\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{l88\_glib\_001 (TMaVdVSm7CGRwQnsM52d6Rj9VMgeoH6smgH)}
\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 $ m3\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_abian : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r2\_glib\_000 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ r1\_glib\_000 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_glib\_000 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_glib\_000 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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 .  {\unicdcdadad} X2 .  \\
{\unicdcdadad} X3 .  (r1\_glib\_000~X0~X2~X3~X1){\unicdbdjded}((r2\_glib\_000~X0~X2~X3~X1){\unicdcdcdid}\\
(r2\_glib\_000~X0~X3~X2~X1)))\end{array}
\label{hyp:ehbdgdpfhgmgjgcgpfadadad}
\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 .  (m3\_glib\_001~\\
X1~X0){\unicdbdjdcd}(m2\_finseq\_1~X1~(k2\_xboole\_0~(k6\_glib\_000~X0)~(k7\_glib\_000~\\
X0))))\end{array}
\label{hyp:egehpfngddpfhgmgjgcgpfadadbd}
\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 .  (m2\_finseq\_1~\\
X1~(k2\_xboole\_0~(k6\_glib\_000~X0)~(k7\_glib\_000~X0))){\unicdbdjdcd}((m3\_glib\_001~\\
X1~X0){\unicdbdjded}((\preoh v1\_abian~(k3\_finseq\_1~X1)){\unicdcdcdhd}((k1\_funct\_1~X1~np\_\_1 \in k6\_glib\_000~\\
X0){\unicdcdcdhd}({\unicdcdadad} X2 .  ((\preoh v1\_abian~X2){\unicdcdcdhd}(m1\_subset\_1~X2~k5\_numbers)){\unicdbdjdcd}\\
((\preoh r1\_xxreal\_0~(k3\_finseq\_1~X1)~X2){\unicdbdjdcd}(r1\_glib\_000~X0~(k1\_funct\_1~\\
X1~X2)~(k1\_funct\_1~X1~(k2\_nat\_1~X2~np\_\_2))~(k1\_funct\_1~X1~(k2\_nat\_1~\\
X2~np\_\_1)))))))))\end{array}
\label{hyp:egddpfhgmgjgcgpfadadbd}
\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 .  (m3\_glib\_001~\\
X1~X0){\unicdbdjdcd}((v2\_glib\_001~X1~X0){\unicdbdjded}({\unicdcdadad} X2 .  ((\preoh v1\_abian~X2){\unicdcdcdhd}(m1\_subset\_1~\\
X2~k5\_numbers)){\unicdbdjdcd}((\preoh r1\_xxreal\_0~(k3\_finseq\_1~X1)~X2){\unicdbdjdcd}(k1\_funct\_1~\\
(k10\_glib\_000~X0)~(k1\_funct\_1~X1~(k2\_nat\_1~X2~np\_\_1))=k1\_funct\_1~\\
X1~X2)))))\end{array}
\label{hyp:egcdfdpfhgmgjgcgpfadadbd}
\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 .  (r2\_glib\_000~X0~X1~X2~X3){\unicdbdjded}((X3 \in k7\_glib\_000~X0){\unicdcdcdhd}((k1\_funct\_1~\\
(k10\_glib\_000~X0)~X3=X1){\unicdcdcdhd}(k1\_funct\_1~(k11\_glib\_000~X0)~X3=X2))))\end{array}
\label{hyp:egbdedpfhgmgjgcgpfadadad}
\end{equation}
\begin{theorem}\label{thm:mgididpfhgmgjgcgpfadadbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}(v1\_glib\_000~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m3\_glib\_001~\\
X1~X0){\unicdbdjdcd}((v2\_glib\_001~X1~X0){\unicdbdjded}({\unicdcdadad} X2 .  ((\preoh v1\_abian~X2){\unicdcdcdhd}(m1\_subset\_1~\\
X2~k5\_numbers)){\unicdbdjdcd}((\preoh r1\_xxreal\_0~(k3\_finseq\_1~X1)~X2){\unicdbdjdcd}(r2\_glib\_000~\\
X0~(k1\_funct\_1~X1~X2)~(k1\_funct\_1~X1~(k2\_nat\_1~X2~np\_\_2))~(k1\_funct\_1~\\
X1~(k2\_nat\_1~X2~np\_\_1)))))))\end{array}$$
\end{theorem}
\end{document}
