\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{t49\_yellow\_7 (TMEgfM5TgiKYxrUN1X3jzSEtHHnUxhiG6ar)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_yellow\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_yellow\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_lattice3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r2\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}((v3\_lattice3~\\
X0){\unicdcdcdhd}(l1\_orders\_2~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (r1\_yellow\_0~X0~X1){\unicdcdcdhd}(r2\_yellow\_0~\\
X0~X1))\end{array}
\label{hyp:ehbdhdpfjhfgmgmgpghhpfad}
\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 .  \\
((r2\_yellow\_0~X0~X1){\unicdcdcdid}(r1\_yellow\_0~(k7\_lattice3~X0)~X1)){\unicdbdjdcd}(k2\_yellow\_0~\\
X0~X1=k1\_yellow\_0~(k7\_lattice3~X0)~X1))\end{array}
\label{hyp:ehbdddpfjhfgmgmgpghhpfhd}
\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 .  \\
((r1\_yellow\_0~X0~X1){\unicdcdcdid}(r2\_yellow\_0~(k7\_lattice3~X0)~X1)){\unicdbdjdcd}(k1\_yellow\_0~\\
X0~X1=k2\_yellow\_0~(k7\_lattice3~X0)~X1))\end{array}
\label{hyp:ehbdcdpfjhfgmgmgpghhpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~\\
(k7\_lattice3~X0)){\unicdcdcdhd}(v1\_orders\_2~(k7\_lattice3~X0)))\end{array}
\label{hyp:ggdggdpfmgbgehehjgdgfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}((v1\_orders\_2~(k7\_lattice3~X0)){\unicdcdcdhd}\\
(l1\_orders\_2~(k7\_lattice3~X0)))\end{array}
\label{hyp:egehpflghdpfmgbgehehjgdgfgdd}
\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 .  \\
(v1\_relat\_1~X1){\unicdbdjdcd}(k5\_yellow\_2~X0~X1=k2\_yellow\_0~X0~(k10\_xtuple\_0~\\
X1)))\end{array}
\label{hyp:eggdpfjhfgmgmgpghhpfcd}
\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 .  \\
(v1\_relat\_1~X1){\unicdbdjdcd}(k4\_yellow\_2~X0~X1=k1\_yellow\_0~X0~(k10\_xtuple\_0~\\
X1)))\end{array}
\label{hyp:egfdpfjhfgmgmgpghhpfcd}
\end{equation}
\begin{theorem}\label{thm:ehedjdpfjhfgmgmgpghhpfhd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}((v3\_lattice3~\\
X0){\unicdcdcdhd}(l1\_orders\_2~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~\\
X1)){\unicdbdjdcd}((k4\_yellow\_2~X0~X1=k5\_yellow\_2~(k7\_lattice3~X0)~X1){\unicdcdcdhd}(k5\_yellow\_2~\\
X0~X1=k4\_yellow\_2~(k7\_lattice3~X0)~X1)))\end{array}$$
\end{theorem}
\end{document}
