\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{t35\_lopclset (TMMj3sRGZnPQjh3vxBfnB5k54qVQesP83mN)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v10\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v17\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_filter\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k12\_lopclset : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k13\_lopclset : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_lopclset : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m1\_lattice4 : {{\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}((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~\\
X0){\unicdcdcdhd}((v17\_lattices~X0){\unicdcdcdhd}(l3\_lattices~X0))))){\unicdbdjdcd}(k13\_lopclset~\\
X0=k8\_lopclset~X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdddpfmgpgahdgmgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~\\
X0){\unicdcdcdhd}((v17\_lattices~X0){\unicdcdcdhd}(l3\_lattices~X0))))){\unicdbdjdcd}((v1\_funct\_1~(\\
k8\_lopclset~X0)){\unicdcdcdhd}((v1\_funct\_2~(k8\_lopclset~X0)~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~(k12\_lopclset~X0))){\unicdcdcdhd}(v3\_funct\_2~(k8\_lopclset~\\
X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~(k12\_lopclset~X0)))))\end{array}
\label{hyp:ggdghdpfmgpgahdgmgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~\\
X0){\unicdcdcdhd}((v17\_lattices~X0){\unicdcdcdhd}(l3\_lattices~X0))))){\unicdbdjdcd}(m1\_lattice4~(\\
k13\_lopclset~X0)~X0~(k12\_lopclset~X0))\end{array}
\label{hyp:egehpflgbdddpfmgpgahdgmgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~\\
X0){\unicdcdcdhd}((v17\_lattices~X0){\unicdcdcdhd}(l3\_lattices~X0))))){\unicdbdjdcd}((\preoh v2\_struct\_0~\\
(k12\_lopclset~X0)){\unicdcdcdhd}((v10\_lattices~(k12\_lopclset~X0)){\unicdcdcdhd}(l3\_lattices~\\
(k12\_lopclset~X0))))\end{array}
\label{hyp:egehpflgbdcdpfmgpgahdgmgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}(l3\_lattices~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v10\_lattices~X1){\unicdcdcdhd}(l3\_lattices~\\
X1))){\unicdbdjdcd}((r1\_filter\_1~X0~X1){\unicdbdjded}({\unicdcdaddd} X2 .  (m1\_lattice4~X2~X0~X1){\unicdcdcdhd}\\
(v3\_funct\_2~X2~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)))))\end{array}
\label{hyp:egcdpfmgbgehehjgdgfged}
\end{equation}
\begin{theorem}\label{thm:ehddfdpfmgpgahdgmgdhfgeh}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~\\
X0){\unicdcdcdhd}((v17\_lattices~X0){\unicdcdcdhd}(l3\_lattices~X0))))){\unicdbdjdcd}(r1\_filter\_1~X0~\\
(k12\_lopclset~X0))\end{array}$$
\end{theorem}
\end{document}
