\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{t27\_card\_5 (TMKxsekDdXFHuNP2nbj69UQ7d2nHYYjyFBv)}
\maketitle
Let $ v1\_card\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_ordinal2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_card\_5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_ordinal2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_ordinal2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_ordinal1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r2\_wellord2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_card\_1~X1){\unicdbdjdcd}(((r1\_tarski~X0~X1){\unicdcdcdhd}(k1\_card\_1~\\
X0 \in k1\_card\_5~X1)){\unicdbdjdcd}((k3\_ordinal2~X0 \in X1){\unicdcdcdhd}(k3\_tarski~X0 \in X1)))\end{array}
\label{hyp:ehcdgdpfdgbgchegpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v3\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v3\_ordinal1~X2){\unicdbdjdcd}(((r1\_tarski~X0~X1){\unicdcdcdhd}(X1 \in X2)){\unicdbdjdcd}(X0 \in X2))))\end{array}
\label{hyp:ehbdcdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (r1\_ordinal1~(k1\_card\_1~X0)~(k1\_card\_1~\\
X1)){\unicdbdjded}({\unicdcdaddd} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~X2)){\unicdcdcdhd}((k9\_xtuple\_0~\\
X2=X1){\unicdcdcdhd}(r1\_tarski~X0~(k10\_xtuple\_0~X2))))\end{array}
\label{hyp:ehbdcdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{r2\_wellord2}~{X0}}~{X0}}}}\label{hyp:chfgggmgfgihjgghjgehjhpfchcdpfhhfgmgmgpgchegcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{r1\_tarski}~{X0}}~{X0}}}}\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v3\_ordinal1~X0){\unicdcdcdhd}(v3\_ordinal1~X1)){\unicdbdjdcd}(\\
(r1\_ordinal1~X0~X1){\unicdbdjded}(r1\_tarski~X0~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchbdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_card\_1}~{X0}})}{\unicdbdjdcd}{({{v1\_card\_1}~{({{k1\_card\_5}~{X0}})}})}}}\label{hyp:egehpflgbdpfdgbgchegpffd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{v1\_card\_1}~{({{k1\_card\_1}~{X0}})}}}\label{hyp:egehpflgbdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v5\_ordinal1~X0){\unicdcdcdhd}((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0))){\unicdbdjdcd}\\
(k4\_ordinal2~X0=k3\_ordinal2~(k10\_xtuple\_0~X0))\end{array}
\label{hyp:egfdpfpgchegjgogbgmgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}(k3\_card\_3~X0=\\
k3\_tarski~(k10\_xtuple\_0~X0))\end{array}
\label{hyp:egedpfdgbgchegpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_card\_1~X1){\unicdbdjdcd}((X1=k1\_card\_1~X0){\unicdbdjded}(r2\_wellord2~\\
X0~X1))\end{array}
\label{hyp:egcdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v3\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{({{v1\_ordinal1}~{X0}})}{\unicdcdcdhd}{({{v2\_ordinal1}~{X0}})}})}}}\label{hyp:dgdgbdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_card\_1}~{X0}})}{\unicdbdjdcd}{({{v3\_ordinal1}~{X0}})}}}\label{hyp:dgdgbdpfdgbgchegpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdhdpfdgbgchegpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_card\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_card\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v5\_ordinal1~X2){\unicdcdcdhd}(v1\_ordinal2~\\
X2)))){\unicdbdjdcd}(((k9\_xtuple\_0~X2=X0){\unicdcdcdhd}((r1\_tarski~(k10\_xtuple\_0~X2)~\\
X1){\unicdcdcdhd}(X0 \in k1\_card\_5~X1))){\unicdbdjdcd}((k4\_ordinal2~X2 \in X1){\unicdcdcdhd}(k3\_card\_3~X2 \in \\
X1)))))\end{array}$$
\end{theorem}
\end{document}
