\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{t27\_waybel\_7 (TMbKq9tp4eJi1KVnZp98qy654Y64EehV8vz)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_yellow\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v13\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_waybel\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_waybel\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r2\_waybel\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_yellow\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_yellow\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k12\_lattice3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v11\_waybel\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_waybel\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xboole\_0 : {\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 $ k3\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_yellow\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_waybel\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v10\_waybel\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_yellow\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{r1\_xboole\_0}~{({{{k4\_xboole\_0}~{X0}}~{X1}})}}~{X1}}}}\label{hyp:ehhdjdpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~\\
X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}((v1\_yellow\_0~X0){\unicdcdcdhd}(l1\_orders\_2~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v2\_waybel\_0~X1~X0){\unicdcdcdhd}((v13\_waybel\_0~\\
X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))))){\unicdbdjdcd}((\\
v1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjded}(\preoh k3\_yellow\_0~X0 \in X1)))\end{array}
\label{hyp:ehedpfhhbgjhcgfgmgpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X0 \in X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X2))){\unicdbdjdcd}(m1\_subset\_1~X0~X2)\end{array}
\label{hyp:ehedpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v5\_orders\_2~X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}(l1\_orders\_2~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v13\_waybel\_0~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0)))){\unicdbdjdcd}((v2\_waybel\_0~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}(((X2 \in X1){\unicdcdcdhd}(X3 \in X1)){\unicdbdjdcd}(k12\_lattice3~X0~X2~X3 \in X1))))))\end{array}
\label{hyp:ehedbdpfhhbgjhcgfgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~\\
X0){\unicdcdcdhd}((v11\_waybel\_1~X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}\\
(l1\_orders\_2~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v2\_waybel\_0~\\
X1~X0){\unicdcdcdhd}((v13\_waybel\_0~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0)))))){\unicdbdjdcd}(((v1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(v2\_waybel\_7~X1~\\
X0)){\unicdbdjded}(v3\_waybel\_7~X1~X0)))\end{array}
\label{hyp:ehcdcdpfhhbgjhcgfgmgpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v2\_waybel\_0~X1~(k3\_yellow\_1~\\
X0)){\unicdcdcdhd}((v13\_waybel\_0~X1~(k3\_yellow\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k3\_yellow\_1~X0))))))){\unicdbdjdcd}((v2\_waybel\_7~X1~(k3\_yellow\_1~\\
X0)){\unicdbdjded}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~X0)){\unicdbdjdcd}((X2 \in X1){\unicdcdcdid}\\
(k6\_subset\_1~X0~X2 \in X1))))\end{array}
\label{hyp:ehcdbdpfhhbgjhcgfgmgpfhd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k3\_yellow\_0}~{({{k3\_yellow\_1}~{X0}})}}={k1\_xboole\_0}}}\label{hyp:ehbdidpfjhfgmgmgpghhpfbd}
\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}((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}
\label{hyp:ehbdhdpfjhfgmgmgpghhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{r1\_xboole\_0}~{X0}}~{X1}})}{\unicdbdjdcd}{({{{r1\_xboole\_0}~{X1}}~{X0}})}}}}\label{hyp:dhjhngngfgehchjhpfchbdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k6\_subset\_1}~{X0}}~{X1}}={{{k4\_xboole\_0}~{X0}}~{X1}}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v2\_struct\_0~(k3\_yellow\_1~X0)){\unicdcdcdhd}((v1\_orders\_2~(k3\_yellow\_1~\\
X0)){\unicdcdcdhd}((v3\_orders\_2~(k3\_yellow\_1~X0)){\unicdcdcdhd}((v4\_orders\_2~(k3\_yellow\_1~\\
X0)){\unicdcdcdhd}(v5\_orders\_2~(k3\_yellow\_1~X0)))))\end{array}
\label{hyp:ggdghdpfjhfgmgmgpghhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_orders\_2~(k3\_yellow\_1~X0)){\unicdcdcdhd}(v11\_waybel\_1~(k3\_yellow\_1~\\
X0))\end{array}
\label{hyp:ggdgbdpfhhbgjhcgfgmgpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_orders\_2~(k3\_yellow\_1~X0)){\unicdcdcdhd}(l1\_orders\_2~(k3\_yellow\_1~\\
X0))\end{array}
\label{hyp:egehpflgddpfjhfgmgmgpghhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (r1\_xboole\_0~X0~X1){\unicdbdjded}(k3\_xboole\_0~X0~X1=\\
k1\_xboole\_0)\end{array}
\label{hyp:eghdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
{\unicdcdadad} X2 .  (r2\_waybel\_7~X0~X1~X2){\unicdbdjded}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}(((v3\_pre\_topc~X3~X0){\unicdcdcdhd}(X2 \in X3)){\unicdbdjdcd}\\
(X3 \in X1))))\end{array}
\label{hyp:egfdpfhhbgjhcgfgmgpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
{\unicdcdadad} X2 .  (r1\_waybel\_7~X0~X1~X2){\unicdbdjded}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}(((v3\_pre\_topc~X3~X0){\unicdcdcdhd}(X2 \in X3)){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  \preoh (X4 \in X1){\unicdcdcdhd}(r1\_xboole\_0~X3~X4)))))\end{array}
\label{hyp:egedpfhhbgjhcgfgmgpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(v11\_waybel\_1~\\
X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}\\
((v5\_orders\_2~X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}((v3\_yellow\_0~\\
X0){\unicdcdcdhd}((v2\_waybel\_1~X0){\unicdcdcdhd}(v10\_waybel\_1~X0))))))))))\end{array}
\label{hyp:dgdgidpfhhbgjhcgfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}((v3\_yellow\_0~X0){\unicdbdjdcd}((v1\_yellow\_0~\\
X0){\unicdcdcdhd}(v2\_yellow\_0~X0)))\end{array}
\label{hyp:dgdgedpfjhfgmgmgpghhpfad}
\end{equation}
\begin{theorem}\label{thm:ehcdhdpfhhbgjhcgfgmgpfhd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v2\_waybel\_0~X1~(k3\_yellow\_1~\\
(u1\_struct\_0~X0))){\unicdcdcdhd}((v13\_waybel\_0~X1~(k3\_yellow\_1~(u1\_struct\_0~\\
X0))){\unicdcdcdhd}((v3\_waybel\_7~X1~(k3\_yellow\_1~(u1\_struct\_0~X0))){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(u1\_struct\_0~(k3\_yellow\_1~(u1\_struct\_0~X0))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (r1\_waybel\_7~X0~X1~X2){\unicdbdjded}(r2\_waybel\_7~X0~X1~X2)))\end{array}$$
\end{theorem}
\end{document}
