\documentclass{article}
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\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
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\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\begin{document}
\title{t58\_sin\_cos9 (TMZnPqhdJmh17hVh4rkRSXZZ5XxyHXdbhjL)}
\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 $ k6\_sin\_cos9 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ np\_\_4 : {\iota}$ be given.
Let $ k32\_sin\_cos : {\iota}$ be given.
Let $ k2\_sin\_cos4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k30\_sin\_cos : {\iota}$ 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}(k2\_sin\_cos4~(k6\_sin\_cos9~\\
X0)=X0))\end{array}
\label{hyp:ehfdcdpfdhjgogpfdgpgdhjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(k1\_seq\_1~k30\_sin\_cos~(k10\_real\_1~k32\_sin\_cos~np\_\_4)=np\_\_1){\unicdcdcdhd}\\
((k2\_sin\_cos4~(k10\_real\_1~k32\_sin\_cos~np\_\_4)=np\_\_1){\unicdcdcdhd}((k1\_seq\_1~\\
k30\_sin\_cos~(k8\_real\_1~(k10\_real\_1~np\_\_3~np\_\_4)~k32\_sin\_cos)=\\
k1\_real\_1~np\_\_1){\unicdcdcdhd}(k2\_sin\_cos4~(k8\_real\_1~(k10\_real\_1~np\_\_3~np\_\_4)~\\
k32\_sin\_cos)=k1\_real\_1~np\_\_1)))\end{array}
\label{hyp:ehbdidpfdhjgogpfdgpgdhjd}
\end{equation}
\begin{theorem}\label{thm:ehfdidpfdhjgogpfdgpgdhjd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}(((r1\_xxreal\_0~(k1\_real\_1~\\
np\_\_1)~X0){\unicdcdcdhd}((r1\_xxreal\_0~X0~np\_\_1){\unicdcdcdhd}(k6\_sin\_cos9~X0=k8\_real\_1~\\
(k10\_real\_1~np\_\_3~np\_\_4)~k32\_sin\_cos))){\unicdbdjdcd}(X0=k1\_real\_1~np\_\_1))\end{array}$$
\end{theorem}
\end{document}
