\documentclass{article}
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\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{l6\_sin\_cos9 (TMRrrPrGXC1rFbyrZRDcAmsEe5iUYaQEeJx)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k2\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k32\_sin\_cos : {\iota}$ be given.
Let $ k1\_fdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k30\_sin\_cos : {\iota}$ be given.
Let $ k1\_real\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k5\_square\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k16\_sin\_cos : {\iota}$ be given.
Let $ r1\_fdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_rfunct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k19\_sin\_cos : {\iota}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}((k1\_seq\_1~k16\_sin\_cos~\\
X0{\unicdcdgdad}k6\_numbers){\unicdbdjdcd}((r1\_fdiff\_1~(k3\_rfunct\_1~k1\_numbers~k1\_numbers~\\
k19\_sin\_cos~k16\_sin\_cos)~X0){\unicdcdcdhd}(k1\_fdiff\_1~(k3\_rfunct\_1~k1\_numbers~\\
k1\_numbers~k19\_sin\_cos~k16\_sin\_cos)~X0=k1\_real\_1~(k10\_real\_1~\\
np\_\_1~(k5\_square\_1~(k1\_seq\_1~k16\_sin\_cos~X0))))))\end{array}
\label{hyp:ehedhdpfggegjgggggpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}r1\_tarski~(k2\_rcomp\_1~k6\_numbers~k32\_sin\_cos)~(k1\_relset\_1~k1\_numbers~\\
k30\_sin\_cos)\end{array}
\label{hyp:ehcdpfdhjgogpfdgpgdhjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}(\preoh (X0 \in k1\_relset\_1~k1\_numbers~\\
k30\_sin\_cos){\unicdcdcdhd}(k1\_seq\_1~k16\_sin\_cos~X0=k6\_numbers))\end{array}
\label{hyp:ehcdpfggegjgggggpfid}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (r1\_tarski~X0~X1){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X0){\unicdbdjdcd}\\
(X2 \in X1))\end{array}
\label{hyp:egddpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
{{k30\_sin\_cos}={{{{{k3\_rfunct\_1}~{k1\_numbers}}~{k1\_numbers}}~{k19\_sin\_cos}}~{k16\_sin\_cos}}}\label{hyp:egcdhdpfdhjgogpfdgpgdh}
\end{equation}
\begin{theorem}\label{thm:mggdpfdhjgogpfdgpgdhjd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}((X0 \in k2\_rcomp\_1~k6\_numbers~\\
k32\_sin\_cos){\unicdbdjdcd}(k1\_fdiff\_1~k30\_sin\_cos~X0=k1\_real\_1~(k10\_real\_1~\\
np\_\_1~(k5\_square\_1~(k1\_seq\_1~k16\_sin\_cos~X0)))))\end{array}$$
\end{theorem}
\end{document}
