\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{t42\_topgen\_3 (TMUypQQwu9TmwGD4aF6J5pTKZuuuQPazf5d)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_topgen\_3 : {{\iota}{\unicdbdjdcd}{{\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 $ k1\_tops\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k15\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k14\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ 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}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((m1\_subset\_1~\\
X3~X0){\unicdcdcdhd}(m1\_subset\_1~X4~X0)){\unicdbdjdcd}(k15\_funcop\_1~X0~X1~X2~X3~X4=k14\_funcop\_1~\\
X1~X2~X3~X4)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdfdpfggfhogdgpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(m1\_subset\_1~(k8\_subset\_1~X0~X1~X2)~(k1\_zfmisc\_1~X0))\end{array}
\label{hyp:egehpflgidpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_pre\_topc~(k7\_topgen\_3~X0~X1)){\unicdcdcdhd}((v2\_pre\_topc~\\
(k7\_topgen\_3~X0~X1)){\unicdcdcdhd}(l1\_pre\_topc~(k7\_topgen\_3~X0~X1)))\end{array}
\label{hyp:egehpflghdpfehpgahhgfgogpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_pre\_topc~X2){\unicdcdcdhd}((v2\_pre\_topc~\\
X2){\unicdcdcdhd}(l1\_pre\_topc~X2))){\unicdbdjdcd}((X2=k7\_topgen\_3~X0~X1){\unicdbdjded}((u1\_struct\_0~\\
X2=X0){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X2))){\unicdbdjdcd}(k1\_tops\_1~X2~X3=k15\_funcop\_1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X2))~X3~X0~X3~(k8\_subset\_1~(u1\_struct\_0~X2)~X3~X1)))))\end{array}
\label{hyp:egidpfehpgahhgfgogpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((X0=X1){\unicdbdjdcd}(k14\_funcop\_1~\\
X0~X1~X2~X3=X2)){\unicdcdcdhd}((X0{\unicdcdgdad}X1){\unicdbdjdcd}(k14\_funcop\_1~X0~X1~X2~X3=X3))\end{array}
\label{hyp:egidpfggfhogdgpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)){\unicdbdjdcd}((v1\_subset\_1~\\
X1~X0){\unicdbdjded}(X1{\unicdcdgdad}X0))\end{array}
\label{hyp:eggdpfdhfhcgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedcdpfehpgahhgfgogpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_subset\_1~\\
X2~(u1\_struct\_0~(k7\_topgen\_3~X0~X1))){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k7\_topgen\_3~X0~X1))))){\unicdbdjdcd}(k1\_tops\_1~(k7\_topgen\_3~\\
X0~X1)~X2=k8\_subset\_1~(u1\_struct\_0~(k7\_topgen\_3~X0~X1))~X2~X1))\end{array}$$
\end{theorem}
\end{document}
