\documentclass{article}
\newtheorem{axiom}{Axiom}
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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\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
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\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{l14\_topreal2 (TMKiruZtcHKjHcg6HGx3KxivtgShjR4tAuc)}
\maketitle
Let $ k19\_euclid : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k1\_rltopsp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k15\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k17\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k18\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Assume the following.
\begin{equation}
{{{k4\_struct\_0}~{({{k15\_euclid}~{np\_\_2}})}}={{{k19\_euclid}~{k6\_numbers}}~{k6\_numbers}}}\label{hyp:ehfdedpffgfhdgmgjgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(k1\_rltopsp1~(k15\_euclid~np\_\_2)~(k19\_euclid~k6\_numbers~k6\_numbers)~\\
(k19\_euclid~k6\_numbers~np\_\_1)=ReplSep~(toset~({\uniddcgcg} X0 : \iota .  m1\_subset\_1~\\
X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))))~({\uniddcgcg} X0 : \iota .  (k17\_euclid~\\
X0=k6\_numbers){\unicdcdcdhd}((r1\_xxreal\_0~(k18\_euclid~X0)~np\_\_1){\unicdcdcdhd}(r1\_xxreal\_0~\\
k6\_numbers~(k18\_euclid~X0))))~({\uniddcgcg} X0 : \iota .  X0)){\unicdcdcdhd}((k1\_rltopsp1~\\
(k15\_euclid~np\_\_2)~(k19\_euclid~k6\_numbers~np\_\_1)~(k19\_euclid~\\
np\_\_1~np\_\_1)=ReplSep~(toset~({\uniddcgcg} X0 : \iota .  m1\_subset\_1~X0~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))))~({\uniddcgcg} X0 : \iota .  (r1\_xxreal\_0~(k17\_euclid~\\
X0)~np\_\_1){\unicdcdcdhd}((r1\_xxreal\_0~k6\_numbers~(k17\_euclid~X0)){\unicdcdcdhd}(k18\_euclid~\\
X0=np\_\_1)))~({\uniddcgcg} X0 : \iota .  X0)){\unicdcdcdhd}((k1\_rltopsp1~(k15\_euclid~np\_\_2)~\\
(k19\_euclid~k6\_numbers~k6\_numbers)~(k19\_euclid~np\_\_1~k6\_numbers)=\\
ReplSep~(toset~({\uniddcgcg} X0 : \iota .  m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))))~({\uniddcgcg} X0 : \iota .  (r1\_xxreal\_0~(k17\_euclid~X0)~np\_\_1){\unicdcdcdhd}(\\
(r1\_xxreal\_0~k6\_numbers~(k17\_euclid~X0)){\unicdcdcdhd}(k18\_euclid~X0=k6\_numbers)))~\\
({\uniddcgcg} X0 : \iota .  X0)){\unicdcdcdhd}(k1\_rltopsp1~(k15\_euclid~np\_\_2)~(k19\_euclid~\\
np\_\_1~k6\_numbers)~(k19\_euclid~np\_\_1~np\_\_1)=ReplSep~(toset~({\uniddcgcg} X0 : \\
\iota .  m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))))~({\uniddcgcg} X0 : \\
\iota .  (k17\_euclid~X0=np\_\_1){\unicdcdcdhd}((r1\_xxreal\_0~(k18\_euclid~X0)~np\_\_1){\unicdcdcdhd}\\
(r1\_xxreal\_0~k6\_numbers~(k18\_euclid~X0))))~({\uniddcgcg} X0 : \iota .  X0))))\end{array}
\label{hyp:ehbdddpfehpgahchfgbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{{k18\_euclid}~{({{{k19\_euclid}~{k6\_numbers}}~{np\_\_1}})}}={np\_\_1}}\label{hyp:mghdpfehpgahchfgbgmgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}\preoh k19\_euclid~k6\_numbers~k6\_numbers \in k1\_rltopsp1~(k15\_euclid~np\_\_2)~\\
(k19\_euclid~np\_\_1~k6\_numbers)~(k19\_euclid~np\_\_1~np\_\_1)\end{array}
\label{hyp:mgbdcdpfehpgahchfgbgmgcd}
\end{equation}
\begin{theorem}\label{thm:mgbdedpfehpgahchfgbgmgcd}
$$\begin{array}{c}\preoh k19\_euclid~k6\_numbers~np\_\_1 \in k1\_rltopsp1~(k15\_euclid~np\_\_2)~\\
(k19\_euclid~k6\_numbers~k6\_numbers)~(k19\_euclid~np\_\_1~k6\_numbers)\end{array}$$
\end{theorem}
\end{document}
