\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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\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t58\_power (TMLrtM9bmxDxV6UCRuPXrtm3aPBN3rsBZj1)}
\maketitle
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k5\_power : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k3\_power : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v6\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_rat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
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){\unicdbdjdcd}((v1\_xboole\_0~X0){\unicdcdcdid}((v2\_xxreal\_0~X1){\unicdcdcdid}(v3\_xxreal\_0~X0)))))\end{array}
\label{hyp:ehgdpfchfgbgmg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\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}(\preoh (\preoh r1\_xxreal\_0~X1~X0){\unicdcdcdhd}((\preoh r1\_xxreal\_0~X2~k6\_numbers){\unicdcdcdhd}\\
((\preoh r1\_xxreal\_0~np\_\_1~X2){\unicdcdcdhd}(r1\_xxreal\_0~(k3\_power~X2~X0)~(k3\_power~\\
X2~X1)))))))\end{array}
\label{hyp:ehedadpfahpghhfgch}
\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){\unicdcdcdhd}(v3\_xxreal\_0~X1)){\unicdbdjdcd}(v3\_xxreal\_0~X0)))\end{array}
\label{hyp:ehcdpfchfgbgmg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}((\\
(r1\_xxreal\_0~X0~X1){\unicdcdcdhd}(r1\_xxreal\_0~X1~X0)){\unicdbdjdcd}(X0=X1)))\end{array}
\label{hyp:ehbdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k1\_xboole\_0}}~{k4\_ordinal1}}\label{hyp:ehbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
{{{r1\_xxreal\_0}~{np\_\_1}}~{np\_\_1}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdpfchbd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{v6\_membered}~{k4\_ordinal1}}\label{hyp:ggdggdpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{k1\_xboole\_0}}\label{hyp:ggdgbdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xreal\_0~X0){\unicdcdcdhd}(v1\_xreal\_0~X1)){\unicdbdjdcd}(v1\_xreal\_0~\\
(k5\_power~X0~X1))\end{array}
\label{hyp:egehpflgfdpfahpghhfgch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}(\preoh (\preoh \\
r1\_xxreal\_0~X0~k6\_numbers){\unicdcdcdhd}((X0{\unicdcdgdad}np\_\_1){\unicdcdcdhd}((\preoh r1\_xxreal\_0~X1~k6\_numbers){\unicdcdcdhd}\\
(\preoh {\unicdcdadad} X2 .  (v1\_xreal\_0~X2){\unicdbdjdcd}((X2=k5\_power~X0~X1){\unicdbdjded}(k3\_power~\\
X0~X2=X1)))))))\end{array}
\label{hyp:egddpfahpghhfgch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xxreal\_0~X0){\unicdcdcdhd}(v1\_xxreal\_0~X1)){\unicdbdjdcd}(\\
(r1\_xxreal\_0~X0~X1){\unicdcdcdid}(r1\_xxreal\_0~X1~X0))\end{array}
\label{hyp:dgpgogogfgdgehfgegogfgdhdhpfchbdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{X0}})}}}\label{hyp:dgdgedpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v3\_membered}~{X0}})}{\unicdbdjdcd}{({{v2\_membered}~{X0}})}}}\label{hyp:dgdgedpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_xxreal\_0~X0){\unicdcdcdhd}(v2\_xxreal\_0~X0)){\unicdbdjdcd}((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((v1\_xxreal\_0~X0){\unicdcdcdhd}(\preoh v3\_xxreal\_0~X0)))\end{array}
\label{hyp:dgdgddpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v4\_membered}~{X0}})}{\unicdbdjdcd}{({{v3\_membered}~{X0}})}}}\label{hyp:dgdgddpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k5\_numbers}})}{\unicdbdjdcd}{({\preoh{{{v3\_xxreal\_0}~{X0}}}})}}}\label{hyp:dgdgcdpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v5\_membered}~{X0}})}{\unicdbdjdcd}{({{v4\_membered}~{X0}})}}}\label{hyp:dgdgcdpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_rat\_1}~{X0}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgbdpfchbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v6\_membered}~{X0}})}{\unicdbdjdcd}{({{v5\_membered}~{X0}})}}}\label{hyp:dgdgbdpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v4\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
(v1\_rat\_1~X1))\end{array}
\label{hyp:dgdgbdfdpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v2\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
(v1\_xxreal\_0~X1))\end{array}
\label{hyp:dgdgbdddpfngfgngcgfgchfgeg}
\end{equation}
\begin{theorem}\label{thm:ehfdidpfahpghhfgch}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xreal\_0~X2){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~X0~k6\_numbers){\unicdcdcdhd}((\preoh r1\_xxreal\_0~\\
np\_\_1~X0){\unicdcdcdhd}((\preoh r1\_xxreal\_0~X1~k6\_numbers){\unicdcdcdhd}((\preoh r1\_xxreal\_0~X2~X1){\unicdcdcdhd}\\
(r1\_xxreal\_0~(k5\_power~X0~X1)~(k5\_power~X0~X2))))))))\end{array}$$
\end{theorem}
\end{document}
