\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{t14\_glib\_004 (TMV6GLsNC7gCzLfaAZrKL2ueNEvZNFiKD2k)}
\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 $ v2\_glib\_000 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_glib\_003 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_glib\_003 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v5\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m3\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r2\_glib\_004 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k1\_glib\_004 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k10\_glib\_003 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ r1\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
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\_glib\_003~\\
X0){\unicdcdcdhd}(v7\_glib\_003~X0))))))){\unicdcdcdhd}(m3\_glib\_001~X1~X0)){\unicdbdjdcd}(m1\_subset\_1~\\
(k10\_glib\_003~X0~X1)~k1\_numbers)\end{array}
\label{hyp:egehpflgbdadpfhgmgjgcgpfadaddd}
\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){\unicdcdcdhd}((v2\_glib\_000~X0){\unicdcdcdhd}\\
((v1\_glib\_003~X0){\unicdcdcdhd}(v7\_glib\_003~X0)))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \\
{\unicdcdadad} X3 .  (m1\_subset\_1~X3~k1\_numbers){\unicdbdjdcd}((({\unicdcdaddd} X4 .  ((v2\_glib\_001~\\
X4~X0){\unicdcdcdhd}(m3\_glib\_001~X4~X0)){\unicdcdcdhd}(r1\_glib\_001~X0~X1~X2~X4)){\unicdbdjdcd}((X3=k1\_glib\_004~\\
X0~X1~X2){\unicdbdjded}({\unicdcdaddd} X4 .  ((v2\_glib\_001~X4~X0){\unicdcdcdhd}((v5\_glib\_001~X4~X0){\unicdcdcdhd}\\
(m3\_glib\_001~X4~X0))){\unicdcdcdhd}((r2\_glib\_004~X0~X4~X1~X2){\unicdcdcdhd}(X3=k10\_glib\_003~\\
X0~X4))))){\unicdcdcdhd}(({\unicdcdadad} X4 .  ((v2\_glib\_001~X4~X0){\unicdcdcdhd}(m3\_glib\_001~X4~\\
X0)){\unicdbdjdcd}(\preoh r1\_glib\_001~X0~X1~X2~X4)){\unicdbdjdcd}((X3=k1\_glib\_004~X0~X1~X2){\unicdbdjded}(X3=\\
k6\_numbers)))))\end{array}
\label{hyp:egddpfhgmgjgcgpfadaded}
\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){\unicdcdcdhd}((v1\_glib\_003~X0){\unicdcdcdhd}\\
(v7\_glib\_003~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v2\_glib\_001~X1~X0){\unicdcdcdhd}((v5\_glib\_001~\\
X1~X0){\unicdcdcdhd}(m3\_glib\_001~X1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (r2\_glib\_004~\\
X0~X1~X2~X3){\unicdbdjded}((r1\_glib\_001~X0~X2~X3~X1){\unicdcdcdhd}({\unicdcdadad} X4 .  ((v2\_glib\_001~\\
X4~X0){\unicdcdcdhd}((v5\_glib\_001~X4~X0){\unicdcdcdhd}(m3\_glib\_001~X4~X0))){\unicdbdjdcd}((r1\_glib\_001~\\
X0~X2~X3~X4){\unicdbdjdcd}(r1\_xxreal\_0~(k10\_glib\_003~X0~X1)~(k10\_glib\_003~X0~\\
X4)))))))\end{array}
\label{hyp:egcdpfhgmgjgcgpfadaded}
\end{equation}
\begin{theorem}\label{thm:ehbdedpfhgmgjgcgpfadaded}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}((v1\_glib\_000~X0){\unicdcdcdhd}((v2\_glib\_000~X0){\unicdcdcdhd}\\
((v1\_glib\_003~X0){\unicdcdcdhd}(v7\_glib\_003~X0)))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v2\_glib\_001~\\
X1~X0){\unicdcdcdhd}((v5\_glib\_001~X1~X0){\unicdcdcdhd}(m3\_glib\_001~X1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
{\unicdcdadad} X3 .  (r2\_glib\_004~X0~X1~X2~X3){\unicdbdjdcd}(k1\_glib\_004~X0~X2~X3=k10\_glib\_003~\\
X0~X1)))\end{array}$$
\end{theorem}
\end{document}
