\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{t20\_conlat\_2 (TMGzf6gBvP9jKgmFmUg3toSPEoBv3nt53sk)}
\maketitle
Let $ v1\_conlat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_conlat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_conlat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_conlat\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ k8\_conlat\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_conlat\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_conlat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u3\_conlat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_conlat\_1~X0){\unicdcdcdhd}((v2\_conlat\_1~X0){\unicdcdcdhd}(l1\_conlat\_1~\\
X0))){\unicdbdjdcd}(k7\_conlat\_2~(k7\_conlat\_2~X0)=X0)\end{array}
\label{hyp:ehbdhdpfdgpgogmgbgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v1\_conlat\_1~X0){\unicdcdcdhd}(l1\_conlat\_1~X0)){\unicdcdcdhd}\\
(l2\_conlat\_1~X1~X0)){\unicdbdjdcd}((v4\_conlat\_1~(k8\_conlat\_2~X0~X1)~(k7\_conlat\_2~\\
X0)){\unicdcdcdhd}(l2\_conlat\_1~(k8\_conlat\_2~X0~X1)~(k7\_conlat\_2~X0)))\end{array}
\label{hyp:egehpflgidpfdgpgogmgbgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_conlat\_1~X0){\unicdcdcdhd}(l1\_conlat\_1~X0)){\unicdbdjdcd}((\preoh v1\_conlat\_1~\\
(k7\_conlat\_2~X0)){\unicdcdcdhd}((v2\_conlat\_1~(k7\_conlat\_2~X0)){\unicdcdcdhd}(l1\_conlat\_1~\\
(k7\_conlat\_2~X0))))\end{array}
\label{hyp:egehpflghdpfdgpgogmgbgehpfcd}
\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 .  \\
(l2\_conlat\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v4\_conlat\_1~X2~(k7\_conlat\_2~\\
X0)){\unicdcdcdhd}(l2\_conlat\_1~X2~(k7\_conlat\_2~X0))){\unicdbdjdcd}((X2=k8\_conlat\_2~X0~\\
X1){\unicdbdjded}((u2\_conlat\_1~(k7\_conlat\_2~X0)~X2=u3\_conlat\_1~X0~X1){\unicdcdcdhd}(u3\_conlat\_1~\\
(k7\_conlat\_2~X0)~X2=u2\_conlat\_1~X0~X1)))))\end{array}
\label{hyp:egidpfdgpgogmgbgehpfcd}
\end{equation}
\begin{theorem}\label{thm:ehcdadpfdgpgogmgbgehpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_conlat\_1~X0){\unicdcdcdhd}((v2\_conlat\_1~X0){\unicdcdcdhd}(l1\_conlat\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v4\_conlat\_1~X1~X0){\unicdcdcdhd}((\preoh v5\_conlat\_1~X1~X0){\unicdcdcdhd}\\
((v7\_conlat\_1~X1~X0){\unicdcdcdhd}(l2\_conlat\_1~X1~X0)))){\unicdbdjdcd}(k8\_conlat\_2~(k7\_conlat\_2~\\
X0)~(k8\_conlat\_2~X0~X1)=X1))\end{array}$$
\end{theorem}
\end{document}
