\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{t50\_yellow\_7 (TMa4J4wqEQLScEaGvMVHPVXBsUChz7Zhw49)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funcop\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_lattice3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_waybel\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_waybel\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_yellow\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_yellow\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}((v3\_lattice3~\\
X0){\unicdcdcdhd}(l1\_orders\_2~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~\\
X1)){\unicdbdjdcd}((k4\_yellow\_2~X0~X1=k5\_yellow\_2~(k7\_lattice3~X0)~X1){\unicdcdcdhd}(k5\_yellow\_2~\\
X0~X1=k4\_yellow\_2~(k7\_lattice3~X0)~X1)))\end{array}
\label{hyp:ehedjdpfjhfgmgmgpghhpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}(u1\_struct\_0~X0=u1\_struct\_0~(k7\_lattice3~\\
X0))\end{array}
\label{hyp:ehddpfjhfgmgmgpghhpfgd}
\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 .  \\
((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_funcop\_1~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_funcop\_1~X2))){\unicdbdjdcd}(((k9\_xtuple\_0~\\
X1=k9\_xtuple\_0~X2){\unicdcdcdhd}({\unicdcdadad} X3 .  (X3 \in k9\_xtuple\_0~X1){\unicdbdjdcd}(k5\_yellow\_2~\\
X0~(k1\_funct\_1~X1~X3)=k5\_yellow\_2~X0~(k1\_funct\_1~X2~X3)))){\unicdbdjdcd}(r1\_funct\_2~\\
(k9\_xtuple\_0~X1)~(u1\_struct\_0~X0)~(k9\_xtuple\_0~X2)~(u1\_struct\_0~\\
X0)~(k5\_waybel\_5~X0~X1)~(k5\_waybel\_5~X0~X2)))))\end{array}
\label{hyp:ehbdcdpfhhbgjhcgfgmgpffd}
\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 .  \\
((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_funcop\_1~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_funcop\_1~X2))){\unicdbdjdcd}(((k9\_xtuple\_0~\\
X1=k9\_xtuple\_0~X2){\unicdcdcdhd}({\unicdcdadad} X3 .  (X3 \in k9\_xtuple\_0~X1){\unicdbdjdcd}(k4\_yellow\_2~\\
X0~(k1\_funct\_1~X1~X3)=k4\_yellow\_2~X0~(k1\_funct\_1~X2~X3)))){\unicdbdjdcd}(r1\_funct\_2~\\
(k9\_xtuple\_0~X1)~(u1\_struct\_0~X0)~(k9\_xtuple\_0~X2)~(u1\_struct\_0~\\
X0)~(k4\_waybel\_5~X0~X1)~(k4\_waybel\_5~X0~X2)))))\end{array}
\label{hyp:ehbdbdpfhhbgjhcgfgmgpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_funcop\_1~\\
X0))){\unicdbdjdcd}((v1\_relat\_1~(k1\_funct\_1~X0~X1)){\unicdcdcdhd}(v1\_funct\_1~(k1\_funct\_1~\\
X0~X1)))\end{array}
\label{hyp:ggdgidpfggfhogdgpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~\\
(k7\_lattice3~X0)){\unicdcdcdhd}(v1\_orders\_2~(k7\_lattice3~X0)))\end{array}
\label{hyp:ggdggdpfmgbgehehjgdgfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}((v1\_orders\_2~(k7\_lattice3~X0)){\unicdcdcdhd}\\
(l1\_orders\_2~(k7\_lattice3~X0)))\end{array}
\label{hyp:egehpflghdpfmgbgehehjgdgfgdd}
\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}\\
((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_funcop\_1~X1)))){\unicdbdjdcd}((v1\_funct\_1~\\
(k4\_waybel\_5~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(k4\_waybel\_5~X0~X1)~(k9\_xtuple\_0~\\
X1)~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~(k4\_waybel\_5~X0~X1)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k9\_xtuple\_0~X1)~(u1\_struct\_0~X0))))))\end{array}
\label{hyp:egehpflgedpfhhbgjhcgfgmgpffd}
\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 .  \\
((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_funcop\_1~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(k9\_xtuple\_0~X1)~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k9\_xtuple\_0~\\
X1)~(u1\_struct\_0~X0)))))){\unicdbdjdcd}((X2=k5\_waybel\_5~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(X3 \in k9\_xtuple\_0~X1){\unicdbdjdcd}(k1\_funct\_1~X2~X3=k5\_yellow\_2~X0~(k1\_funct\_1~\\
X1~X3))))))\end{array}
\label{hyp:egcdpfhhbgjhcgfgmgpffd}
\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 .  \\
((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_funcop\_1~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(k9\_xtuple\_0~X1)~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k9\_xtuple\_0~\\
X1)~(u1\_struct\_0~X0)))))){\unicdbdjdcd}((X2=k4\_waybel\_5~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(X3 \in k9\_xtuple\_0~X1){\unicdbdjdcd}(k1\_funct\_1~X2~X3=k4\_yellow\_2~X0~(k1\_funct\_1~\\
X1~X3))))))\end{array}
\label{hyp:egbdpfhhbgjhcgfgmgpffd}
\end{equation}
\begin{theorem}\label{thm:ehfdadpfjhfgmgmgpghhpfhd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}((v3\_lattice3~\\
X0){\unicdcdcdhd}(l1\_orders\_2~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~\\
X1){\unicdcdcdhd}(v1\_funcop\_1~X1))){\unicdbdjdcd}((r1\_funct\_2~(k9\_xtuple\_0~X1)~(u1\_struct\_0~\\
X0)~(k9\_xtuple\_0~X1)~(u1\_struct\_0~(k7\_lattice3~X0))~(k4\_waybel\_5~\\
X0~X1)~(k5\_waybel\_5~(k7\_lattice3~X0)~X1)){\unicdcdcdhd}(r1\_funct\_2~(k9\_xtuple\_0~\\
X1)~(u1\_struct\_0~X0)~(k9\_xtuple\_0~X1)~(u1\_struct\_0~(k7\_lattice3~\\
X0))~(k5\_waybel\_5~X0~X1)~(k4\_waybel\_5~(k7\_lattice3~X0)~X1))))\end{array}$$
\end{theorem}
\end{document}
