\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{t30\_conlat\_1 (TMXLDRQqPc55nMqJzgNgjgQBJSSm6ne9deU)}
\maketitle
Let $ v1\_conlat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_conlat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_conlat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v7\_conlat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l2\_conlat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r2\_conlat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_conlat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_conlat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u3\_conlat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u2\_conlat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l5\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_conlat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v9\_conlat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v8\_conlat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~X1)){\unicdbdjded}(r1\_tarski~\\
X0~X1)\end{array}
\label{hyp:ehddpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_conlat\_1~X0){\unicdcdcdhd}(l1\_conlat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v5\_conlat\_1~X1~X0){\unicdcdcdhd}((v7\_conlat\_1~X1~X0){\unicdcdcdhd}(l2\_conlat\_1~X1~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((\preoh v5\_conlat\_1~X2~X0){\unicdcdcdhd}((v7\_conlat\_1~X2~X0){\unicdcdcdhd}(l2\_conlat\_1~\\
X2~X0))){\unicdbdjdcd}((r2\_conlat\_1~X0~X1~X2){\unicdbdjded}(r1\_tarski~(u3\_conlat\_1~X0~X2)~\\
(u3\_conlat\_1~X0~X1)))))\end{array}
\label{hyp:ehcdidpfdgpgogmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_conlat\_1~X0){\unicdcdcdhd}(l1\_conlat\_1~X0)){\unicdbdjdcd}((u2\_conlat\_1~\\
X0~(k5\_conlat\_1~X0)=u1\_struct\_0~X0){\unicdcdcdhd}(u3\_conlat\_1~X0~(k6\_conlat\_1~\\
X0)=u4\_struct\_0~X0))\end{array}
\label{hyp:ehcdddpfdgpgogmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l5\_struct\_0~X0){\unicdcdcdhd}(l2\_conlat\_1~X1~X0)){\unicdbdjdcd}\\
(m1\_subset\_1~(u3\_conlat\_1~X0~X1)~(k1\_zfmisc\_1~(u4\_struct\_0~X0)))\end{array}
\label{hyp:egehpffhddpfdgpgogmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l5\_struct\_0~X0){\unicdcdcdhd}(l2\_conlat\_1~X1~X0)){\unicdbdjdcd}\\
(m1\_subset\_1~(u2\_conlat\_1~X0~X1)~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))\end{array}
\label{hyp:egehpffhcdpfdgpgogmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_conlat\_1}~{X0}})}{\unicdbdjdcd}{({{l5\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfdgpgogmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_conlat\_1~X0){\unicdcdcdhd}(l1\_conlat\_1~X0)){\unicdbdjdcd}((v4\_conlat\_1~\\
(k6\_conlat\_1~X0)~X0){\unicdcdcdhd}((\preoh v5\_conlat\_1~(k6\_conlat\_1~X0)~X0){\unicdcdcdhd}((v7\_conlat\_1~\\
(k6\_conlat\_1~X0)~X0){\unicdcdcdhd}((v9\_conlat\_1~(k6\_conlat\_1~X0)~X0){\unicdcdcdhd}(l2\_conlat\_1~\\
(k6\_conlat\_1~X0)~X0)))))\end{array}
\label{hyp:egehpflggdpfdgpgogmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_conlat\_1~X0){\unicdcdcdhd}(l1\_conlat\_1~X0)){\unicdbdjdcd}((v4\_conlat\_1~\\
(k5\_conlat\_1~X0)~X0){\unicdcdcdhd}((\preoh v5\_conlat\_1~(k5\_conlat\_1~X0)~X0){\unicdcdcdhd}((v7\_conlat\_1~\\
(k5\_conlat\_1~X0)~X0){\unicdcdcdhd}((v8\_conlat\_1~(k5\_conlat\_1~X0)~X0){\unicdcdcdhd}(l2\_conlat\_1~\\
(k5\_conlat\_1~X0)~X0)))))\end{array}
\label{hyp:egehpflgfdpfdgpgogmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_conlat\_1~X0){\unicdcdcdhd}(l1\_conlat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v5\_conlat\_1~X1~X0){\unicdcdcdhd}((v7\_conlat\_1~X1~X0){\unicdcdcdhd}(l2\_conlat\_1~X1~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((\preoh v5\_conlat\_1~X2~X0){\unicdcdcdhd}((v7\_conlat\_1~X2~X0){\unicdcdcdhd}(l2\_conlat\_1~\\
X2~X0))){\unicdbdjdcd}((r2\_conlat\_1~X0~X1~X2){\unicdbdjded}(r1\_tarski~(u2\_conlat\_1~X0~X1)~\\
(u2\_conlat\_1~X0~X2)))))\end{array}
\label{hyp:egbdgdpfdgpgogmgbgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddadpfdgpgogmgbgehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_conlat\_1~X0){\unicdcdcdhd}(l1\_conlat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v5\_conlat\_1~X1~X0){\unicdcdcdhd}((v7\_conlat\_1~X1~X0){\unicdcdcdhd}(l2\_conlat\_1~X1~X0))){\unicdbdjdcd}\\
((r2\_conlat\_1~X0~X1~(k5\_conlat\_1~X0)){\unicdcdcdhd}(r2\_conlat\_1~X0~(k6\_conlat\_1~\\
X0)~X1)))\end{array}$$
\end{theorem}
\end{document}
