\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{t34\_openlatt (TMXdEnvefgrmjUWGpveU4uBgNVhTjU3X1ib)}
\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 $ v1\_lattice2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_lattice4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k6\_openlatt : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k17\_openlatt : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k18\_openlatt : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k4\_filter\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\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}((v1\_lattice2~X0){\unicdcdcdhd}(l3\_lattices~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}(k3\_funct\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~(k6\_openlatt~\\
(k17\_openlatt~X0)))~(k18\_openlatt~X0)~(k4\_filter\_0~X0~X1~X2)=k4\_filter\_0~\\
(k6\_openlatt~(k17\_openlatt~X0))~(k3\_funct\_2~(u1\_struct\_0~X0)~\\
(u1\_struct\_0~(k6\_openlatt~(k17\_openlatt~X0)))~(k18\_openlatt~\\
X0)~X1)~(k3\_funct\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~(k6\_openlatt~\\
(k17\_openlatt~X0)))~(k18\_openlatt~X0)~X2))))\end{array}
\label{hyp:ehddddpfpgahfgogmgbgeheh}
\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}((v1\_lattice2~X0){\unicdcdcdhd}(l3\_lattices~X0))))){\unicdbdjdcd}((\preoh v2\_struct\_0~\\
(k17\_openlatt~X0)){\unicdcdcdhd}((v1\_pre\_topc~(k17\_openlatt~X0)){\unicdcdcdhd}(v2\_pre\_topc~\\
(k17\_openlatt~X0))))\end{array}
\label{hyp:ggdgbdadpfpgahfgogmgbgeheh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k6\_openlatt~X0)){\unicdcdcdhd}((v10\_lattices~(k6\_openlatt~\\
X0)){\unicdcdcdhd}(l3\_lattices~(k6\_openlatt~X0))))\end{array}
\label{hyp:egehpflggdpfpgahfgogmgbgeheh}
\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}((v1\_lattice2~X0){\unicdcdcdhd}(l3\_lattices~X0))))){\unicdbdjdcd}(m1\_lattice4~(k18\_openlatt~\\
X0)~X0~(k6\_openlatt~(k17\_openlatt~X0)))\end{array}
\label{hyp:egehpflgbdidpfpgahfgogmgbgeheh}
\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}((v1\_lattice2~X0){\unicdcdcdhd}(l3\_lattices~X0))))){\unicdbdjdcd}((v1\_pre\_topc~(\\
k17\_openlatt~X0)){\unicdcdcdhd}(l1\_pre\_topc~(k17\_openlatt~X0)))\end{array}
\label{hyp:egehpflgbdhdpfpgahfgogmgbgeheh}
\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}({\unicdcdadad} X2 .  (m1\_lattice4~X2~X0~X1){\unicdbdjdcd}((r1\_lattice4~X0~X1~X2){\unicdbdjded}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~X0)){\unicdbdjdcd}(k3\_funct\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X1)~X2~(k4\_filter\_0~X0~X3~X4)=k4\_filter\_0~X1~(k3\_funct\_2~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X1)~X2~X3)~(k3\_funct\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X1)~X2~X4)))))))\end{array}
\label{hyp:egddpfmgbgehehjgdgfged}
\end{equation}
\begin{theorem}\label{thm:ehddedpfpgahfgogmgbgeheh}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~\\
X0){\unicdcdcdhd}((v1\_lattice2~X0){\unicdcdcdhd}(l3\_lattices~X0))))){\unicdbdjdcd}(r1\_lattice4~X0~\\
(k6\_openlatt~(k17\_openlatt~X0))~(k18\_openlatt~X0))\end{array}$$
\end{theorem}
\end{document}
