\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}
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\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{t6\_pepin (TMa78fEQhmxVGnSZT6VCq4sDemTnA7gPKW2)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ r1\_nat\_d : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_nat\_d : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_nat\_d : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\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}({\unicdcdadad} X2 .  \\
(v7\_ordinal1~X2){\unicdbdjdcd}(((r1\_nat\_d~X0~X1){\unicdcdcdhd}(r1\_nat\_d~X0~X2)){\unicdbdjded}(r1\_nat\_d~\\
X0~(k6\_nat\_d~X1~X2)))))\end{array}
\label{hyp:ehfdadpfogfghhehpgog}
\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}(\preoh (k6\_numbers{\unicdcdgdad}X0){\unicdcdcdhd}(r1\_xxreal\_0~\\
X0~k6\_numbers))\end{array}
\label{hyp:ehddpfogbgehpfbd}
\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~k6\_numbers){\unicdbdjdcd}(k6\_nat\_d~X1~X0=k6\_nat\_d~X0~(k4\_nat\_d~\\
X1~X0))))\end{array}
\label{hyp:ehcdidpfogbgehpfeg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{{{k4\_nat\_d}~{X0}}~{X0}}={k6\_numbers}})}}}\label{hyp:ehcdfdpfogbgehpfeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}(k4\_nat\_d~\\
(k3\_xcmplx\_0~X0~X1)~X0=k6\_numbers))\end{array}
\label{hyp:ehbdddpfogbgehpfeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v7\_ordinal1~X1)){\unicdbdjdcd}(\\
r1\_nat\_d~X0~X0)\end{array}
\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfogbgehpfeg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdaddd} X0 .  {{({\preoh{{{v1\_xboole\_0}~{X0}}}})}{\unicdcdcdhd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:chdgfdpfpgchegjgogbgmgbd}
\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){\unicdbdjded}({\unicdcdaddd} X2 .  (v7\_ordinal1~X2){\unicdcdcdhd}(X1=k3\_xcmplx\_0~\\
X0~X2))))\end{array}
\label{hyp:egddpfogbgehpfeg}
\end{equation}
\begin{theorem}\label{thm:ehgdpfahfgahjgog}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}((\\
X0{\unicdcdgdad}k6\_numbers){\unicdbdjdcd}((r1\_nat\_d~X0~X1){\unicdbdjded}(k4\_nat\_d~X1~X0=k6\_numbers))))\end{array}$$
\end{theorem}
\end{document}
