\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{t17\_yellow\_1 (TMaYkUUMwDFK8nUeTvTov8yWTofCs1pZqRt)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_yellow\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k13\_lattice3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k12\_lattice3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_yellow\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k11\_lattice3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k10\_lattice3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k9\_setfam\_1 : {{\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 $ v2\_lattice3 : {{\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 $ v3\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_lattice3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v10\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_lattice3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ g1\_orders\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_yellow\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
(k2\_yellow\_1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
(k2\_yellow\_1~X0))){\unicdbdjdcd}((k3\_xboole\_0~X1~X2 \in X0){\unicdbdjdcd}(k11\_lattice3~(k2\_yellow\_1~\\
X0)~X1~X2=k3\_xboole\_0~X1~X2))))\end{array}
\label{hyp:ehjdpfjhfgmgmgpghhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
(k2\_yellow\_1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
(k2\_yellow\_1~X0))){\unicdbdjdcd}((k2\_xboole\_0~X1~X2 \in X0){\unicdbdjdcd}(k10\_lattice3~(k2\_yellow\_1~\\
X0)~X1~X2=k2\_xboole\_0~X1~X2))))\end{array}
\label{hyp:ehidpfjhfgmgmgpghhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{\preoh{{({{X0} \in {X1}})}}}{\unicdcdcdhd}{({{v1\_xboole\_0}~{X1}})}}}}\label{hyp:ehhdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k3\_yellow\_1}~{X0}}={{k2\_yellow\_1}~{({{k9\_setfam\_1}~{X0}})}}}}\label{hyp:ehedpfjhfgmgmgpghhpfbd}
\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 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v5\_orders\_2~X0){\unicdcdcdhd}((v2\_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}(k12\_lattice3~X0~X1~X2=k11\_lattice3~\\
X0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdcdpfmgbgehehjgdgfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k3\_yellow\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k3\_yellow\_1~\\
X0))){\unicdbdjdcd}((k3\_xboole\_0~X1~X2 \in k9\_setfam\_1~X0){\unicdcdcdhd}(k2\_xboole\_0~X1~X2 \in \\
k9\_setfam\_1~X0)))\end{array}
\label{hyp:mgbdjdpfjhfgmgmgpghhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_orders\_2~(k2\_yellow\_1~X0)){\unicdcdcdhd}((v3\_orders\_2~(k2\_yellow\_1~\\
X0)){\unicdcdcdhd}((v4\_orders\_2~(k2\_yellow\_1~X0)){\unicdcdcdhd}(v5\_orders\_2~(k2\_yellow\_1~\\
X0))))\end{array}
\label{hyp:ggdgfdpfjhfgmgmgpghhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_lattices~(k1\_lattice3~X0)){\unicdcdcdhd}(v10\_lattices~(k1\_lattice3~\\
X0))\end{array}
\label{hyp:ggdgcdpfmgbgehehjgdgfgdd}
\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 .  (\preoh v2\_struct\_0~(k1\_lattice3~X0)){\unicdcdcdhd}(v3\_lattices~(k1\_lattice3~\\
X0))\end{array}
\label{hyp:ggdgbdpfmgbgehehjgdgfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_orders\_2~(k2\_yellow\_1~X0)){\unicdcdcdhd}(l1\_orders\_2~(k2\_yellow\_1~\\
X0))\end{array}
\label{hyp:egehpflgcdpfjhfgmgmgpghhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_lattices~(k1\_lattice3~X0)){\unicdcdcdhd}(l3\_lattices~(k1\_lattice3~\\
X0))\end{array}
\label{hyp:egehpflgbdpfmgbgehehjgdgfgdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k3\_yellow\_1}~{X0}}={{k3\_lattice3}~{({{k1\_lattice3}~{X0}})}}}}\label{hyp:egcdpfjhfgmgmgpghhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k2\_yellow\_1}~{X0}}={{{g1\_orders\_2}~{X0}}~{({{k1\_yellow\_1}~{X0}})}}}}\label{hyp:egbdpfjhfgmgmgpghhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdhdpfjhfgmgmgpghhpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k3\_yellow\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k3\_yellow\_1~\\
X0))){\unicdbdjdcd}((k13\_lattice3~(k3\_yellow\_1~X0)~X1~X2=k2\_xboole\_0~X1~X2){\unicdcdcdhd}\\
(k12\_lattice3~(k3\_yellow\_1~X0)~X1~X2=k3\_xboole\_0~X1~X2)))\end{array}$$
\end{theorem}
\end{document}
