\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{t18\_necklace (TMZSaejHz6iEvXyeJMZ97NFZqe9bBW85Rbv)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_orders\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_necklace : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_relat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_necklace : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_necklace : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 : \iota{\unicdbdjdcd}o .  {\unicdcdadad} X1 : \iota{\unicdbdjdcd}\iota .  {\unicdcdadad} X2 : \iota{\unicdbdjdcd}\iota .  \\
{\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~X4){\unicdcdcdhd}(v1\_relat\_1~X3)){\unicdbdjdcd}(\\
(X3=ReplSep~(toset~({\uniddcgcg} X5 : \iota .  m1\_subset\_1~X5~X4))~({\uniddcgcg} X5 : \iota .  \\
X0~X5)~({\uniddcgcg} X5 : \iota .  k4\_tarski~(X2~X5)~(X1~X5))){\unicdbdjdcd}(k2\_relat\_1~X3=\\
ReplSep~(toset~({\uniddcgcg} X5 : \iota .  m1\_subset\_1~X5~X4))~({\uniddcgcg} X5 : \iota .  X0~\\
X5)~({\uniddcgcg} X5 : \iota .  k4\_tarski~(X1~X5)~(X2~X5))))\end{array}
\label{hyp:dhbdpfogfgdglgmgbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~X0))){\unicdbdjdcd}(k4\_subset\_1~X0~X1~X2=\\
k2\_xboole\_0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(k3\_relset\_1~X0~X1~X2=k2\_relat\_1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}(m1\_subset\_1~(u1\_orders\_2~X0)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))))\end{array}
\label{hyp:egehpffhbdpfpgchegfgchdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(m1\_subset\_1~(k3\_relset\_1~X0~X1~X2)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X1~X0)))\end{array}
\label{hyp:egehpflgddpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}((v1\_orders\_2~(k2\_necklace~X0)){\unicdcdcdhd}\\
(l1\_orders\_2~(k2\_necklace~X0)))\end{array}
\label{hyp:egehpflgcdpfogfgdglgmgbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}((v1\_orders\_2~(k1\_necklace~X0)){\unicdcdcdhd}\\
(l1\_orders\_2~(k1\_necklace~X0)))\end{array}
\label{hyp:egehpflgbdpfogfgdglgmgbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}(k4\_necklace~X0=k2\_necklace~(k1\_necklace~\\
X0))\end{array}
\label{hyp:egjdpfogfgdglgmgbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_orders\_2~X1){\unicdcdcdhd}(\\
l1\_orders\_2~X1)){\unicdbdjdcd}((X1=k2\_necklace~X0){\unicdbdjded}((u1\_struct\_0~X1=u1\_struct\_0~\\
X0){\unicdcdcdhd}(u1\_orders\_2~X1=k4\_subset\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~\\
(u1\_struct\_0~X0))~(u1\_orders\_2~X0)~(k3\_relset\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)~(u1\_orders\_2~X0))))))\end{array}
\label{hyp:eghdpfogfgdglgmgbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_orders\_2~X1){\unicdcdcdhd}(\\
l1\_orders\_2~X1)){\unicdbdjdcd}((X1=k1\_necklace~X0){\unicdbdjded}((u1\_struct\_0~X1=X0){\unicdcdcdhd}\\
(u1\_orders\_2~X1=ReplSep~(toset~({\uniddcgcg} X2 : \iota .  m1\_subset\_1~X2~k5\_numbers))~\\
({\uniddcgcg} X2 : \iota .  \preoh r1\_xxreal\_0~X0~(k2\_nat\_1~X2~np\_\_1))~({\uniddcgcg} X2 : \iota .  \\
k4\_tarski~X2~(k2\_nat\_1~X2~np\_\_1))))))\end{array}
\label{hyp:eggdpfogfgdglgmgbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(v1\_relat\_1~X2)\end{array}
\label{hyp:dgdgbdpfchfgmgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdidpfogfgdglgmgbgdgfg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}(u1\_orders\_2~(k4\_necklace~X0)=k2\_xboole\_0~\\
(ReplSep~(toset~({\uniddcgcg} X1 : \iota .  m1\_subset\_1~X1~k5\_numbers))~({\uniddcgcg} X1 : \\
\iota .  \preoh r1\_xxreal\_0~X0~(k2\_nat\_1~X1~np\_\_1))~({\uniddcgcg} X1 : \iota .  k4\_tarski~\\
X1~(k2\_nat\_1~X1~np\_\_1)))~(ReplSep~(toset~({\uniddcgcg} X1 : \iota .  m1\_subset\_1~\\
X1~k5\_numbers))~({\uniddcgcg} X1 : \iota .  \preoh r1\_xxreal\_0~X0~(k2\_nat\_1~X1~np\_\_1))~\\
({\uniddcgcg} X1 : \iota .  k4\_tarski~(k2\_nat\_1~X1~np\_\_1)~X1)))\end{array}$$
\end{theorem}
\end{document}
