\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{t15\_yellow18 (TMTnc9nUX55FBkjQCXEuHNKBEYoJgc5EPVH)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v12\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r2\_yellow18 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v21\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_yellow18 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_altcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k5\_altcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k3\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k8\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ v9\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v16\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m2\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_altcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_funct\_4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_altcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ u2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~\\
X1))){\unicdbdjdcd}((r2\_yellow18~X0~X1){\unicdbdjded}((u1\_struct\_0~X1=u1\_struct\_0~X0){\unicdcdcdhd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
(m1\_subset\_1~X6~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~\\
(u1\_struct\_0~X1)){\unicdbdjdcd}(((X5=X2){\unicdcdcdhd}((X6=X3){\unicdcdcdhd}(X7=X4))){\unicdbdjdcd}((k1\_altcat\_1~\\
X0~X2~X3=k1\_altcat\_1~X1~X6~X5){\unicdcdcdhd}(\preoh (k1\_altcat\_1~X0~X2~X3{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}\\
((k1\_altcat\_1~X0~X3~X4{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}({\unicdcdaddd} X8 .  (m1\_subset\_1~\\
X8~(k1\_altcat\_1~X0~X2~X3)){\unicdcdcdhd}({\unicdcdaddd} X9 .  (m1\_subset\_1~X9~(k1\_altcat\_1~\\
X0~X3~X4)){\unicdcdcdhd}({\unicdcdaddd} X10 .  (m1\_subset\_1~X10~(k1\_altcat\_1~X1~X6~X5)){\unicdcdcdhd}\\
({\unicdcdaddd} X11 .  (m1\_subset\_1~X11~(k1\_altcat\_1~X1~X7~X6)){\unicdcdcdhd}((X10=X8){\unicdcdcdhd}\\
((X11=X9){\unicdcdcdhd}(k5\_altcat\_1~X1~X7~X6~X5~X11~X10{\unicdcdgdad}k5\_altcat\_1~X0~X2~X3~X4~\\
X8~X9))))))))))))))))))))\end{array}
\label{hyp:ehjdpfjhfgmgmgpghhbdid}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 : \iota{\unicdbdjdcd}\iota{\unicdbdjdcd}\iota{\unicdbdjdcd}\iota .  {\unicdcdadad} X1 : \iota{\unicdbdjdcd}\iota .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  \\
{\unicdcdadad} X4 .  (({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X4)){\unicdbdjdcd}(k3\_functor0~\\
X4~X3~X2~X5=X1~X5)){\unicdcdcdhd}(({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X4)){\unicdbdjdcd}\\
({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~X4)){\unicdbdjdcd}((k1\_altcat\_1~\\
X4~X5~X6{\unicdcdgdad}k1\_xboole\_0){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~(k1\_altcat\_1~\\
X4~X5~X6)){\unicdbdjdcd}(k8\_functor0~X4~X3~X2~X5~X6~X7=X0~X5~X6~X7))))){\unicdcdcdhd}(({\unicdcdadad} X5 .  \\
(m1\_subset\_1~X5~(u1\_struct\_0~X4)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~\\
(u1\_struct\_0~X4)){\unicdbdjdcd}((X1~X5=X1~X6){\unicdbdjdcd}(X5=X6)))){\unicdcdcdhd}(({\unicdcdadad} X5 .  (m1\_subset\_1~\\
X5~(u1\_struct\_0~X4)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~\\
X4)){\unicdbdjdcd}((k1\_altcat\_1~X4~X5~X6{\unicdcdgdad}k1\_xboole\_0){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~\\
X7~(k1\_altcat\_1~X4~X5~X6)){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_subset\_1~X8~(k1\_altcat\_1~\\
X4~X5~X6)){\unicdbdjdcd}((X0~X5~X6~X7=X0~X5~X6~X8){\unicdbdjdcd}(X7=X8))))))){\unicdcdcdhd}({\unicdcdadad} X5 .  \\
(m1\_subset\_1~X5~(u1\_struct\_0~X3)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~\\
(u1\_struct\_0~X3)){\unicdbdjdcd}((k1\_altcat\_1~X3~X5~X6{\unicdcdgdad}k1\_xboole\_0){\unicdbdjdcd}({\unicdcdadad} X7 .  \\
(m1\_subset\_1~X7~(k1\_altcat\_1~X3~X5~X6)){\unicdbdjdcd}({\unicdcdaddd} X8 .  (m1\_subset\_1~\\
X8~(u1\_struct\_0~X4)){\unicdcdcdhd}({\unicdcdaddd} X9 .  (m1\_subset\_1~X9~(u1\_struct\_0~\\
X4)){\unicdcdcdhd}({\unicdcdaddd} X10 .  (m1\_subset\_1~X10~(k1\_altcat\_1~X4~X8~X9)){\unicdcdcdhd}((\\
X6=X1~X8){\unicdcdcdhd}((X5=X1~X9){\unicdcdcdhd}((k1\_altcat\_1~X4~X8~X9{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}(X7=\\
X0~X8~X9~X10))))))))))))))){\unicdbdjdcd}(v21\_functor0~X2~X4~X3)\end{array}
\label{hyp:dhbdcdpfjhfgmgmgpghhbdid}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}\\
((v11\_altcat\_1~X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0))))){\unicdcdcdhd}\\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}((v11\_altcat\_1~X1){\unicdcdcdhd}((\\
v12\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~X1)))))){\unicdbdjdcd}((v9\_functor0~(k2\_yellow18~\\
X0~X1)~X0~X1){\unicdcdcdhd}((v16\_functor0~(k2\_yellow18~X0~X1)~X0~X1){\unicdcdcdhd}(m2\_functor0~\\
(k2\_yellow18~X0~X1)~X0~X1)))\end{array}
\label{hyp:egehpflgcdpfjhfgmgmgpghhbdid}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v11\_altcat\_1~\\
X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}((v11\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~\\
X1){\unicdcdcdhd}(l2\_altcat\_1~X1))))){\unicdbdjdcd}((r2\_yellow18~X0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (\\
(v9\_functor0~X2~X0~X1){\unicdcdcdhd}((v16\_functor0~X2~X0~X1){\unicdcdcdhd}(m2\_functor0~X2~\\
X0~X1))){\unicdbdjdcd}((X2=k2\_yellow18~X0~X1){\unicdbdjded}(({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}(k3\_functor0~X0~X1~X2~X3=X3)){\unicdcdcdhd}({\unicdcdadad} X3 .  (\\
m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}((k1\_altcat\_1~X0~X3~X4{\unicdcdgdad}k1\_xboole\_0){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
(m1\_subset\_1~X5~(k1\_altcat\_1~X0~X3~X4)){\unicdbdjdcd}(k8\_functor0~X0~X1~X2~X3~\\
X4~X5=X5))))))))))\end{array}
\label{hyp:egfdpfjhfgmgmgpghhbdid}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_altcat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l2\_altcat\_1~X1)){\unicdbdjdcd}((r2\_yellow18~X0~X1){\unicdbdjded}(\\
(u1\_struct\_0~X1=u1\_struct\_0~X0){\unicdcdcdhd}((u1\_altcat\_1~X1=k2\_funct\_4~\\
(u1\_altcat\_1~X0)){\unicdcdcdhd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~\\
X1)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X7 .  \\
(m1\_subset\_1~X7~(u1\_struct\_0~X1)){\unicdbdjdcd}(((X5=X2){\unicdcdcdhd}((X6=X3){\unicdcdcdhd}(X7=X4))){\unicdbdjdcd}\\
(k4\_altcat\_1~(u1\_struct\_0~X1)~(u1\_altcat\_1~X1)~(u2\_altcat\_1~X1)~\\
X5~X6~X7=k1\_functor0~(k1\_binop\_1~(u1\_altcat\_1~X0)~X3~X2)~(k1\_binop\_1~\\
(u1\_altcat\_1~X0)~X4~X3)~(k1\_binop\_1~(u1\_altcat\_1~X0)~X4~X2)~(k4\_altcat\_1~\\
(u1\_struct\_0~X0)~(u1\_altcat\_1~X0)~(u2\_altcat\_1~X0)~X4~X3~X2)))))))))))))\end{array}
\label{hyp:egddpfjhfgmgmgpghhbdid}
\end{equation}
\begin{theorem}\label{thm:ehbdfdpfjhfgmgmgpghhbdid}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v11\_altcat\_1~\\
X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}((v11\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~\\
X1){\unicdcdcdhd}(l2\_altcat\_1~X1))))){\unicdbdjdcd}((r2\_yellow18~X0~X1){\unicdbdjdcd}(v21\_functor0~\\
(k2\_yellow18~X0~X1)~X0~X1)))\end{array}$$
\end{theorem}
\end{document}
