\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{t41\_waybel20 (TMbTNVp2VdCQvQzUZ17MS9RZzRzGger3PNT)}
\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 $ v3\_waybel\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_yellow\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_waybel20 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_waybel20 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_eqrel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_waybel20 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_eqrel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_eqrel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r3\_orders\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_yellow\_0 : {{\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~X1){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}\\
(X0 \in X1))\end{array}
\label{hyp:ehcdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v3\_relat\_2~X1){\unicdcdcdhd}((v8\_relat\_2~X1){\unicdcdcdhd}((v1\_partfun1~\\
X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)))))){\unicdbdjdcd}\\
(k8\_eqrel\_1~X0~X1=k7\_eqrel\_1~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgidpffgbhchfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_orders\_2~X0){\unicdcdcdhd}(l1\_orders\_2~\\
X0))){\unicdbdjdcd}({\unicdcdaddd} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_finset\_1~X1){\unicdcdcdhd}((v1\_waybel\_0~X1~\\
X0){\unicdcdcdhd}(v2\_waybel\_0~X1~X0)))))\end{array}
\label{hyp:chdgcdpfhhbgjhcgfgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v3\_relat\_2~X1){\unicdcdcdhd}((v8\_relat\_2~X1){\unicdcdcdhd}((v1\_partfun1~\\
X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)))))){\unicdbdjdcd}\\
(m1\_subset\_1~(k7\_eqrel\_1~X0~X1)~(k1\_zfmisc\_1~(k1\_zfmisc\_1~X0)))\end{array}
\label{hyp:egehpflghdpffgbhchfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (m1\_subset\_1~X2~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(m1\_subset\_1~(k6\_eqrel\_1~X0~\\
X1~X2~X3)~(k1\_zfmisc\_1~X1))\end{array}
\label{hyp:egehpflggdpffgbhchfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((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}((v3\_waybel\_3~X0){\unicdcdcdhd}(l1\_orders\_2~X0)))))))){\unicdcdcdhd}((\preoh v1\_xboole\_0~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~(k3\_yellow\_3~X0~\\
X0)))))){\unicdbdjdcd}((v1\_orders\_2~(k5\_waybel20~X0~X1)){\unicdcdcdhd}((v3\_orders\_2~(\\
k5\_waybel20~X0~X1)){\unicdcdcdhd}((v4\_orders\_2~(k5\_waybel20~X0~X1)){\unicdcdcdhd}((v5\_orders\_2~\\
(k5\_waybel20~X0~X1)){\unicdcdcdhd}((v1\_lattice3~(k5\_waybel20~X0~X1)){\unicdcdcdhd}((v2\_lattice3~\\
(k5\_waybel20~X0~X1)){\unicdcdcdhd}((v3\_lattice3~(k5\_waybel20~X0~X1)){\unicdcdcdhd}((v3\_waybel\_3~\\
(k5\_waybel20~X0~X1)){\unicdcdcdhd}(l1\_orders\_2~(k5\_waybel20~X0~X1))))))))))\end{array}
\label{hyp:egehpflgfdpfhhbgjhcgfgmgcdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l1\_orders\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k3\_yellow\_3~X0~X0))))){\unicdbdjdcd}((v1\_partfun1~(k2\_waybel20~\\
X0~X1)~(u1\_struct\_0~X0)){\unicdcdcdhd}((v3\_relat\_2~(k2\_waybel20~X0~X1)){\unicdcdcdhd}((\\
v8\_relat\_2~(k2\_waybel20~X0~X1)){\unicdcdcdhd}(m1\_subset\_1~(k2\_waybel20~X0~\\
X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)))))))\end{array}
\label{hyp:egehpflgcdpfhhbgjhcgfgmgcdad}
\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}\\
((v3\_waybel\_3~X0){\unicdcdcdhd}(l1\_orders\_2~X0)))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~(k3\_yellow\_3~X0~\\
X0))))){\unicdbdjdcd}((v1\_waybel20~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_orders\_2~X2){\unicdcdcdhd}\\
((v3\_orders\_2~X2){\unicdcdcdhd}((v4\_orders\_2~X2){\unicdcdcdhd}((v5\_orders\_2~X2){\unicdcdcdhd}((v1\_lattice3~\\
X2){\unicdcdcdhd}((v2\_lattice3~X2){\unicdcdcdhd}((v3\_lattice3~X2){\unicdcdcdhd}((v3\_waybel\_3~X2){\unicdcdcdhd}\\
(l1\_orders\_2~X2))))))))){\unicdbdjdcd}((X2=k5\_waybel20~X0~X1){\unicdbdjded}((u1\_struct\_0~\\
X2=k8\_eqrel\_1~(u1\_struct\_0~X0)~(k2\_waybel20~X0~X1)){\unicdcdcdhd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X2)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(u1\_struct\_0~X2)){\unicdbdjdcd}((r3\_orders\_2~X2~X3~X4){\unicdbdjded}(r3\_orders\_2~X0~(k2\_yellow\_0~\\
X0~X3)~(k2\_yellow\_0~X0~X4))))))))))\end{array}
\label{hyp:egfdpfhhbgjhcgfgmgcdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v3\_relat\_2~X1){\unicdcdcdhd}((v8\_relat\_2~X1){\unicdcdcdhd}((v1\_partfun1~\\
X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(k1\_zfmisc\_1~X0))){\unicdbdjdcd}\\
((X2=k7\_eqrel\_1~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}((X3 \in X2){\unicdbdjded}({\unicdcdaddd} X4 .  (X4 \in X0){\unicdcdcdhd}(X3=k6\_eqrel\_1~X0~X0~X1~X4))))))\end{array}
\label{hyp:egddpffgbhchfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v1\_xboole\_0~X1))\end{array}
\label{hyp:dgdgbdpfdhfhcgdhfgehpfbd}
\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:ehedbdpfhhbgjhcgfgmgcdad}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~\\
X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}((v3\_lattice3~X0){\unicdcdcdhd}\\
((v3\_waybel\_3~X0){\unicdcdcdhd}(l1\_orders\_2~X0)))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~(k3\_yellow\_3~X0~\\
X0))))){\unicdbdjdcd}((v1\_waybel20~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
(k5\_waybel20~X0~X1))){\unicdbdjded}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}(X2=k6\_eqrel\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(k2\_waybel20~\\
X0~X1)~X3)))))\end{array}$$
\end{theorem}
\end{document}
