\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{t19\_lattice6 (TMPtpeZSxw9n5uLbmcZKTB8msD7DNCZAgK8)}
\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 $ v2\_lattice6 : {{\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 $ k5\_lattices : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v4\_lattice6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_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 $ v13\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_lattice6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ 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 $ v5\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k13\_lattice3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k10\_lattice3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k12\_lattice3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ 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 $ v2\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r3\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v15\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v14\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}((v13\_lattices~\\
X0){\unicdcdcdhd}((v2\_lattice6~X0){\unicdcdcdhd}(l3\_lattices~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}((X1=k5\_lattices~X0){\unicdbdjded}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh r1\_lattice6~X0~X1~X2))))\end{array}
\label{hyp:ehidpfmgbgehehjgdgfggd}
\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~X0)){\unicdbdjdcd}((X2{\unicdcdgdad}X3){\unicdbdjdcd}((((r1\_lattice6~X0~X2~X1){\unicdcdcdhd}(r1\_lattice6~\\
X0~X3~X1)){\unicdbdjdcd}(X1=k4\_lattices~X0~X3~X2)){\unicdcdcdhd}(((r1\_lattice6~X0~X1~X2){\unicdcdcdhd}\\
(r1\_lattice6~X0~X1~X3)){\unicdbdjdcd}(X1=k3\_lattices~X0~X3~X2)))))))\end{array}
\label{hyp:ehcdpfmgbgehehjgdgfggd}
\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}((v4\_lattice6~X1~X0){\unicdbdjdcd}(v3\_waybel\_6~(k4\_lattice3~X0~X1)~(k3\_lattice3~\\
X0))))\end{array}
\label{hyp:ehbdidpfmgbgehehjgdgfggd}
\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}((v2\_lattice6~X0){\unicdcdcdhd}(l3\_lattices~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}((v4\_lattice6~X1~X0){\unicdbdjded}({\unicdcdaddd} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)){\unicdcdcdhd}((r1\_lattice6~X0~X1~X2){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~X0)){\unicdbdjdcd}((r1\_lattice6~X0~X1~X3){\unicdbdjdcd}(X3=X2)))))))\end{array}
\label{hyp:ehbdfdpfmgbgehehjgdgfggd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v5\_orders\_2~X0){\unicdcdcdhd}((v1\_lattice3~\\
X0){\unicdcdcdhd}(l1\_orders\_2~X0))){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(\\
m1\_subset\_1~X2~(u1\_struct\_0~X0)))){\unicdbdjdcd}(k13\_lattice3~X0~X1~X2=k10\_lattice3~\\
X0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdddpfmgbgehehjgdgfgdd}
\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}((k4\_lattices~X0~X1~X2=k12\_lattice3~\\
(k3\_lattice3~X0)~(k4\_lattice3~X0~X1)~(k4\_lattice3~X0~X2)){\unicdcdcdhd}(k3\_lattices~\\
X0~X1~X2=k13\_lattice3~(k3\_lattice3~X0)~(k4\_lattice3~X0~X1)~(k4\_lattice3~\\
X0~X2)))))\end{array}
\label{hyp:mgddddpfmgbgehehjgdgfggd}
\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}(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}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}\\
(l3\_lattices~X0))){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~X0))){\unicdbdjdcd}(m1\_subset\_1~\\
(k4\_lattice3~X0~X1)~(u1\_struct\_0~(k3\_lattice3~X0)))\end{array}
\label{hyp:egehpflgedpfmgbgehehjgdgfgdd}
\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}(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\_lattice6~X0~X1~X2){\unicdbdjded}((X1{\unicdcdgdad}\\
X2){\unicdcdcdhd}((r3\_lattices~X0~X2~X1){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}(\preoh (r3\_lattices~X0~X2~X3){\unicdcdcdhd}((r3\_lattices~X0~X3~X1){\unicdcdcdhd}((X3{\unicdcdgdad}X1){\unicdcdcdhd}\\
(X3{\unicdcdgdad}X2))))))))))\end{array}
\label{hyp:egfdpfmgbgehehjgdgfggd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}((v3\_waybel\_6~X1~X0){\unicdbdjded}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (X1=k10\_lattice3~X0~X2~X3){\unicdcdcdhd}((X2{\unicdcdgdad}X1){\unicdcdcdhd}(X3{\unicdcdgdad}\\
X1)))))))\end{array}
\label{hyp:egddpfhhbgjhcgfgmgpfgd}
\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 .  (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){\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:ehbdjdpfmgbgehehjgdgfggd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}((v4\_lattice3~\\
X0){\unicdcdcdhd}((v2\_lattice6~X0){\unicdcdcdhd}(l3\_lattices~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}((X1{\unicdcdgdad}k5\_lattices~X0){\unicdbdjdcd}((v4\_lattice6~X1~X0){\unicdbdjded}\\
(v3\_waybel\_6~(k4\_lattice3~X0~X1)~(k3\_lattice3~X0)))))\end{array}$$
\end{theorem}
\end{document}
