\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{t25\_necklace (TMQ12Didd5PagZ6UajWFLNmfXLVPzZy8Spc)}
\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 $ k1\_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 $ u1\_orders\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}(\preoh \\
(X1 \in u1\_struct\_0~(k4\_necklace~X0)){\unicdcdcdhd}(r1\_xxreal\_0~X0~X1)))\end{array}
\label{hyp:ehcdcdpfogfgdglgmgbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}((\\
\preoh r1\_xxreal\_0~X0~(k1\_nat\_1~X1~np\_\_1)){\unicdbdjdcd}(k4\_tarski~X1~(k1\_nat\_1~X1~\\
np\_\_1) \in u1\_orders\_2~(k4\_necklace~X0))))\end{array}
\label{hyp:ehcdbdpfogfgdglgmgbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (k4\_tarski~X0~X1=\\
k4\_tarski~X2~X3){\unicdbdjdcd}((X0=X2){\unicdcdcdhd}(X1=X3))\end{array}
\label{hyp:ehbdpfihehfhahmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\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}
\label{hyp:ehbdjdpfogfgdglgmgbgdgfg}
\end{equation}
\begin{theorem}\label{thm:ehcdfdpfogfgdglgmgbgdgfg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v7\_ordinal1~X2){\unicdbdjdcd}(((X1 \in u1\_struct\_0~(k4\_necklace~X0)){\unicdcdcdhd}(X2 \in u1\_struct\_0~\\
(k4\_necklace~X0))){\unicdbdjdcd}(((X1{\unicdcdgdad}k1\_nat\_1~X2~np\_\_1){\unicdcdcdhd}(X2{\unicdcdgdad}k1\_nat\_1~X1~\\
np\_\_1)){\unicdcdcdid}(k4\_tarski~X1~X2 \in u1\_orders\_2~(k4\_necklace~X0))))))\end{array}$$
\end{theorem}
\end{document}
