\documentclass{article}
\newtheorem{axiom}{Axiom}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
\newcommand\unicdcdadad{\forall}
\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
\newcommand\uniddcgcg{\lambda}
\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t25\_kurato\_1 (TMYHZVxRpPTDCtGpMZvMTfBnMZNgdMP6Mwt)}
\maketitle
Let $ k1\_tops\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_topmetr : {\iota}$ be given.
Let $ k2\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_kurato\_1 : {\iota}$ be given.
Let $ k2\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_4 : {\iota}$ be given.
Let $ k1\_xxreal\_0 : {\iota}$ be given.
Let $ k4\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ np\_\_5 : {\iota}$ be given.
Let $ k3\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}k1\_tops\_1~k3\_topmetr~k6\_kurato\_1=k4\_subset\_1~k1\_numbers~(k2\_rcomp\_1~\\
np\_\_4~np\_\_5)~(k2\_rcomp\_1~np\_\_5~k1\_xxreal\_0)\end{array}
\label{hyp:ehcdddpflgfhchbgehpgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}k3\_subset\_1~(u1\_struct\_0~k3\_topmetr)~(k2\_pre\_topc~k3\_topmetr~\\
(k3\_subset\_1~(u1\_struct\_0~k3\_topmetr)~(k2\_pre\_topc~k3\_topmetr~\\
(k3\_subset\_1~(u1\_struct\_0~k3\_topmetr)~(k2\_pre\_topc~k3\_topmetr~\\
(k3\_subset\_1~(u1\_struct\_0~k3\_topmetr)~k6\_kurato\_1))))))=k2\_rcomp\_1~\\
np\_\_4~k1\_xxreal\_0\end{array}
\label{hyp:ehcdcdpflgfhchbgehpgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}k3\_subset\_1~(u1\_struct\_0~k3\_topmetr)~(k2\_pre\_topc~k3\_topmetr~\\
(k3\_subset\_1~(u1\_struct\_0~k3\_topmetr)~k6\_kurato\_1))=k4\_subset\_1~\\
k1\_numbers~(k2\_rcomp\_1~np\_\_4~np\_\_5)~(k2\_rcomp\_1~np\_\_5~k1\_xxreal\_0)\end{array}
\label{hyp:ehbdidpflgfhchbgehpgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{{u1\_struct\_0}~{k3\_topmetr}}={k1\_numbers}}\label{hyp:ehbdhdpfehpgahngfgehch}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k6\_kurato\_1}}~{({{k1\_zfmisc\_1}~{({{u1\_struct\_0}~{k3\_topmetr}})}})}}\label{hyp:egehpflggdpflgfhchbgehpgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{({{v2\_pre\_topc}~{k3\_topmetr}})}{\unicdcdcdhd}{({{l1\_pre\_topc}~{k3\_topmetr}})}}\label{hyp:egehpflgddpfehpgahngfgehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)){\unicdbdjdcd}(m1\_subset\_1~\\
(k3\_subset\_1~X0~X1)~(k1\_zfmisc\_1~X0))\end{array}
\label{hyp:egehpflgddpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l1\_pre\_topc~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0)))){\unicdbdjdcd}(m1\_subset\_1~(k2\_pre\_topc~X0~X1)~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0)))\end{array}
\label{hyp:egehpflgcdpfahchfgpfehpgahdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))){\unicdbdjdcd}(k1\_tops\_1~X0~X1=k3\_subset\_1~(u1\_struct\_0~\\
X0)~(k2\_pre\_topc~X0~(k3\_subset\_1~(u1\_struct\_0~X0)~X1))))\end{array}
\label{hyp:egbdpfehpgahdhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdfdpflgfhchbgehpgpfbd}
$$\begin{array}{c}k1\_tops\_1~k3\_topmetr~(k2\_pre\_topc~k3\_topmetr~(k1\_tops\_1~k3\_topmetr~\\
k6\_kurato\_1))=k2\_rcomp\_1~np\_\_4~k1\_xxreal\_0\end{array}$$
\end{theorem}
\end{document}
