\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}
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\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{t19\_necklace (TMcVoQLTWg219ZW8Yzp5rxR9pyGdbi4UApG)}
\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 $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\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}
\label{hyp:ehbdidpfogfgdglgmgbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X2=k2\_xboole\_0~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(X3 \in X2){\unicdbdjded}((X3 \in X0){\unicdcdcdid}(X3 \in X1)))\end{array}
\label{hyp:egddpfihcgpgpgmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:ehbdjdpfogfgdglgmgbgdgfg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (X1 \in u1\_orders\_2~(k4\_necklace~\\
X0)){\unicdbdjded}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~k5\_numbers){\unicdcdcdhd}((\preoh r1\_xxreal\_0~\\
X0~(k2\_nat\_1~X2~np\_\_1)){\unicdcdcdhd}((X1=k4\_tarski~X2~(k2\_nat\_1~X2~np\_\_1)){\unicdcdcdid}\\
(X1=k4\_tarski~(k2\_nat\_1~X2~np\_\_1)~X2)))))\end{array}$$
\end{theorem}
\end{document}
