\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{t31\_openlatt (TMchfgS7WkEcsYpxJxPqtSVGtcnuUXhUncT)}
\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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_openlatt : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k17\_openlatt : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_openlatt : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_tarski : {{\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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ g3\_lattices : {{\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 $ k5\_openlatt : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_openlatt : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_openlatt : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_pre\_topc : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_openlatt : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_lattices : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_lattices : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~\\
X1~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0)~X0))))){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~\\
(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0)~X0)))))){\unicdbdjdcd}({\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
(g3\_lattices~X0~X1~X2=g3\_lattices~X3~X4~X5){\unicdbdjdcd}((X0=X3){\unicdcdcdhd}((X1=X4){\unicdcdcdhd}\\
(X2=X5))))\end{array}
\label{hyp:ggchfgfgpfhgddpfmgbgehehjgdgfgdh}
\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}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}((v1\_funct\_1~(k5\_openlatt~X0)){\unicdcdcdhd}((v1\_funct\_2~(k5\_openlatt~\\
X0)~(k2\_zfmisc\_1~(k1\_openlatt~X0)~(k1\_openlatt~X0))~(k1\_openlatt~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~(k5\_openlatt~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k1\_openlatt~X0)~(k1\_openlatt~X0))~(k1\_openlatt~\\
X0))))))\end{array}
\label{hyp:egehpflgfdpfpgahfgogmgbgeheh}
\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}((v1\_funct\_1~(k4\_openlatt~X0)){\unicdcdcdhd}((v1\_funct\_2~(k4\_openlatt~\\
X0)~(k2\_zfmisc\_1~(k1\_openlatt~X0)~(k1\_openlatt~X0))~(k1\_openlatt~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~(k4\_openlatt~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k1\_openlatt~X0)~(k1\_openlatt~X0))~(k1\_openlatt~\\
X0))))))\end{array}
\label{hyp:egehpflgedpfpgahfgogmgbgeheh}
\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 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~\\
X1~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0)~X0))))){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~\\
(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0)~X0)))))){\unicdbdjdcd}((v3\_lattices~(g3\_lattices~X0~X1~\\
X2)){\unicdcdcdhd}(l3\_lattices~(g3\_lattices~X0~X1~X2)))\end{array}
\label{hyp:egehpfhgddpfmgbgehehjgdgfgdh}
\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}(k6\_openlatt~X0=g3\_lattices~(k1\_openlatt~X0)~(k4\_openlatt~\\
X0)~(k5\_openlatt~X0))\end{array}
\label{hyp:egedpfpgahfgogmgbgeheh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_pre\_topc}~{X0}})}{\unicdbdjdcd}{({{{k1\_openlatt}~{X0}}={{u1\_pre\_topc}~{X0}}})}}}\label{hyp:egbdpfpgahfgogmgbgeheh}
\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}((v3\_lattices~X0){\unicdbdjdcd}(X0=g3\_lattices~\\
(u1\_struct\_0~X0)~(u2\_lattices~X0)~(u1\_lattices~X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghddpfmgbgehehjgdgfgdh}
\end{equation}
\begin{theorem}\label{thm:ehddbdpfpgahfgogmgbgeheh}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~\\
X0){\unicdcdcdhd}((v1\_lattice2~X0){\unicdcdcdhd}(l3\_lattices~X0))))){\unicdbdjdcd}(u1\_struct\_0~(k6\_openlatt~\\
(k17\_openlatt~X0))=ReplSep~(toset~({\uniddcgcg} X1 : \iota .  m1\_subset\_1~X1~\\
(k1\_zfmisc\_1~(k9\_openlatt~X0))))~({\uniddcgcg} X1 : \iota .  True)~({\uniddcgcg} X1 : \\
\iota .  k3\_tarski~X1))\end{array}$$
\end{theorem}
\end{document}
