\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\_nat\_d (TMbswvytmJzdY7g65pnPqHDXcvyxWAcpZqE)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_int\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_int\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_int\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}((\\
k2\_xcmplx\_0~X0~X1=k6\_numbers){\unicdbdjdcd}((X0=k6\_numbers){\unicdcdcdhd}(X1=k6\_numbers))))\end{array}
\label{hyp:ehhdpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_int\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_int\_1~X1){\unicdbdjdcd}(((r1\_xxreal\_0~\\
k6\_numbers~X1){\unicdbdjdcd}((r1\_xxreal\_0~X0~X1){\unicdcdcdid}(k6\_int\_1~X1~X0=X1))){\unicdcdcdhd}((\\
r1\_xxreal\_0~(k4\_xcmplx\_0~X0)~X1){\unicdbdjdcd}((r1\_xxreal\_0~k6\_numbers~X1){\unicdcdcdid}\\
(k6\_int\_1~X1~X0=k2\_xcmplx\_0~X0~X1)))))\end{array}
\label{hyp:ehgdddpfogbgehpfeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}((\preoh r1\_xxreal\_0~X0~k6\_numbers){\unicdbdjdcd}(\\
{\unicdcdadad} X1 .  (v1\_int\_1~X1){\unicdbdjdcd}((r1\_xxreal\_0~k6\_numbers~(k6\_int\_1~\\
X1~X0)){\unicdcdcdhd}(\preoh r1\_xxreal\_0~X0~(k6\_int\_1~X1~X0)))))\end{array}
\label{hyp:ehgdcdpfogbgehpfeg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_int\_1}~{X0}})}{\unicdbdjdcd}{({{{{k6\_int\_1}~{X0}}~{X0}}={k6\_numbers}})}}}\label{hyp:ehfdadpfjgogehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}(\preoh \\
(r1\_xxreal\_0~X0~X1){\unicdcdcdhd}({\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}(X1{\unicdcdgdad}k2\_xcmplx\_0~\\
X0~X2))))\end{array}
\label{hyp:ehbdadpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdaddd} X0 .  {{v7\_ordinal1}~{X0}}}\label{hyp:chdgedpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdaddd} X0 .  {{v1\_int\_1}~{X0}}}\label{hyp:chdgcdpfjgogehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}(v7\_ordinal1~\\
(k6\_int\_1~X0~X1)))\end{array}
\label{hyp:mgcdpfogbgehpfeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_int\_1~X0){\unicdcdcdhd}(v1\_int\_1~X1)){\unicdbdjdcd}(v1\_int\_1~\\
(k6\_int\_1~X0~X1))\end{array}
\label{hyp:egehpflggdpfjgogehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_int\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_int\_1~X1){\unicdbdjdcd}(((X1{\unicdcdgdad}k6\_numbers){\unicdbdjdcd}\\
(k6\_int\_1~X0~X1=k6\_xcmplx\_0~X0~(k3\_xcmplx\_0~(k5\_int\_1~X0~X1)~X1))){\unicdcdcdhd}\\
((X1=k6\_numbers){\unicdbdjdcd}(k6\_int\_1~X0~X1=k6\_numbers))))\end{array}
\label{hyp:egbdadpfjgogehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{v1\_int\_1}~{X0}})}}}\label{hyp:dgdgcdpfjgogehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehgdfdpfogbgehpfeg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_int\_1~X1){\unicdbdjdcd}(k6\_int\_1~\\
(k6\_int\_1~X1~X0)~X0=k6\_int\_1~X1~X0))\end{array}$$
\end{theorem}
\end{document}
