\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{t63\_topreal9 (TMJ2iDrs6ov4viqkWCyW3RABj2yXVppstr4)}
\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 $ 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 $ k10\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k19\_euclid : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_jgraph\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k7\_jgraph\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\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 $ k3\_topreal9 : {{\iota}{\unicdbdjdcd}{{\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 $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k14\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k11\_metric\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k10\_metric\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k2\_topreal9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ k4\_ordinal1 : {\iota}$ be given.
Let $ v6\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}(u1\_struct\_0~(k15\_euclid~X0)=u1\_struct\_0~\\
(k14\_euclid~X0))\end{array}
\label{hyp:ehidpfehpgahchfgbgmgdd}
\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}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~(k14\_euclid~\\
np\_\_2))){\unicdbdjdcd}((X3=k19\_euclid~X0~X1){\unicdbdjdcd}(k11\_metric\_1~(k14\_euclid~np\_\_2)~\\
X3~X2=k5\_jgraph\_6~X0~X1~X2)))))\end{array}
\label{hyp:ehedjdpfehpgahchfgbgmgjd}
\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}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~(k14\_euclid~\\
np\_\_2))){\unicdbdjdcd}((X3=k19\_euclid~X0~X1){\unicdbdjdcd}(k10\_metric\_1~(k14\_euclid~np\_\_2)~\\
X3~X2=k7\_jgraph\_6~X0~X1~X2)))))\end{array}
\label{hyp:ehedhdpfehpgahchfgbgmgjd}
\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=\\
k3\_rlvect\_1~(k15\_euclid~X0)~(k1\_rlvect\_1~(k15\_euclid~X0)~X3~(k10\_real\_1~\\
np\_\_1~np\_\_2))~(k1\_rlvect\_1~(k15\_euclid~X0)~X4~(k10\_real\_1~np\_\_1~\\
np\_\_2))){\unicdcdcdhd}((X7=X4){\unicdcdcdhd}((X8=X5){\unicdcdcdhd}((X3{\unicdcdgdad}X4){\unicdcdcdhd}((X3 \in k3\_topreal9~X0~X5~\\
X1){\unicdcdcdhd}((X4 \in k2\_topreal9~X0~X5~X1){\unicdcdcdhd}({\unicdcdadad} X9 .  (m1\_subset\_1~X9~(u1\_struct\_0~\\
(k15\_euclid~X0))){\unicdbdjdcd}(\preoh (X9{\unicdcdgdad}X3){\unicdcdcdhd}((k2\_tarski~X3~X9=k9\_subset\_1~(\\
u1\_struct\_0~(k15\_euclid~X0))~(k4\_topreal9~X0~X3~X4)~(k3\_topreal9~\\
X0~X5~X1)){\unicdcdcdhd}(((X4 \in k3\_topreal9~X0~X5~X1){\unicdbdjdcd}(X9=X4)){\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~(k3\_rlvect\_1~(k15\_euclid~X0)~(k1\_rlvect\_1~(\\
k15\_euclid~X0)~X3~(k10\_real\_1~np\_\_1~np\_\_2))~(k1\_rlvect\_1~(k15\_euclid~\\
X0)~X4~(k10\_real\_1~np\_\_1~np\_\_2))))~(k5\_algstr\_0~(k15\_euclid~X0)~\\
(k3\_rlvect\_1~(k15\_euclid~X0)~(k1\_rlvect\_1~(k15\_euclid~X0)~X3~(\\
k10\_real\_1~np\_\_1~np\_\_2))~(k1\_rlvect\_1~(k15\_euclid~X0)~X4~(k10\_real\_1~\\
np\_\_1~np\_\_2)))~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~(k3\_rlvect\_1~(k15\_euclid~X0)~(k1\_rlvect\_1~(\\
k15\_euclid~X0)~X3~(k10\_real\_1~np\_\_1~np\_\_2))~(k1\_rlvect\_1~(k15\_euclid~\\
X0)~X4~(k10\_real\_1~np\_\_1~np\_\_2))))~(k5\_algstr\_0~(k15\_euclid~X0)~\\
(k3\_rlvect\_1~(k15\_euclid~X0)~(k1\_rlvect\_1~(k15\_euclid~X0)~X3~(\\
k10\_real\_1~np\_\_1~np\_\_2))~(k1\_rlvect\_1~(k15\_euclid~X0)~X4~(k10\_real\_1~\\
np\_\_1~np\_\_2)))~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))))){\unicdbdjdcd}((X4 \in k3\_topreal9~X0~X5~\\
X1){\unicdcdcdid}(X9=k3\_rlvect\_1~(k15\_euclid~X0)~(k1\_rlvect\_1~(k15\_euclid~\\
X0)~(k3\_rlvect\_1~(k15\_euclid~X0)~(k1\_rlvect\_1~(k15\_euclid~X0)~\\
X3~(k10\_real\_1~np\_\_1~np\_\_2))~(k1\_rlvect\_1~(k15\_euclid~X0)~X4~(k10\_real\_1~\\
np\_\_1~np\_\_2)))~(k9\_real\_1~np\_\_1~X2))~(k1\_rlvect\_1~(k15\_euclid~\\
X0)~X4~X2))))))))))))))))))))))\end{array}
\label{hyp:ehddidpfehpgahchfgbgmgjd}
\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 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k15\_euclid~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~(k14\_euclid~X0))){\unicdbdjdcd}(\\
(X2=X3){\unicdbdjdcd}(k11\_metric\_1~(k14\_euclid~X0)~X3~X1=k3\_topreal9~X0~X2~\\
X1)))))\end{array}
\label{hyp:ehbdfdpfehpgahchfgbgmgjd}
\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 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k15\_euclid~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~(k14\_euclid~X0))){\unicdbdjdcd}(\\
(X2=X3){\unicdbdjdcd}(k10\_metric\_1~(k14\_euclid~X0)~X3~X1=k2\_topreal9~X0~X2~\\
X1)))))\end{array}
\label{hyp:ehbdedpfehpgahchfgbgmgjd}
\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}
{{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 .  ((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}
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:ehgdddpfehpgahchfgbgmgjd}
$$\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=k3\_rlvect\_1~(k15\_euclid~np\_\_2)~(k1\_rlvect\_1~\\
(k15\_euclid~np\_\_2)~X4~(k10\_real\_1~np\_\_1~np\_\_2))~(k1\_rlvect\_1~(\\
k15\_euclid~np\_\_2)~X5~(k10\_real\_1~np\_\_1~np\_\_2))){\unicdcdcdhd}((X7=X5){\unicdcdcdhd}((X8=\\
k19\_euclid~X0~X1){\unicdcdcdhd}((X4{\unicdcdgdad}X5){\unicdcdcdhd}((X4 \in k5\_jgraph\_6~X0~X1~X2){\unicdcdcdhd}((X5 \in k7\_jgraph\_6~\\
X0~X1~X2){\unicdcdcdhd}({\unicdcdadad} X9 .  (m1\_subset\_1~X9~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))){\unicdbdjdcd}(\preoh (X9{\unicdcdgdad}X4){\unicdcdcdhd}((k2\_tarski~X4~X9=k9\_subset\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~(k4\_topreal9~np\_\_2~X4~X5)~(k5\_jgraph\_6~X0~X1~\\
X2)){\unicdcdcdhd}(((X5 \in k3\_topreal9~np\_\_2~(k19\_euclid~X0~X1)~X2){\unicdbdjdcd}(X9=X5)){\unicdcdcdhd}\\
((X3=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~(k3\_rlvect\_1~(k15\_euclid~np\_\_2)~\\
(k1\_rlvect\_1~(k15\_euclid~np\_\_2)~X4~(k10\_real\_1~np\_\_1~np\_\_2))~(\\
k1\_rlvect\_1~(k15\_euclid~np\_\_2)~X5~(k10\_real\_1~np\_\_1~np\_\_2))))~\\
(k5\_algstr\_0~(k15\_euclid~np\_\_2)~(k3\_rlvect\_1~(k15\_euclid~np\_\_2)~\\
(k1\_rlvect\_1~(k15\_euclid~np\_\_2)~X4~(k10\_real\_1~np\_\_1~np\_\_2))~(\\
k1\_rlvect\_1~(k15\_euclid~np\_\_2)~X5~(k10\_real\_1~np\_\_1~np\_\_2)))~(\\
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~(k3\_rlvect\_1~(k15\_euclid~np\_\_2)~\\
(k1\_rlvect\_1~(k15\_euclid~np\_\_2)~X4~(k10\_real\_1~np\_\_1~np\_\_2))~(\\
k1\_rlvect\_1~(k15\_euclid~np\_\_2)~X5~(k10\_real\_1~np\_\_1~np\_\_2))))~\\
(k5\_algstr\_0~(k15\_euclid~np\_\_2)~(k3\_rlvect\_1~(k15\_euclid~np\_\_2)~\\
(k1\_rlvect\_1~(k15\_euclid~np\_\_2)~X4~(k10\_real\_1~np\_\_1~np\_\_2))~(\\
k1\_rlvect\_1~(k15\_euclid~np\_\_2)~X5~(k10\_real\_1~np\_\_1~np\_\_2)))~(\\
k19\_euclid~X0~X1))))~(k9\_real\_1~(k18\_rvsum\_1~(k11\_euclid~np\_\_2~\\
(k8\_euclid~np\_\_2~X6~X8)))~(k3\_square\_1~X2)))))~(k8\_real\_1~np\_\_2~\\
(k18\_rvsum\_1~(k11\_euclid~np\_\_2~(k8\_euclid~np\_\_2~X7~X6))))){\unicdbdjdcd}((\\
X5 \in k3\_topreal9~np\_\_2~(k19\_euclid~X0~X1)~X2){\unicdcdcdid}(X9=k3\_rlvect\_1~(\\
k15\_euclid~np\_\_2)~(k1\_rlvect\_1~(k15\_euclid~np\_\_2)~(k3\_rlvect\_1~\\
(k15\_euclid~np\_\_2)~(k1\_rlvect\_1~(k15\_euclid~np\_\_2)~X4~(k10\_real\_1~\\
np\_\_1~np\_\_2))~(k1\_rlvect\_1~(k15\_euclid~np\_\_2)~X5~(k10\_real\_1~np\_\_1~\\
np\_\_2)))~(k9\_real\_1~np\_\_1~X3))~(k1\_rlvect\_1~(k15\_euclid~np\_\_2)~\\
X5~X3))))))))))))))))))))))\end{array}$$
\end{theorem}
\end{document}
