\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{t56\_sppol\_2 (TMGyzo69RFDV5nM6VDHATbtefW81wTcBQhh)}
\maketitle
Let $ k1\_topreal1 : {\iota}$ be given.
Let $ k1\_sppol\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ c1\_\_xreal\_0 : {\iota}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k15\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k1\_rltopsp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k19\_euclid : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_1){\unicdcdcdhd}(m2\_subset\_1~np\_\_1~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_1~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_1~k1\_numbers))\end{array}
\label{hyp:dhahdgbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k6\_numbers}}~{k1\_numbers}}\label{hyp:mgbdjdpfbgchjhehngpfad}
\end{equation}
Assume the following.
\begin{equation}
{{c1\_\_xreal\_0}={k6\_numbers}}\label{hyp:egfgpfdgbdpfpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xreal\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_xreal\_0~X3){\unicdbdjdcd}(k1\_sppol\_2~X0~X1~\\
X2~X3=k4\_subset\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~(k4\_subset\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~(k1\_rltopsp1~(k15\_euclid~np\_\_2)~\\
(k19\_euclid~X0~X2)~(k19\_euclid~X0~X3))~(k1\_rltopsp1~(k15\_euclid~\\
np\_\_2)~(k19\_euclid~X0~X3)~(k19\_euclid~X1~X3)))~(k4\_subset\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~(k1\_rltopsp1~(k15\_euclid~np\_\_2)~(k19\_euclid~\\
X1~X3)~(k19\_euclid~X1~X2))~(k1\_rltopsp1~(k15\_euclid~np\_\_2)~(k19\_euclid~\\
X1~X2)~(k19\_euclid~X0~X2)))))))\end{array}
\label{hyp:egddpfdhahahpgmgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}k1\_topreal1=k4\_subset\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~(k4\_subset\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~(k1\_rltopsp1~(k15\_euclid~np\_\_2)~\\
(k19\_euclid~k6\_numbers~k6\_numbers)~(k19\_euclid~k6\_numbers~np\_\_1))~\\
(k1\_rltopsp1~(k15\_euclid~np\_\_2)~(k19\_euclid~k6\_numbers~np\_\_1)~\\
(k19\_euclid~np\_\_1~np\_\_1)))~(k4\_subset\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~(k1\_rltopsp1~(k15\_euclid~np\_\_2)~(k19\_euclid~np\_\_1~np\_\_1)~\\
(k19\_euclid~np\_\_1~k6\_numbers))~(k1\_rltopsp1~(k15\_euclid~np\_\_2)~\\
(k19\_euclid~np\_\_1~k6\_numbers)~(k19\_euclid~k6\_numbers~k6\_numbers)))\end{array}
\label{hyp:egcdpfehpgahchfgbgmgbd}
\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:ehfdgdpfdhahahpgmgpfcd}
${{k1\_topreal1}={{{{{k1\_sppol\_2}~{k6\_numbers}}~{np\_\_1}}~{k6\_numbers}}~{np\_\_1}}}$.
\end{theorem}
\end{document}
