\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{t65\_card\_2 (TMLqF5kevMeJFKrX769HpkwVA11TAGuz21z)}
\maketitle
Let $ v1\_card\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_card\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r2\_wellord2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_card\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k3\_card\_3~(k2\_card\_3~(k7\_funcop\_1~X0~X1))=\\
k2\_zfmisc\_1~X1~X0\end{array}
\label{hyp:ehcdfdpfdgbgchegpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k7\_funcop\_1}~{X0}}~{X1}}={{{k2\_funcop\_1}~{X0}}~{X1}}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflghdpfggfhogdgpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (r2\_wellord2~(k2\_zfmisc\_1~X0~X1)~(k2\_zfmisc\_1~\\
X1~X0)){\unicdcdcdhd}(k1\_card\_1~(k2\_zfmisc\_1~X0~X1)=k1\_card\_1~(k2\_zfmisc\_1~\\
X1~X0))\end{array}
\label{hyp:mgfdpfdgbgchegpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_card\_1~X1){\unicdbdjdcd}(v1\_card\_3~(k2\_funcop\_1~\\
X0~X1))\end{array}
\label{hyp:ggdgcdpfdgbgchegpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_relat\_1~(k2\_funcop\_1~X0~X1)){\unicdcdcdhd}(v1\_funct\_1~\\
(k2\_funcop\_1~X0~X1))\end{array}
\label{hyp:ggdgbdpfggfhogdgpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_card\_3~X0))){\unicdbdjdcd}\\
(k6\_card\_3~X0=k1\_card\_1~(k3\_card\_3~(k2\_card\_3~X0)))\end{array}
\label{hyp:eghdpfdgbgchegpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_card\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_card\_1~X1){\unicdbdjdcd}(k2\_card\_2~\\
X0~X1=k1\_card\_1~(k2\_zfmisc\_1~X0~X1)))\end{array}
\label{hyp:egcdpfdgbgchegpfcd}
\end{equation}
\begin{theorem}\label{thm:ehgdfdpfdgbgchegpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_card\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_card\_1~X1){\unicdbdjdcd}(k6\_card\_3~\\
(k7\_funcop\_1~X0~X1)=k2\_card\_2~X0~X1))\end{array}$$
\end{theorem}
\end{document}
