\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{t50\_kurato\_1 (TMYouDvNLybZqvYWSswapb9AAdZbkNVUsJE)}
\maketitle
Let $ k1\_enumset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_topmetr : {\iota}$ be given.
Let $ k6\_kurato\_1 : {\iota}$ be given.
Let $ k1\_tops\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_xxreal\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_xxreal\_0 : {\iota}$ be given.
Let $ k1\_xxreal\_0 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}(k1\_tops\_1~X0~\\
(k2\_pre\_topc~X0~X1)=k1\_tops\_1~X0~(k2\_pre\_topc~X0~(k1\_tops\_1~X0~\\
(k2\_pre\_topc~X0~X1)))))\end{array}
\label{hyp:ehfdpfehegmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  \preoh (X0 \in k1\_enumset1~(k1\_tops\_1~k3\_topmetr~k6\_kurato\_1)~\\
(k1\_tops\_1~k3\_topmetr~(k2\_pre\_topc~k3\_topmetr~k6\_kurato\_1))~\\
(k1\_tops\_1~k3\_topmetr~(k2\_pre\_topc~k3\_topmetr~(k1\_tops\_1~k3\_topmetr~\\
k6\_kurato\_1)))){\unicdcdcdhd}(X0=k1\_numbers)\end{array}
\label{hyp:ehedjdpflgfhchbgehpgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}k2\_pre\_topc~k3\_topmetr~(k1\_tops\_1~k3\_topmetr~k6\_kurato\_1){\unicdcdgdad}k1\_tops\_1~\\
k3\_topmetr~(k2\_pre\_topc~k3\_topmetr~(k1\_tops\_1~k3\_topmetr~k6\_kurato\_1))\end{array}
\label{hyp:ehedcdpflgfhchbgehpgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~k3\_topmetr))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (v1\_xxreal\_0~X2){\unicdbdjdcd}(\\
(X0=k2\_rcomp\_1~X1~X2){\unicdbdjdcd}(v3\_pre\_topc~X0~k3\_topmetr))))\end{array}
\label{hyp:ehedadpfcgpgchdhfhlgpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~X1)){\unicdbdjded}(r1\_tarski~\\
X0~X1)\end{array}
\label{hyp:ehddpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}k2\_pre\_topc~k3\_topmetr~(k1\_tops\_1~k3\_topmetr~(k2\_pre\_topc~k3\_topmetr~\\
k6\_kurato\_1)){\unicdcdgdad}k1\_tops\_1~k3\_topmetr~(k2\_pre\_topc~k3\_topmetr~\\
k6\_kurato\_1)\end{array}
\label{hyp:ehcdidpflgfhchbgehpgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(l1\_pre\_topc~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X1))){\unicdbdjdcd}(((v3\_pre\_topc~X3~X1){\unicdbdjdcd}(k1\_tops\_1~X1~X3=X3)){\unicdcdcdhd}((k1\_tops\_1~\\
X0~X2=X2){\unicdbdjdcd}(v3\_pre\_topc~X2~X0))))))\end{array}
\label{hyp:ehcdddpfehpgahdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k1\_numbers}={{{k4\_xxreal\_1}~{k2\_xxreal\_0}}~{k1\_xxreal\_0}}}\label{hyp:ehcdcdedpfihihchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{{u1\_struct\_0}~{k3\_topmetr}}={k1\_numbers}}\label{hyp:ehbdhdpfehpgahngfgehch}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{r1\_tarski}~{X0}}~{X0}}}}\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xxreal\_0~X0){\unicdcdcdhd}(v1\_xxreal\_0~X1)){\unicdbdjdcd}(\\
k2\_rcomp\_1~X0~X1=k4\_xxreal\_1~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfchdgpgngahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xxreal\_0}~{k2\_xxreal\_0}}\label{hyp:ggdgcdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xxreal\_0}~{k1\_xxreal\_0}}\label{hyp:ggdgbdpfihihchfgbgmgpfad}
\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 .  ((v1\_xxreal\_0~X0){\unicdcdcdhd}(v1\_xxreal\_0~X1)){\unicdbdjdcd}(\\
m1\_subset\_1~(k2\_rcomp\_1~X0~X1)~(k1\_zfmisc\_1~k1\_numbers))\end{array}
\label{hyp:egehpflgcdpfchdgpgngahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k1\_xxreal\_0}={k1\_numbers}}\label{hyp:egcdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (X3=k1\_enumset1~\\
X0~X1~X2){\unicdbdjded}({\unicdcdadad} X4 .  (X4 \in X3){\unicdbdjded}(\preoh (X4{\unicdcdgdad}X0){\unicdcdcdhd}((X4{\unicdcdgdad}X1){\unicdcdcdhd}(X4{\unicdcdgdad}X2))))\end{array}
\label{hyp:egbdpffgogfhngdhfgehbd}
\end{equation}
\begin{theorem}\label{thm:ehfdadpflgfhchbgehpgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  \preoh (X0 \in k1\_enumset1~(k2\_pre\_topc~k3\_topmetr~k6\_kurato\_1)~\\
(k2\_pre\_topc~k3\_topmetr~(k1\_tops\_1~k3\_topmetr~k6\_kurato\_1))~\\
(k2\_pre\_topc~k3\_topmetr~(k1\_tops\_1~k3\_topmetr~(k2\_pre\_topc~k3\_topmetr~\\
k6\_kurato\_1)))){\unicdcdcdhd}(X0=k1\_numbers)\end{array}$$
\end{theorem}
\end{document}
