\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{t26\_waybel26 (TMLLEBgvnYuupBFkoZaKJACugbgMq79AvKE)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_waybel25 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_waybel26 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_waybel\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_yellow\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_pre\_topc : {{\iota}{\unicdbdjdcd}{\iota}}$ 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 $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r5\_waybel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_waybel18 : {\iota}$ be given.
Let $ v1\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_waybel18 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_monoid\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
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 .  ((\preoh \\
v2\_struct\_0~X1){\unicdcdcdhd}((v3\_orders\_2~X1){\unicdcdcdhd}((v4\_orders\_2~X1){\unicdcdcdhd}((v5\_orders\_2~\\
X1){\unicdcdcdhd}(l1\_orders\_2~X1))))){\unicdbdjdcd}(((r5\_waybel\_1~X0~X1){\unicdcdcdhd}(v3\_waybel\_3~\\
X0)){\unicdbdjdcd}(v3\_waybel\_3~X1)))\end{array}
\label{hyp:ehjdpfhhbgjhcgfgmgbdfd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_orders\_2~X1)){\unicdbdjdcd}((r5\_waybel\_1~X0~X1){\unicdbdjdcd}(\\
r5\_waybel\_1~X1~X0)))\end{array}
\label{hyp:ehgdpfhhbgjhcgfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}(r5\_waybel\_1~(k2\_yellow\_1~(u1\_pre\_topc~X0))~(k1\_waybel26~\\
X0~k9\_waybel18))\end{array}
\label{hyp:ehgdpfhhbgjhcgfgmgcdgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((\preoh v7\_struct\_0~X1){\unicdcdcdhd}((\\
v2\_pre\_topc~X1){\unicdcdcdhd}((v6\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~X1))))){\unicdbdjdcd}(\preoh (\\
v1\_lattice3~(k1\_waybel26~X0~X1)){\unicdcdcdhd}(v7\_pre\_topc~X1)))\end{array}
\label{hyp:ehcdfdpfhhbgjhcgfgmgcdgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~\\
X0){\unicdcdcdhd}((v6\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~X0))))){\unicdbdjdcd}((\preoh v7\_pre\_topc~\\
X0){\unicdbdjdcd}(r1\_waybel18~k9\_waybel18~X0))\end{array}
\label{hyp:ehcdedpfhhbgjhcgfgmgcdgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_pre\_topc~X1){\unicdcdcdhd}((v6\_pre\_topc~\\
X1){\unicdcdcdhd}((v1\_waybel25~X1){\unicdcdcdhd}(l1\_pre\_topc~X1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh \\
v2\_struct\_0~X2){\unicdcdcdhd}((v2\_pre\_topc~X2){\unicdcdcdhd}((v6\_pre\_topc~X2){\unicdcdcdhd}((v1\_waybel25~\\
X2){\unicdcdcdhd}(l1\_pre\_topc~X2))))){\unicdbdjdcd}(((r1\_waybel18~X1~X2){\unicdcdcdhd}((v3\_lattice3~\\
(k1\_waybel26~X0~X2)){\unicdcdcdhd}(v3\_waybel\_3~(k1\_waybel26~X0~X2)))){\unicdbdjdcd}((v3\_lattice3~\\
(k1\_waybel26~X0~X1)){\unicdcdcdhd}(v3\_waybel\_3~(k1\_waybel26~X0~X1))))))\end{array}
\label{hyp:ehcdddpfhhbgjhcgfgmgcdgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~(k2\_yellow\_1~X0)){\unicdcdcdhd}\\
(v1\_orders\_2~(k2\_yellow\_1~X0)))\end{array}
\label{hyp:ggdggdpfjhfgmgmgpghhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{({{v1\_pre\_topc}~{k9\_waybel18}})}{\unicdcdcdhd}{({{v6\_pre\_topc}~{k9\_waybel18}})}}\label{hyp:ggdggdpfhhbgjhcgfgmgbdid}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_orders\_2~(k2\_yellow\_1~X0)){\unicdcdcdhd}((v3\_orders\_2~(k2\_yellow\_1~\\
X0)){\unicdcdcdhd}((v4\_orders\_2~(k2\_yellow\_1~X0)){\unicdcdcdhd}(v5\_orders\_2~(k2\_yellow\_1~\\
X0))))\end{array}
\label{hyp:ggdgfdpfjhfgmgmgpghhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(\preoh v2\_struct\_0~k9\_waybel18){\unicdcdcdhd}((v1\_pre\_topc~k9\_waybel18){\unicdcdcdhd}(v2\_pre\_topc~\\
k9\_waybel18))\end{array}
\label{hyp:ggdgfdpfhhbgjhcgfgmgbdid}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(\preoh v7\_struct\_0~k9\_waybel18){\unicdcdcdhd}((v1\_pre\_topc~k9\_waybel18){\unicdcdcdhd}(v1\_waybel25~\\
k9\_waybel18))\end{array}
\label{hyp:ggdgedpfhhbgjhcgfgmgcdgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}\\
(l1\_pre\_topc~X0))){\unicdcdcdhd}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_pre\_topc~X1){\unicdcdcdhd}((\\
v6\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~X1))))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k1\_waybel26~\\
X0~X1)){\unicdcdcdhd}((v1\_orders\_2~(k1\_waybel26~X0~X1)){\unicdcdcdhd}(v5\_orders\_2~(k1\_waybel26~\\
X0~X1))))\end{array}
\label{hyp:ggdgcdpfhhbgjhcgfgmgcdgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}\\
(l1\_pre\_topc~X0))){\unicdcdcdhd}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~\\
X1)))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k1\_waybel26~X0~X1)){\unicdcdcdhd}((v1\_monoid\_0~(k1\_waybel26~\\
X0~X1)){\unicdcdcdhd}((v1\_orders\_2~(k1\_waybel26~X0~X1)){\unicdcdcdhd}((v3\_orders\_2~(k1\_waybel26~\\
X0~X1)){\unicdcdcdhd}(v4\_orders\_2~(k1\_waybel26~X0~X1))))))\end{array}
\label{hyp:ggdgbdpfhhbgjhcgfgmgcdgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(u1\_pre\_topc~X0))\end{array}
\label{hyp:ggdgbdpfahchfgpfehpgahdg}
\end{equation}
Assume the following.
\begin{equation}
{{({{v1\_pre\_topc}~{k9\_waybel18}})}{\unicdcdcdhd}{({{l1\_pre\_topc}~{k9\_waybel18}})}}\label{hyp:egehpflgjdpfhhbgjhcgfgmgbdid}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_orders\_2~(k2\_yellow\_1~X0)){\unicdcdcdhd}(l1\_orders\_2~(k2\_yellow\_1~\\
X0))\end{array}
\label{hyp:egehpflgcdpfjhfgmgmgpghhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}\\
(l1\_pre\_topc~X0))){\unicdcdcdhd}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~\\
X1)))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k1\_waybel26~X0~X1)){\unicdcdcdhd}((v1\_orders\_2~(k1\_waybel26~\\
X0~X1)){\unicdcdcdhd}(l1\_orders\_2~(k1\_waybel26~X0~X1))))\end{array}
\label{hyp:egehpflgbdpfhhbgjhcgfgmgcdgd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_pre\_topc}~{X0}})}{\unicdbdjdcd}{({{({{v7\_pre\_topc}~{X0}})}{\unicdbdjdcd}{({{v6\_pre\_topc}~{X0}})}})}}}\label{hyp:dgdghdpfahchfgpfehpgahdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(v3\_lattice3~\\
X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}(v2\_lattice3~X0))))\end{array}
\label{hyp:dgdgbdpfjhfgmgmgpghhpfad}
\end{equation}
\begin{theorem}\label{thm:ehcdgdpfhhbgjhcgfgmgcdgd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((\preoh v7\_struct\_0~X1){\unicdcdcdhd}((\\
v2\_pre\_topc~X1){\unicdcdcdhd}((v6\_pre\_topc~X1){\unicdcdcdhd}((v1\_waybel25~X1){\unicdcdcdhd}(l1\_pre\_topc~\\
X1)))))){\unicdbdjdcd}(((v3\_lattice3~(k1\_waybel26~X0~X1)){\unicdcdcdhd}(v3\_waybel\_3~(\\
k1\_waybel26~X0~X1))){\unicdbdjdcd}(v3\_waybel\_3~(k2\_yellow\_1~(u1\_pre\_topc~\\
X0)))))\end{array}$$
\end{theorem}
\end{document}
