\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{t1\_glib\_005 (TMbeakweKAFax4s31xuddjSsAGnB9S8w3W9)}
\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 $ v1\_glib\_003 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_glib\_003 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k7\_glib\_000 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m3\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r5\_glib\_005 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_abian : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ 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 $ k1\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k5\_glib\_003 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{({{v7\_ordinal1}~{X0}})}{\unicdcdcdhd}{({\preoh{{{v1\_abian}~{X0}}}})}})}{\unicdbdjdcd}{({{{r1\_xxreal\_0}~{np\_\_1}}~{X0}})}}}\label{hyp:ehbdcdpfbgcgjgbgog}
\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}((\preoh (\preoh v3\_glib\_001~X1~X0){\unicdcdcdhd}(k3\_finseq\_1~X1=np\_\_1)){\unicdcdcdhd}(\preoh (k3\_finseq\_1~\\
X1{\unicdcdgdad}np\_\_1){\unicdcdcdhd}(v3\_glib\_001~X1~X0))))\end{array}
\label{hyp:mgjdcdpfhgmgjgcgpfadadbd}
\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 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~(k7\_glib\_000~X0)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~(k7\_glib\_000~\\
X0)){\unicdcdcdhd}(v4\_valued\_0~X1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m3\_glib\_001~X2~X0){\unicdbdjdcd}(\\
(r5\_glib\_005~X0~X1~X2){\unicdbdjded}({\unicdcdadad} X3 .  ((v7\_ordinal1~X3){\unicdcdcdhd}(\preoh v1\_abian~\\
X3)){\unicdbdjdcd}((\preoh r1\_xxreal\_0~(k3\_finseq\_1~X2)~X3){\unicdbdjdcd}((\preoh (r2\_glib\_000~X0~\\
(k1\_funct\_1~X2~X3)~(k1\_funct\_1~X2~(k1\_nat\_1~X3~np\_\_2))~(k1\_funct\_1~\\
X2~(k1\_nat\_1~X3~np\_\_1))){\unicdcdcdhd}(r1\_xxreal\_0~(k1\_funct\_1~(k5\_glib\_003~\\
X0)~(k1\_funct\_1~X2~(k1\_nat\_1~X3~np\_\_1)))~(k1\_funct\_1~X1~(k1\_funct\_1~\\
X2~(k1\_nat\_1~X3~np\_\_1))))){\unicdcdcdhd}(\preoh (\preoh r2\_glib\_000~X0~(k1\_funct\_1~X2~X3)~\\
(k1\_funct\_1~X2~(k1\_nat\_1~X3~np\_\_2))~(k1\_funct\_1~X2~(k1\_nat\_1~X3~\\
np\_\_1))){\unicdcdcdhd}(r1\_xxreal\_0~(k1\_funct\_1~X1~(k1\_funct\_1~X2~(k1\_nat\_1~\\
X3~np\_\_1)))~k6\_numbers))))))))\end{array}
\label{hyp:egidpfhgmgjgcgpfadadfd}
\end{equation}
\begin{theorem}\label{thm:ehbdpfhgmgjgcgpfadadfd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}((v1\_glib\_000~X0){\unicdcdcdhd}((v1\_glib\_003~X0){\unicdcdcdhd}\\
(v7\_glib\_003~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~(k7\_glib\_000~X0)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~(k7\_glib\_000~\\
X0)){\unicdcdcdhd}(v4\_valued\_0~X1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m3\_glib\_001~X2~X0){\unicdbdjdcd}(\\
(v3\_glib\_001~X2~X0){\unicdbdjdcd}(r5\_glib\_005~X0~X1~X2))))\end{array}$$
\end{theorem}
\end{document}
