\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{t14\_topreala (TMSdUh5LQZeiHDsAmCUAig8hTt1bWWkBZEw)}
\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 $ 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 $ 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 $ v2\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_t\_0topsp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v5\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_tops\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_funct\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k3\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}((v2\_funct\_1~X0){\unicdbdjdcd}\\
(k2\_funct\_1~(k2\_funct\_1~X0)=X0))\end{array}
\label{hyp:ehedddpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~\\
X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)))))){\unicdbdjdcd}\\
(((v2\_funct\_1~X2){\unicdcdcdhd}(v2\_funct\_2~X2~(u1\_struct\_0~X1))){\unicdbdjdcd}((r2\_funct\_2~\\
(u1\_struct\_0~X1)~(u1\_struct\_0~X1)~(k1\_partfun1~(u1\_struct\_0~X1)~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)~(k2\_tops\_2~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X1)~X2)~X2)~(k3\_struct\_0~X1)){\unicdcdcdhd}((\\
r2\_funct\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(k1\_partfun1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X1)~(u1\_struct\_0~X1)~(u1\_struct\_0~X0)~X2~(k2\_tops\_2~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X1)~X2))~(k3\_struct\_0~X0)){\unicdcdcdhd}((v2\_funct\_1~\\
(k2\_tops\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)~X2)){\unicdcdcdhd}(v2\_funct\_2~\\
(k2\_tops\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)~X2)~(u1\_struct\_0~\\
X0))))))))\end{array}
\label{hyp:ehedbdpfhgchdgbgehpfbd}
\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 v2\_struct\_0~X1){\unicdcdcdhd}((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X1)))))){\unicdbdjdcd}(((v2\_funct\_1~X2){\unicdcdcdhd}(v2\_funct\_2~\\
X2~(u1\_struct\_0~X1))){\unicdbdjdcd}((v5\_pre\_topc~X2~X0~X1){\unicdbdjded}(v1\_t\_0topsp~(k2\_tops\_2~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X1)~X2)~X1~X0)))))\end{array}
\label{hyp:ehbdddpfehpgahchfgbgmgbg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v2\_funct\_1~X0))){\unicdbdjdcd}\\
((v1\_relat\_1~(k2\_funct\_1~X0)){\unicdcdcdhd}((v1\_funct\_1~(k2\_funct\_1~X0)){\unicdcdcdhd}\\
(v2\_funct\_1~(k2\_funct\_1~X0))))\end{array}
\label{hyp:ggdggdpfggfhogdgehpfbd}
\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 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))))){\unicdbdjdcd}\\
((v1\_funct\_1~(k2\_tops\_2~X0~X1~X2)){\unicdcdcdhd}((v1\_funct\_2~(k2\_tops\_2~X0~\\
X1~X2)~X1~X0){\unicdcdcdhd}(m1\_subset\_1~(k2\_tops\_2~X0~X1~X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X1~X0)))))\end{array}
\label{hyp:egehpflgcdpfehpgahdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))))){\unicdbdjdcd}\\
((v3\_funct\_2~X2~X0~X1){\unicdbdjdcd}(k2\_tops\_2~X0~X1~X2=k2\_funct\_1~X2))\end{array}
\label{hyp:egedpfehpgahdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(((v1\_funct\_1~X2){\unicdcdcdhd}((v2\_funct\_1~X2){\unicdcdcdhd}(v2\_funct\_2~\\
X2~X1))){\unicdbdjdcd}((v1\_funct\_1~X2){\unicdcdcdhd}(v3\_funct\_2~X2~X0~X1)))\end{array}
\label{hyp:dgdggdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(v1\_relat\_1~X2)\end{array}
\label{hyp:dgdgbdpfchfgmgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdedpfehpgahchfgbgmgbg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X1)))))){\unicdbdjdcd}(((v2\_funct\_1~X2){\unicdcdcdhd}(v2\_funct\_2~\\
X2~(u1\_struct\_0~X1))){\unicdbdjdcd}((v1\_t\_0topsp~X2~X0~X1){\unicdbdjded}(v5\_pre\_topc~(k2\_tops\_2~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X1)~X2)~X1~X0)))))\end{array}$$
\end{theorem}
\end{document}
