\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{l91\_geomtrap (TMQQ1FesprrDMgtNjsoPE9Ncox5J3CLZtcr)}
\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 $ k7\_geomtrap : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r1\_analmetr : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r2\_analoaf : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ r2\_geomtrap : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ g1\_geomtrap : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_geomtrap : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_geomtrap : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_geomtrap : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_geomtrap : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u1\_midsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_analoaf : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
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~(k7\_geomtrap~X0~X5~X6))){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_subset\_1~\\
X8~(u1\_struct\_0~(k7\_geomtrap~X0~X5~X6))){\unicdbdjdcd}({\unicdcdadad} X9 .  (m1\_subset\_1~\\
X9~(u1\_struct\_0~(k7\_geomtrap~X0~X5~X6))){\unicdbdjdcd}({\unicdcdadad} X10 .  (m1\_subset\_1~\\
X10~(u1\_struct\_0~(k7\_geomtrap~X0~X5~X6))){\unicdbdjdcd}(((X1=X7){\unicdcdcdhd}((X2=X8){\unicdcdcdhd}\\
((X3=X9){\unicdcdcdhd}(X4=X10)))){\unicdbdjdcd}((r2\_analoaf~(k7\_geomtrap~X0~X5~X6)~X7~X8~\\
X9~X10){\unicdbdjded}(r2\_geomtrap~X0~X5~X6~X1~X2~X3~X4)))))))))))))\end{array}
\label{hyp:ehededpfhgfgpgngehchbgah}
\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~X0)){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_subset\_1~X8~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X9 .  (m1\_subset\_1~X9~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X10 .  (\\
m1\_subset\_1~X10~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X11 .  (m1\_subset\_1~\\
X11~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X12 .  (m1\_subset\_1~X12~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}(((r1\_analmetr~X0~X1~X2){\unicdcdcdhd}((r2\_geomtrap~X0~X1~X2~X3~X4~X5~X9){\unicdcdcdhd}\\
((r2\_geomtrap~X0~X1~X2~X3~X4~X6~X10){\unicdcdcdhd}((r2\_geomtrap~X0~X1~X2~X3~X4~X7~\\
X11){\unicdcdcdhd}((r2\_geomtrap~X0~X1~X2~X3~X4~X8~X12){\unicdcdcdhd}(r2\_geomtrap~X0~X1~X2~X5~\\
X6~X7~X8)))))){\unicdbdjdcd}((X3=X4){\unicdcdcdid}(r2\_geomtrap~X0~X1~X2~X9~X10~X11~X12)))))))))))))))\end{array}
\label{hyp:ehedbdpfhgfgpgngehchbgah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~\\
X1~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0)~X0))))){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0)~(k2\_zfmisc\_1~X0~X0))))){\unicdbdjdcd}({\unicdcdadad} X3 .  {\unicdcdadad} X4 .  \\
{\unicdcdadad} X5 .  (g1\_geomtrap~X0~X1~X2=g1\_geomtrap~X3~X4~X5){\unicdbdjdcd}((X0=X3){\unicdcdcdhd}\\
((X1=X4){\unicdcdcdhd}(X2=X5))))\end{array}
\label{hyp:ggchfgfgpfhgbdpfhgfgpgngehchbgah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\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)))))))))){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~X0)))){\unicdbdjdcd}((v1\_geomtrap~(k7\_geomtrap~\\
X0~X1~X2)){\unicdcdcdhd}(l1\_geomtrap~(k7\_geomtrap~X0~X1~X2)))\end{array}
\label{hyp:egehpflghdpfhgfgpgngehchbgah}
\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\_funct\_1~(k6\_geomtrap~X0)){\unicdcdcdhd}((v1\_funct\_2~(\\
k6\_geomtrap~X0)~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~\\
(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~(k6\_geomtrap~X0)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~\\
(u1\_struct\_0~X0))))))\end{array}
\label{hyp:egehpflggdpfhgfgpgngehchbgah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\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)))))))))){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~X0)))){\unicdbdjdcd}(m1\_subset\_1~(k5\_geomtrap~\\
X0~X1~X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0))~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0)))))\end{array}
\label{hyp:egehpflgfdpfhgfgpgngehchbgah}
\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}(k7\_geomtrap~X0~\\
X1~X2=g1\_geomtrap~(u1\_struct\_0~X0)~(k6\_geomtrap~X0)~(k5\_geomtrap~\\
X0~X1~X2))))\end{array}
\label{hyp:egjdpfhgfgpgngehchbgah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_geomtrap~X0){\unicdbdjdcd}((v1\_geomtrap~X0){\unicdbdjdcd}(X0=g1\_geomtrap~\\
(u1\_struct\_0~X0)~(u1\_midsp\_1~X0)~(u1\_analoaf~X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdpfhgfgpgngehchbgah}
\end{equation}
\begin{theorem}\label{thm:mgjdbdpfhgfgpgngehchbgah}
$$\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~(k7\_geomtrap~X0~X1~X2))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~(k7\_geomtrap~X0~X1~X2))){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~\\
X5~(u1\_struct\_0~(k7\_geomtrap~X0~X1~X2))){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~\\
X6~(u1\_struct\_0~(k7\_geomtrap~X0~X1~X2))){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~\\
X7~(u1\_struct\_0~(k7\_geomtrap~X0~X1~X2))){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_subset\_1~\\
X8~(u1\_struct\_0~(k7\_geomtrap~X0~X1~X2))){\unicdbdjdcd}({\unicdcdadad} X9 .  (m1\_subset\_1~\\
X9~(u1\_struct\_0~(k7\_geomtrap~X0~X1~X2))){\unicdbdjdcd}({\unicdcdadad} X10 .  (m1\_subset\_1~\\
X10~(u1\_struct\_0~(k7\_geomtrap~X0~X1~X2))){\unicdbdjdcd}({\unicdcdadad} X11 .  (m1\_subset\_1~\\
X11~(u1\_struct\_0~(k7\_geomtrap~X0~X1~X2))){\unicdbdjdcd}({\unicdcdadad} X12 .  (m1\_subset\_1~\\
X12~(u1\_struct\_0~(k7\_geomtrap~X0~X1~X2))){\unicdbdjdcd}(((r1\_analmetr~X0~X1~\\
X2){\unicdcdcdhd}((r2\_analoaf~(k7\_geomtrap~X0~X1~X2)~X3~X4~X5~X6){\unicdcdcdhd}((r2\_analoaf~\\
(k7\_geomtrap~X0~X1~X2)~X3~X4~X7~X8){\unicdcdcdhd}((r2\_analoaf~(k7\_geomtrap~X0~\\
X1~X2)~X3~X4~X9~X10){\unicdcdcdhd}((r2\_analoaf~(k7\_geomtrap~X0~X1~X2)~X3~X4~X11~X12){\unicdcdcdhd}\\
(r2\_analoaf~(k7\_geomtrap~X0~X1~X2)~X5~X7~X9~X11)))))){\unicdbdjdcd}((X3=X4){\unicdcdcdid}\\
(r2\_analoaf~(k7\_geomtrap~X0~X1~X2)~X6~X8~X10~X12)))))))))))))))\end{array}$$
\end{theorem}
\end{document}
