\documentclass{article}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdcdadjd{\notin}
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\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t3\_nat\_lat (TMVQFgjorNhGyffz22BK8QmRMAE9ki2UBsR)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_nat\_lat : {\iota}$ be given.
Let $ r1\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_nat\_d : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_nat\_d : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v6\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}((\\
r1\_nat\_d~X0~X1){\unicdbdjded}(k5\_nat\_d~X0~X1=X1)))\end{array}
\label{hyp:ehededpfogfghhehpgog}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~(u1\_struct\_0~k3\_nat\_lat)){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(u1\_struct\_0~k3\_nat\_lat))){\unicdbdjdcd}(k1\_lattices~k3\_nat\_lat~\\
X0~X1=k5\_nat\_d~X0~X1)\end{array}
\label{hyp:jgfgbdpfogbgehpfmgbgeh}
\end{equation}
Assume the following.
\begin{equation}
{{v6\_membered}~{({{u1\_struct\_0}~{k3\_nat\_lat}})}}\label{hyp:ggdgbdpfogbgehpfmgbgeh}
\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}
\begin{array}{c}(\preoh v2\_struct\_0~k3\_nat\_lat){\unicdcdcdhd}((v3\_lattices~k3\_nat\_lat){\unicdcdcdhd}(l3\_lattices~\\
k3\_nat\_lat))\end{array}
\label{hyp:egehpflgddpfogbgehpfmgbgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_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}((r1\_lattices~X0~X1~X2){\unicdbdjded}(k1\_lattices~X0~X1~X2=\\
X2))))\end{array}
\label{hyp:egddpfmgbgehehjgdgfgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v6\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
(v7\_ordinal1~X1))\end{array}
\label{hyp:dgdgbdhdpfngfgngcgfgchfgeg}
\end{equation}
\begin{theorem}\label{thm:ehddpfogbgehpfmgbgeh}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~k3\_nat\_lat)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~k3\_nat\_lat)){\unicdbdjdcd}((r1\_lattices~k3\_nat\_lat~\\
X0~X1){\unicdbdjdcd}(r1\_nat\_d~X0~X1)))\end{array}$$
\end{theorem}
\end{document}
