\documentclass{article}
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\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
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\begin{document}
\title{l10\_nat\_lat (TMRWCCNcsJQ5tp9cX6hq99T3XKyDpo6be5A)}
\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 $ k2\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_nat\_lat : {\iota}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_nat\_d : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v6\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{{{k6\_nat\_d}~{X0}}~{np\_\_1}}={np\_\_1}})}}}\label{hyp:ehfdbdpfogfghhehpgog}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_1){\unicdcdcdhd}(m2\_subset\_1~np\_\_1~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_1~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_1~k1\_numbers))\end{array}
\label{hyp:dhahdgbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\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}(k2\_lattices~k3\_nat\_lat~\\
X0~X1=k6\_nat\_d~X0~X1)\end{array}
\label{hyp:jgfgcdpfogbgehpfmgbgeh}
\end{equation}
Assume the following.
\begin{equation}
{{v6\_membered}~{k4\_ordinal1}}\label{hyp:ggdggdpfngfgngcgfgchfgeg}
\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}
{{{m1\_subset\_1}~{k4\_nat\_lat}}~{({{u1\_struct\_0}~{k3\_nat\_lat}})}}\label{hyp:egehpflgedpfogbgehpfmgbgeh}
\end{equation}
Assume the following.
\begin{equation}
{{k4\_nat\_lat}={np\_\_1}}\label{hyp:egedpfogbgehpfmgbgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v7\_ordinal1~X1)){\unicdbdjdcd}(\\
k6\_nat\_d~X0~X1=k6\_nat\_d~X1~X0)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflggdpfogbgehpfeg}
\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:mgbdadpfogbgehpfmgbgeh}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~k3\_nat\_lat)){\unicdbdjdcd}((k2\_lattices~\\
k3\_nat\_lat~k4\_nat\_lat~X0=k4\_nat\_lat){\unicdcdcdhd}(k2\_lattices~k3\_nat\_lat~\\
X0~k4\_nat\_lat=k4\_nat\_lat))\end{array}$$
\end{theorem}
\end{document}
