\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\_openlatt (TMG4DuBJWTRkvZa6YxPUEtQ1NztT31JBLBi)}
\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 $ r2\_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 $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_lattices : {{\iota}{\unicdbdjdcd}{\iota}}$ 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 $ k15\_openlatt : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k16\_openlatt : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_openlatt : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_openlatt : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v11\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_lattice4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ l1\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_pre\_topc : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_openlatt : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_filter\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
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}(k6\_lattices~(k6\_openlatt~X0)=u1\_struct\_0~X0)\end{array}
\label{hyp:ehjdpfpgahfgogmgbgeheh}
\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}(k3\_funct\_2~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~(k15\_openlatt~X0))~(k16\_openlatt~X0)~(k6\_lattices~\\
X0)=k7\_openlatt~X0)\end{array}
\label{hyp:ehcdidpfpgahfgogmgbgeheh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))))){\unicdcdcdhd}(m1\_subset\_1~X3~X0))){\unicdbdjdcd}(k3\_funct\_2~X0~\\
X1~X2~X3=k1\_funct\_1~X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfggfhogdgehpfcd}
\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}(k18\_openlatt~X0=\\
k8\_openlatt~X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdidpfpgahfgogmgbgeheh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}((v11\_lattices~\\
X0){\unicdcdcdhd}(l3\_lattices~X0)))){\unicdbdjdcd}(k16\_openlatt~X0=k8\_openlatt~X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdgdpfpgahfgogmgbgeheh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(u1\_struct\_0~X0))\end{array}
\label{hyp:ggdgcdpfdhehchfhdgehpfad}
\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 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}\\
(l3\_lattices~X0))){\unicdcdcdhd}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v10\_lattices~X1){\unicdcdcdhd}(\\
l3\_lattices~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_lattice4~X2~X0~X1){\unicdbdjdcd}((v1\_funct\_1~\\
X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)))))))\end{array}
\label{hyp:egehpfngbdpfmgbgehehjgdgfged}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l3\_lattices}~{X0}})}{\unicdbdjdcd}{({{({{l1\_lattices}~{X0}})}{\unicdcdcdhd}{({{l2\_lattices}~{X0}})}})}}}\label{hyp:egehpfmgddpfmgbgehehjgdgfgdh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_lattices}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfmgbgehehjgdgfgdh}
\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}(l2\_lattices~X0)){\unicdbdjdcd}(m1\_subset\_1~\\
(k6\_lattices~X0)~(u1\_struct\_0~X0))\end{array}
\label{hyp:egehpflggdpfmgbgehehjgdgfgdh}
\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}((v11\_lattices~\\
X0){\unicdcdcdhd}(l3\_lattices~X0)))){\unicdbdjdcd}(m1\_lattice4~(k16\_openlatt~X0)~X0~(k15\_openlatt~\\
X0))\end{array}
\label{hyp:egehpflgbdgdpfpgahfgogmgbgeheh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}((v11\_lattices~\\
X0){\unicdcdcdhd}(l3\_lattices~X0)))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k15\_openlatt~X0)){\unicdcdcdhd}\\
((v10\_lattices~(k15\_openlatt~X0)){\unicdcdcdhd}(l3\_lattices~(k15\_openlatt~\\
X0))))\end{array}
\label{hyp:egehpflgbdfdpfpgahfgogmgbgeheh}
\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}((r2\_lattice4~X0~X1~X2){\unicdbdjded}\\
(k3\_funct\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)~X2~(k6\_lattices~\\
X0)=k6\_lattices~X1))))\end{array}
\label{hyp:egedpfmgbgehehjgdgfged}
\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}({\unicdcdadad} X1 .  ((v1\_pre\_topc~\\
X1){\unicdcdcdhd}(l1\_pre\_topc~X1)){\unicdbdjdcd}((X1=k17\_openlatt~X0){\unicdbdjded}((u1\_struct\_0~\\
X1=k7\_openlatt~X0){\unicdcdcdhd}(u1\_pre\_topc~X1=ReplSep~(toset~({\uniddcgcg} X2 : \iota .  \\
m1\_subset\_1~X2~(k1\_zfmisc\_1~(k9\_openlatt~X0))))~({\uniddcgcg} X2 : \iota .  \\
True)~({\uniddcgcg} X2 : \iota .  k3\_tarski~X2)))))\end{array}
\label{hyp:egbdcdpfpgahfgogmgbgeheh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l3\_lattices~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~\\
X0){\unicdcdcdhd}(v3\_filter\_0~X0))){\unicdbdjdcd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}\\
((v11\_lattices~X0){\unicdcdcdhd}(v3\_filter\_0~X0)))))\end{array}
\label{hyp:dgdgcdpfggjgmgehfgchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l3\_lattices~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~\\
X0){\unicdcdcdhd}(v1\_lattice2~X0))){\unicdbdjdcd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}\\
((v13\_lattices~X0){\unicdcdcdhd}(v3\_filter\_0~X0)))))\end{array}
\label{hyp:dgdgbdpfmgbgehehjgdgfgcd}
\end{equation}
\begin{theorem}\label{thm:ehddfdpfpgahfgogmgbgeheh}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~\\
X0){\unicdcdcdhd}((v1\_lattice2~X0){\unicdcdcdhd}(l3\_lattices~X0))))){\unicdbdjdcd}(r2\_lattice4~X0~\\
(k6\_openlatt~(k17\_openlatt~X0))~(k18\_openlatt~X0))\end{array}$$
\end{theorem}
\end{document}
