\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{t52\_yellow\_0 (TMd43Z1m1sY37UHZRTyRhdS6fFUyZXeqm6R)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r2\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r2\_lattice3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_lattice3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
{\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}(((r2\_lattice3~\\
X0~X1~X2){\unicdbdjdcd}(r2\_lattice3~X0~(k3\_xboole\_0~X1~(u1\_struct\_0~X0))~X2)){\unicdcdcdhd}\\
(((r2\_lattice3~X0~(k3\_xboole\_0~X1~(u1\_struct\_0~X0))~X2){\unicdbdjdcd}(r2\_lattice3~\\
X0~X1~X2)){\unicdcdcdhd}(((r1\_lattice3~X0~X1~X2){\unicdbdjdcd}(r1\_lattice3~X0~(k3\_xboole\_0~\\
X1~(u1\_struct\_0~X0))~X2)){\unicdcdcdhd}((r1\_lattice3~X0~(k3\_xboole\_0~X1~(u1\_struct\_0~\\
X0))~X2){\unicdbdjdcd}(r1\_lattice3~X0~X1~X2))))))\end{array}
\label{hyp:ehfdpfjhfgmgmgpghhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
{\unicdcdadad} X2 .  ((r2\_yellow\_0~X0~X1){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(\\
u1\_struct\_0~X0)){\unicdbdjdcd}((r1\_lattice3~X0~X1~X3){\unicdbdjded}(r1\_lattice3~X0~X2~X3)))){\unicdbdjdcd}\\
(k2\_yellow\_0~X0~X1=k2\_yellow\_0~X0~X2))\end{array}
\label{hyp:ehedjdpfjhfgmgmgpghhpfad}
\end{equation}
\begin{theorem}\label{thm:ehfdcdpfjhfgmgmgpghhpfad}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((r2\_yellow\_0~X0~X1){\unicdcdcdid}(r2\_yellow\_0~X0~(k3\_xboole\_0~X1~(u1\_struct\_0~\\
X0)))){\unicdbdjdcd}(k2\_yellow\_0~X0~X1=k2\_yellow\_0~X0~(k3\_xboole\_0~X1~(u1\_struct\_0~\\
X0))))\end{array}$$
\end{theorem}
\end{document}
