\documentclass{article}
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\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t18\_nat\_5 (TMYycQNWTPvjba7ZGroZY6aNedAPvkhgbzr)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_int\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_moebius1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k24\_binop\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k6\_nat\_d : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_nat\_d : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k3\_int\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_int\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}(\preoh \\
(\preoh r1\_xxreal\_0~X0~k6\_numbers){\unicdcdcdhd}(r1\_xxreal\_0~(k6\_nat\_d~X0~X1)~k6\_numbers)))\end{array}
\label{hyp:ehfdidpfogfghhehpgog}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}((\\
r1\_nat\_d~X0~X1){\unicdbdjdcd}(k6\_nat\_d~X0~X1=X0)))\end{array}
\label{hyp:ehedjdpfogfghhehpgog}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}((\\
X1 \in k3\_moebius1~X0){\unicdbdjded}((\preoh r1\_xxreal\_0~X1~k6\_numbers){\unicdcdcdhd}(r1\_nat\_d~\\
X1~X0))))\end{array}
\label{hyp:ehddjdpfngpgfgcgjgfhdhbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v7\_ordinal1~X1){\unicdcdcdhd}(\\
\preoh v1\_xboole\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v7\_ordinal1~X2){\unicdcdcdhd}(\preoh v1\_xboole\_0~\\
X2)){\unicdbdjdcd}((r1\_int\_2~X1~X2){\unicdbdjdcd}(k6\_nat\_d~X0~(k24\_binop\_2~X1~X2)=k24\_binop\_2~\\
(k6\_nat\_d~X0~X1)~(k6\_nat\_d~X0~X2)))))\end{array}
\label{hyp:ehbdhdpfogbgehpffd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v7\_ordinal1~X1)){\unicdbdjdcd}(\\
k6\_nat\_d~X0~X1=k3\_int\_2~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogbgehpfeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v7\_ordinal1~X1)){\unicdbdjdcd}(\\
k24\_binop\_2~X0~X1=k3\_xcmplx\_0~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdedpfcgjgogpgahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v7\_ordinal1~X1)){\unicdbdjdcd}(\\
v7\_ordinal1~(k3\_xcmplx\_0~X0~X1))\end{array}
\label{hyp:ggdgcdpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_int\_1~X0){\unicdcdcdhd}(v1\_int\_1~X1)){\unicdbdjdcd}(v7\_ordinal1~\\
(k3\_int\_2~X0~X1))\end{array}
\label{hyp:egehpflgddpfjgogehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v7\_ordinal1~X2){\unicdbdjdcd}((X2=k3\_int\_2~X0~X1){\unicdbdjded}((r1\_nat\_d~X2~X0){\unicdcdcdhd}((r1\_nat\_d~\\
X2~X1){\unicdcdcdhd}({\unicdcdadad} X3 .  (v7\_ordinal1~X3){\unicdbdjdcd}(((r1\_nat\_d~X3~X0){\unicdcdcdhd}(r1\_nat\_d~\\
X3~X1)){\unicdbdjdcd}(r1\_nat\_d~X3~X2))))))))\end{array}
\label{hyp:egfdpfogbgehpfeg}
\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:ehbdidpfogbgehpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v7\_ordinal1~X1){\unicdcdcdhd}(\\
\preoh v1\_xboole\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v7\_ordinal1~X2){\unicdcdcdhd}(\preoh v1\_xboole\_0~\\
X2)){\unicdbdjdcd}(\preoh (r1\_int\_2~X1~X2){\unicdcdcdhd}((X0 \in k3\_moebius1~(k24\_binop\_2~X1~X2)){\unicdcdcdhd}\\
({\unicdcdadad} X3 .  (v7\_ordinal1~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (v7\_ordinal1~X4){\unicdbdjdcd}(\\
\preoh (X3 \in k3\_moebius1~X1){\unicdcdcdhd}((X4 \in k3\_moebius1~X2){\unicdcdcdhd}(X0=k24\_binop\_2~\\
X3~X4)))))))))\end{array}$$
\end{theorem}
\end{document}
