\documentclass{article}
\newtheorem{axiom}{Axiom}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
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\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{l3\_sin\_cos8 (TMQQJkmDyJgQcBoU6D8kVVUgeyGRAMRdGpP)}
\maketitle
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_square\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_sin\_cos2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_sin\_cos2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k3\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_sin\_cos2 : {\iota}$ be given.
Let $ k1\_sin\_cos2 : {\iota}$ be given.
Let $ k8\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_sin\_cos2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_square\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_sin\_cos2 : {{\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}((k9\_real\_1~(k5\_square\_1~(k1\_seq\_1~\\
k4\_sin\_cos2~X0))~(k5\_square\_1~(k1\_seq\_1~k1\_sin\_cos2~X0))=np\_\_1){\unicdcdcdhd}\\
(k9\_real\_1~(k8\_real\_1~(k1\_seq\_1~k4\_sin\_cos2~X0)~(k1\_seq\_1~k4\_sin\_cos2~\\
X0))~(k8\_real\_1~(k1\_seq\_1~k1\_sin\_cos2~X0)~(k1\_seq\_1~k1\_sin\_cos2~\\
X0))=np\_\_1))\end{array}
\label{hyp:ehbdedpfdhjgogpfdgpgdhcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k1\_numbers){\unicdcdcdhd}(v1\_xreal\_0~\\
X1)){\unicdbdjdcd}(k9\_real\_1~X0~X1=k6\_xcmplx\_0~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k1\_numbers){\unicdcdcdhd}(v1\_xreal\_0~\\
X1)){\unicdbdjdcd}(k8\_real\_1~X0~X1=k3\_xcmplx\_0~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgidpfchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k6\_sin\_cos2}~{X0}}={{k5\_sin\_cos2}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfdhjgogpfdgpgdhcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}(k5\_square\_1~X0=k3\_square\_1~\\
X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfdhbhfhbgchfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k3\_sin\_cos2}~{X0}}={{k2\_sin\_cos2}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfdhjgogpfdgpgdhcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{({{k3\_square\_1}~{X0}})}})}}}\label{hyp:ggdgcdpfdhbhfhbgchfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k1\_numbers){\unicdcdcdhd}(v1\_xreal\_0~\\
X1)){\unicdbdjdcd}(m1\_subset\_1~(k8\_real\_1~X0~X1)~k1\_numbers)\end{array}
\label{hyp:egehpflgidpfchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{m1\_subset\_1}~{({{k6\_sin\_cos2}~{X0}})}}~{k1\_numbers}}}\label{hyp:egehpflggdpfdhjgogpfdgpgdhcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{m1\_subset\_1}~{({{k3\_sin\_cos2}~{X0}})}}~{k1\_numbers}}}\label{hyp:egehpflgddpfdhjgogpfdgpgdhcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k5\_sin\_cos2}~{X0}}={{{k1\_seq\_1}~{k4\_sin\_cos2}}~{X0}}}}\label{hyp:egedpfdhjgogpfdgpgdhcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k2\_sin\_cos2}~{X0}}={{{k1\_seq\_1}~{k1\_sin\_cos2}}~{X0}}}}\label{hyp:egcdpfdhjgogpfdgpgdhcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xcmplx\_0}~{X0}})}{\unicdbdjdcd}{({{{k3\_square\_1}~{X0}}={{{k3\_xcmplx\_0}~{X0}}~{X0}}})}}}\label{hyp:egbdpfdhbhfhbgchfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xcmplx\_0}~{X0}})}}}\label{hyp:dgdgddpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgbdpfihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:mgddpfdhjgogpfdgpgdhid}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}((k6\_xcmplx\_0~(k5\_square\_1~(k6\_sin\_cos2~\\
X0))~(k5\_square\_1~(k3\_sin\_cos2~X0))=np\_\_1){\unicdcdcdhd}(k6\_xcmplx\_0~(k3\_xcmplx\_0~\\
(k6\_sin\_cos2~X0)~(k6\_sin\_cos2~X0))~(k3\_xcmplx\_0~(k3\_sin\_cos2~\\
X0)~(k3\_sin\_cos2~X0))=np\_\_1))\end{array}$$
\end{theorem}
\end{document}
