\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{t20\_necklace (TMSD7jcHAd9ebKe7MxRcDh3Ew8HwCybdEQo)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_necklace : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_necklace : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_necklace : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_orders\_2 : {{\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 $ 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.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}((v1\_orders\_2~(k4\_necklace~X0)){\unicdcdcdhd}\\
(l1\_orders\_2~(k4\_necklace~X0)))\end{array}
\label{hyp:egehpflgedpfogfgdglgmgbgdgfg}
\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}
\begin{theorem}\label{thm:ehcdadpfogfgdglgmgbgdgfg}
${{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{{u1\_struct\_0}~{({{k4\_necklace}~{X0}})}}={X0}})}}}$.
\end{theorem}
\end{document}
