\documentclass{article}
\newtheorem{axiom}{Axiom}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t41\_sin\_cos9 (TMVUtYBQ3W1asfiCZ2m1s1bc8rn7C8BSGmd)}
\maketitle
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k29\_sin\_cos : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_sin\_cos4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k19\_sin\_cos : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k16\_sin\_cos : {\iota}$ be given.
Let $ k4\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_real\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}((k1\_seq\_1~k19\_sin\_cos~k6\_numbers=\\
np\_\_1){\unicdcdcdhd}((k1\_seq\_1~k16\_sin\_cos~k6\_numbers=k6\_numbers){\unicdcdcdhd}((k1\_seq\_1~\\
k19\_sin\_cos~(k4\_xcmplx\_0~X0)=k1\_seq\_1~k19\_sin\_cos~X0){\unicdcdcdhd}(k1\_seq\_1~\\
k16\_sin\_cos~(k4\_xcmplx\_0~X0)=k1\_real\_1~(k1\_seq\_1~k16\_sin\_cos~\\
X0)))))\end{array}
\label{hyp:ehddadpfdhjgogpfdgpgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}((k1\_seq\_1~k19\_sin\_cos~\\
X0{\unicdcdgdad}k6\_numbers){\unicdbdjdcd}(k1\_seq\_1~k29\_sin\_cos~X0=k1\_sin\_cos4~X0))\end{array}
\label{hyp:ehbdfdpfdhjgogpfdgpgdhjd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k6\_numbers}}~{k1\_numbers}}\label{hyp:mgbdjdpfbgchjhehngpfad}
\end{equation}
Assume the following.
\begin{equation}
{{{r1\_xxreal\_0}~{k6\_numbers}}~{np\_\_1}}\label{hyp:mgbdcdpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(k1\_seq\_1~k29\_sin\_cos~k6\_numbers=k6\_numbers){\unicdcdcdhd}(\preoh r1\_xxreal\_0~\\
(k1\_seq\_1~k29\_sin\_cos~np\_\_1)~np\_\_1)\end{array}
\label{hyp:mgbdbdidpfdhjgogpfdgpgdh}
\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:ehedbdpfdhjgogpfdgpgdhjd}
$$\begin{array}{c}(k1\_seq\_1~k29\_sin\_cos~k6\_numbers=k6\_numbers){\unicdcdcdhd}(k1\_sin\_cos4~\\
k6\_numbers=k6\_numbers)\end{array}$$
\end{theorem}
\end{document}
