\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\_waybel17 (TMLHRNZZsbcgW31Gt8s2iuab2AWUtMUpcu6)}
\maketitle
Let $ v2\_pre\_topc : {{\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 $ v3\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_waybel11 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_waybel\_9 : {{\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 $ u1\_struct\_0 : {{\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 $ v2\_waybel\_8 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_waybel\_8 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r3\_orders\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_waybel\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_waybel\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ 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}(l1\_orders\_2~X0)))))){\unicdbdjdcd}\\
((v2\_waybel\_8~X0){\unicdbdjded}((v3\_waybel\_3~X0){\unicdcdcdhd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}(\preoh (r1\_waybel\_3~X0~X1~X2){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}(\preoh (X3 \in u1\_struct\_0~(k1\_waybel\_8~X0)){\unicdcdcdhd}((r3\_orders\_2~X0~X1~\\
X3){\unicdcdcdhd}(r3\_orders\_2~X0~X3~X2)))))))))\end{array}
\label{hyp:ehhdpfhhbgjhcgfgmgpfid}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_pre\_topc~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\_lattice3~X0){\unicdcdcdhd}((v3\_waybel\_3~X0){\unicdcdcdhd}((v4\_waybel11~X0){\unicdcdcdhd}(l1\_waybel\_9~\\
X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v2\_pre\_topc~X1){\unicdcdcdhd}((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}((v3\_waybel\_3~X1){\unicdcdcdhd}((v4\_waybel11~X1){\unicdcdcdhd}\\
(l1\_waybel\_9~X1)))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)))))){\unicdbdjdcd}((v5\_pre\_topc~\\
X2~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~(u1\_struct\_0~X1)){\unicdbdjdcd}((r1\_waybel\_3~X1~X4~(k3\_funct\_2~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X1)~X2~X3)){\unicdbdjded}({\unicdcdaddd} X5 .  (m1\_subset\_1~\\
X5~(u1\_struct\_0~X0)){\unicdcdcdhd}((r1\_waybel\_3~X0~X5~X3){\unicdcdcdhd}(r1\_waybel\_3~X1~X4~\\
(k3\_funct\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)~X2~X5))))))))))\end{array}
\label{hyp:ehcdddpfhhbgjhcgfgmgbdhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_pre\_topc~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\_lattice3~X0){\unicdcdcdhd}((v4\_waybel11~X0){\unicdcdcdhd}(l1\_waybel\_9~X0))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v2\_pre\_topc~X1){\unicdcdcdhd}((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}((v4\_waybel11~X1){\unicdcdcdhd}(l1\_waybel\_9~X1))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~X0)~\\
(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X1)))))){\unicdbdjdcd}(((v2\_waybel\_8~X1){\unicdcdcdhd}(\\
{\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~X1)){\unicdbdjdcd}((X4 \in u1\_struct\_0~(k1\_waybel\_8~X1)){\unicdbdjdcd}((r3\_orders\_2~\\
X1~X4~(k3\_funct\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)~X2~X3)){\unicdbdjded}({\unicdcdaddd} X5 .  \\
(m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdcdcdhd}((X5 \in u1\_struct\_0~(k1\_waybel\_8~\\
X0)){\unicdcdcdhd}((r3\_orders\_2~X0~X5~X3){\unicdcdcdhd}(r3\_orders\_2~X1~X4~(k3\_funct\_2~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X1)~X2~X5)))))))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~\\
X1)){\unicdbdjdcd}((r1\_waybel\_3~X1~X4~(k3\_funct\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X1)~X2~X3)){\unicdbdjded}({\unicdcdaddd} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdcdcdhd}((r1\_waybel\_3~\\
X0~X5~X3){\unicdcdcdhd}(r1\_waybel\_3~X1~X4~(k3\_funct\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X1)~X2~X5))))))))))\end{array}
\label{hyp:mgedgdpfhhbgjhcgfgmgbdhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_pre\_topc~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\_lattice3~X0){\unicdcdcdhd}((v4\_waybel11~X0){\unicdcdcdhd}(l1\_waybel\_9~X0))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v2\_pre\_topc~X1){\unicdcdcdhd}((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}((v4\_waybel11~X1){\unicdcdcdhd}(l1\_waybel\_9~X1))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~X0)~\\
(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X1)))))){\unicdbdjdcd}(((v2\_waybel\_8~X0){\unicdcdcdhd}(\\
(v2\_waybel\_8~X1){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X1)){\unicdbdjdcd}((r1\_waybel\_3~\\
X1~X4~(k3\_funct\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)~X2~X3)){\unicdbdjded}({\unicdcdaddd} X5 .  \\
(m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdcdcdhd}((r1\_waybel\_3~X0~X5~X3){\unicdcdcdhd}(r1\_waybel\_3~\\
X1~X4~(k3\_funct\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)~X2~X5))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~X1)){\unicdbdjdcd}((X4 \in u1\_struct\_0~(k1\_waybel\_8~X1)){\unicdbdjdcd}((r3\_orders\_2~\\
X1~X4~(k3\_funct\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)~X2~X3)){\unicdbdjded}({\unicdcdaddd} X5 .  \\
(m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdcdcdhd}((X5 \in u1\_struct\_0~(k1\_waybel\_8~\\
X0)){\unicdcdcdhd}((r3\_orders\_2~X0~X5~X3){\unicdcdcdhd}(r3\_orders\_2~X1~X4~(k3\_funct\_2~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X1)~X2~X5))))))))))))\end{array}
\label{hyp:mgedfdpfhhbgjhcgfgmgbdhd}
\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}
\begin{theorem}\label{thm:ehcdhdpfhhbgjhcgfgmgbdhd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_pre\_topc~X0){\unicdcdcdhd}((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~\\
X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}\\
((v3\_lattice3~X0){\unicdcdcdhd}((v4\_waybel11~X0){\unicdcdcdhd}(l1\_waybel\_9~X0))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v2\_pre\_topc~X1){\unicdcdcdhd}((v3\_orders\_2~X1){\unicdcdcdhd}((v4\_orders\_2~\\
X1){\unicdcdcdhd}((v5\_orders\_2~X1){\unicdcdcdhd}((v1\_lattice3~X1){\unicdcdcdhd}((v2\_lattice3~X1){\unicdcdcdhd}\\
((v3\_lattice3~X1){\unicdcdcdhd}((v4\_waybel11~X1){\unicdcdcdhd}(l1\_waybel\_9~X1))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~X0)~\\
(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X1)))))){\unicdbdjdcd}(((v2\_waybel\_8~X0){\unicdcdcdhd}(\\
v2\_waybel\_8~X1)){\unicdbdjdcd}((v5\_pre\_topc~X2~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~\\
X1)){\unicdbdjdcd}((X4 \in u1\_struct\_0~(k1\_waybel\_8~X1)){\unicdbdjdcd}((r3\_orders\_2~X1~X4~\\
(k3\_funct\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)~X2~X3)){\unicdbdjded}({\unicdcdaddd} X5 .  \\
(m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdcdcdhd}((X5 \in u1\_struct\_0~(k1\_waybel\_8~\\
X0)){\unicdcdcdhd}((r3\_orders\_2~X0~X5~X3){\unicdcdcdhd}(r3\_orders\_2~X1~X4~(k3\_funct\_2~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X1)~X2~X5)))))))))))))\end{array}$$
\end{theorem}
\end{document}
