\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{t38\_parsp\_2 (TMZZroxSqLNSWjfQPXvdtUTUs9BoBkdoAvW)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_parsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_parsp\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_parsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_parsp\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ r2\_parsp\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ r1\_parsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_parsp\_1~X0){\unicdcdcdhd}((v1\_parsp\_2~\\
X0){\unicdcdcdhd}(l1\_parsp\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\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}(\preoh (r2\_parsp\_2~X0~X1~X2~X3~X4){\unicdcdcdhd}(r1\_parsp\_1~X0~\\
X1~X4~X2~X3))))))\end{array}
\label{hyp:ehddgdpfahbgchdhahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_parsp\_1~X0){\unicdcdcdhd}((v1\_parsp\_2~\\
X0){\unicdcdcdhd}(l1\_parsp\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (\preoh r1\_parsp\_2~X0~X1~X2~X3){\unicdcdcdhd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh r2\_parsp\_2~X0~\\
X1~X2~X3~X4))))))\end{array}
\label{hyp:ehddedpfahbgchdhahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_parsp\_1~X0){\unicdcdcdhd}((v1\_parsp\_2~\\
X0){\unicdcdcdhd}(l1\_parsp\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\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}((r2\_parsp\_2~X0~X1~X2~X3~X4){\unicdbdjdcd}((\preoh r1\_parsp\_2~X0~\\
X1~X2~X3){\unicdcdcdhd}((\preoh r1\_parsp\_2~X0~X2~X1~X4){\unicdcdcdhd}((\preoh r1\_parsp\_2~X0~X3~X4~X1){\unicdcdcdhd}(\\
(\preoh r1\_parsp\_2~X0~X4~X3~X2){\unicdcdcdhd}((\preoh r1\_parsp\_2~X0~X1~X3~X2){\unicdcdcdhd}((\preoh r1\_parsp\_2~\\
X0~X2~X1~X3){\unicdcdcdhd}((\preoh r1\_parsp\_2~X0~X2~X3~X1){\unicdcdcdhd}((\preoh r1\_parsp\_2~X0~X3~X1~X2){\unicdcdcdhd}\\
((\preoh r1\_parsp\_2~X0~X3~X2~X1){\unicdcdcdhd}((\preoh r1\_parsp\_2~X0~X2~X4~X1){\unicdcdcdhd}((\preoh r1\_parsp\_2~\\
X0~X1~X2~X4){\unicdcdcdhd}((\preoh r1\_parsp\_2~X0~X1~X4~X2){\unicdcdcdhd}((\preoh r1\_parsp\_2~X0~X4~X1~X2){\unicdcdcdhd}\\
((\preoh r1\_parsp\_2~X0~X4~X2~X1){\unicdcdcdhd}((\preoh r1\_parsp\_2~X0~X3~X1~X4){\unicdcdcdhd}((\preoh r1\_parsp\_2~\\
X0~X1~X3~X4){\unicdcdcdhd}((\preoh r1\_parsp\_2~X0~X1~X4~X3){\unicdcdcdhd}((\preoh r1\_parsp\_2~X0~X4~X1~X3){\unicdcdcdhd}\\
((\preoh r1\_parsp\_2~X0~X4~X3~X1){\unicdcdcdhd}((\preoh r1\_parsp\_2~X0~X4~X2~X3){\unicdcdcdhd}((\preoh r1\_parsp\_2~\\
X0~X2~X3~X4){\unicdcdcdhd}((\preoh r1\_parsp\_2~X0~X2~X4~X3){\unicdcdcdhd}((\preoh r1\_parsp\_2~X0~X3~X2~X4){\unicdcdcdhd}\\
(\preoh r1\_parsp\_2~X0~X3~X4~X2)))))))))))))))))))))))))))))\end{array}
\label{hyp:ehcdidpfahbgchdhahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_parsp\_1~X0){\unicdcdcdhd}((v1\_parsp\_2~\\
X0){\unicdcdcdhd}(l1\_parsp\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\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}((r2\_parsp\_2~X0~X1~X2~X3~X4){\unicdbdjdcd}((X1{\unicdcdgdad}X2){\unicdcdcdhd}((X2{\unicdcdgdad}\\
X3){\unicdcdcdhd}((X3{\unicdcdgdad}X1){\unicdcdcdhd}((X1{\unicdcdgdad}X4){\unicdcdcdhd}((X2{\unicdcdgdad}X4){\unicdcdcdhd}(X3{\unicdcdgdad}X4)))))))))))\end{array}
\label{hyp:ehcdgdpfahbgchdhahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_parsp\_1~X0){\unicdcdcdhd}(l1\_parsp\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\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~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~\\
X6~(u1\_struct\_0~X0)){\unicdbdjdcd}(((r1\_parsp\_1~X0~X3~X4~X1~X2){\unicdcdcdhd}(r1\_parsp\_1~\\
X0~X1~X2~X5~X6)){\unicdbdjdcd}((X1=X2){\unicdcdcdid}(r1\_parsp\_1~X0~X3~X4~X5~X6)))))))))\end{array}
\label{hyp:ehcdgdpfahbgchdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_parsp\_1~X0){\unicdcdcdhd}(l1\_parsp\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\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}\\
((r1\_parsp\_1~X0~X1~X2~X3~X4){\unicdbdjdcd}((r1\_parsp\_1~X0~X2~X1~X3~X4){\unicdcdcdhd}((r1\_parsp\_1~\\
X0~X1~X2~X4~X3){\unicdcdcdhd}((r1\_parsp\_1~X0~X2~X1~X4~X3){\unicdcdcdhd}((r1\_parsp\_1~X0~X3~X4~X1~\\
X2){\unicdcdcdhd}((r1\_parsp\_1~X0~X4~X3~X1~X2){\unicdcdcdhd}((r1\_parsp\_1~X0~X3~X4~X2~X1){\unicdcdcdhd}(r1\_parsp\_1~\\
X0~X4~X3~X2~X1))))))))))))\end{array}
\label{hyp:ehcdddpfahbgchdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_parsp\_1~X0){\unicdcdcdhd}((v1\_parsp\_2~\\
X0){\unicdcdcdhd}(l1\_parsp\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (X1{\unicdcdgdad}X2){\unicdcdcdhd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}(r1\_parsp\_2~X0~\\
X1~X2~X3)))))\end{array}
\label{hyp:ehbdedpfahbgchdhahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_parsp\_1~X0){\unicdcdcdhd}((v1\_parsp\_2~\\
X0){\unicdcdcdhd}(l1\_parsp\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}((r1\_parsp\_2~X0~X1~X2~X3){\unicdbdjdcd}((\\
r1\_parsp\_2~X0~X1~X3~X2){\unicdcdcdhd}((r1\_parsp\_2~X0~X3~X2~X1){\unicdcdcdhd}((r1\_parsp\_2~X0~\\
X2~X1~X3){\unicdcdcdhd}((r1\_parsp\_2~X0~X2~X3~X1){\unicdcdcdhd}(r1\_parsp\_2~X0~X3~X1~X2)))))))))\end{array}
\label{hyp:ehbdadpfahbgchdhahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_parsp\_1~X0){\unicdcdcdhd}((v1\_parsp\_2~\\
X0){\unicdcdcdhd}(l1\_parsp\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\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}((r2\_parsp\_2~X0~X1~X2~X3~X4){\unicdbdjded}((\preoh r1\_parsp\_2~X0~\\
X1~X2~X3){\unicdcdcdhd}((r1\_parsp\_1~X0~X1~X2~X3~X4){\unicdcdcdhd}(r1\_parsp\_1~X0~X1~X3~X2~X4))))))))\end{array}
\label{hyp:egddpfahbgchdhahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_parsp\_1~X0){\unicdcdcdhd}((v1\_parsp\_2~\\
X0){\unicdcdcdhd}(l1\_parsp\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}((r1\_parsp\_2~X0~X1~X2~X3){\unicdbdjded}(r1\_parsp\_1~\\
X0~X1~X2~X1~X3)))))\end{array}
\label{hyp:egcdpfahbgchdhahpfcd}
\end{equation}
\begin{theorem}\label{thm:ehddidpfahbgchdhahpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_parsp\_1~X0){\unicdcdcdhd}((v1\_parsp\_2~\\
X0){\unicdcdcdhd}(l1\_parsp\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (X1{\unicdcdgdad}X2){\unicdcdcdhd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (r1\_parsp\_2~\\
X0~X1~X2~X3){\unicdcdcdhd}((X3{\unicdcdgdad}X1){\unicdcdcdhd}(X3{\unicdcdgdad}X2)))))))\end{array}$$
\end{theorem}
\end{document}
