\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{t31\_topalg\_6 (TMWiqGj899x1NeG9sxMJK6ktqrKMi1Urdiy)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_topalg\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k4\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k2\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_topalg\_6 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_topalg\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_topalg\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_xxreal\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xxreal\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xxreal\_1 : {{\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 $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_topalg\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_topalg\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v2\_membered~X0){\unicdbdjdcd}((\preoh v1\_xboole\_0~X0){\unicdbdjded}(r1\_xxreal\_0~\\
(k2\_xxreal\_2~X0)~(k1\_xxreal\_2~X0)))\end{array}
\label{hyp:ehedadpfihihchfgbgmgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}((X0 \in \\
k9\_xtuple\_0~X1){\unicdbdjdcd}(k1\_funct\_1~X1~X0 \in k10\_xtuple\_0~X1))\end{array}
\label{hyp:ehddpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v7\_topalg\_6~X1~X0){\unicdcdcdhd}(m2\_subset\_1~X1~(k4\_partfun1~k1\_numbers~\\
(k2\_struct\_0~X0))~(k1\_topalg\_6~X0))){\unicdbdjdcd}(k9\_xtuple\_0~X1=k1\_rcomp\_1~\\
(k2\_xxreal\_2~(k9\_xtuple\_0~X1))~(k1\_xxreal\_2~(k9\_xtuple\_0~X1))))\end{array}
\label{hyp:ehcdhdpfehpgahbgmghgpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xxreal\_0~X2){\unicdbdjdcd}((X0 \in k1\_xxreal\_1~X1~X2){\unicdbdjded}((r1\_xxreal\_0~X1~X0){\unicdcdcdhd}\\
(r1\_xxreal\_0~X0~X2)))))\end{array}
\label{hyp:ehbdpfihihchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xxreal\_0~X0){\unicdcdcdhd}(v1\_xxreal\_0~X1)){\unicdbdjdcd}(\\
r1\_xxreal\_0~X0~X0)\end{array}
\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~X0~X1){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xreal\_0~X0){\unicdcdcdhd}(v1\_xreal\_0~X1)){\unicdbdjdcd}(k1\_rcomp\_1~\\
X0~X1=k1\_xxreal\_1~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfchdgpgngahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdcdcdhd}\\
((v5\_topalg\_6~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_topalg\_6~X0)))){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(k9\_xtuple\_0~X1))\end{array}
\label{hyp:ggdgjdpfehpgahbgmghgpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l1\_pre\_topc~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_topalg\_6~\\
X0))){\unicdbdjdcd}(v3\_membered~(k9\_xtuple\_0~X1))\end{array}
\label{hyp:ggdgidpfehpgahbgmghgpfgd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_pre\_topc}~{X0}})}{\unicdbdjdcd}{({\preoh{{{v1\_xboole\_0}~{({{k1\_topalg\_6}~{X0}})}}}})}}}\label{hyp:ggdghdpfehpgahbgmghgpfgd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{v4\_funct\_1}~{({{{k4\_partfun1}~{X0}}~{X1}})}}}}\label{hyp:ggdgedpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {\preoh{{{v1\_xboole\_0}~{({{{k4\_partfun1}~{X0}}~{X1}})}}}}}}\label{hyp:ggdgbdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdcdcdhd}\\
((v6\_topalg\_6~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_topalg\_6~X0)))){\unicdbdjdcd}((v1\_xreal\_0~\\
(k1\_xxreal\_2~(k9\_xtuple\_0~X1))){\unicdcdcdhd}(v1\_xxreal\_0~(k1\_xxreal\_2~(\\
k9\_xtuple\_0~X1))))\end{array}
\label{hyp:ggdgbdcdpfehpgahbgmghgpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdcdcdhd}\\
((v5\_topalg\_6~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_topalg\_6~X0)))){\unicdbdjdcd}((v1\_xreal\_0~\\
(k2\_xxreal\_2~(k9\_xtuple\_0~X1))){\unicdcdcdhd}(v1\_xxreal\_0~(k2\_xxreal\_2~(\\
k9\_xtuple\_0~X1))))\end{array}
\label{hyp:ggdgbdadpfehpgahbgmghgpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}(m1\_subset\_1~(k1\_topalg\_6~X0)~(k1\_zfmisc\_1~\\
(k4\_partfun1~k1\_numbers~(k2\_struct\_0~X0))))\end{array}
\label{hyp:egehpflgbdpfehpgahbgmghgpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v5\_topalg\_6~X1~X0){\unicdcdcdhd}(m2\_subset\_1~X1~(k4\_partfun1~k1\_numbers~\\
(k2\_struct\_0~X0))~(k1\_topalg\_6~X0))){\unicdbdjdcd}(k2\_topalg\_6~X0~X1=k1\_funct\_1~\\
X1~(k2\_xxreal\_2~(k9\_xtuple\_0~X1))))\end{array}
\label{hyp:egjdpfehpgahbgmghgpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v6\_topalg\_6~X1~X0){\unicdcdcdhd}(m2\_subset\_1~X1~(k4\_partfun1~k1\_numbers~\\
(k2\_struct\_0~X0))~(k1\_topalg\_6~X0))){\unicdbdjdcd}(k3\_topalg\_6~X0~X1=k1\_funct\_1~\\
X1~(k1\_xxreal\_2~(k9\_xtuple\_0~X1))))\end{array}
\label{hyp:egbdadpfehpgahbgmghgpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_topalg\_6~\\
X0)){\unicdbdjdcd}((v7\_topalg\_6~X1~X0){\unicdbdjdcd}((v5\_topalg\_6~X1~X0){\unicdcdcdhd}(v6\_topalg\_6~\\
X1~X0))))\end{array}
\label{hyp:dgdgjdpfehpgahbgmghgpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v4\_funct\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v4\_funct\_1~X1))\end{array}
\label{hyp:dgdgjdpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v4\_funct\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}(\\
(v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)))\end{array}
\label{hyp:dgdgidpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v3\_membered}~{X0}})}{\unicdbdjdcd}{({{v2\_membered}~{X0}})}}}\label{hyp:dgdgedpfngfgngcgfgchfgeg}
\end{equation}
\begin{theorem}\label{thm:ehddbdpfehpgahbgmghgpfgd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v7\_topalg\_6~X1~X0){\unicdcdcdhd}(m2\_subset\_1~X1~(k4\_partfun1~k1\_numbers~\\
(k2\_struct\_0~X0))~(k1\_topalg\_6~X0))){\unicdbdjdcd}((k2\_topalg\_6~X0~X1 \in k10\_xtuple\_0~\\
X1){\unicdcdcdhd}(k3\_topalg\_6~X0~X1 \in k10\_xtuple\_0~X1)))\end{array}$$
\end{theorem}
\end{document}
