\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{t20\_waybel30 (TMXPDn2yiAdAra22qCzuSRkaBz3UZxRK6Hw)}
\maketitle
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\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_waybel19 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_yellow\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_yellow\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_waybel\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_yellow\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_waybel11 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ g1\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_pre\_topc : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_borsuk\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_waybel19 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ g1\_orders\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_orders\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l1\_waybel\_9 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_yellow\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k5\_setfam\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k8\_mcart\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
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}((v1\_lattice3~X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}((v3\_lattice3~X0){\unicdcdcdhd}\\
(l1\_orders\_2~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v3\_orders\_2~X1){\unicdcdcdhd}((v4\_orders\_2~\\
X1){\unicdcdcdhd}((v5\_orders\_2~X1){\unicdcdcdhd}((v1\_lattice3~X1){\unicdcdcdhd}((v2\_lattice3~X1){\unicdcdcdhd}\\
((v3\_lattice3~X1){\unicdcdcdhd}(l1\_orders\_2~X1))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v2\_pre\_topc~\\
X2){\unicdcdcdhd}((v2\_waybel19~X2){\unicdcdcdhd}(m1\_yellow\_9~X2~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v2\_pre\_topc~\\
X3){\unicdcdcdhd}((v2\_waybel19~X3){\unicdcdcdhd}(m1\_yellow\_9~X3~X1))){\unicdbdjdcd}((v3\_waybel\_3~(\\
k2\_yellow\_1~(k5\_waybel11~X1))){\unicdbdjdcd}(u1\_pre\_topc~(k2\_borsuk\_1~X2~\\
X3)=k2\_waybel19~(k3\_yellow\_3~X0~X1))))))\end{array}
\label{hyp:ehbdjdpfhhbgjhcgfgmgddad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (g1\_orders\_2~X0~X1=g1\_orders\_2~\\
X2~X3){\unicdbdjdcd}((X0=X2){\unicdcdcdhd}(X1=X3)))\end{array}
\label{hyp:ggchfgfgpfhgbdpfpgchegfgchdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v2\_lattice3~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdcdcdhd}\\
((v2\_lattice3~X1){\unicdcdcdhd}(l1\_orders\_2~X1))){\unicdbdjdcd}((v1\_orders\_2~(k3\_yellow\_3~\\
X0~X1)){\unicdcdcdhd}(v2\_lattice3~(k3\_yellow\_3~X0~X1)))\end{array}
\label{hyp:ggdgidpfjhfgmgmgpghhpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_lattice3~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdcdcdhd}\\
((v1\_lattice3~X1){\unicdcdcdhd}(l1\_orders\_2~X1))){\unicdbdjdcd}((v1\_orders\_2~(k3\_yellow\_3~\\
X0~X1)){\unicdcdcdhd}(v1\_lattice3~(k3\_yellow\_3~X0~X1)))\end{array}
\label{hyp:ggdghdpfjhfgmgmgpghhpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v4\_orders\_2~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdcdcdhd}\\
((v4\_orders\_2~X1){\unicdcdcdhd}(l1\_orders\_2~X1))){\unicdbdjdcd}((v1\_orders\_2~(k3\_yellow\_3~\\
X0~X1)){\unicdcdcdhd}(v4\_orders\_2~(k3\_yellow\_3~X0~X1)))\end{array}
\label{hyp:ggdggdpfjhfgmgmgpghhpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v5\_orders\_2~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdcdcdhd}\\
((v5\_orders\_2~X1){\unicdcdcdhd}(l1\_orders\_2~X1))){\unicdbdjdcd}((v1\_orders\_2~(k3\_yellow\_3~\\
X0~X1)){\unicdcdcdhd}(v5\_orders\_2~(k3\_yellow\_3~X0~X1)))\end{array}
\label{hyp:ggdgfdpfjhfgmgmgpghhpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v3\_orders\_2~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdcdcdhd}\\
((v3\_orders\_2~X1){\unicdcdcdhd}(l1\_orders\_2~X1))){\unicdbdjdcd}((v1\_orders\_2~(k3\_yellow\_3~\\
X0~X1)){\unicdcdcdhd}(v3\_orders\_2~(k3\_yellow\_3~X0~X1)))\end{array}
\label{hyp:ggdgedpfjhfgmgmgpghhpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}\\
((v3\_lattice3~X0){\unicdcdcdhd}(l1\_orders\_2~X0)))){\unicdcdcdhd}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(\\
(v5\_orders\_2~X1){\unicdcdcdhd}((v3\_lattice3~X1){\unicdcdcdhd}(l1\_orders\_2~X1))))){\unicdbdjdcd}((\\
v1\_orders\_2~(k3\_yellow\_3~X0~X1)){\unicdcdcdhd}(v3\_lattice3~(k3\_yellow\_3~X0~\\
X1)))\end{array}
\label{hyp:ggdgbdadpfjhfgmgmgpghhpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}(m1\_subset\_1~(u1\_orders\_2~X0)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))))\end{array}
\label{hyp:egehpffhbdpfpgchegfgchdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_yellow\_9~X1~X0){\unicdbdjdcd}\\
(l1\_waybel\_9~X1))\end{array}
\label{hyp:egehpfngbdpfjhfgmgmgpghhpfjd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_waybel\_9}~{X0}})}{\unicdbdjdcd}{({{({{l1\_pre\_topc}~{X0}})}{\unicdcdcdhd}{({{l1\_orders\_2}~{X0}})}})}}}\label{hyp:egehpfmgbdpfhhbgjhcgfgmgpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l1\_orders\_2~X0){\unicdcdcdhd}(l1\_orders\_2~X1)){\unicdbdjdcd}(\\
(v1\_orders\_2~(k3\_yellow\_3~X0~X1)){\unicdcdcdhd}(l1\_orders\_2~(k3\_yellow\_3~\\
X0~X1)))\end{array}
\label{hyp:egehpflgddpfjhfgmgmgpghhpfdd}
\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}((v1\_lattice3~X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}((v3\_lattice3~X0){\unicdcdcdhd}\\
(l1\_orders\_2~X0))))))){\unicdbdjdcd}(m1\_subset\_1~(k2\_waybel19~X0)~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~(u1\_struct\_0~X0))))\end{array}
\label{hyp:egehpflgcdpfhhbgjhcgfgmgbdjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdcdcdhd}\\
((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~X1))){\unicdbdjdcd}((v1\_pre\_topc~(k2\_borsuk\_1~\\
X0~X1)){\unicdcdcdhd}((v2\_pre\_topc~(k2\_borsuk\_1~X0~X1)){\unicdcdcdhd}(l1\_pre\_topc~(k2\_borsuk\_1~\\
X0~X1))))\end{array}
\label{hyp:egehpflgcdpfcgpgchdhfhlgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_waybel\_9~X1){\unicdbdjdcd}((\\
m1\_yellow\_9~X1~X0){\unicdbdjded}(g1\_orders\_2~(u1\_struct\_0~X1)~(u1\_orders\_2~\\
X1)=g1\_orders\_2~(u1\_struct\_0~X0)~(u1\_orders\_2~X0))))\end{array}
\label{hyp:egedpfjhfgmgmgpghhpfjd}
\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}((v1\_lattice3~X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}((v3\_lattice3~X0){\unicdcdcdhd}\\
(l1\_orders\_2~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}((X1=k2\_waybel19~X0){\unicdbdjded}({\unicdcdadad} X2 .  \\
((v2\_pre\_topc~X2){\unicdcdcdhd}((v2\_waybel19~X2){\unicdcdcdhd}(m1\_yellow\_9~X2~X0))){\unicdbdjdcd}(\\
X1=u1\_pre\_topc~X2))))\end{array}
\label{hyp:egedpfhhbgjhcgfgmgbdjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_orders\_2~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_orders\_2~X2){\unicdcdcdhd}(l1\_orders\_2~X2)){\unicdbdjdcd}((X2=k3\_yellow\_3~X0~X1){\unicdbdjded}\\
((u1\_struct\_0~X2=k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}\\
(u1\_orders\_2~X2=k2\_yellow\_3~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~\\
(u1\_struct\_0~X1)~(u1\_struct\_0~X1)~(u1\_orders\_2~X0)~(u1\_orders\_2~\\
X1))))))\end{array}
\label{hyp:egcdpfjhfgmgmgpghhpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_pre\_topc~\\
X2){\unicdcdcdhd}((v2\_pre\_topc~X2){\unicdcdcdhd}(l1\_pre\_topc~X2))){\unicdbdjdcd}((X2=k2\_borsuk\_1~\\
X0~X1){\unicdbdjded}((u1\_struct\_0~X2=k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X1)){\unicdcdcdhd}(u1\_pre\_topc~X2=ReplSep~(toset~({\uniddcgcg} X3 : \iota .  m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~X2)))))~({\uniddcgcg} X3 : \iota .  \\
r1\_tarski~X3~(ReplSep2~(toset~({\uniddcgcg} X4 : \iota .  m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))))~({\uniddcgcg} X4 : \iota .  toset~({\uniddcgcg} X5 : \iota .  m1\_subset\_1~\\
X5~(k1\_zfmisc\_1~(u1\_struct\_0~X1))))~({\uniddcgcg} X4 : \iota .  {\uniddcgcg} X5 : \iota .  \\
(X4 \in u1\_pre\_topc~X0){\unicdcdcdhd}(X5 \in u1\_pre\_topc~X1))~({\uniddcgcg} X4 : \iota .  {\uniddcgcg} X5 : \\
\iota .  k8\_mcart\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)~X4~X5)))~({\uniddcgcg} X3 : \\
\iota .  k5\_setfam\_1~(u1\_struct\_0~X2)~X3))))))\end{array}
\label{hyp:egcdpfcgpgchdhfhlgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_orders\_2}~{X0}})}{\unicdbdjdcd}{({{({{v1\_lattice3}~{X0}})}{\unicdbdjdcd}{({\preoh{{{v2\_struct\_0}~{X0}}}})}})}}}\label{hyp:dgdgbdpfmgbgehehjgdgfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}((v1\_pre\_topc~X0){\unicdbdjdcd}(X0=g1\_pre\_topc~\\
(u1\_struct\_0~X0)~(u1\_pre\_topc~X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdpfahchfgpfehpgahdg}
\end{equation}
\begin{theorem}\label{thm:ehcdadpfhhbgjhcgfgmgddad}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~\\
X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}((v3\_lattice3~X0){\unicdcdcdhd}\\
(l1\_orders\_2~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v3\_orders\_2~X1){\unicdcdcdhd}((v4\_orders\_2~\\
X1){\unicdcdcdhd}((v5\_orders\_2~X1){\unicdcdcdhd}((v1\_lattice3~X1){\unicdcdcdhd}((v2\_lattice3~X1){\unicdcdcdhd}\\
((v3\_lattice3~X1){\unicdcdcdhd}(l1\_orders\_2~X1))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v2\_pre\_topc~\\
X2){\unicdcdcdhd}((v2\_waybel19~X2){\unicdcdcdhd}(m1\_yellow\_9~X2~(k3\_yellow\_3~X0~X1)))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v2\_pre\_topc~X3){\unicdcdcdhd}((v2\_waybel19~X3){\unicdcdcdhd}(m1\_yellow\_9~\\
X3~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v2\_pre\_topc~X4){\unicdcdcdhd}((v2\_waybel19~X4){\unicdcdcdhd}(m1\_yellow\_9~\\
X4~X1))){\unicdbdjdcd}((v3\_waybel\_3~(k2\_yellow\_1~(k5\_waybel11~X1))){\unicdbdjdcd}(g1\_pre\_topc~\\
(u1\_struct\_0~X2)~(u1\_pre\_topc~X2)=k2\_borsuk\_1~X3~X4))))))\end{array}$$
\end{theorem}
\end{document}
