\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{t43\_waybel34 (TMbcdaKbekDXiEwTXYPZ7XZEK1Wk5KxhCbU)}
\maketitle
Let $ v2\_setfam\_1 : {{\iota}{\unicdbdjdcd}{o}}$ 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\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\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 $ k8\_waybel34 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_waybel34 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_altcat\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_altcat\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v11\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v12\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_yellow21 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r2\_altcat\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_altcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_altcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v22\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_yellow21 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k3\_yellow21 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
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 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~X1)){\unicdbdjded}(r1\_tarski~\\
X0~X1)\end{array}
\label{hyp:ehddpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~X1){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}\\
(X0 \in X1))\end{array}
\label{hyp:ehcdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v2\_setfam\_1~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}(l1\_orders\_2~X1)))))){\unicdbdjdcd}((m1\_subset\_1~X1~(u1\_struct\_0~(k4\_waybel34~\\
X0))){\unicdbdjded}((v1\_orders\_2~X1){\unicdcdcdhd}((v3\_lattice3~X1){\unicdcdcdhd}(u1\_struct\_0~X1 \in \\
X0)))))\end{array}
\label{hyp:ehbdddpfhhbgjhcgfgmgdded}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(u1\_struct\_0~X0))\end{array}
\label{hyp:ggdgcdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_altcat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_altcat\_2~X1~X0){\unicdbdjdcd}\\
(l2\_altcat\_1~X1))\end{array}
\label{hyp:egehpfngbdpfbgmgehdgbgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_altcat\_1}~{X0}})}{\unicdbdjdcd}{({{l1\_altcat\_1}~{X0}})}}}\label{hyp:egehpfmgcdpfbgmgehdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_altcat\_1}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfbgmgehdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~(k8\_waybel34~X0)){\unicdcdcdhd}\\
((v2\_altcat\_1~(k8\_waybel34~X0)){\unicdcdcdhd}((v6\_altcat\_1~(k8\_waybel34~\\
X0)){\unicdcdcdhd}((v3\_altcat\_2~(k8\_waybel34~X0)~(k4\_waybel34~X0)){\unicdcdcdhd}(m1\_altcat\_2~\\
(k8\_waybel34~X0)~(k4\_waybel34~X0))))))\end{array}
\label{hyp:egehpflgidpfhhbgjhcgfgmgdded}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~(k4\_waybel34~X0)){\unicdcdcdhd}\\
((v2\_altcat\_1~(k4\_waybel34~X0)){\unicdcdcdhd}((v6\_altcat\_1~(k4\_waybel34~\\
X0)){\unicdcdcdhd}((v11\_altcat\_1~(k4\_waybel34~X0)){\unicdcdcdhd}((v12\_altcat\_1~(k4\_waybel34~\\
X0)){\unicdcdcdhd}((v2\_yellow21~(k4\_waybel34~X0)){\unicdcdcdhd}(l2\_altcat\_1~(k4\_waybel34~\\
X0))))))))\end{array}
\label{hyp:egehpflgedpfhhbgjhcgfgmgdded}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_altcat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l2\_altcat\_1~X1){\unicdbdjdcd}((\\
m1\_altcat\_2~X1~X0){\unicdbdjded}((r1\_tarski~(u1\_struct\_0~X1)~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((r2\_altcat\_2~(k2\_zfmisc\_1~(u1\_struct\_0~X1)~(u1\_struct\_0~\\
X1))~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~(u1\_altcat\_1~\\
X1)~(u1\_altcat\_1~X0)){\unicdcdcdhd}(r2\_altcat\_2~(k3\_zfmisc\_1~(u1\_struct\_0~\\
X1)~(u1\_struct\_0~X1)~(u1\_struct\_0~X1))~(k3\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~(u2\_altcat\_1~X1)~(u2\_altcat\_1~\\
X0))))))\end{array}
\label{hyp:egbdbdpfbgmgehdgbgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((v2\_altcat\_1~X1){\unicdcdcdhd}((v6\_altcat\_1~X1){\unicdcdcdhd}((v3\_altcat\_2~X1~(k4\_waybel34~\\
X0)){\unicdcdcdhd}(m1\_altcat\_2~X1~(k4\_waybel34~X0)))))){\unicdbdjdcd}((X1=k8\_waybel34~\\
X0){\unicdbdjded}(({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k4\_waybel34~X0))){\unicdbdjdcd}\\
(m1\_subset\_1~X2~(u1\_struct\_0~X1))){\unicdcdcdhd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~(k4\_waybel34~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~(k4\_waybel34~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~\\
X1)){\unicdbdjdcd}(((X4=X2){\unicdcdcdhd}(X5=X3)){\unicdbdjdcd}((k1\_altcat\_1~(k4\_waybel34~X0)~X2~X3=\\
k1\_xboole\_0){\unicdcdcdid}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(k1\_altcat\_1~(k4\_waybel34~\\
X0)~X2~X3)){\unicdbdjdcd}((X6 \in k1\_altcat\_1~X1~X4~X5){\unicdbdjded}(v22\_waybel\_0~(k5\_yellow21~\\
(k4\_waybel34~X0)~X2~X3~X6)~(k3\_yellow21~(k4\_waybel34~X0)~X2)~(k3\_yellow21~\\
(k4\_waybel34~X0)~X3)))))))))))))\end{array}
\label{hyp:egbdadpfhhbgjhcgfgmgdded}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({\preoh{{{v2\_setfam\_1}~{X0}}}})}{\unicdbdjdcd}{({\preoh{{{v1\_xboole\_0}~{X0}}}})}}}\label{hyp:dgdgcdpfdhfgehggbgngpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedddpfhhbgjhcgfgmgdded}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v2\_setfam\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v3\_orders\_2~X1){\unicdcdcdhd}\\
((v4\_orders\_2~X1){\unicdcdcdhd}((v5\_orders\_2~X1){\unicdcdcdhd}((v1\_lattice3~X1){\unicdcdcdhd}((v2\_lattice3~\\
X1){\unicdcdcdhd}(l1\_orders\_2~X1)))))){\unicdbdjdcd}((m1\_subset\_1~X1~(u1\_struct\_0~(k8\_waybel34~\\
X0))){\unicdbdjded}((v1\_orders\_2~X1){\unicdcdcdhd}((v3\_lattice3~X1){\unicdcdcdhd}(u1\_struct\_0~X1 \in \\
X0)))))\end{array}$$
\end{theorem}
\end{document}
