\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{t11\_openlatt (TMVQqQx44gnkheNg1wWg3seiy1PL22w6o2e)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v10\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v19\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v20\_lattices : {{\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 $ u1\_struct\_0 : {{\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 $ k7\_openlatt : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
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}((v1\_relat\_1~(k8\_openlatt~X0)){\unicdcdcdhd}(v1\_funct\_1~\\
(k8\_openlatt~X0)))\end{array}
\label{hyp:egehpflgidpfpgahfgogmgbgeheh}
\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}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~\\
X1)){\unicdbdjdcd}((X1=k8\_openlatt~X0){\unicdbdjded}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}((k9\_xtuple\_0~X1=u1\_struct\_0~X0){\unicdcdcdhd}(k1\_funct\_1~X1~X2=ReplSep~\\
(toset~({\uniddcgcg} X3 : \iota .  (\preoh v1\_xboole\_0~X3){\unicdcdcdhd}((v19\_lattices~X3~X0){\unicdcdcdhd}\\
((v20\_lattices~X3~X0){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0)))))))~({\uniddcgcg} X3 : \iota .  (X3 \in k7\_openlatt~X0){\unicdcdcdhd}(X2 \in X3))~({\uniddcgcg} X3 : \\
\iota .  X3))))))\end{array}
\label{hyp:eggdpfpgahfgogmgbgeheh}
\end{equation}
\begin{theorem}\label{thm:ehbdbdpfpgahfgogmgbgeheh}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}((v11\_lattices~\\
X0){\unicdcdcdhd}(l3\_lattices~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v19\_lattices~\\
X1~X0){\unicdcdcdhd}((v20\_lattices~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}((X1 \in \\
k1\_funct\_1~(k8\_openlatt~X0)~X2){\unicdbdjded}((X1 \in k7\_openlatt~X0){\unicdcdcdhd}(X2 \in X1)))))\end{array}$$
\end{theorem}
\end{document}
