\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{t5\_topalg\_4 (TMSxL5NC79xeEKTB62obC78ykehskG367Tm)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_algstr\_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 $ v1\_group\_6 : {{\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 $ v3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_topalg\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k2\_group\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k10\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l3\_algstr\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l3\_algstr\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~\\
X2){\unicdcdcdhd}(l3\_algstr\_0~X2)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((\preoh v2\_struct\_0~X3){\unicdcdcdhd}(l3\_algstr\_0~\\
X3)){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X2)){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X2)))))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_funct\_1~\\
X5){\unicdcdcdhd}((v1\_funct\_2~X5~(u1\_struct\_0~X1)~(u1\_struct\_0~X3)){\unicdcdcdhd}(m1\_subset\_1~\\
X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X1)~(u1\_struct\_0~X3)))))){\unicdbdjdcd}\\
(((v2\_funct\_2~X4~(u1\_struct\_0~X2)){\unicdcdcdhd}(v2\_funct\_2~X5~(u1\_struct\_0~\\
X3))){\unicdbdjdcd}(v2\_funct\_2~(k1\_topalg\_4~X0~X1~X2~X3~X4~X5)~(u1\_struct\_0~(\\
k2\_group\_7~(k2\_tarski~np\_\_1~np\_\_2)~(k10\_finseq\_1~X2~X3))))))))))\end{array}
\label{hyp:ehedpfehpgahbgmghgpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l3\_algstr\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l3\_algstr\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~\\
X2){\unicdcdcdhd}(l3\_algstr\_0~X2)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((\preoh v2\_struct\_0~X3){\unicdcdcdhd}(l3\_algstr\_0~\\
X3)){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X2)){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X2)))))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_funct\_1~\\
X5){\unicdcdcdhd}((v1\_funct\_2~X5~(u1\_struct\_0~X1)~(u1\_struct\_0~X3)){\unicdcdcdhd}(m1\_subset\_1~\\
X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X1)~(u1\_struct\_0~X3)))))){\unicdbdjdcd}\\
(((v2\_funct\_1~X4){\unicdcdcdhd}(v2\_funct\_1~X5)){\unicdbdjdcd}(v2\_funct\_1~(k1\_topalg\_4~\\
X0~X1~X2~X3~X4~X5))))))))\end{array}
\label{hyp:ehddpfehpgahbgmghgpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l3\_algstr\_0~X0)){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
(l3\_algstr\_0~X1)){\unicdcdcdhd}(((\preoh v2\_struct\_0~X2){\unicdcdcdhd}(l3\_algstr\_0~X2)){\unicdcdcdhd}((\\
(\preoh v2\_struct\_0~X3){\unicdcdcdhd}(l3\_algstr\_0~X3)){\unicdcdcdhd}(((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~\\
X4~(u1\_struct\_0~X0)~(u1\_struct\_0~X2)){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X2)))))){\unicdcdcdhd}((v1\_funct\_1~\\
X5){\unicdcdcdhd}((v1\_funct\_2~X5~(u1\_struct\_0~X1)~(u1\_struct\_0~X3)){\unicdcdcdhd}(m1\_subset\_1~\\
X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X1)~(u1\_struct\_0~X3))))))))))){\unicdbdjdcd}\\
((v1\_funct\_1~(k1\_topalg\_4~X0~X1~X2~X3~X4~X5)){\unicdcdcdhd}((v1\_funct\_2~(k1\_topalg\_4~\\
X0~X1~X2~X3~X4~X5)~(u1\_struct\_0~(k2\_group\_7~(k2\_tarski~np\_\_1~np\_\_2)~\\
(k10\_finseq\_1~X0~X1)))~(u1\_struct\_0~(k2\_group\_7~(k2\_tarski~np\_\_1~\\
np\_\_2)~(k10\_finseq\_1~X2~X3)))){\unicdcdcdhd}(m1\_subset\_1~(k1\_topalg\_4~X0~X1~\\
X2~X3~X4~X5)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~(k2\_group\_7~\\
(k2\_tarski~np\_\_1~np\_\_2)~(k10\_finseq\_1~X0~X1)))~(u1\_struct\_0~(k2\_group\_7~\\
(k2\_tarski~np\_\_1~np\_\_2)~(k10\_finseq\_1~X2~X3))))))))\end{array}
\label{hyp:egehpflgbdpfehpgahbgmghgpfed}
\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\_funct\_1~X2){\unicdcdcdhd}(v3\_funct\_2~X2~X0~X1)){\unicdbdjdcd}\\
((v1\_funct\_1~X2){\unicdcdcdhd}((v2\_funct\_1~X2){\unicdcdcdhd}(v2\_funct\_2~X2~X1))))\end{array}
\label{hyp:dgdgfdpfggfhogdgehpfcd}
\end{equation}
\begin{theorem}\label{thm:ehfdpfehpgahbgmghgpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_group\_1~\\
X1){\unicdcdcdhd}((v3\_group\_1~X1){\unicdcdcdhd}(l3\_algstr\_0~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~\\
X2){\unicdcdcdhd}((v2\_group\_1~X2){\unicdcdcdhd}((v3\_group\_1~X2){\unicdcdcdhd}(l3\_algstr\_0~X2)))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((\preoh v2\_struct\_0~X3){\unicdcdcdhd}((v2\_group\_1~X3){\unicdcdcdhd}((v3\_group\_1~\\
X3){\unicdcdcdhd}(l3\_algstr\_0~X3)))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~\\
X4~(u1\_struct\_0~X0)~(u1\_struct\_0~X2)){\unicdcdcdhd}((v1\_group\_6~X4~X0~X2){\unicdcdcdhd}(\\
m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X2))))))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_funct\_1~X5){\unicdcdcdhd}((v1\_funct\_2~X5~(u1\_struct\_0~\\
X1)~(u1\_struct\_0~X3)){\unicdcdcdhd}((v1\_group\_6~X5~X1~X3){\unicdcdcdhd}(m1\_subset\_1~X5~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X1)~(u1\_struct\_0~X3))))))){\unicdbdjdcd}\\
(((v3\_funct\_2~X4~(u1\_struct\_0~X0)~(u1\_struct\_0~X2)){\unicdcdcdhd}(v3\_funct\_2~\\
X5~(u1\_struct\_0~X1)~(u1\_struct\_0~X3))){\unicdbdjdcd}(v3\_funct\_2~(k1\_topalg\_4~\\
X0~X1~X2~X3~X4~X5)~(u1\_struct\_0~(k2\_group\_7~(k2\_tarski~np\_\_1~np\_\_2)~\\
(k10\_finseq\_1~X0~X1)))~(u1\_struct\_0~(k2\_group\_7~(k2\_tarski~np\_\_1~\\
np\_\_2)~(k10\_finseq\_1~X2~X3))))))))))\end{array}$$
\end{theorem}
\end{document}
