_cos~X0))=k2\_sin\_cos4~(k7\_xcmplx\_0~\\
(k2\_xcmplx\_0~X0~X1)~np\_\_2))))\end{array}$$
\end{theorem}
\end{document}
