\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{t50\_wellord1 (TMcw7ZYDD73Rctx1cpVziBsChF8VZDnwXxs)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_wellord1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r3\_wellord1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_relat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r4\_wellord1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_wellord1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_wellord1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k7\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_relat\_1~X1){\unicdbdjdcd}(r1\_tarski~(k1\_wellord1~\\
X1~X0)~(k1\_relat\_1~X1))\end{array}
\label{hyp:ehjdpfhhfgmgmgpgchegbd}
\end{equation}
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){\unicdcdcdhd}(v1\_funct\_1~X2)){\unicdbdjdcd}((r3\_wellord1~X0~X1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
\preoh (X3 \in k1\_relat\_1~X0){\unicdcdcdhd}({\unicdcdadad} X4 .  \preoh (X4 \in k1\_relat\_1~X1){\unicdcdcdhd}(k7\_relat\_1~\\
X2~(k1\_wellord1~X0~X3)=k1\_wellord1~X1~X4))))))\end{array}
\label{hyp:ehedjdpfhhfgmgmgpgchegbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\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}(((v2\_wellord1~\\
X1){\unicdcdcdhd}((r1\_tarski~X0~(k1\_relat\_1~X1)){\unicdcdcdhd}(r3\_wellord1~X1~X2~X3))){\unicdbdjdcd}\\
((r3\_wellord1~(k2\_wellord1~X1~X0)~(k2\_wellord1~X2~(k7\_relat\_1~\\
X3~X0))~(k5\_relat\_1~X3~X0)){\unicdcdcdhd}(r4\_wellord1~(k2\_wellord1~X1~X0)~(k2\_wellord1~\\
X2~(k7\_relat\_1~X3~X0)))))))\end{array}
\label{hyp:ehedidpfhhfgmgmgpgchegbd}
\end{equation}
\begin{theorem}\label{thm:ehfdadpfhhfgmgmgpgchegbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_relat\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~X2)){\unicdbdjdcd}(((v2\_wellord1~X0){\unicdcdcdhd}(r3\_wellord1~\\
X0~X1~X2)){\unicdbdjdcd}({\unicdcdadad} X3 .  \preoh (X3 \in k1\_relat\_1~X0){\unicdcdcdhd}({\unicdcdadad} X4 .  \preoh (X4 \in \\
k1\_relat\_1~X1){\unicdcdcdhd}(r4\_wellord1~(k2\_wellord1~X0~(k1\_wellord1~X0~X3))~\\
(k2\_wellord1~X1~(k1\_wellord1~X1~X4))))))))\end{array}$$
\end{theorem}
\end{document}
