\documentclass{article}
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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}
\newcommand\unicdcdbdgd{\setminus}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t69\_sin\_cos9 (TMKSqsHiFL3XPq33oFAwpUsgLDXDFH1mbGh)}
\maketitle
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.
Let $ k1\_real\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k2\_sin\_cos4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_sin\_cos9 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_sin\_cos4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}(((r1\_xxreal\_0~(k1\_real\_1~\\
np\_\_1)~X0){\unicdcdcdhd}(r1\_xxreal\_0~X0~np\_\_1)){\unicdbdjdcd}(k1\_sin\_cos4~(k5\_sin\_cos9~\\
X0)=X0))\end{array}
\label{hyp:ehfdbdpfdhjgogpfdgpgdhjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}(k2\_sin\_cos4~X0=k10\_real\_1~np\_\_1~\\
(k1\_sin\_cos4~X0))\end{array}
\label{hyp:ehbdcdpfdhjgogpfdgpgdhfd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}(m1\_subset\_1~(k5\_sin\_cos9~\\
X0)~k1\_numbers)\end{array}
\label{hyp:egehpflgfdpfdhjgogpfdgpgdhjd}
\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:ehgdjdpfdhjgogpfdgpgdhjd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}(((r1\_xxreal\_0~(k1\_real\_1~\\
np\_\_1)~X0){\unicdcdcdhd}(r1\_xxreal\_0~X0~np\_\_1)){\unicdbdjdcd}(k2\_sin\_cos4~(k5\_sin\_cos9~\\
X0)=k10\_real\_1~np\_\_1~X0))\end{array}$$
\end{theorem}
\end{document}
