\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{t58\_topreal9 (TMMyhcrD72L1qxvMb8s33Rc3vx816FPvVb9)}
\maketitle
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ 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 $ m2\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k1\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k19\_euclid : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_real\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k23\_rvsum\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k7\_square\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_quin\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k18\_rvsum\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k11\_euclid : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_euclid : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k9\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_square\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_jgraph\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_topreal9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_jgraph\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k3\_topreal9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_topreal9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_numbers : {\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.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xreal\_0~X2){\unicdbdjdcd}(k3\_topreal9~np\_\_2~(k19\_euclid~X0~X1)~X2=k5\_jgraph\_6~\\
X0~X1~X2)))\end{array}
\label{hyp:ehfdcdpfehpgahchfgbgmgjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xreal\_0~X2){\unicdbdjdcd}(k1\_topreal9~np\_\_2~(k19\_euclid~X0~X1)~X2=k6\_jgraph\_6~\\
X0~X1~X2)))\end{array}
\label{hyp:ehfdadpfehpgahchfgbgmgjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~\\
X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (v1\_xreal\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(u1\_struct\_0~(k15\_euclid~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(\\
u1\_struct\_0~(k15\_euclid~X0))){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~\\
(k15\_euclid~X0))){\unicdbdjdcd}({\unicdcdadad} X6 .  (m2\_finseq\_2~X6~k1\_numbers~(k1\_euclid~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X7 .  (m2\_finseq\_2~X7~k1\_numbers~(k1\_euclid~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X8 .  (m2\_finseq\_2~X8~k1\_numbers~(k1\_euclid~X0)){\unicdbdjdcd}(\preoh (X6=\\
X3){\unicdcdcdhd}((X7=X4){\unicdcdcdhd}((X8=X5){\unicdcdcdhd}((X3{\unicdcdgdad}X4){\unicdcdcdhd}((X3 \in k1\_topreal9~X0~X5~X1){\unicdcdcdhd}\\
((X2=k10\_real\_1~(k7\_real\_1~(k1\_real\_1~(k8\_real\_1~np\_\_2~(k23\_rvsum\_1~\\
(k5\_algstr\_0~(k15\_euclid~X0)~X4~X3)~(k5\_algstr\_0~(k15\_euclid~X0)~\\
X3~X5))))~(k7\_square\_1~(k2\_quin\_1~(k18\_rvsum\_1~(k11\_euclid~X0~\\
(k8\_euclid~X0~X7~X6)))~(k8\_real\_1~np\_\_2~(k23\_rvsum\_1~(k5\_algstr\_0~\\
(k15\_euclid~X0)~X4~X3)~(k5\_algstr\_0~(k15\_euclid~X0)~X3~X5)))~(k9\_real\_1~\\
(k18\_rvsum\_1~(k11\_euclid~X0~(k8\_euclid~X0~X6~X8)))~(k3\_square\_1~\\
X1)))))~(k8\_real\_1~np\_\_2~(k18\_rvsum\_1~(k11\_euclid~X0~(k8\_euclid~\\
X0~X7~X6))))){\unicdcdcdhd}({\unicdcdadad} X9 .  (m1\_subset\_1~X9~(u1\_struct\_0~(k15\_euclid~\\
X0))){\unicdbdjdcd}(\preoh (k1\_tarski~X9=k9\_subset\_1~(u1\_struct\_0~(k15\_euclid~\\
X0))~(k4\_topreal9~X0~X3~X4)~(k3\_topreal9~X0~X5~X1)){\unicdcdcdhd}(X9=k3\_rlvect\_1~\\
(k15\_euclid~X0)~(k1\_rlvect\_1~(k15\_euclid~X0)~X3~(k9\_real\_1~np\_\_1~\\
X2))~(k1\_rlvect\_1~(k15\_euclid~X0)~X4~X2))))))))))))))))))\end{array}
\label{hyp:ehddhdpfehpgahchfgbgmgjd}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xreal\_0~X0){\unicdcdcdhd}(v1\_xreal\_0~X1)){\unicdbdjdcd}(m1\_subset\_1~\\
(k19\_euclid~X0~X1)~(u1\_struct\_0~(k15\_euclid~np\_\_2)))\end{array}
\label{hyp:egehpflgbdjdpffgfhdgmgjgeg}
\end{equation}
\begin{theorem}\label{thm:ehfdidpfehpgahchfgbgmgjd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xreal\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_xreal\_0~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~\\
X5~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}({\unicdcdadad} X6 .  (m2\_finseq\_2~\\
X6~k1\_numbers~(k1\_euclid~np\_\_2)){\unicdbdjdcd}({\unicdcdadad} X7 .  (m2\_finseq\_2~X7~\\
k1\_numbers~(k1\_euclid~np\_\_2)){\unicdbdjdcd}({\unicdcdadad} X8 .  (m2\_finseq\_2~X8~k1\_numbers~\\
(k1\_euclid~np\_\_2)){\unicdbdjdcd}(\preoh (X6=X4){\unicdcdcdhd}((X7=X5){\unicdcdcdhd}((X8=k19\_euclid~X0~X1){\unicdcdcdhd}\\
((X2=k10\_real\_1~(k7\_real\_1~(k1\_real\_1~(k8\_real\_1~np\_\_2~(k23\_rvsum\_1~\\
(k5\_algstr\_0~(k15\_euclid~np\_\_2)~X5~X4)~(k5\_algstr\_0~(k15\_euclid~\\
np\_\_2)~X4~(k19\_euclid~X0~X1)))))~(k7\_square\_1~(k2\_quin\_1~(k18\_rvsum\_1~\\
(k11\_euclid~np\_\_2~(k8\_euclid~np\_\_2~X7~X6)))~(k8\_real\_1~np\_\_2~(k23\_rvsum\_1~\\
(k5\_algstr\_0~(k15\_euclid~np\_\_2)~X5~X4)~(k5\_algstr\_0~(k15\_euclid~\\
np\_\_2)~X4~(k19\_euclid~X0~X1))))~(k9\_real\_1~(k18\_rvsum\_1~(k11\_euclid~\\
np\_\_2~(k8\_euclid~np\_\_2~X6~X8)))~(k3\_square\_1~X3)))))~(k8\_real\_1~\\
np\_\_2~(k18\_rvsum\_1~(k11\_euclid~np\_\_2~(k8\_euclid~np\_\_2~X7~X6))))){\unicdcdcdhd}\\
((X4{\unicdcdgdad}X5){\unicdcdcdhd}((X4 \in k6\_jgraph\_6~X0~X1~X3){\unicdcdcdhd}({\unicdcdadad} X9 .  (m1\_subset\_1~\\
X9~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}(\preoh (k1\_tarski~X9=k9\_subset\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~(k4\_topreal9~np\_\_2~X4~X5)~(k5\_jgraph\_6~\\
X0~X1~X3)){\unicdcdcdhd}(X9=k3\_rlvect\_1~(k15\_euclid~np\_\_2)~(k1\_rlvect\_1~(k15\_euclid~\\
np\_\_2)~X4~(k9\_real\_1~np\_\_1~X2))~(k1\_rlvect\_1~(k15\_euclid~np\_\_2)~\\
X5~X2))))))))))))))))))\end{array}$$
\end{theorem}
\end{document}
