\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=}
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\newcommand\unicdcdcdjd{\cap}
\newcommand\unicdcdadad{\forall}
\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t50\_fintopo6 (TMQrkjXYMEX9Kfo4xWP24KAExqY8wD17cV9)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\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 $ v3\_fintopo6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r3\_fintopo6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ v2\_fintopo6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m2\_finseq\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
(\preoh (v2\_fintopo6~X1~X0){\unicdcdcdhd}((r1\_tarski~(k2\_relset\_1~(u1\_struct\_0~\\
X0)~X1)~X2){\unicdcdcdhd}((k1\_funct\_1~X1~np\_\_1=X3){\unicdcdcdhd}((k1\_funct\_1~X1~(k3\_finseq\_1~\\
X1)=X4){\unicdcdcdhd}({\unicdcdadad} X5 .  (m2\_finseq\_1~X5~(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (v2\_fintopo6~\\
X5~X0){\unicdcdcdhd}((r1\_tarski~(k2\_relset\_1~(u1\_struct\_0~X0)~X5)~X2){\unicdcdcdhd}((k1\_funct\_1~\\
X5~np\_\_1=X3){\unicdcdcdhd}((k1\_funct\_1~X5~(k3\_finseq\_1~X5)=X4){\unicdcdcdhd}({\unicdcdadad} X6 .  \\
(m2\_finseq\_1~X6~(u1\_struct\_0~X0)){\unicdbdjdcd}(((v2\_fintopo6~X6~X0){\unicdcdcdhd}((r1\_tarski~\\
(k2\_relset\_1~(u1\_struct\_0~X0)~X6)~X2){\unicdcdcdhd}((k1\_funct\_1~X6~np\_\_1=X3){\unicdcdcdhd}\\
(k1\_funct\_1~X6~(k3\_finseq\_1~X6)=X4)))){\unicdbdjdcd}(r1\_xxreal\_0~(k3\_finseq\_1~\\
X5)~(k3\_finseq\_1~X6)))))))))))))))))\end{array}
\label{hyp:mggdbdpfggjgogehpgahpggd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m2\_finseq\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
((r3\_fintopo6~X0~X1~X2~X3~X4){\unicdbdjded}((v2\_fintopo6~X1~X0){\unicdcdcdhd}((r1\_tarski~\\
(k2\_relset\_1~(u1\_struct\_0~X0)~X1)~X2){\unicdcdcdhd}((k1\_funct\_1~X1~np\_\_1=X3){\unicdcdcdhd}\\
((k1\_funct\_1~X1~(k3\_finseq\_1~X1)=X4){\unicdcdcdhd}({\unicdcdadad} X5 .  (m2\_finseq\_1~\\
X5~(u1\_struct\_0~X0)){\unicdbdjdcd}(((v2\_fintopo6~X5~X0){\unicdcdcdhd}((r1\_tarski~(k2\_relset\_1~\\
(u1\_struct\_0~X0)~X5)~X2){\unicdcdcdhd}((k1\_funct\_1~X5~np\_\_1=X3){\unicdcdcdhd}(k1\_funct\_1~\\
X5~(k3\_finseq\_1~X5)=X4)))){\unicdbdjdcd}(r1\_xxreal\_0~(k3\_finseq\_1~X1)~(k3\_finseq\_1~\\
X5)))))))))))))\end{array}
\label{hyp:egidpfggjgogehpgahpggd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}((v3\_fintopo6~\\
X1~X0){\unicdbdjded}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (X2 \in X1){\unicdcdcdhd}((X3 \in X1){\unicdcdcdhd}({\unicdcdadad} X4 .  \\
(m2\_finseq\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (v2\_fintopo6~X4~X0){\unicdcdcdhd}((r1\_tarski~\\
(k2\_relset\_1~(u1\_struct\_0~X0)~X4)~X1){\unicdcdcdhd}((k1\_funct\_1~X4~np\_\_1=X2){\unicdcdcdhd}\\
(k1\_funct\_1~X4~(k3\_finseq\_1~X4)=X3)))))))))))\end{array}
\label{hyp:eghdpfggjgogehpgahpggd}
\end{equation}
\begin{theorem}\label{thm:ehfdadpfggjgogehpgahpggd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}((v3\_fintopo6~\\
X1~X0){\unicdbdjded}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (X2 \in X1){\unicdcdcdhd}((X3 \in X1){\unicdcdcdhd}({\unicdcdadad} X4 .  \\
(m2\_finseq\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh r3\_fintopo6~X0~X4~X1~X2~X3))))))))\end{array}$$
\end{theorem}
\end{document}
