\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{t86\_chord (TMVCKC7ZU3q2MEfxyzmT3xZgCpnwN15FEkW)}
\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 $ m3\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v5\_chord : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_glib\_000 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k14\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_glib\_000 : {{\iota}{\unicdbdjdcd}{{\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 $ k1\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\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}((r5\_glib\_000~X0~X1){\unicdbdjded}((m1\_glib\_000~\\
X0~X1){\unicdcdcdhd}(m1\_glib\_000~X1~X0))))\end{array}
\label{hyp:ehidhdpfhgmgjgcgpfadadad}
\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}({\unicdcdadad} X2 .  (m3\_glib\_001~X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m3\_glib\_001~X3~X1){\unicdbdjdcd}((X2=X3){\unicdbdjdcd}(k14\_glib\_001~X0~X2=k14\_glib\_001~\\
X1~X3)))))\end{array}
\label{hyp:ehbdbdadpfhgmgjgcgpfadadbd}
\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\_glib\_000~\\
X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (r1\_glib\_000~X1~X2~X3~\\
X4){\unicdbdjdcd}(r1\_glib\_000~X0~X2~X3~X4)))\end{array}
\label{hyp:mgddhdpfhgmgjgcgpfadadad}
\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}((v5\_chord~X1~X0){\unicdbdjded}({\unicdcdaddd} X2 .  ((v7\_ordinal1~X2){\unicdcdcdhd}(\preoh v1\_abian~\\
X2)){\unicdcdcdhd}({\unicdcdaddd} X3 .  ((v7\_ordinal1~X3){\unicdcdcdhd}(\preoh v1\_abian~X3)){\unicdcdcdhd}((\preoh r1\_xxreal\_0~\\
X3~(k1\_nat\_1~X2~np\_\_2)){\unicdcdcdhd}((r1\_xxreal\_0~X3~(k3\_finseq\_1~X1)){\unicdcdcdhd}((\\
k1\_funct\_1~X1~X2{\unicdcdgdad}k1\_funct\_1~X1~X3){\unicdcdcdhd}(({\unicdcdaddd} X4 .  r1\_glib\_000~X0~\\
(k1\_funct\_1~X1~X2)~(k1\_funct\_1~X1~X3)~X4){\unicdcdcdhd}({\unicdcdadad} X4 .  \preoh (X4 \in k14\_glib\_001~\\
X0~X1){\unicdcdcdhd}(r1\_glib\_000~X0~(k1\_funct\_1~X1~X2)~(k1\_funct\_1~X1~X3)~X4))))))))))\end{array}
\label{hyp:egbdadpfdgigpgcheg}
\end{equation}
\begin{theorem}\label{thm:ehidgdpfdgigpgcheg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}(v1\_glib\_000~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~\\
X1){\unicdcdcdhd}((v4\_relat\_1~X1~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_finset\_1~\\
X1){\unicdcdcdhd}(v1\_glib\_000~X1))))){\unicdbdjdcd}((r5\_glib\_000~X0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (\\
m3\_glib\_001~X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  (m3\_glib\_001~X3~X1){\unicdbdjdcd}(((X2=X3){\unicdcdcdhd}\\
(v5\_chord~X2~X0)){\unicdbdjdcd}(v5\_chord~X3~X1))))))\end{array}$$
\end{theorem}
\end{document}
