\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{t23\_euclmetr (TMYNxKcn2n7LF79ngfHT14abbg9H39fZheS)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_analmetr : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_analmetr : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_rlvect\_1 : {{\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 $ r1\_analmetr : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_analmetr : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_euclmetr : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_euclmetr : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_euclmetr : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_euclmetr : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_euclmetr : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_euclmetr : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_euclmetr : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_conaffm : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_conaffm : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_numbers : {\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 $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ v7\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_analoaf : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_analoaf : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_analoaf : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_analmetr : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_diraf : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v11\_aff\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_aff\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_aff\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_aff\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_analoaf : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_translac : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_analmetr : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_analmetr~X0){\unicdcdcdhd}(l1\_analmetr~\\
X0))){\unicdbdjdcd}((v1\_euclmetr~X0){\unicdbdjded}(v3\_conaffm~X0))\end{array}
\label{hyp:ehidpffgfhdgmgngfgehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_analmetr~X0){\unicdcdcdhd}(l1\_analmetr~\\
X0))){\unicdbdjdcd}((v5\_conaffm~X0){\unicdbdjdcd}(v3\_conaffm~X0))\end{array}
\label{hyp:ehgdpfdgpgogbgggggng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v5\_rlvect\_1~X0){\unicdcdcdhd}\\
((v6\_rlvect\_1~X0){\unicdcdcdhd}((v7\_rlvect\_1~X0){\unicdcdcdhd}((v8\_rlvect\_1~X0){\unicdcdcdhd}(l1\_rlvect\_1~\\
X0)))))))))){\unicdbdjdcd}(({\unicdcdaddd} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}\\
({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k1\_numbers){\unicdbdjdcd}((k3\_rlvect\_1~\\
X0~(k1\_rlvect\_1~X0~X1~X3)~(k1\_rlvect\_1~X0~X2~X4)=k4\_struct\_0~X0){\unicdbdjdcd}\\
((X3=k6\_numbers){\unicdcdcdhd}(X4=k6\_numbers))))))){\unicdbdjdcd}((\preoh v7\_struct\_0~(k2\_analoaf~\\
X0)){\unicdcdcdhd}((v2\_analoaf~(k2\_analoaf~X0)){\unicdcdcdhd}(l1\_analoaf~(k2\_analoaf~\\
X0)))))\end{array}
\label{hyp:ehcdgdpfbgogbgmgpgbggg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_analmetr~X0){\unicdcdcdhd}(l1\_analmetr~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((\\
v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}((v5\_rlvect\_1~\\
X1){\unicdcdcdhd}((v6\_rlvect\_1~X1){\unicdcdcdhd}((v7\_rlvect\_1~X1){\unicdcdcdhd}((v8\_rlvect\_1~X1){\unicdcdcdhd}\\
(l1\_rlvect\_1~X1)))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X1)){\unicdbdjdcd}(((r1\_analmetr~\\
X1~X2~X3){\unicdcdcdhd}(X0=k2\_analmetr~X1~X2~X3)){\unicdbdjdcd}(v7\_euclmetr~X0)))))\end{array}
\label{hyp:ehcdcdpffgfhdgmgngfgehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_analmetr~X0){\unicdcdcdhd}(l1\_analmetr~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((\\
v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}((v5\_rlvect\_1~\\
X1){\unicdcdcdhd}((v6\_rlvect\_1~X1){\unicdcdcdhd}((v7\_rlvect\_1~X1){\unicdcdcdhd}((v8\_rlvect\_1~X1){\unicdcdcdhd}\\
(l1\_rlvect\_1~X1)))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X1)){\unicdbdjdcd}(((r1\_analmetr~\\
X1~X2~X3){\unicdcdcdhd}(X0=k2\_analmetr~X1~X2~X3)){\unicdbdjdcd}(v5\_conaffm~X0)))))\end{array}
\label{hyp:ehcdadpffgfhdgmgngfgehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v5\_rlvect\_1~X0){\unicdcdcdhd}\\
((v6\_rlvect\_1~X0){\unicdcdcdhd}((v7\_rlvect\_1~X0){\unicdcdcdhd}((v8\_rlvect\_1~X0){\unicdcdcdhd}(l1\_rlvect\_1~\\
X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}(k3\_analmetr~(\\
k2\_analmetr~X0~X1~X2)=k2\_diraf~(k2\_analoaf~X0))))\end{array}
\label{hyp:ehcdadpfbgogbgmgngfgehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v5\_rlvect\_1~X0){\unicdcdcdhd}\\
((v6\_rlvect\_1~X0){\unicdcdcdhd}((v7\_rlvect\_1~X0){\unicdcdcdhd}((v8\_rlvect\_1~X0){\unicdcdcdhd}(l1\_rlvect\_1~\\
X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v7\_struct\_0~X1){\unicdcdcdhd}((v2\_analoaf~X1){\unicdcdcdhd}\\
(l1\_analoaf~X1))){\unicdbdjdcd}((X1=k2\_analoaf~X0){\unicdbdjdcd}(v11\_aff\_2~(k2\_diraf~\\
X1))))\end{array}
\label{hyp:ehbdhdpfahbgahegfgdhbggg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v5\_rlvect\_1~X0){\unicdcdcdhd}\\
((v6\_rlvect\_1~X0){\unicdcdcdhd}((v7\_rlvect\_1~X0){\unicdcdcdhd}((v8\_rlvect\_1~X0){\unicdcdcdhd}(l1\_rlvect\_1~\\
X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v7\_struct\_0~X1){\unicdcdcdhd}((v2\_analoaf~X1){\unicdcdcdhd}\\
(l1\_analoaf~X1))){\unicdbdjdcd}((X1=k2\_analoaf~X0){\unicdbdjdcd}(v7\_aff\_2~(k2\_diraf~X1))))\end{array}
\label{hyp:ehbdgdpfahbgahegfgdhbggg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v5\_rlvect\_1~X0){\unicdcdcdhd}\\
((v6\_rlvect\_1~X0){\unicdcdcdhd}((v7\_rlvect\_1~X0){\unicdcdcdhd}((v8\_rlvect\_1~X0){\unicdcdcdhd}(l1\_rlvect\_1~\\
X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v7\_struct\_0~X1){\unicdcdcdhd}((v2\_analoaf~X1){\unicdcdcdhd}\\
(l1\_analoaf~X1))){\unicdbdjdcd}((X1=k2\_analoaf~X0){\unicdbdjdcd}(v4\_aff\_2~(k2\_diraf~X1))))\end{array}
\label{hyp:ehbdedpfahbgahegfgdhbggg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v5\_rlvect\_1~X0){\unicdcdcdhd}\\
((v6\_rlvect\_1~X0){\unicdcdcdhd}((v7\_rlvect\_1~X0){\unicdcdcdhd}((v8\_rlvect\_1~X0){\unicdcdcdhd}(l1\_rlvect\_1~\\
X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v7\_struct\_0~X1){\unicdcdcdhd}((v2\_analoaf~X1){\unicdcdcdhd}\\
(l1\_analoaf~X1))){\unicdbdjdcd}((X1=k2\_analoaf~X0){\unicdbdjdcd}(v2\_aff\_2~(k2\_diraf~X1))))\end{array}
\label{hyp:ehbdddpfahbgahegfgdhbggg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v2\_analoaf~X0){\unicdcdcdhd}(l1\_analoaf~\\
X0))){\unicdbdjdcd}((v1\_analoaf~(k2\_diraf~X0)){\unicdcdcdhd}(v1\_translac~(k2\_diraf~X0)))\end{array}
\label{hyp:ggdgddpfahbgahegfgdhbggg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v5\_rlvect\_1~X0){\unicdcdcdhd}\\
((v6\_rlvect\_1~X0){\unicdcdcdhd}((v7\_rlvect\_1~X0){\unicdcdcdhd}((v8\_rlvect\_1~X0){\unicdcdcdhd}(l1\_rlvect\_1~\\
X0)))))))))){\unicdbdjdcd}((v1\_analoaf~(k2\_analoaf~X0)){\unicdcdcdhd}(l1\_analoaf~(k2\_analoaf~\\
X0)))\end{array}
\label{hyp:egehpflgcdpfbgogbgmgpgbggg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_analmetr~X0){\unicdcdcdhd}(l1\_analmetr~\\
X0))){\unicdbdjdcd}((v6\_euclmetr~X0){\unicdbdjded}(v11\_aff\_2~(k3\_analmetr~X0)))\end{array}
\label{hyp:eggdpffgfhdgmgngfgehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_analmetr~X0){\unicdcdcdhd}(l1\_analmetr~\\
X0))){\unicdbdjdcd}((v5\_euclmetr~X0){\unicdbdjded}(v7\_aff\_2~(k3\_analmetr~X0)))\end{array}
\label{hyp:egfdpffgfhdgmgngfgehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_analmetr~X0){\unicdcdcdhd}(l1\_analmetr~\\
X0))){\unicdbdjdcd}((v4\_euclmetr~X0){\unicdbdjded}(v1\_translac~(k3\_analmetr~X0)))\end{array}
\label{hyp:egedpffgfhdgmgngfgehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_analmetr~X0){\unicdcdcdhd}(l1\_analmetr~\\
X0))){\unicdbdjdcd}((v3\_euclmetr~X0){\unicdbdjded}(v4\_aff\_2~(k3\_analmetr~X0)))\end{array}
\label{hyp:egddpffgfhdgmgngfgehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_analmetr~X0){\unicdcdcdhd}(l1\_analmetr~\\
X0))){\unicdbdjdcd}((v2\_euclmetr~X0){\unicdbdjded}(v2\_aff\_2~(k3\_analmetr~X0)))\end{array}
\label{hyp:egcdpffgfhdgmgngfgehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v5\_rlvect\_1~X0){\unicdcdcdhd}\\
((v6\_rlvect\_1~X0){\unicdcdcdhd}((v7\_rlvect\_1~X0){\unicdcdcdhd}((v8\_rlvect\_1~X0){\unicdcdcdhd}(l1\_rlvect\_1~\\
X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}((r1\_analmetr~\\
X0~X1~X2){\unicdbdjded}(({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdaddd} X4 .  \\
(m1\_subset\_1~X4~k1\_numbers){\unicdcdcdhd}({\unicdcdaddd} X5 .  (m1\_subset\_1~X5~k1\_numbers){\unicdcdcdhd}\\
(X3=k3\_rlvect\_1~X0~(k1\_rlvect\_1~X0~X1~X4)~(k1\_rlvect\_1~X0~X2~X5))))){\unicdcdcdhd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~k1\_numbers){\unicdbdjdcd}((k3\_rlvect\_1~X0~(k1\_rlvect\_1~X0~X1~X3)~(k1\_rlvect\_1~\\
X0~X2~X4)=k4\_struct\_0~X0){\unicdbdjdcd}((X3=k6\_numbers){\unicdcdcdhd}(X4=k6\_numbers)))))))))\end{array}
\label{hyp:egbdpfbgogbgmgngfgehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_analmetr~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(v3\_analmetr~\\
X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(v2\_analmetr~X0)))\end{array}
\label{hyp:dgdgbdpfbgogbgmgngfgehch}
\end{equation}
\begin{theorem}\label{thm:ehcdddpffgfhdgmgngfgehch}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_analmetr~X0){\unicdcdcdhd}(l1\_analmetr~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((\\
v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}((v5\_rlvect\_1~\\
X1){\unicdcdcdhd}((v6\_rlvect\_1~X1){\unicdcdcdhd}((v7\_rlvect\_1~X1){\unicdcdcdhd}((v8\_rlvect\_1~X1){\unicdcdcdhd}\\
(l1\_rlvect\_1~X1)))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X1)){\unicdbdjdcd}(((r1\_analmetr~\\
X1~X2~X3){\unicdcdcdhd}(X0=k2\_analmetr~X1~X2~X3)){\unicdbdjdcd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_analmetr~\\
X0){\unicdcdcdhd}((v1\_euclmetr~X0){\unicdcdcdhd}((v2\_euclmetr~X0){\unicdcdcdhd}((v3\_euclmetr~X0){\unicdcdcdhd}\\
((v4\_euclmetr~X0){\unicdcdcdhd}((v5\_euclmetr~X0){\unicdcdcdhd}((v6\_euclmetr~X0){\unicdcdcdhd}((v7\_euclmetr~\\
X0){\unicdcdcdhd}(l1\_analmetr~X0))))))))))))))\end{array}$$
\end{theorem}
\end{document}
