\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{t38\_lattice2 (TMMB6wjNvoaw8QRCsWLWn2g2eHxvsXa84sS)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v10\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r3\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_lattice2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v8\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v9\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v6\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v3\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v8\_lattices~X0){\unicdcdcdhd}((v9\_lattices~\\
X0){\unicdcdcdhd}(l3\_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}(k2\_lattices~X0~X1~X2=X1))))\end{array}
\label{hyp:ehedpfmgbgehehjgdgfgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}(l3\_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}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(u1\_struct\_0~(k1\_lattice2~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(u1\_struct\_0~(k1\_lattice2~X0))){\unicdbdjdcd}(((X1=X3){\unicdcdcdhd}(X2=X4)){\unicdbdjdcd}((k4\_lattices~\\
X0~X1~X2=k3\_lattices~(k1\_lattice2~X0)~X3~X4){\unicdcdcdhd}(k3\_lattices~X0~X1~\\
X2=k4\_lattices~(k1\_lattice2~X0)~X3~X4)))))))\end{array}
\label{hyp:ehddhdpfmgbgehehjgdgfgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v6\_lattices~\\
X0){\unicdcdcdhd}((v8\_lattices~X0){\unicdcdcdhd}((v9\_lattices~X0){\unicdcdcdhd}(l3\_lattices~X0))))){\unicdcdcdhd}\\
((m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)))){\unicdbdjdcd}((r3\_lattices~X0~X1~X2){\unicdbdjded}(r1\_lattices~X0~X1~X2))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchddpfmgbgehehjgdgfgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v6\_lattices~\\
X0){\unicdcdcdhd}(l1\_lattices~X0))){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(\\
m1\_subset\_1~X2~(u1\_struct\_0~X0)))){\unicdbdjdcd}(k4\_lattices~X0~X1~X2=k2\_lattices~\\
X0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfmgbgehehjgdgfgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v4\_lattices~\\
X0){\unicdcdcdhd}(l2\_lattices~X0))){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(\\
m1\_subset\_1~X2~(u1\_struct\_0~X0)))){\unicdbdjdcd}(k3\_lattices~X0~X1~X2=k1\_lattices~\\
X0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfmgbgehehjgdgfgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}(l3\_lattices~\\
X0))){\unicdbdjdcd}((v3\_lattices~(k1\_lattice2~X0)){\unicdcdcdhd}(v10\_lattices~(k1\_lattice2~\\
X0)))\end{array}
\label{hyp:ggdgidpfmgbgehehjgdgfgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l3\_lattices~X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~\\
(k1\_lattice2~X0)){\unicdcdcdhd}(v3\_lattices~(k1\_lattice2~X0)))\end{array}
\label{hyp:ggdgbdpfmgbgehehjgdgfgcd}
\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 .  (l3\_lattices~X0){\unicdbdjdcd}((v3\_lattices~(k1\_lattice2~X0)){\unicdcdcdhd}\\
(l3\_lattices~(k1\_lattice2~X0)))\end{array}
\label{hyp:egehpflgbdpfmgbgehehjgdgfgcd}
\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 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v6\_lattices~\\
X0){\unicdcdcdhd}(l1\_lattices~X0))){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(\\
m1\_subset\_1~X2~(u1\_struct\_0~X0)))){\unicdbdjdcd}(k4\_lattices~X0~X1~X2=k4\_lattices~\\
X0~X2~X1)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgedpfmgbgehehjgdgfgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l3\_lattices~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(v10\_lattices~\\
X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v4\_lattices~X0){\unicdcdcdhd}((v5\_lattices~X0){\unicdcdcdhd}\\
((v6\_lattices~X0){\unicdcdcdhd}((v7\_lattices~X0){\unicdcdcdhd}((v8\_lattices~X0){\unicdcdcdhd}(v9\_lattices~\\
X0))))))))\end{array}
\label{hyp:dgdgbdpfmgbgehehjgdgfgdh}
\end{equation}
\begin{theorem}\label{thm:ehddidpfmgbgehehjgdgfgcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}(l3\_lattices~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}((r3\_lattices~X0~X1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~(k1\_lattice2~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~(u1\_struct\_0~(k1\_lattice2~X0))){\unicdbdjdcd}(((X1=X3){\unicdcdcdhd}(\\
X2=X4)){\unicdbdjdcd}(r3\_lattices~(k1\_lattice2~X0)~X4~X3)))))))\end{array}$$
\end{theorem}
\end{document}
