\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=}
\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}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t59\_nat\_3 (TMMTVMYp7WBvCoAKai8u7ek4f23JFVsaCD9)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_int\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k13\_nat\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_newton : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k11\_nat\_3 : {{\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 $ np\_\_1 : {\iota}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ r1\_int\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh \\
v1\_xboole\_0~X1){\unicdcdcdhd}(v7\_ordinal1~X1)){\unicdbdjdcd}((k11\_nat\_3~X1~X0{\unicdcdgdad}k6\_numbers){\unicdbdjdcd}\\
(k1\_seq\_1~(k13\_nat\_3~X1)~X0=k1\_newton~X0~(k11\_nat\_3~X1~X0))))\end{array}
\label{hyp:ehfdgdpfogbgehpfdd}
\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~np\_\_1){\unicdbdjdcd}(k11\_nat\_3~(k1\_newton~X0~X1)~X0=X1)))\end{array}
\label{hyp:ehcdfdpfogbgehpfdd}
\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}(\\
v7\_ordinal1~(k1\_newton~X0~X1))\end{array}
\label{hyp:ggdgedpfogfghhehpgog}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{k1\_xboole\_0}}\label{hyp:ggdgbdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v7\_ordinal1~X0)){\unicdcdcdhd}\\
(v7\_ordinal1~X1)){\unicdbdjdcd}(\preoh v1\_xboole\_0~(k1\_newton~X0~X1))\end{array}
\label{hyp:ggdgbdpfogbgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}((v1\_int\_2~X0){\unicdbdjded}((\preoh r1\_xxreal\_0~X0~\\
np\_\_1){\unicdcdcdhd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}(\preoh (r1\_int\_1~X1~X0){\unicdcdcdhd}((X1{\unicdcdgdad}\\
np\_\_1){\unicdcdcdhd}(X1{\unicdcdgdad}X0))))))\end{array}
\label{hyp:egedpfjgogehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~X0)){\unicdbdjdcd}((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~X0)))\end{array}
\label{hyp:dgdgbdpfogbgehpfdd}
\end{equation}
\begin{theorem}\label{thm:ehfdjdpfogbgehpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh \\
v1\_xboole\_0~X1){\unicdcdcdhd}(v7\_ordinal1~X1)){\unicdbdjdcd}(k1\_seq\_1~(k13\_nat\_3~(k1\_newton~\\
X0~X1))~X0=k1\_newton~X0~X1))\end{array}$$
\end{theorem}
\end{document}
