\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{t36\_midsp\_1 (TMVxvN3FeSNTkwvrVoVg1BHtJHwwUzCkpBL)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_midsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_midsp\_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 $ r2\_midsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k8\_midsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_midsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_midsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_midsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_midsp\_1~X0){\unicdcdcdhd}(l1\_midsp\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0))){\unicdbdjdcd}((r2\_midsp\_1~X0~X1~X2){\unicdbdjdcd}(k4\_midsp\_1~\\
X0~X1=k4\_midsp\_1~X0~X2))))\end{array}
\label{hyp:ehcdhdpfngjgegdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_midsp\_1~X0){\unicdcdcdhd}\\
(l1\_midsp\_1~X0))){\unicdcdcdhd}(m1\_subset\_1~X1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)))){\unicdbdjdcd}(k5\_midsp\_1~X0~X1=k4\_midsp\_1~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfngjgegdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_midsp\_1~X0){\unicdcdcdhd}(l1\_midsp\_1~\\
X0))){\unicdbdjdcd}({\unicdcdaddd} X1 .  m1\_midsp\_1~X1~X0)\end{array}
\label{hyp:fgihjgdhehfgogdgfgpfngbdpfngjgegdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_midsp\_1~X0){\unicdcdcdhd}(l1\_midsp\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_midsp\_1~X1~X0){\unicdbdjdcd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))))))\end{array}
\label{hyp:egehpfngbdpfngjgegdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((m1\_subset\_1~X2~X0){\unicdcdcdhd}(m1\_subset\_1~X3~X1)))){\unicdbdjdcd}\\
(m1\_subset\_1~(k1\_domain\_1~X0~X1~X2~X3)~(k2\_zfmisc\_1~X0~X1))\end{array}
\label{hyp:egehpflgbdpfegpgngbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_midsp\_1~X0){\unicdcdcdhd}(l1\_midsp\_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}(k8\_midsp\_1~X0~X1~X2=k5\_midsp\_1~\\
X0~(k1\_domain\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X1~X2))))\end{array}
\label{hyp:egbdadpfngjgegdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(v1\_xboole\_0~X2))\end{array}
\label{hyp:dgdgddpfchfgmgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddgdpfngjgegdhahpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_midsp\_1~X0){\unicdcdcdhd}(l1\_midsp\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
((r2\_midsp\_1~X0~(k1\_domain\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~\\
X1~X2)~(k1\_domain\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X3~X4)){\unicdbdjdcd}(\\
k8\_midsp\_1~X0~X1~X2=k8\_midsp\_1~X0~X3~X4))))))\end{array}$$
\end{theorem}
\end{document}
