\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{t4\_t\_0topsp (TMQekkXQ5uvWufeNB9DxD52kyyH1EgM8j3i)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k3\_t\_0topsp : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_t\_0topsp : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_eqrel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_t\_0topsp : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\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 $ k7\_eqrel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_eqrel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k11\_borsuk\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k12\_borsuk\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_eqrel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ l1\_struct\_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 $ v5\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_t\_0topsp : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_pre\_topc : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v3\_relat\_2~X2){\unicdcdcdhd}((v8\_relat\_2~\\
X2){\unicdcdcdhd}((v1\_partfun1~X2~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X1~X1)))))){\unicdbdjdcd}(\preoh (X0 \in k7\_eqrel\_1~X1~X2){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~X1){\unicdbdjdcd}(X0{\unicdcdgdad}k6\_eqrel\_1~X1~X1~X2~X3)))\end{array}
\label{hyp:ehddgdpffgbhchfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~X1){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}\\
(X0 \in X1))\end{array}
\label{hyp:ehcdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m1\_eqrel\_1~X1~(u1\_struct\_0~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}(X2 \in k3\_funct\_2~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~(k11\_borsuk\_1~X0~X1))~(k12\_borsuk\_1~\\
X0~X1)~X2)))\end{array}
\label{hyp:ehcdidpfcgpgchdhfhlgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v3\_relat\_2~X2){\unicdcdcdhd}((v8\_relat\_2~\\
X2){\unicdcdcdhd}((v1\_partfun1~X2~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0)))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (X3 \in X0){\unicdbdjdcd}((X1 \in k6\_eqrel\_1~X0~X0~X2~X3){\unicdbdjded}\\
(k6\_eqrel\_1~X0~X0~X2~X3=k6\_eqrel\_1~X0~X0~X2~X1)))\end{array}
\label{hyp:ehcdddpffgbhchfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v3\_relat\_2~X1){\unicdcdcdhd}((v8\_relat\_2~X1){\unicdcdcdhd}((v1\_partfun1~\\
X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)))))){\unicdbdjdcd}\\
(k8\_eqrel\_1~X0~X1=k7\_eqrel\_1~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgidpffgbhchfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(u1\_struct\_0~X0))\end{array}
\label{hyp:ggdgcdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_pre\_topc}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfahchfgpfehpgahdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}((v1\_funct\_1~(k4\_t\_0topsp~X0)){\unicdcdcdhd}((v1\_funct\_2~(k4\_t\_0topsp~\\
X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~(k3\_t\_0topsp~X0))){\unicdcdcdhd}((v5\_pre\_topc~\\
(k4\_t\_0topsp~X0)~X0~(k3\_t\_0topsp~X0)){\unicdcdcdhd}(m1\_subset\_1~(k4\_t\_0topsp~\\
X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~(\\
k3\_t\_0topsp~X0))))))))\end{array}
\label{hyp:egehpflgedpfehpfadehpgahdhah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))))){\unicdcdcdhd}(m1\_subset\_1~X3~X0))){\unicdbdjdcd}(m1\_subset\_1~(\\
k3\_funct\_2~X0~X1~X2~X3)~X1)\end{array}
\label{hyp:egehpflgddpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdbdjdcd}((\preoh v1\_xboole\_0~\\
(k2\_t\_0topsp~X0)){\unicdcdcdhd}(m1\_eqrel\_1~(k2\_t\_0topsp~X0)~(u1\_struct\_0~\\
X0)))\end{array}
\label{hyp:egehpflgcdpfehpfadehpgahdhah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdbdjdcd}((v1\_partfun1~\\
(k1\_t\_0topsp~X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}((v3\_relat\_2~(k1\_t\_0topsp~\\
X0)){\unicdcdcdhd}((v8\_relat\_2~(k1\_t\_0topsp~X0)){\unicdcdcdhd}(m1\_subset\_1~(k1\_t\_0topsp~\\
X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)))))))\end{array}
\label{hyp:egehpflgbdpfehpfadehpgahdhah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdcdcdhd}\\
(m1\_eqrel\_1~X1~(u1\_struct\_0~X0))){\unicdbdjdcd}((v1\_pre\_topc~(k11\_borsuk\_1~\\
X0~X1)){\unicdcdcdhd}((v2\_pre\_topc~(k11\_borsuk\_1~X0~X1)){\unicdcdcdhd}(l1\_pre\_topc~(k11\_borsuk\_1~\\
X0~X1))))\end{array}
\label{hyp:egehpflgbdbdpfcgpgchdhfhlgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_eqrel\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_pre\_topc~X2){\unicdcdcdhd}\\
((v2\_pre\_topc~X2){\unicdcdcdhd}(l1\_pre\_topc~X2))){\unicdbdjdcd}((X2=k11\_borsuk\_1~X0~X1){\unicdbdjded}\\
((u1\_struct\_0~X2=X1){\unicdcdcdhd}(u1\_pre\_topc~X2=ReplSep~(toset~({\uniddcgcg} X3 : \\
\iota .  m1\_subset\_1~X3~(k1\_zfmisc\_1~X1)))~({\uniddcgcg} X3 : \iota .  k3\_tarski~\\
X3 \in u1\_pre\_topc~X0)~({\uniddcgcg} X3 : \iota .  X3))))))\end{array}
\label{hyp:eghdpfcgpgchdhfhlgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}(k4\_t\_0topsp~X0=k12\_borsuk\_1~X0~(k2\_t\_0topsp~X0))\end{array}
\label{hyp:eggdpfehpfadehpgahdhah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}(k3\_t\_0topsp~X0=k11\_borsuk\_1~X0~(k2\_t\_0topsp~X0))\end{array}
\label{hyp:egfdpfehpfadehpgahdhah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdbdjdcd}(k2\_t\_0topsp~\\
X0=k8\_eqrel\_1~(u1\_struct\_0~X0)~(k1\_t\_0topsp~X0))\end{array}
\label{hyp:egedpfehpfadehpgahdhah}
\end{equation}
\begin{theorem}\label{thm:ehedpfehpfadehpgahdhah}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(k3\_funct\_2~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~(k3\_t\_0topsp~X0))~(k4\_t\_0topsp~\\
X0)~X1=k6\_eqrel\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(k1\_t\_0topsp~\\
X0)~X1))\end{array}$$
\end{theorem}
\end{document}
