\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{t109\_tmap\_1 (TMFxv1DkT2Metz7kDG5DFuxdXM9uoDE1DzB)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_tmap\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k8\_tmap\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_tmap\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ 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 $ v5\_pre\_topc : {{\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 $ r1\_tmap\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~\\
X1)~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X1)~(u1\_struct\_0~X0)))))){\unicdbdjdcd}((v5\_pre\_topc~X2~X1~X0){\unicdbdjded}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X1)){\unicdbdjdcd}(r1\_tmap\_1~X1~X0~\\
X2~X3)))))\end{array}
\label{hyp:ehededpfehngbgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(m1\_pre\_topc~X1~X0)){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X1)){\unicdbdjdcd}(r1\_tmap\_1~X1~(k8\_tmap\_1~\\
X0~X1)~(k2\_tmap\_1~X0~(k8\_tmap\_1~X0~X1)~(k9\_tmap\_1~X0~X1)~X1)~X2)))\end{array}
\label{hyp:ehbdadhdpfehngbgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}\\
(l1\_pre\_topc~X0))){\unicdcdcdhd}(m1\_pre\_topc~X1~X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~(k8\_tmap\_1~\\
X0~X1)){\unicdcdcdhd}((v1\_pre\_topc~(k8\_tmap\_1~X0~X1)){\unicdcdcdhd}(v2\_pre\_topc~(k8\_tmap\_1~\\
X0~X1))))\end{array}
\label{hyp:ggdgfdpfehngbgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_pre\_topc~X1~X0){\unicdbdjdcd}\\
(l1\_pre\_topc~X1))\end{array}
\label{hyp:egehpfngbdpfahchfgpfehpgahdg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_pre\_topc}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfahchfgpfehpgahdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}\\
(l1\_pre\_topc~X0))){\unicdcdcdhd}(m1\_pre\_topc~X1~X0)){\unicdbdjdcd}((v1\_funct\_1~(k9\_tmap\_1~\\
X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(k9\_tmap\_1~X0~X1)~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
(k8\_tmap\_1~X0~X1))){\unicdcdcdhd}(m1\_subset\_1~(k9\_tmap\_1~X0~X1)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~(k8\_tmap\_1~X0~X1)))))))\end{array}
\label{hyp:egehpflgjdpfehngbgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}\\
(l1\_pre\_topc~X0))){\unicdcdcdhd}(m1\_pre\_topc~X1~X0)){\unicdbdjdcd}((v1\_pre\_topc~(k8\_tmap\_1~\\
X0~X1)){\unicdcdcdhd}((v2\_pre\_topc~(k8\_tmap\_1~X0~X1)){\unicdcdcdhd}(l1\_pre\_topc~(k8\_tmap\_1~\\
X0~X1))))\end{array}
\label{hyp:egehpflgidpfehngbgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((l1\_struct\_0~X0){\unicdcdcdhd}\\
((l1\_struct\_0~X1){\unicdcdcdhd}(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X1)))))){\unicdcdcdhd}(l1\_struct\_0~X3)))){\unicdbdjdcd}\\
((v1\_funct\_1~(k2\_tmap\_1~X0~X1~X2~X3)){\unicdcdcdhd}((v1\_funct\_2~(k2\_tmap\_1~\\
X0~X1~X2~X3)~(u1\_struct\_0~X3)~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~(k2\_tmap\_1~\\
X0~X1~X2~X3)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X3)~(u1\_struct\_0~\\
X1))))))\end{array}
\label{hyp:egehpflgcdpfehngbgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_pre\_topc~X1~X0){\unicdbdjdcd}(v2\_pre\_topc~X1))\end{array}
\label{hyp:dgdgbdpfahchfgpfehpgahdg}
\end{equation}
\begin{theorem}\label{thm:ehbdadjdpfehngbgahpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(m1\_pre\_topc~X1~X0)){\unicdbdjdcd}(\\
(v1\_funct\_1~(k2\_tmap\_1~X0~(k8\_tmap\_1~X0~X1)~(k9\_tmap\_1~X0~X1)~X1)){\unicdcdcdhd}\\
((v1\_funct\_2~(k2\_tmap\_1~X0~(k8\_tmap\_1~X0~X1)~(k9\_tmap\_1~X0~X1)~X1)~\\
(u1\_struct\_0~X1)~(u1\_struct\_0~(k8\_tmap\_1~X0~X1))){\unicdcdcdhd}((v5\_pre\_topc~\\
(k2\_tmap\_1~X0~(k8\_tmap\_1~X0~X1)~(k9\_tmap\_1~X0~X1)~X1)~X1~(k8\_tmap\_1~\\
X0~X1)){\unicdcdcdhd}(m1\_subset\_1~(k2\_tmap\_1~X0~(k8\_tmap\_1~X0~X1)~(k9\_tmap\_1~\\
X0~X1)~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X1)~(u1\_struct\_0~\\
(k8\_tmap\_1~X0~X1)))))))))\end{array}$$
\end{theorem}
\end{document}
