\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\preoh[1]{\lnot #1}
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\begin{document}
\title{l27\_nat\_lat (TMXrxreNzDMfiy8WKZcNKz3YsXNT44J6nqk)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_nat\_lat : {\iota}$ be given.
Let $ k1\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_nat\_d : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_lattices : {{\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 $ v1\_xboole\_0 : {{\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}({\unicdcdadad} X2 .  \\
(v7\_ordinal1~X2){\unicdbdjdcd}(k5\_nat\_d~X0~(k5\_nat\_d~X1~X2)=k5\_nat\_d~(k5\_nat\_d~\\
X0~X1)~X2)))\end{array}
\label{hyp:ehedddpfogfghhehpgog}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~(u1\_struct\_0~k10\_nat\_lat)){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(u1\_struct\_0~k10\_nat\_lat))){\unicdbdjdcd}(k1\_lattices~k10\_nat\_lat~\\
X0~X1=k5\_nat\_d~X0~X1)\end{array}
\label{hyp:jgfgddpfogbgehpfmgbgeh}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v2\_struct\_0}~{k10\_nat\_lat}}}})}{\unicdcdcdhd}{({{v3\_lattices}~{k10\_nat\_lat}})}}\label{hyp:ggdggdpfogbgehpfmgbgeh}
\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}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_lattices~\\
X0)){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)))){\unicdbdjdcd}(m1\_subset\_1~(k1\_lattices~X0~X1~X2)~(u1\_struct\_0~X0))\end{array}
\label{hyp:egehpflgbdpfmgbgehehjgdgfgdh}
\end{equation}
Assume the following.
\begin{equation}
{{({{v3\_lattices}~{k10\_nat\_lat}})}{\unicdcdcdhd}{({{l3\_lattices}~{k10\_nat\_lat}})}}\label{hyp:egehpflgbdadpfogbgehpfmgbgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v7\_ordinal1~X1)){\unicdbdjdcd}(\\
k5\_nat\_d~X0~X1=k5\_nat\_d~X1~X0)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgfdpfogbgehpfeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~k10\_nat\_lat)){\unicdbdjdcd}((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}(v7\_ordinal1~X0))\end{array}
\label{hyp:dgdgedpfogbgehpfmgbgeh}
\end{equation}
\begin{theorem}\label{thm:mgcdhdpfogbgehpfmgbgeh}
$$\begin{array}{c}({\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~k10\_nat\_lat)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~k10\_nat\_lat)){\unicdbdjdcd}(k1\_lattices~k10\_nat\_lat~\\
X0~X1=k1\_lattices~k10\_nat\_lat~X1~X0))){\unicdcdcdhd}({\unicdcdadad} X0 .  (m1\_subset\_1~\\
X0~(u1\_struct\_0~k10\_nat\_lat)){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
k10\_nat\_lat)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~k10\_nat\_lat)){\unicdbdjdcd}\\
(k1\_lattices~k10\_nat\_lat~X0~(k1\_lattices~k10\_nat\_lat~X1~X2)=k1\_lattices~\\
k10\_nat\_lat~(k1\_lattices~k10\_nat\_lat~X0~X1)~X2))))\end{array}$$
\end{theorem}
\end{document}
