\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\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t74\_sin\_cos6 (TMYaNmvccN6sSWXoMEGuPp6sKL85dgvcxSX)}
\maketitle
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ k3\_sin\_cos6 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k18\_sin\_cos : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k21\_sin\_cos : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k20\_sin\_cos : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k17\_sin\_cos : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_sin\_cos6 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_sin\_cos6 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}(((r1\_xxreal\_0~(k1\_real\_1~np\_\_1)~\\
X0){\unicdcdcdhd}(r1\_xxreal\_0~X0~np\_\_1)){\unicdbdjdcd}(k18\_sin\_cos~(k3\_sin\_cos6~X0)=X0))\end{array}
\label{hyp:ehgdidpfdhjgogpfdgpgdhgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}((k21\_sin\_cos~k6\_numbers=np\_\_1){\unicdcdcdhd}\\
((k18\_sin\_cos~k6\_numbers=k6\_numbers){\unicdcdcdhd}((k20\_sin\_cos~(k4\_xcmplx\_0~\\
X0)=k20\_sin\_cos~X0){\unicdcdcdhd}(k17\_sin\_cos~(k4\_xcmplx\_0~X0)=k4\_xcmplx\_0~\\
(k17\_sin\_cos~X0)))))\end{array}
\label{hyp:ehddbdpfdhjgogpfdgpgdh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k3\_sin\_cos6}~{X0}}={{k2\_sin\_cos6}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfdhjgogpfdgpgdhgd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k2\_sin\_cos6}~{X0}}={{{k1\_seq\_1}~{k1\_sin\_cos6}}~{X0}}}}\label{hyp:egcdpfdhjgogpfdgpgdhgd}
\end{equation}
\begin{theorem}\label{thm:ehhdedpfdhjgogpfdgpgdhgd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}(((r1\_xxreal\_0~(k1\_real\_1~np\_\_1)~\\
X0){\unicdcdcdhd}((r1\_xxreal\_0~X0~np\_\_1){\unicdcdcdhd}(k3\_sin\_cos6~X0=k6\_numbers))){\unicdbdjdcd}\\
(X0=k6\_numbers))\end{array}$$
\end{theorem}
\end{document}
