\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{t42\_wellord1 (TMMVYJGPssLLeeFZ9V7ZURmDPQxKeMxMjM5)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r4\_wellord1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r3\_wellord1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_relat\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_relat\_1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}(v1\_funct\_1~X3)){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  ((v1\_relat\_1~X4){\unicdcdcdhd}(v1\_funct\_1~X4)){\unicdbdjdcd}(((r3\_wellord1~\\
X0~X1~X3){\unicdcdcdhd}(r3\_wellord1~X1~X2~X4)){\unicdbdjdcd}(r3\_wellord1~X0~X2~(k3\_relat\_1~\\
X3~X4)))))))\end{array}
\label{hyp:ehedbdpfhhfgmgmgpgchegbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdcdcdhd}((\\
v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1))){\unicdbdjdcd}((v1\_relat\_1~(k3\_relat\_1~X0~\\
X1)){\unicdcdcdhd}(v1\_funct\_1~(k3\_relat\_1~X0~X1)))\end{array}
\label{hyp:ggdgcdpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_relat\_1~X1){\unicdbdjdcd}((r4\_wellord1~\\
X0~X1){\unicdbdjded}({\unicdcdaddd} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~X2)){\unicdcdcdhd}(r3\_wellord1~\\
X0~X1~X2))))\end{array}
\label{hyp:egidpfhhfgmgmgpgchegbd}
\end{equation}
\begin{theorem}\label{thm:ehedcdpfhhfgmgmgpgchegbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_relat\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_relat\_1~X2){\unicdbdjdcd}(((r4\_wellord1~X0~X1){\unicdcdcdhd}(r4\_wellord1~X1~X2)){\unicdbdjdcd}(\\
r4\_wellord1~X0~X2))))\end{array}$$
\end{theorem}
\end{document}
