\documentclass{article}
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\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
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\begin{document}
\title{t51\_sin\_cos (TMGfC8scm6wmRcBNsACk6ik75iq9DNckc7f)}
\maketitle
Let $ k26\_sin\_cos : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k5\_complex1 : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k25\_sin\_cos : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k11\_arytm\_3 : {\iota}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k24\_sin\_cos : {\iota}$ be given.
Let $ k16\_complex1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ c2\_\_arytm\_0 : {\iota}$ be given.
Let $ c1\_\_xreal\_0 : {\iota}$ be given.
Let $ k1\_xxreal\_0 : {\iota}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_complex1}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfdgpgngahmgfgihbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}(k26\_sin\_cos~X0=k25\_sin\_cos~\\
X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdgdpfdhjgogpfdgpgdh}
\end{equation}
Assume the following.
\begin{equation}
{{k11\_arytm\_3}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdbdpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{{{k1\_seq\_1}~{k24\_sin\_cos}}~{k6\_numbers}}={np\_\_1}}\label{hyp:mgidhdpfdhjgogpfdgpgdh}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k6\_numbers}}~{k1\_numbers}}\label{hyp:mgbdjdpfbgchjhehngpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_xboole\_0~(k16\_complex1~k6\_numbers)){\unicdcdcdhd}(v1\_xreal\_0~(k16\_complex1~\\
k6\_numbers))\end{array}
\label{hyp:ggdgddpfdgpgngahmgfgihbd}
\end{equation}
Assume the following.
\begin{equation}
{{c2\_\_arytm\_0}={k6\_numbers}}\label{hyp:egfgpfdgcdpfpfbgchjhehngpfad}
\end{equation}
Assume the following.
\begin{equation}
{{c1\_\_xreal\_0}={k6\_numbers}}\label{hyp:egfgpfdgbdpfpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{k1\_xxreal\_0}={k1\_numbers}}\label{hyp:egcdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{{k25\_sin\_cos}~{X0}}={{{k1\_seq\_1}~{k24\_sin\_cos}}~{X0}}})}}}\label{hyp:egcdddpfdhjgogpfdgpgdh}
\end{equation}
\begin{theorem}\label{thm:ehfdbdpfdhjgogpfdgpgdh}
${{{k26\_sin\_cos}~{k6\_numbers}}={np\_\_1}}$.
\end{theorem}
\end{document}
