\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{t105\_card\_3 (TMcu2KdsijLaua52vJoadbysZuACz3DdsBW)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r4\_wellord1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_relat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r3\_wellord1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v2\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}((v1\_finset\_1~\\
(k9\_xtuple\_0~X0)){\unicdbdjdcd}(v1\_finset\_1~(k10\_xtuple\_0~X0)))\end{array}
\label{hyp:ehidpfggjgogdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_finset\_1~X0)){\unicdbdjdcd}(v1\_finset\_1~\\
(k1\_relat\_1~X0))\end{array}
\label{hyp:ggdgcdidpfggjgogdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(\preoh v1\_finset\_1~X0)){\unicdbdjdcd}(\preoh v1\_finset\_1~\\
(k1\_relat\_1~X0))\end{array}
\label{hyp:ggdgbdedpfdgbgchegpfdd}
\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}
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){\unicdbdjded}((\\
k9\_xtuple\_0~X2=k1\_relat\_1~X0){\unicdcdcdhd}((k10\_xtuple\_0~X2=k1\_relat\_1~\\
X1){\unicdcdcdhd}((v2\_funct\_1~X2){\unicdcdcdhd}({\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (k4\_tarski~X3~X4 \in \\
X0){\unicdbdjded}((X3 \in k1\_relat\_1~X0){\unicdcdcdhd}((X4 \in k1\_relat\_1~X0){\unicdcdcdhd}(k4\_tarski~(k1\_funct\_1~\\
X2~X3)~(k1\_funct\_1~X2~X4) \in X1))))))))))\end{array}
\label{hyp:eghdpfhhfgmgmgpgchegbd}
\end{equation}
\begin{theorem}\label{thm:ehbdadfdpfdgbgchegpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_relat\_1~X1){\unicdbdjdcd}(((r4\_wellord1~\\
X0~X1){\unicdcdcdhd}(v1\_finset\_1~X0)){\unicdbdjdcd}(v1\_finset\_1~X1)))\end{array}$$
\end{theorem}
\end{document}
