\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{t180\_glib\_001 (TMdMnybv5hrwGiyDF5wzKxwQeyFpMGwBvVE)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_glib\_000 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r5\_glib\_000 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ r1\_glib\_000 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ r2\_glib\_000 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ r3\_glib\_000 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ r4\_glib\_000 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k10\_subset\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k11\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_glib\_000 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k12\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_glib\_000 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}}$ be given.
Let $ k10\_glib\_000 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k11\_glib\_000 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}(v1\_glib\_000~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~\\
X1){\unicdcdcdhd}((v4\_relat\_1~X1~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_finset\_1~\\
X1){\unicdcdcdhd}(v1\_glib\_000~X1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  \\
{\unicdcdadad} X5 .  {\unicdcdadad} X6 .  (r5\_glib\_000~X0~X1){\unicdbdjdcd}(((r1\_glib\_000~X0~X3~\\
X4~X2){\unicdbdjdcd}(r1\_glib\_000~X1~X3~X4~X2)){\unicdcdcdhd}(((r2\_glib\_000~X0~X3~X4~X2){\unicdbdjdcd}(r2\_glib\_000~\\
X1~X3~X4~X2)){\unicdcdcdhd}(((r3\_glib\_000~X0~X5~X6~X2){\unicdbdjdcd}(r3\_glib\_000~X1~X5~X6~X2)){\unicdcdcdhd}\\
((r4\_glib\_000~X0~X5~X6~X2){\unicdbdjdcd}(r4\_glib\_000~X1~X5~X6~X2)))))))\end{array}
\label{hyp:ehididpfhgmgjgcgpfadadad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}\\
((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}(v1\_glib\_000~X0))))){\unicdcdcdhd}((\\
v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}\\
((v1\_finset\_1~X1){\unicdcdcdhd}(v1\_glib\_000~X1)))))){\unicdbdjdcd}((r5\_glib\_000~X0~X1){\unicdbdjdcd}\\
(r5\_glib\_000~X1~X0))\end{array}
\label{hyp:dhjhngngfgehchjhpfchfdpfhgmgjgcgpfadadad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{m1\_subset\_1}~{({{k10\_subset\_1}~{X0}})}}~{X0}}}\label{hyp:egehpflgbdadpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}(v1\_glib\_000~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \\
{\unicdcdadad} X3 .  ((r1\_glib\_000~X0~X1~X2~X3){\unicdbdjdcd}(k2\_glib\_001~X0~X1~X2~X3=k11\_finseq\_1~\\
X1~X3~X2)){\unicdcdcdhd}((\preoh r1\_glib\_000~X0~X1~X2~X3){\unicdbdjdcd}(k2\_glib\_001~X0~X1~X2~X3=k1\_glib\_001~\\
X0~(k10\_subset\_1~(k6\_glib\_000~X0)))))\end{array}
\label{hyp:egfdpfhgmgjgcgpfadadbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}(v1\_glib\_000~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(k6\_glib\_000~X0)){\unicdbdjdcd}(k1\_glib\_001~X0~X1=k12\_finseq\_1~(k6\_glib\_000~\\
X0)~X1))\end{array}
\label{hyp:egedpfhgmgjgcgpfadadbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}(v1\_glib\_000~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~\\
X1){\unicdcdcdhd}((v4\_relat\_1~X1~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_finset\_1~\\
X1){\unicdcdcdhd}(v1\_glib\_000~X1))))){\unicdbdjdcd}((r5\_glib\_000~X0~X1){\unicdbdjded}((k6\_glib\_000~\\
X0=k6\_glib\_000~X1){\unicdcdcdhd}((k7\_glib\_000~X0=k7\_glib\_000~X1){\unicdcdcdhd}((r1\_funct\_2~\\
(k7\_glib\_000~X0)~(k6\_glib\_000~X0)~(k7\_glib\_000~X1)~(k6\_glib\_000~\\
X1)~(k10\_glib\_000~X0)~(k10\_glib\_000~X1)){\unicdcdcdhd}(r1\_funct\_2~(k7\_glib\_000~\\
X0)~(k6\_glib\_000~X0)~(k7\_glib\_000~X1)~(k6\_glib\_000~X1)~(k11\_glib\_000~\\
X0)~(k11\_glib\_000~X1)))))))\end{array}
\label{hyp:egddedpfhgmgjgcgpfadadad}
\end{equation}
\begin{theorem}\label{thm:ehbdidadpfhgmgjgcgpfadadbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}(v1\_glib\_000~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~\\
X1){\unicdcdcdhd}((v4\_relat\_1~X1~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_finset\_1~\\
X1){\unicdcdcdhd}(v1\_glib\_000~X1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  \\
(r5\_glib\_000~X0~X1){\unicdbdjdcd}(k2\_glib\_001~X0~X2~X4~X3=k2\_glib\_001~X1~X2~X4~\\
X3)))\end{array}$$
\end{theorem}
\end{document}
