\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{t2\_jordan4 (TMXS6ruuJ43GQbAGYZtkBJxam495WqdHMZS)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_nat\_d : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_nat\_d : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ v1\_xreal\_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}((\\
r1\_xxreal\_0~X0~X1){\unicdbdjdcd}(k7\_nat\_d~X1~(k7\_nat\_d~X1~X0)=X0)))\end{array}
\label{hyp:ehfdidpfogbgehpfeg}
\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}(\preoh (r1\_xxreal\_0~X0~X1){\unicdcdcdhd}((\preoh r1\_xxreal\_0~X2~X1){\unicdcdcdhd}\\
(r1\_xxreal\_0~(k7\_nat\_d~X2~X0)~(k7\_nat\_d~X1~X0))))))\end{array}
\label{hyp:ehfdgdpfogbgehpfeg}
\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}((r1\_xxreal\_0~X0~X1){\unicdbdjdcd}(r1\_xxreal\_0~(k7\_nat\_d~\\
X2~X1)~(k7\_nat\_d~X2~X0)))))\end{array}
\label{hyp:ehedbdpfogbgehpfeg}
\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}((r1\_xxreal\_0~X0~X1){\unicdbdjdcd}(k7\_nat\_d~(k2\_xcmplx\_0~\\
X1~X2)~X0=k6\_xcmplx\_0~(k2\_xcmplx\_0~X1~X2)~X0))))\end{array}
\label{hyp:ehddhdpfogbgehpfeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}((\\
k7\_nat\_d~X0~X1=k6\_numbers){\unicdbdjdcd}(r1\_xxreal\_0~X0~X1)))\end{array}
\label{hyp:ehddgdpfogbgehpfeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xreal\_0~X2){\unicdbdjdcd}(((r1\_xxreal\_0~X0~k6\_numbers){\unicdcdcdhd}(r1\_xxreal\_0~\\
X1~X2)){\unicdbdjdcd}(r1\_xxreal\_0~(k2\_xcmplx\_0~X1~X0)~X2))))\end{array}
\label{hyp:ehddfdpfihchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}(k7\_nat\_d~\\
(k2\_xcmplx\_0~X0~X1)~X1=X0))\end{array}
\label{hyp:ehddedpfogbgehpfeg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{{r1\_xxreal\_0}~{k6\_numbers}}~{X0}})}}}\label{hyp:ehcdpfogbgehpfbd}
\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}((\\
\preoh r1\_xxreal\_0~X1~X0){\unicdbdjdcd}(k4\_nat\_d~X0~X1=X0)))\end{array}
\label{hyp:ehcdedpfogbgehpfeg}
\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}((k4\_nat\_d~X0~X1=k6\_numbers){\unicdbdjdcd}(k4\_nat\_d~(k2\_xcmplx\_0~\\
X0~X2)~X1=k4\_nat\_d~X2~X1))))\end{array}
\label{hyp:ehbdhdpfogbgehpfeg}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}(((r1\_xxreal\_0~\\
k6\_numbers~X0){\unicdbdjdcd}(r1\_xxreal\_0~X1~(k2\_xcmplx\_0~X0~X1))){\unicdcdcdhd}(((r1\_xxreal\_0~\\
X1~(k2\_xcmplx\_0~X0~X1)){\unicdbdjdcd}(r1\_xxreal\_0~k6\_numbers~X0)){\unicdcdcdhd}((\preoh (\preoh r1\_xxreal\_0~\\
X0~k6\_numbers){\unicdcdcdhd}(r1\_xxreal\_0~(k2\_xcmplx\_0~X0~X1)~X1)){\unicdcdcdhd}((\preoh (\preoh r1\_xxreal\_0~\\
(k2\_xcmplx\_0~X0~X1)~X1){\unicdcdcdhd}(r1\_xxreal\_0~X0~k6\_numbers)){\unicdcdcdhd}(((r1\_xxreal\_0~\\
k6\_numbers~X0){\unicdbdjdcd}(r1\_xxreal\_0~(k6\_xcmplx\_0~X1~X0)~X1)){\unicdcdcdhd}(((r1\_xxreal\_0~\\
(k6\_xcmplx\_0~X1~X0)~X1){\unicdbdjdcd}(r1\_xxreal\_0~k6\_numbers~X0)){\unicdcdcdhd}((\preoh (\preoh r1\_xxreal\_0~\\
X0~k6\_numbers){\unicdcdcdhd}(r1\_xxreal\_0~X1~(k6\_xcmplx\_0~X1~X0))){\unicdcdcdhd}(\preoh (\preoh r1\_xxreal\_0~\\
X1~(k6\_xcmplx\_0~X1~X0)){\unicdcdcdhd}(r1\_xxreal\_0~X0~k6\_numbers))))))))))\end{array}
\label{hyp:mgedpfhhdhjgfgchahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xreal\_0~X2){\unicdbdjdcd}((r1\_xxreal\_0~X0~(k6\_xcmplx\_0~X1~X2)){\unicdbdjdcd}(r1\_xxreal\_0~\\
(k2\_xcmplx\_0~X0~X2)~X1))))\end{array}
\label{hyp:mgcdidpfihchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgcdpfihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehcdpfkgpgchegbgoged}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}((\\
r1\_xxreal\_0~X1~X0){\unicdbdjdcd}((r1\_xxreal\_0~(k2\_xcmplx\_0~X1~X1)~X0){\unicdcdcdid}((k4\_nat\_d~\\
X0~X1=k6\_xcmplx\_0~X0~X1){\unicdcdcdhd}(k4\_nat\_d~X0~X1=k7\_nat\_d~X0~X1)))))\end{array}$$
\end{theorem}
\end{document}
