\documentclass{article}
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\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
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\begin{document}
\title{t37\_sin\_cos3 (TMW92zRw5JmurDHeBfmxPAoMEvAUSyk6d8W)}
\maketitle
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k15\_sin\_cos : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_binop\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_binop\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_complex1 : {\iota}$ be given.
Let $ k4\_binop\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_numbers : {\iota}$ be given.
Let $ k2\_sin\_cos3 : {\iota}$ be given.
Let $ k1\_sin\_cos3 : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_sin\_cos3 : {\iota}$ be given.
Let $ k3\_sin\_cos3 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_numbers){\unicdbdjdcd}(k15\_sin\_cos~(k1\_binop\_2~\\
X0)=k4\_binop\_2~(k10\_funct\_2~k2\_numbers~k2\_numbers~k4\_sin\_cos3~\\
X0)~(k10\_funct\_2~k2\_numbers~k2\_numbers~k3\_sin\_cos3~X0))\end{array}
\label{hyp:ehcdgdpfdhjgogpfdgpgdhdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xcmplx\_0~X0){\unicdbdjdcd}(k10\_funct\_2~k2\_numbers~k2\_numbers~\\
k4\_sin\_cos3~(k5\_binop\_2~k7\_complex1~X0)=k10\_funct\_2~k2\_numbers~\\
k2\_numbers~k2\_sin\_cos3~X0)\end{array}
\label{hyp:ehbdidpfdhjgogpfdgpgdhdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xcmplx\_0~X0){\unicdbdjdcd}(k10\_funct\_2~k2\_numbers~k2\_numbers~\\
k3\_sin\_cos3~(k5\_binop\_2~k7\_complex1~X0)=k5\_binop\_2~k7\_complex1~\\
(k10\_funct\_2~k2\_numbers~k2\_numbers~k1\_sin\_cos3~X0))\end{array}
\label{hyp:ehbdhdpfdhjgogpfdgpgdhdd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k7\_complex1}}~{k2\_numbers}}\label{hyp:egehpflghdpfdgpgngahmgfgihbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xcmplx\_0~X0){\unicdcdcdhd}(v1\_xcmplx\_0~X1)){\unicdbdjdcd}(\\
m1\_subset\_1~(k5\_binop\_2~X0~X1)~k2\_numbers)\end{array}
\label{hyp:egehpflgfdpfcgjgogpgahpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k2\_numbers}})}{\unicdbdjdcd}{({{v1\_xcmplx\_0}~{X0}})}}}\label{hyp:dgdgddpfihdgngahmgihpfad}
\end{equation}
\begin{theorem}\label{thm:ehddhdpfdhjgogpfdgpgdhdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xcmplx\_0~X0){\unicdbdjdcd}(k15\_sin\_cos~(k1\_binop\_2~(k5\_binop\_2~\\
k7\_complex1~X0))=k4\_binop\_2~(k10\_funct\_2~k2\_numbers~k2\_numbers~\\
k2\_sin\_cos3~X0)~(k5\_binop\_2~k7\_complex1~(k10\_funct\_2~k2\_numbers~\\
k2\_numbers~k1\_sin\_cos3~X0)))\end{array}$$
\end{theorem}
\end{document}
