\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{t36\_waybel27 (TMZWL2mcmu2d9n7DwVtDV6nc8YKRVgQ5uMr)}
\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 $ r5\_waybel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_waybel27 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ 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 $ v23\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k4\_waybel27 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_orders\_2 : {{\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}((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 .  ((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}(l1\_orders\_2~X2))))))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v3\_orders\_2~X3){\unicdcdcdhd}((v4\_orders\_2~X3){\unicdcdcdhd}((v5\_orders\_2~\\
X3){\unicdcdcdhd}((v1\_lattice3~X3){\unicdcdcdhd}((v2\_lattice3~X3){\unicdcdcdhd}((v3\_lattice3~X3){\unicdcdcdhd}\\
(l1\_orders\_2~X3))))))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~\\
X4~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)))))){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
((v1\_funct\_1~X5){\unicdcdcdhd}((v1\_funct\_2~X5~(u1\_struct\_0~X2)~(u1\_struct\_0~\\
X3)){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X2)~(u1\_struct\_0~X3)))))){\unicdbdjdcd}(((v23\_waybel\_0~X4~X0~X1){\unicdcdcdhd}(v23\_waybel\_0~\\
X5~X2~X3)){\unicdbdjdcd}(v23\_waybel\_0~(k4\_waybel27~X0~X1~X2~X3~X4~X5)~(k2\_waybel27~\\
X1~X2)~(k2\_waybel27~X0~X3))))))))\end{array}
\label{hyp:ehddfdpfhhbgjhcgfgmgcdhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}(l1\_orders\_2~\\
X0)))){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v3\_orders\_2~X1){\unicdcdcdhd}((v5\_orders\_2~\\
X1){\unicdcdcdhd}(l1\_orders\_2~X1)))){\unicdcdcdhd}(((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v3\_orders\_2~\\
X2){\unicdcdcdhd}((v5\_orders\_2~X2){\unicdcdcdhd}(l1\_orders\_2~X2)))){\unicdcdcdhd}(((\preoh v2\_struct\_0~\\
X3){\unicdcdcdhd}((v3\_orders\_2~X3){\unicdcdcdhd}((v5\_orders\_2~X3){\unicdcdcdhd}(l1\_orders\_2~X3)))){\unicdcdcdhd}\\
(((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X1)){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X1)))))){\unicdcdcdhd}((v1\_funct\_1~X5){\unicdcdcdhd}((v1\_funct\_2~X5~(\\
u1\_struct\_0~X2)~(u1\_struct\_0~X3)){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X2)~(u1\_struct\_0~X3))))))))))){\unicdbdjdcd}((\\
v1\_funct\_1~(k4\_waybel27~X0~X1~X2~X3~X4~X5)){\unicdcdcdhd}((v1\_funct\_2~(k4\_waybel27~\\
X0~X1~X2~X3~X4~X5)~(u1\_struct\_0~(k2\_waybel27~X1~X2))~(u1\_struct\_0~\\
(k2\_waybel27~X0~X3))){\unicdcdcdhd}(m1\_subset\_1~(k4\_waybel27~X0~X1~X2~X3~X4~X5)~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~(k2\_waybel27~X1~X2))~(\\
u1\_struct\_0~(k2\_waybel27~X0~X3)))))))\end{array}
\label{hyp:egehpflgedpfhhbgjhcgfgmgcdhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdcdcdhd}\\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v3\_orders\_2~X1){\unicdcdcdhd}((v5\_orders\_2~X1){\unicdcdcdhd}(l1\_orders\_2~\\
X1))))){\unicdbdjdcd}((v1\_orders\_2~(k2\_waybel27~X0~X1)){\unicdcdcdhd}(l1\_orders\_2~(k2\_waybel27~\\
X0~X1)))\end{array}
\label{hyp:egehpflgcdpfhhbgjhcgfgmgcdhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_orders\_2~X1){\unicdbdjdcd}((\\
r5\_waybel\_1~X0~X1){\unicdbdjded}({\unicdcdaddd} 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)))))){\unicdcdcdhd}(v23\_waybel\_0~\\
X2~X0~X1))))\end{array}
\label{hyp:egidpfhhbgjhcgfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_orders\_2}~{X0}})}{\unicdbdjdcd}{({{({{v2\_lattice3}~{X0}})}{\unicdbdjdcd}{({\preoh{{{v2\_struct\_0}~{X0}}}})}})}}}\label{hyp:dgdgcdpfmgbgehehjgdgfgdd}
\end{equation}
\begin{theorem}\label{thm:ehddgdpfhhbgjhcgfgmgcdhd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~\\
X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}((v3\_lattice3~X0){\unicdcdcdhd}\\
(l1\_orders\_2~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v3\_orders\_2~X1){\unicdcdcdhd}((v4\_orders\_2~\\
X1){\unicdcdcdhd}((v5\_orders\_2~X1){\unicdcdcdhd}((v1\_lattice3~X1){\unicdcdcdhd}((v2\_lattice3~X1){\unicdcdcdhd}\\
((v3\_lattice3~X1){\unicdcdcdhd}(l1\_orders\_2~X1))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v3\_orders\_2~\\
X2){\unicdcdcdhd}((v4\_orders\_2~X2){\unicdcdcdhd}((v5\_orders\_2~X2){\unicdcdcdhd}((v1\_lattice3~X2){\unicdcdcdhd}\\
((v2\_lattice3~X2){\unicdcdcdhd}((v3\_lattice3~X2){\unicdcdcdhd}(l1\_orders\_2~X2))))))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v3\_orders\_2~X3){\unicdcdcdhd}((v4\_orders\_2~X3){\unicdcdcdhd}((v5\_orders\_2~\\
X3){\unicdcdcdhd}((v1\_lattice3~X3){\unicdcdcdhd}((v2\_lattice3~X3){\unicdcdcdhd}((v3\_lattice3~X3){\unicdcdcdhd}\\
(l1\_orders\_2~X3))))))){\unicdbdjdcd}(((r5\_waybel\_1~X0~X1){\unicdcdcdhd}(r5\_waybel\_1~X2~\\
X3)){\unicdbdjdcd}(r5\_waybel\_1~(k2\_waybel27~X1~X2)~(k2\_waybel27~X0~X3))))))\end{array}$$
\end{theorem}
\end{document}
