\documentclass{article}
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\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}
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\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{t37\_transgeo (TMbXkGQ92KuALqBx88k2rufmZDPhDP4geuz)}
\maketitle
Let $ v7\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_analoaf : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_analoaf : {{\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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_diraf : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r3\_transgeo : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}}$ be given.
Let $ v4\_transgeo : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ g1\_analoaf : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_analoaf : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_analoaf : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_transgeo : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_diraf : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}(((v1\_funct\_1~X4){\unicdcdcdhd}((\\
v1\_funct\_2~X4~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1))))){\unicdcdcdhd}((v1\_funct\_1~X5){\unicdcdcdhd}((v1\_funct\_2~X5~X2~X3){\unicdcdcdhd}(m1\_subset\_1~\\
X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X2~X3)))))))){\unicdbdjdcd}(r1\_funct\_2~X0~X1~X2~\\
X3~X4~X4)\end{array}
\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0)~(k2\_zfmisc\_1~X0~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  \\
(g1\_analoaf~X0~X1=g1\_analoaf~X2~X3){\unicdbdjdcd}((X0=X2){\unicdcdcdhd}(X1=X3)))\end{array}
\label{hyp:ggchfgfgpfhgbdpfbgogbgmgpgbggg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v7\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}(v1\_zfmisc\_1~\\
(u1\_struct\_0~X0))\end{array}
\label{hyp:ggdghdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}(\preoh v1\_zfmisc\_1~\\
(u1\_struct\_0~X0))\end{array}
\label{hyp:ggdggdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(u1\_struct\_0~X0))\end{array}
\label{hyp:ggdgcdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_analoaf~X0){\unicdbdjdcd}(m1\_subset\_1~(u1\_analoaf~X0)~(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:egehpffhbdpfbgogbgmgpgbggg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_analoaf}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfbgogbgmgpgbggg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_analoaf~X0)){\unicdbdjdcd}((v1\_analoaf~\\
(k2\_diraf~X0)){\unicdcdcdhd}(l1\_analoaf~(k2\_diraf~X0)))\end{array}
\label{hyp:egehpflgcdpfegjgchbggg}
\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}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}((v3\_funct\_2~X1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0))))))){\unicdbdjdcd}((v4\_transgeo~X1~X0){\unicdbdjded}(r1\_transgeo~\\
(u1\_struct\_0~X0)~X1~(k1\_diraf~(u1\_struct\_0~X0)~(u1\_analoaf~X0)))))\end{array}
\label{hyp:egidpfehchbgogdhhgfgpg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_analoaf~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((v3\_funct\_2~X1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))))))){\unicdbdjdcd}\\
((r3\_transgeo~X0~X1){\unicdbdjded}(r1\_transgeo~(u1\_struct\_0~X0)~X1~(u1\_analoaf~\\
X0))))\end{array}
\label{hyp:egedpfehchbgogdhhgfgpg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_analoaf~X0)){\unicdbdjdcd}(k2\_diraf~X0=\\
g1\_analoaf~(u1\_struct\_0~X0)~(k1\_diraf~(u1\_struct\_0~X0)~(u1\_analoaf~\\
X0)))\end{array}
\label{hyp:egcdpfegjgchbggg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{({\preoh{{{v7\_struct\_0}~{X0}}}})}{\unicdbdjdcd}{({\preoh{{{v2\_struct\_0}~{X0}}}})}})}}}\label{hyp:dgdgcdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_analoaf~X0){\unicdbdjdcd}((v1\_analoaf~X0){\unicdbdjdcd}(X0=g1\_analoaf~\\
(u1\_struct\_0~X0)~(u1\_analoaf~X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdpfbgogbgmgpgbggg}
\end{equation}
\begin{theorem}\label{thm:ehddhdpfehchbgogdhhgfgpg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v2\_analoaf~X0){\unicdcdcdhd}(l1\_analoaf~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(u1\_struct\_0~\\
(k2\_diraf~X0))~(u1\_struct\_0~(k2\_diraf~X0))){\unicdcdcdhd}((v3\_funct\_2~X1~(\\
u1\_struct\_0~(k2\_diraf~X0))~(u1\_struct\_0~(k2\_diraf~X0))){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~(k2\_diraf~X0))~(u1\_struct\_0~\\
(k2\_diraf~X0)))))))){\unicdbdjdcd}(\preoh (r3\_transgeo~(k2\_diraf~X0)~X1){\unicdcdcdhd}({\unicdcdadad} X2 .  \\
((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((v3\_funct\_2~X2~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))))))){\unicdbdjdcd}\\
(\preoh (r1\_funct\_2~(u1\_struct\_0~(k2\_diraf~X0))~(u1\_struct\_0~(k2\_diraf~\\
X0))~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X1~X2){\unicdcdcdhd}(v4\_transgeo~X2~X0)))))\end{array}$$
\end{theorem}
\end{document}
