\documentclass{article}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\begin{document}
\title{t78\_sin\_cos6 (TMNDbrYRQ58nnVp9ys8xVEhrcWf3DNyDz4P)}
\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 $ k4\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k32\_sin\_cos : {\iota}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k17\_sin\_cos : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k18\_sin\_cos : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k21\_sin\_cos : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k20\_sin\_cos : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\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}((r1\_xxreal\_0~(k1\_real\_1~(k10\_real\_1~\\
k32\_sin\_cos~np\_\_2))~(k3\_sin\_cos6~X0)){\unicdcdcdhd}(r1\_xxreal\_0~(k3\_sin\_cos6~\\
X0)~(k10\_real\_1~k32\_sin\_cos~np\_\_2))))\end{array}
\label{hyp:ehhdgdpfdhjgogpfdgpgdhgd}
\end{equation}
Assume the following.
\begin{equation}
{{{k3\_sin\_cos6}~{np\_\_1}}={{{k10\_real\_1}~{k32\_sin\_cos}}~{np\_\_2}}}\label{hyp:ehhdcdpfdhjgogpfdgpgdhgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}(((r1\_xxreal\_0~(k1\_real\_1~(k10\_real\_1~\\
k32\_sin\_cos~np\_\_2))~X0){\unicdcdcdhd}(r1\_xxreal\_0~X0~(k10\_real\_1~k32\_sin\_cos~\\
np\_\_2))){\unicdbdjdcd}(k3\_sin\_cos6~(k17\_sin\_cos~X0)=X0))\end{array}
\label{hyp:ehgdjdpfdhjgogpfdgpgdhgd}
\end{equation}
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}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}((r1\_xxreal\_0~\\
X0~X1){\unicdbdjded}(r1\_xxreal\_0~(k4\_xcmplx\_0~X1)~(k4\_xcmplx\_0~X0))))\end{array}
\label{hyp:ehcdedpfihchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{{k1\_real\_1}~{X0}}={{k4\_xcmplx\_0}~{X0}}})}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}(k18\_sin\_cos~X0=k17\_sin\_cos~\\
X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdidpfdhjgogpfdgpgdh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{{k1\_real\_1}~{({{k1\_real\_1}~{X0}})}}={X0}})}}}\label{hyp:jgogghpgmgfhehjgghfgogfgdhdhpflgbdpfchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{m1\_subset\_1}~{({{k3\_sin\_cos6}~{X0}})}}~{k1\_numbers}}}\label{hyp:egehpflgddpfdhjgogpfdgpgdhgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}(m1\_subset\_1~(k1\_real\_1~\\
X0)~k1\_numbers)\end{array}
\label{hyp:egehpflgbdpfchfgbgmgpfbd}
\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:ehhdidpfdhjgogpfdgpgdhgd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}(((r1\_xxreal\_0~(k1\_real\_1~np\_\_1)~\\
X0){\unicdcdcdhd}(r1\_xxreal\_0~X0~np\_\_1)){\unicdbdjdcd}(k3\_sin\_cos6~X0=k1\_real\_1~(k3\_sin\_cos6~\\
(k4\_xcmplx\_0~X0))))\end{array}$$
\end{theorem}
\end{document}
