\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{t27\_topreal1 (TMcAVdZbL24rEVAFBHFfznENV527Zj6iq2x)}
\maketitle
Let $ v1\_xboole\_0 : {{\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 $ k15\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ v5\_topreal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_topreal1 : {\iota}$ be given.
Let $ k4\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k9\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k19\_euclid : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_topreal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_topreal1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v6\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdaddd} X0 .  (m2\_finseq\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdcdcdhd}\\
({\unicdcdaddd} X1 .  (m2\_finseq\_1~X1~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdcdcdhd}\\
((v4\_topreal1~X0){\unicdcdcdhd}((v4\_topreal1~X1){\unicdcdcdhd}((k1\_topreal1=k4\_subset\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~(k3\_topreal1~np\_\_2~X0)~(k3\_topreal1~\\
np\_\_2~X1)){\unicdcdcdhd}((k9\_subset\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~(k3\_topreal1~\\
np\_\_2~X0)~(k3\_topreal1~np\_\_2~X1)=k2\_tarski~(k19\_euclid~k6\_numbers~\\
k6\_numbers)~(k19\_euclid~np\_\_1~np\_\_1)){\unicdcdcdhd}((k7\_partfun1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~X0~np\_\_1=k19\_euclid~k6\_numbers~k6\_numbers){\unicdcdcdhd}\\
((k7\_partfun1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~X0~(k3\_finseq\_1~\\
X0)=k19\_euclid~np\_\_1~np\_\_1){\unicdcdcdhd}((k7\_partfun1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~X1~np\_\_1=k19\_euclid~k6\_numbers~k6\_numbers){\unicdcdcdhd}(k7\_partfun1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~X1~(k3\_finseq\_1~X1)=k19\_euclid~\\
np\_\_1~np\_\_1)))))))))\end{array}
\label{hyp:ehcdedpfehpgahchfgbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_2){\unicdcdcdhd}(m2\_subset\_1~np\_\_2~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_2~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_2~k1\_numbers))\end{array}
\label{hyp:dhahdgcdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m2\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjded}{({{{m1\_finseq\_1}~{X1}}~{X0}})}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{v6\_membered}~{k4\_ordinal1}}\label{hyp:ggdggdpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(m1\_finseq\_1~X1~(u1\_struct\_0~\\
(k15\_euclid~X0)))){\unicdbdjdcd}(m1\_subset\_1~(k3\_topreal1~X0~X1)~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k15\_euclid~X0))))\end{array}
\label{hyp:egehpflgddpfehpgahchfgbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2)))){\unicdbdjdcd}((v5\_topreal1~X0){\unicdbdjded}({\unicdcdaddd} X1 .  (m2\_finseq\_1~X1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))){\unicdcdcdhd}((v4\_topreal1~X1){\unicdcdcdhd}(X0=k3\_topreal1~np\_\_2~\\
X1))))\end{array}
\label{hyp:egjdpfehpgahchfgbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2)))){\unicdbdjdcd}((v5\_topreal1~X0){\unicdbdjdcd}(\preoh v1\_xboole\_0~X0))\end{array}
\label{hyp:dgdgbdpfehpgahchfgbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v6\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
(v7\_ordinal1~X1))\end{array}
\label{hyp:dgdgbdhdpfngfgngcgfgchfgeg}
\end{equation}
\begin{theorem}\label{thm:ehcdhdpfehpgahchfgbgmgbd}
$$\begin{array}{c}{\unicdcdaddd} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(\\
u1\_struct\_0~(k15\_euclid~np\_\_2))))){\unicdcdcdhd}({\unicdcdaddd} X1 .  ((\preoh v1\_xboole\_0~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))))){\unicdcdcdhd}\\
((v5\_topreal1~X0){\unicdcdcdhd}((v5\_topreal1~X1){\unicdcdcdhd}((k1\_topreal1=k4\_subset\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~X0~X1){\unicdcdcdhd}(k9\_subset\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~X0~X1=k2\_tarski~(k19\_euclid~k6\_numbers~k6\_numbers)~\\
(k19\_euclid~np\_\_1~np\_\_1))))))\end{array}$$
\end{theorem}
\end{document}
