\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{t10\_lattice6 (TMZLroKbX9LjFcisFTgqZXhPq8Vx1NTpG8k)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v10\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_lattice6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_lattices : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_waybel\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_lattice3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_lattice3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v4\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_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 $ r1\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k16\_lattice3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r3\_lattice3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r3\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k15\_lattice3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v14\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_yellow\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_yellow\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v6\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v9\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v15\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_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}((v4\_lattices~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){\unicdcdcdhd}(r1\_lattices~\\
X0~X2~X1)){\unicdbdjdcd}(X1=X2))))\end{array}
\label{hyp:ehidpfmgbgehehjgdgfgdh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}((v4\_lattice3~\\
X0){\unicdcdcdhd}(l3\_lattices~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (X1=k16\_lattice3~X0~X2){\unicdbdjded}((r3\_lattice3~X0~X1~\\
X2){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}((r3\_lattice3~\\
X0~X3~X2){\unicdbdjdcd}(r3\_lattices~X0~X3~X1))))))\end{array}
\label{hyp:ehddedpfmgbgehehjgdgfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~X1){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}\\
(X0 \in X1))\end{array}
\label{hyp:ehcdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}((v4\_lattice3~\\
X0){\unicdcdcdhd}(l3\_lattices~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (k15\_lattice3~X0~X1=k1\_yellow\_0~\\
(k3\_lattice3~X0)~X1){\unicdcdcdhd}(k16\_lattice3~X0~X1=k2\_yellow\_0~(k3\_lattice3~\\
X0)~X1))\end{array}
\label{hyp:ehcdjdpfjhfgmgmgpghhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}((v14\_lattices~\\
X0){\unicdcdcdhd}(l3\_lattices~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}(r3\_lattices~X0~X1~(k6\_lattices~X0)))\end{array}
\label{hyp:ehbdjdpfmgbgehehjgdgfgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}((v2\_yellow\_0~\\
X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}(l1\_orders\_2~X0))))){\unicdbdjdcd}(v2\_waybel\_6~(k4\_yellow\_0~\\
X0)~X0)\end{array}
\label{hyp:ehbdadpfhhbgjhcgfgmgpfgd}
\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 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}(l3\_lattices~\\
X0))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k3\_lattice3~X0)){\unicdcdcdhd}((v1\_orders\_2~(k3\_lattice3~\\
X0)){\unicdcdcdhd}((v3\_orders\_2~(k3\_lattice3~X0)){\unicdcdcdhd}((v4\_orders\_2~(k3\_lattice3~\\
X0)){\unicdcdcdhd}(v5\_orders\_2~(k3\_lattice3~X0))))))\end{array}
\label{hyp:ggdgedpfmgbgehehjgdgfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}((v14\_lattices~\\
X0){\unicdcdcdhd}(l3\_lattices~X0)))){\unicdbdjdcd}((v1\_orders\_2~(k3\_lattice3~X0)){\unicdcdcdhd}((\\
v3\_orders\_2~(k3\_lattice3~X0)){\unicdcdcdhd}((v4\_orders\_2~(k3\_lattice3~X0)){\unicdcdcdhd}\\
((v5\_orders\_2~(k3\_lattice3~X0)){\unicdcdcdhd}(v2\_yellow\_0~(k3\_lattice3~X0))))))\end{array}
\label{hyp:ggdgcdpfjhfgmgmgpghhpfbd}
\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}((v1\_orders\_2~(k3\_lattice3~X0)){\unicdcdcdhd}((v3\_orders\_2~(k3\_lattice3~\\
X0)){\unicdcdcdhd}((v4\_orders\_2~(k3\_lattice3~X0)){\unicdcdcdhd}((v5\_orders\_2~(k3\_lattice3~\\
X0)){\unicdcdcdhd}((v1\_lattice3~(k3\_lattice3~X0)){\unicdcdcdhd}(v2\_lattice3~(k3\_lattice3~\\
X0)))))))\end{array}
\label{hyp:ggdgbdpfjhfgmgmgpghhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdaddd} X1 .  {{{m1\_subset\_1}~{X1}}~{X0}}}}\label{hyp:fgihjgdhehfgogdgfgpfngbdpfdhfhcgdhfgehpfbd}
\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 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_lattices~X0)){\unicdbdjdcd}(m1\_subset\_1~\\
(k6\_lattices~X0)~(u1\_struct\_0~X0))\end{array}
\label{hyp:egehpflggdpfmgbgehehjgdgfgdh}
\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}((v1\_orders\_2~(k3\_lattice3~X0)){\unicdcdcdhd}((v3\_orders\_2~(k3\_lattice3~\\
X0)){\unicdcdcdhd}((v4\_orders\_2~(k3\_lattice3~X0)){\unicdcdcdhd}((v5\_orders\_2~(k3\_lattice3~\\
X0)){\unicdcdcdhd}(l1\_orders\_2~(k3\_lattice3~X0))))))\end{array}
\label{hyp:egehpflgddpfmgbgehehjgdgfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}((v4\_lattice3~\\
X0){\unicdcdcdhd}(l3\_lattices~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}(k3\_lattice6~X0~X1=k16\_lattice3~X0~(ReplSep~(toset~({\uniddcgcg} X2 : \\
\iota .  m1\_subset\_1~X2~(u1\_struct\_0~X0)))~({\uniddcgcg} X2 : \iota .  (r3\_lattices~\\
X0~X1~X2){\unicdcdcdhd}(X2{\unicdcdgdad}X1))~({\uniddcgcg} X2 : \iota .  X2))))\end{array}
\label{hyp:eggdpfmgbgehehjgdgfggd}
\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}(k4\_lattice3~\\
X0~X1=X1))\end{array}
\label{hyp:egddpfmgbgehehjgdgfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l3\_lattices~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (r3\_lattice3~X0~\\
X1~X2){\unicdbdjded}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}((X3 \in X2){\unicdbdjdcd}\\
(r1\_lattices~X0~X1~X3)))))\end{array}
\label{hyp:egbdgdpfmgbgehehjgdgfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}(k4\_yellow\_0~X0=k2\_yellow\_0~X0~k1\_xboole\_0)\end{array}
\label{hyp:egbdcdpfjhfgmgmgpghhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l3\_lattices~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(v15\_lattices~\\
X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_lattices~X0){\unicdcdcdhd}(v14\_lattices~X0))))\end{array}
\label{hyp:dgdgedpfmgbgehehjgdgfgdh}
\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}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l3\_lattices~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~\\
X0){\unicdcdcdhd}(v4\_lattice3~X0))){\unicdbdjdcd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}\\
(v15\_lattices~X0))))\end{array}
\label{hyp:dgdgbdpflgogbgdhehfgch}
\end{equation}
\begin{theorem}\label{thm:ehbdadpfmgbgehehjgdgfggd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}((v4\_lattice3~\\
X0){\unicdcdcdhd}(l3\_lattices~X0)))){\unicdbdjdcd}((k3\_lattice6~X0~(k6\_lattices~X0)=k6\_lattices~\\
X0){\unicdcdcdhd}(v2\_waybel\_6~(k4\_lattice3~X0~(k6\_lattices~X0))~(k3\_lattice3~\\
X0)))\end{array}$$
\end{theorem}
\end{document}
