\documentclass{article}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
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\begin{document}
\title{t24\_sin\_cos3 (TMR1b9qPhUY59oW6nqLTV4t39sCZxCGXvLx)}
\maketitle
Let $ k10\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_numbers : {\iota}$ be given.
Let $ k4\_sin\_cos3 : {\iota}$ be given.
Let $ k5\_complex1 : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k2\_sin\_cos3 : {\iota}$ be given.
Let $ k5\_binop\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_complex1 : {\iota}$ be given.
Let $ k1\_xcmplx\_0 : {\iota}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xcmplx\_0}~{X0}})}{\unicdbdjdcd}{({{{{k3\_xcmplx\_0}~{X0}}~{k6\_numbers}}={k6\_numbers}})}}}\label{hyp:ehcdpfbgchjgehigng}
\end{equation}
Assume the following.
\begin{equation}
{{{{{{k10\_funct\_2}~{k2\_numbers}}~{k2\_numbers}}~{k2\_sin\_cos3}}~{k5\_complex1}}={np\_\_1}}\label{hyp:ehcdddpfdhjgogpfdgpgdhdd}
\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}
{{k7\_complex1}={k1\_xcmplx\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflghdpfdgpgngahmgfgihbd}
\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 .  {\unicdcdadad} X1 .  ((v1\_xcmplx\_0~X0){\unicdcdcdhd}(v1\_xcmplx\_0~X1)){\unicdbdjdcd}(\\
k5\_binop\_2~X0~X1=k3\_xcmplx\_0~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfcgjgogpgahpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xcmplx\_0}~{k1\_xcmplx\_0}}\label{hyp:ggdgbdpfihdgngahmgihpfad}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k5\_complex1}}~{k2\_numbers}}\label{hyp:egehpflgfdpfdgpgngahmgfgihbd}
\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:ehcdedpfdhjgogpfdgpgdhdd}
${{{{{{k10\_funct\_2}~{k2\_numbers}}~{k2\_numbers}}~{k4\_sin\_cos3}}~{k5\_complex1}}={np\_\_1}}$.
\end{theorem}
\end{document}
