\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{l26\_geomtrap (TMP1NeBKAAKZu8UnpZmCcE2wbiJSqiCJjCt)}
\maketitle
Let $ v2\_struct\_0 : {{\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 $ r1\_geomtrap : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ r3\_analmetr : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}}}$ be given.
Let $ v2\_analmetr : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_analmetr : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r2\_analoaf : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ r4\_analmetr : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ k2\_analmetr : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u1\_analoaf : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_diraf : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_analoaf : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_analmetr : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_analmetr : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_analmetr~X0){\unicdcdcdhd}(l1\_analmetr~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~\\
X6~(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (X1{\unicdcdgdad}X2){\unicdcdcdhd}((\preoh (\preoh (r2\_analoaf~X0~X1~X2~X3~X4){\unicdcdcdhd}\\
(r4\_analmetr~X0~X1~X2~X5~X6)){\unicdcdcdhd}((\preoh (r2\_analoaf~X0~X1~X2~X5~X6){\unicdcdcdhd}(r4\_analmetr~\\
X0~X1~X2~X3~X4)){\unicdcdcdhd}((\preoh (r2\_analoaf~X0~X1~X2~X3~X4){\unicdcdcdhd}(r4\_analmetr~X0~X5~\\
X6~X1~X2)){\unicdcdcdhd}((\preoh (r2\_analoaf~X0~X1~X2~X5~X6){\unicdcdcdhd}(r4\_analmetr~X0~X3~X4~X1~\\
X2)){\unicdcdcdhd}((\preoh (r2\_analoaf~X0~X3~X4~X1~X2){\unicdcdcdhd}(r4\_analmetr~X0~X5~X6~X1~X2)){\unicdcdcdhd}\\
((\preoh (r2\_analoaf~X0~X5~X6~X1~X2){\unicdcdcdhd}(r4\_analmetr~X0~X3~X4~X1~X2)){\unicdcdcdhd}((\preoh (\\
r2\_analoaf~X0~X3~X4~X1~X2){\unicdcdcdhd}(r4\_analmetr~X0~X1~X2~X5~X6)){\unicdcdcdhd}(\preoh (r2\_analoaf~\\
X0~X5~X6~X1~X2){\unicdcdcdhd}(r4\_analmetr~X0~X1~X2~X3~X4))))))))){\unicdcdcdhd}(\preoh r4\_analmetr~\\
X0~X3~X4~X5~X6)))))))))\end{array}
\label{hyp:ehgdcdpfbgogbgmgngfgehch}
\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}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
(m1\_subset\_1~X6~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~\\
(u1\_struct\_0~(k2\_analmetr~X0~X1~X2))){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_subset\_1~\\
X8~(u1\_struct\_0~(k2\_analmetr~X0~X1~X2))){\unicdbdjdcd}({\unicdcdadad} X9 .  (m1\_subset\_1~\\
X9~(u1\_struct\_0~(k2\_analmetr~X0~X1~X2))){\unicdbdjdcd}({\unicdcdadad} X10 .  (m1\_subset\_1~\\
X10~(u1\_struct\_0~(k2\_analmetr~X0~X1~X2))){\unicdbdjdcd}(((X7=X3){\unicdcdcdhd}((X8=X4){\unicdcdcdhd}\\
((X9=X5){\unicdcdcdhd}(X10=X6)))){\unicdbdjdcd}((r2\_analoaf~(k2\_analmetr~X0~X1~X2)~X7~X8~\\
X9~X10){\unicdbdjded}(r1\_geomtrap~X0~X3~X4~X5~X6)))))))))))))\end{array}
\label{hyp:ehedpfhgfgpgngehchbgah}
\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){\unicdbdjdcd}((\preoh v2\_struct\_0~(k2\_analmetr~X0~X1~X2)){\unicdcdcdhd}((v2\_analmetr~\\
(k2\_analmetr~X0~X1~X2)){\unicdcdcdhd}(l1\_analmetr~(k2\_analmetr~X0~X1~X2)))))))\end{array}
\label{hyp:ehddddpfbgogbgmgngfgehch}
\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}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
(m1\_subset\_1~X6~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~\\
(u1\_struct\_0~(k2\_analmetr~X0~X5~X6))){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_subset\_1~\\
X8~(u1\_struct\_0~(k2\_analmetr~X0~X5~X6))){\unicdbdjdcd}({\unicdcdadad} X9 .  (m1\_subset\_1~\\
X9~(u1\_struct\_0~(k2\_analmetr~X0~X5~X6))){\unicdbdjdcd}({\unicdcdadad} X10 .  (m1\_subset\_1~\\
X10~(u1\_struct\_0~(k2\_analmetr~X0~X5~X6))){\unicdbdjdcd}(((X7=X1){\unicdcdcdhd}((X8=X2){\unicdcdcdhd}\\
((X9=X3){\unicdcdcdhd}(X10=X4)))){\unicdbdjdcd}((r4\_analmetr~(k2\_analmetr~X0~X5~X6)~X7~\\
X9~X8~X10){\unicdbdjded}(r3\_analmetr~X0~X1~X3~X2~X4~X5~X6)))))))))))))\end{array}
\label{hyp:ehcdbdpfbgogbgmgngfgehch}
\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}((u1\_struct\_0~\\
(k2\_analmetr~X0~X1~X2)=u1\_struct\_0~X0){\unicdcdcdhd}((u1\_analoaf~(k2\_analmetr~\\
X0~X1~X2)=k1\_diraf~(u1\_struct\_0~X0)~(k1\_analoaf~X0)){\unicdcdcdhd}(u1\_analmetr~\\
(k2\_analmetr~X0~X1~X2)=k1\_analmetr~X0~X1~X2)))))\end{array}
\label{hyp:ehbdjdpfbgogbgmgngfgehch}
\end{equation}
\begin{theorem}\label{thm:mgcdgdpfhgfgpgngehchbgah}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v5\_rlvect\_1~X0){\unicdcdcdhd}\\
((v6\_rlvect\_1~X0){\unicdcdcdhd}((v7\_rlvect\_1~X0){\unicdcdcdhd}((v8\_rlvect\_1~X0){\unicdcdcdhd}(l1\_rlvect\_1~\\
X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
(m1\_subset\_1~X6~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_subset\_1~X8~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
((r1\_analmetr~X0~X1~X2){\unicdbdjdcd}(((\preoh r1\_geomtrap~X0~X3~X4~X5~X6){\unicdcdcdhd}(\preoh r1\_geomtrap~\\
X0~X5~X6~X3~X4)){\unicdcdcdid}(((\preoh r3\_analmetr~X0~X7~X8~X5~X6~X1~X2){\unicdcdcdhd}(\preoh r3\_analmetr~\\
X0~X5~X6~X7~X8~X1~X2)){\unicdcdcdid}((X5=X6){\unicdcdcdid}((r3\_analmetr~X0~X3~X4~X7~X8~X1~X2){\unicdcdcdhd}\\
(r3\_analmetr~X0~X7~X8~X3~X4~X1~X2))))))))))))))\end{array}$$
\end{theorem}
\end{document}
