\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{t8\_topreal5 (TMSM4D8QhqxaEpR79ABj9gjteNbxC5Nc5sG)}
\maketitle
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_topmetr : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_topmetr : {\iota}$ be given.
Let $ v5\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k3\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v3\_membered : {{\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}({\unicdcdadad} X2 .  \\
(v1\_xreal\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_xreal\_0~X3){\unicdbdjdcd}((\preoh r1\_xxreal\_0~\\
X1~X0){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~(u1\_struct\_0~\\
(k4\_topmetr~X0~X1))~(u1\_struct\_0~k3\_topmetr)){\unicdcdcdhd}((v5\_pre\_topc~\\
X4~(k4\_topmetr~X0~X1)~k3\_topmetr){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~(k4\_topmetr~X0~X1))~(u1\_struct\_0~k3\_topmetr))))))){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  (v1\_xreal\_0~X5){\unicdbdjdcd}(\preoh (k1\_funct\_1~X4~X0=X2){\unicdcdcdhd}((k1\_funct\_1~\\
X4~X1=X3){\unicdcdcdhd}((\preoh r1\_xxreal\_0~X2~X5){\unicdcdcdhd}((\preoh r1\_xxreal\_0~X5~X3){\unicdcdcdhd}({\unicdcdadad} X6 .  \\
(m1\_subset\_1~X6~k1\_numbers){\unicdbdjdcd}(\preoh (k1\_funct\_1~X4~X6=X5){\unicdcdcdhd}((\preoh r1\_xxreal\_0~\\
X6~X0){\unicdcdcdhd}(\preoh r1\_xxreal\_0~X1~X6))))))))))))))\end{array}
\label{hyp:ehhdpfehpgahchfgbgmgfd}
\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}((\preoh r1\_xxreal\_0~\\
X1~X0){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~(u1\_struct\_0~\\
(k4\_topmetr~X0~X1))~(u1\_struct\_0~k3\_topmetr)){\unicdcdcdhd}((v5\_pre\_topc~\\
X4~(k4\_topmetr~X0~X1)~k3\_topmetr){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~(k4\_topmetr~X0~X1))~(u1\_struct\_0~k3\_topmetr))))))){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  (v1\_xreal\_0~X5){\unicdbdjdcd}(\preoh (k1\_funct\_1~X4~X0=X2){\unicdcdcdhd}((k1\_funct\_1~\\
X4~X1=X3){\unicdcdcdhd}((\preoh r1\_xxreal\_0~X5~X2){\unicdcdcdhd}((\preoh r1\_xxreal\_0~X3~X5){\unicdcdcdhd}({\unicdcdadad} X6 .  \\
(m1\_subset\_1~X6~k1\_numbers){\unicdbdjdcd}(\preoh (k1\_funct\_1~X4~X6=X5){\unicdcdcdhd}((\preoh r1\_xxreal\_0~\\
X6~X0){\unicdcdcdhd}(\preoh r1\_xxreal\_0~X1~X6))))))))))))))\end{array}
\label{hyp:ehgdpfehpgahchfgbgmgfd}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}(\preoh (\preoh \\
r1\_xxreal\_0~k6\_numbers~(k3\_xcmplx\_0~X0~X1)){\unicdcdcdhd}((\preoh (\preoh r1\_xxreal\_0~\\
X0~k6\_numbers){\unicdcdcdhd}(\preoh r1\_xxreal\_0~k6\_numbers~X1)){\unicdcdcdhd}(\preoh (\preoh r1\_xxreal\_0~\\
k6\_numbers~X0){\unicdcdcdhd}(\preoh r1\_xxreal\_0~X1~k6\_numbers)))))\end{array}
\label{hyp:ehbdddddpfihchfgbgmgpfbd}
\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}
{{{m1\_subset\_1}~{k5\_numbers}}~{({{k1\_zfmisc\_1}~{k1\_numbers}})}}\label{hyp:egehpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_numbers)){\unicdbdjdcd}(v3\_membered~\\
X0)\end{array}
\label{hyp:dgdgidpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
(v1\_xreal\_0~X1))\end{array}
\label{hyp:dgdgbdedpfngfgngcgfgchfgeg}
\end{equation}
\begin{theorem}\label{thm:ehidpfehpgahchfgbgmgfd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~(k4\_topmetr~X0~\\
X1))~(u1\_struct\_0~k3\_topmetr)){\unicdcdcdhd}((v5\_pre\_topc~X2~(k4\_topmetr~\\
X0~X1)~k3\_topmetr){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~(k4\_topmetr~X0~X1))~(u1\_struct\_0~k3\_topmetr))))))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (v1\_xreal\_0~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (v1\_xreal\_0~X4){\unicdbdjdcd}(\preoh (\\
\preoh r1\_xxreal\_0~X1~X0){\unicdcdcdhd}((\preoh r1\_xxreal\_0~k6\_numbers~(k3\_xcmplx\_0~X3~\\
X4)){\unicdcdcdhd}((X3=k1\_funct\_1~X2~X0){\unicdcdcdhd}((X4=k1\_funct\_1~X2~X1){\unicdcdcdhd}({\unicdcdadad} X5 .  \\
(m1\_subset\_1~X5~k1\_numbers){\unicdbdjdcd}(\preoh (k1\_funct\_1~X2~X5=k6\_numbers){\unicdcdcdhd}\\
((\preoh r1\_xxreal\_0~X5~X0){\unicdcdcdhd}(\preoh r1\_xxreal\_0~X1~X5))))))))))))\end{array}$$
\end{theorem}
\end{document}
