\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\_waybel\_4 (TMdxF529dk2TfMc52wAcacqC5ffiwhSMUrc)}
\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\_yellow\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_yellow\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_waybel\_4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_yellow\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_waybel\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v5\_orders\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_orders\_2 : {{\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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k5\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_orders\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_yellow\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{r1\_tarski}~{X0}}~{X0}}}}\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfehbgchdhlgjg}
\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}(l1\_orders\_2~X0))))){\unicdbdjdcd}((v1\_funct\_1~(k3\_yellow\_2~\\
X0)){\unicdcdcdhd}((v1\_funct\_2~(k3\_yellow\_2~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
(k2\_yellow\_1~(k7\_waybel\_0~X0)))){\unicdcdcdhd}(v5\_orders\_3~(k3\_yellow\_2~\\
X0)~X0~(k2\_yellow\_1~(k7\_waybel\_0~X0)))))\end{array}
\label{hyp:ggdgidpfjhfgmgmgpghhpfcd}
\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}(l1\_orders\_2~X0))))){\unicdbdjdcd}((v1\_orders\_2~(\\
k8\_waybel\_4~X0)){\unicdcdcdhd}(l1\_orders\_2~(k8\_waybel\_4~X0)))\end{array}
\label{hyp:egehpflgidpfhhbgjhcgfgmgpfed}
\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}(l1\_orders\_2~X0))))){\unicdbdjdcd}((v1\_funct\_1~(k3\_yellow\_2~\\
X0)){\unicdcdcdhd}((v1\_funct\_2~(k3\_yellow\_2~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
(k2\_yellow\_1~(k7\_waybel\_0~X0)))){\unicdcdcdhd}(m1\_subset\_1~(k3\_yellow\_2~\\
X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~(\\
k2\_yellow\_1~(k7\_waybel\_0~X0))))))))\end{array}
\label{hyp:egehpflgddpfjhfgmgmgpghhpfcd}
\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}(l1\_orders\_2~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~\\
X1){\unicdcdcdhd}((v1\_funct\_2~X1~(u1\_struct\_0~X0)~(u1\_struct\_0~(k2\_yellow\_1~\\
(k7\_waybel\_0~X0)))){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~(k2\_yellow\_1~(k7\_waybel\_0~X0)))))))){\unicdbdjdcd}\\
((X1=k3\_yellow\_2~X0){\unicdbdjded}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}(k3\_funct\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~(k2\_yellow\_1~\\
(k7\_waybel\_0~X0)))~X1~X2=k5\_waybel\_0~X0~X2))))\end{array}
\label{hyp:egedpfjhfgmgmgpghhpfcd}
\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}(l1\_orders\_2~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_orders\_2~\\
X1){\unicdcdcdhd}(l1\_orders\_2~X1)){\unicdbdjdcd}((X1=k8\_waybel\_4~X0){\unicdbdjded}({\unicdcdadad} X2 .  (\preoh (\\
X2 \in u1\_struct\_0~X1){\unicdcdcdhd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~\\
X3~(u1\_struct\_0~X0)~(u1\_struct\_0~(k2\_yellow\_1~(k7\_waybel\_0~X0)))){\unicdcdcdhd}\\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
(k2\_yellow\_1~(k7\_waybel\_0~X0)))))))){\unicdbdjdcd}(\preoh (X2=X3){\unicdcdcdhd}((v5\_orders\_3~\\
X3~X0~(k2\_yellow\_1~(k7\_waybel\_0~X0))){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~X0)){\unicdbdjdcd}(r1\_tarski~(k3\_funct\_2~(u1\_struct\_0~X0)~\\
(u1\_struct\_0~(k2\_yellow\_1~(k7\_waybel\_0~X0)))~X3~X4)~(k5\_waybel\_0~\\
X0~X4))))))){\unicdcdcdhd}((({\unicdcdaddd} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~(k2\_yellow\_1~(k7\_waybel\_0~X0)))){\unicdcdcdhd}\\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
(k2\_yellow\_1~(k7\_waybel\_0~X0)))))))){\unicdcdcdhd}((X2=X3){\unicdcdcdhd}((v5\_orders\_3~\\
X3~X0~(k2\_yellow\_1~(k7\_waybel\_0~X0))){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~X0)){\unicdbdjdcd}(r1\_tarski~(k3\_funct\_2~(u1\_struct\_0~X0)~\\
(u1\_struct\_0~(k2\_yellow\_1~(k7\_waybel\_0~X0)))~X3~X4)~(k5\_waybel\_0~\\
X0~X4)))))){\unicdbdjdcd}(X2 \in u1\_struct\_0~X1)){\unicdcdcdhd}({\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (k4\_tarski~\\
X3~X4 \in u1\_orders\_2~X1){\unicdbdjded}({\unicdcdaddd} X5 .  ((v1\_funct\_1~X5){\unicdcdcdhd}((v1\_funct\_2~\\
X5~(u1\_struct\_0~X0)~(u1\_struct\_0~(k2\_yellow\_1~(k7\_waybel\_0~X0)))){\unicdcdcdhd}\\
(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
(k2\_yellow\_1~(k7\_waybel\_0~X0)))))))){\unicdcdcdhd}({\unicdcdaddd} X6 .  ((v1\_funct\_1~\\
X6){\unicdcdcdhd}((v1\_funct\_2~X6~(u1\_struct\_0~X0)~(u1\_struct\_0~(k2\_yellow\_1~\\
(k7\_waybel\_0~X0)))){\unicdcdcdhd}(m1\_subset\_1~X6~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~(k2\_yellow\_1~(k7\_waybel\_0~X0)))))))){\unicdcdcdhd}\\
((X3=X5){\unicdcdcdhd}((X4=X6){\unicdcdcdhd}((X3 \in u1\_struct\_0~X1){\unicdcdcdhd}((X4 \in u1\_struct\_0~X1){\unicdcdcdhd}\\
(r1\_yellow\_2~(u1\_struct\_0~X0)~(k2\_yellow\_1~(k7\_waybel\_0~X0))~\\
X5~X6))))))))))))\end{array}
\label{hyp:egbdddpfhhbgjhcgfgmgpfed}
\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}
\begin{theorem}\label{thm:ehbdjdpfhhbgjhcgfgmgpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~\\
X0){\unicdcdcdhd}((v1\_yellow\_0~X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}(l1\_orders\_2~X0)))))){\unicdbdjdcd}\\
(k3\_yellow\_2~X0 \in u1\_struct\_0~(k8\_waybel\_4~X0))\end{array}$$
\end{theorem}
\end{document}
