\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\_closure1 (TMUKViKeHgiEfk63JBY2LGs92YAFPTRmbZh)}
\maketitle
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v9\_closure1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_closure1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_mssubfam : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v2\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m3\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_mboolean : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_closure1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r2\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r6\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_closure1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k4\_mssubfam : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_closure1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v2\_closure1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v3\_closure1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v4\_mssubfam : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v5\_mssubfam : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v10\_closure1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l2\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v4\_mssubfam~\\
X2~X0~X1){\unicdcdcdhd}(m3\_pboole~X2~X0~(k1\_mboolean~X0~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_pboole~\\
X3~X0~(k5\_mssubfam~X0~X1)~(k5\_mssubfam~X0~X1)){\unicdbdjdcd}(({\unicdcdadad} X4 .  (m1\_pboole~\\
X4~X0~(k5\_mssubfam~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v2\_relat\_1~X5){\unicdcdcdhd}(m3\_pboole~\\
X5~X0~(k1\_mboolean~X0~X1))){\unicdbdjdcd}(({\unicdcdadad} X6 .  ((v1\_relat\_1~X6){\unicdcdcdhd}((v4\_relat\_1~\\
X6~X0){\unicdcdcdhd}((v1\_funct\_1~X6){\unicdcdcdhd}(v1\_partfun1~X6~X0)))){\unicdbdjdcd}((r1\_pboole~X0~\\
X6~X5){\unicdbdjded}((r1\_pboole~X0~X6~X2){\unicdcdcdhd}(r2\_pboole~X0~X4~X6)))){\unicdbdjdcd}(r6\_pboole~\\
X0~(k2\_closure1~X0~X1~X3~X4)~(k4\_mssubfam~X0~X1~X5))))){\unicdbdjdcd}(v3\_closure1~\\
X3~X0~X1))))\end{array}
\label{hyp:ehddhdpfdgmgpgdhfhchfgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v5\_mssubfam~\\
X2~X0~X1){\unicdcdcdhd}(m3\_pboole~X2~X0~(k1\_mboolean~X0~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_pboole~\\
X3~X0~(k5\_mssubfam~X0~X1)~(k5\_mssubfam~X0~X1)){\unicdbdjdcd}(({\unicdcdadad} X4 .  (m1\_pboole~\\
X4~X0~(k5\_mssubfam~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v2\_relat\_1~X5){\unicdcdcdhd}(m3\_pboole~\\
X5~X0~(k1\_mboolean~X0~X1))){\unicdbdjdcd}(({\unicdcdadad} X6 .  ((v1\_relat\_1~X6){\unicdcdcdhd}((v4\_relat\_1~\\
X6~X0){\unicdcdcdhd}((v1\_funct\_1~X6){\unicdcdcdhd}(v1\_partfun1~X6~X0)))){\unicdbdjdcd}((r1\_pboole~X0~\\
X6~X5){\unicdbdjded}((r1\_pboole~X0~X6~X2){\unicdcdcdhd}(r2\_pboole~X0~X4~X6)))){\unicdbdjdcd}(r6\_pboole~\\
X0~(k2\_closure1~X0~X1~X3~X4)~(k4\_mssubfam~X0~X1~X5))))){\unicdbdjdcd}((v1\_closure1~\\
X3~X0~X1){\unicdcdcdhd}(v2\_closure1~X3~X0~X1)))))\end{array}
\label{hyp:ehddgdpfdgmgpgdhfhchfgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l1\_struct\_0~X0){\unicdcdcdhd}((v10\_closure1~X1~X0){\unicdcdcdhd}\\
(l1\_closure1~X1~X0))){\unicdbdjdcd}(v5\_mssubfam~(u1\_closure1~X0~X1)~(u1\_struct\_0~\\
X0)~(u3\_msualg\_1~X0~X1))\end{array}
\label{hyp:ggdgidpfdgmgpgdhfhchfgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l1\_struct\_0~X0){\unicdcdcdhd}((v9\_closure1~X1~X0){\unicdcdcdhd}\\
(l1\_closure1~X1~X0))){\unicdbdjdcd}(v4\_mssubfam~(u1\_closure1~X0~X1)~(u1\_struct\_0~\\
X0)~(u3\_msualg\_1~X0~X1))\end{array}
\label{hyp:ggdghdpfdgmgpgdhfhchfgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l1\_struct\_0~X0){\unicdcdcdhd}(l2\_msualg\_1~X1~X0)){\unicdbdjdcd}\\
((v1\_relat\_1~(u3\_msualg\_1~X0~X1)){\unicdcdcdhd}((v4\_relat\_1~(u3\_msualg\_1~\\
X0~X1)~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_funct\_1~(u3\_msualg\_1~X0~X1)){\unicdcdcdhd}(v1\_partfun1~\\
(u3\_msualg\_1~X0~X1)~(u1\_struct\_0~X0)))))\end{array}
\label{hyp:egehpffhddpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l1\_struct\_0~X0){\unicdcdcdhd}(l1\_closure1~X1~X0)){\unicdbdjdcd}\\
(m3\_pboole~(u1\_closure1~X0~X1)~(u1\_struct\_0~X0)~(k1\_mboolean~(\\
u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)))\end{array}
\label{hyp:egehpffhbdpfdgmgpgdhfhchfgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_struct\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_closure1~X1~X0){\unicdbdjdcd}\\
(l2\_msualg\_1~X1~X0))\end{array}
\label{hyp:egehpfmgbdpfdgmgpgdhfhchfgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_struct\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_closure1~X1~X0){\unicdbdjdcd}\\
((v9\_closure1~X1~X0){\unicdbdjdcd}(v10\_closure1~X1~X0)))\end{array}
\label{hyp:dgdgedpfdgmgpgdhfhchfgbd}
\end{equation}
\begin{theorem}\label{thm:ehddidpfdgmgpgdhfhchfgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (l1\_struct\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v9\_closure1~X1~X0){\unicdcdcdhd}\\
(l1\_closure1~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_pboole~X2~(u1\_struct\_0~X0)~\\
(k5\_mssubfam~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1))~(k5\_mssubfam~\\
(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1))){\unicdbdjdcd}(({\unicdcdadad} X3 .  (m1\_pboole~\\
X3~(u1\_struct\_0~X0)~(k5\_mssubfam~(u1\_struct\_0~X0)~(u3\_msualg\_1~\\
X0~X1))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v2\_relat\_1~X4){\unicdcdcdhd}(m3\_pboole~X4~(u1\_struct\_0~\\
X0)~(k1\_mboolean~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)))){\unicdbdjdcd}(({\unicdcdadad} X5 .  \\
((v1\_relat\_1~X5){\unicdcdcdhd}((v4\_relat\_1~X5~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_funct\_1~\\
X5){\unicdcdcdhd}(v1\_partfun1~X5~(u1\_struct\_0~X0))))){\unicdbdjdcd}((r1\_pboole~(u1\_struct\_0~\\
X0)~X5~X4){\unicdbdjded}((r1\_pboole~(u1\_struct\_0~X0)~X5~(u1\_closure1~X0~X1)){\unicdcdcdhd}\\
(r2\_pboole~(u1\_struct\_0~X0)~X3~X5)))){\unicdbdjdcd}(r6\_pboole~(u1\_struct\_0~\\
X0)~(k2\_closure1~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~X2~X3)~(k4\_mssubfam~\\
(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~X4))))){\unicdbdjdcd}((v1\_closure1~X2~\\
(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)){\unicdcdcdhd}((v2\_closure1~X2~(u1\_struct\_0~\\
X0)~(u3\_msualg\_1~X0~X1)){\unicdcdcdhd}((v3\_closure1~X2~(u1\_struct\_0~X0)~(u3\_msualg\_1~\\
X0~X1)){\unicdcdcdhd}(m2\_pboole~X2~(u1\_struct\_0~X0)~(k5\_mssubfam~(u1\_struct\_0~\\
X0)~(u3\_msualg\_1~X0~X1))~(k5\_mssubfam~(u1\_struct\_0~X0)~(u3\_msualg\_1~\\
X0~X1)))))))))\end{array}$$
\end{theorem}
\end{document}
