\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{l53\_xxreal\_3 (TManYuHbFtrvwPYhc3H4CNfTN91P5ECwFRv)}
\maketitle
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_xxreal\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k2\_xxreal\_0 : {\iota}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xxreal\_0 : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
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~\\
X0~X1){\unicdbdjded}(r1\_xxreal\_0~(k4\_xcmplx\_0~X1)~(k4\_xcmplx\_0~X0))))\end{array}
\label{hyp:ehcdedpfihchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}((k2\_xxreal\_3~X0 \in k1\_numbers){\unicdbdjded}(\\
X0 \in k1\_numbers))\end{array}
\label{hyp:mgbdfdpfihihchfgbgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xxreal\_0}~{X0}})}{\unicdbdjdcd}{({{{k2\_xxreal\_3}~{({{k2\_xxreal\_3}~{X0}})}}={X0}})}}}\label{hyp:jgogghpgmgfhehjgghfgogfgdhdhpflgcdpfihihchfgbgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}((v1\_xxreal\_0~(k2\_xxreal\_3~X0)){\unicdcdcdhd}\\
(v1\_xreal\_0~(k2\_xxreal\_3~X0)))\end{array}
\label{hyp:ggdgbdpfihihchfgbgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xreal\_0}~{k2\_xxreal\_0}}}}\label{hyp:ggdgbdpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xxreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{({{k2\_xxreal\_3}~{X0}})}})}}}\label{hyp:egehpflgcdpfihihchfgbgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}((\\
(v1\_xreal\_0~X0){\unicdbdjdcd}((X1=k2\_xxreal\_3~X0){\unicdbdjded}({\unicdcdaddd} X2 .  (v1\_xcmplx\_0~\\
X2){\unicdcdcdhd}((X0=X2){\unicdcdcdhd}(X1=k4\_xcmplx\_0~X2))))){\unicdcdcdhd}(((X0=k1\_xxreal\_0){\unicdbdjdcd}\\
((X1=k2\_xxreal\_3~X0){\unicdbdjded}(X1=k2\_xxreal\_0))){\unicdcdcdhd}(\preoh (\preoh v1\_xreal\_0~X0){\unicdcdcdhd}\\
((X0{\unicdcdgdad}k1\_xxreal\_0){\unicdcdcdhd}(\preoh (X1=k2\_xxreal\_3~X0){\unicdbdjded}(X1=k1\_xxreal\_0)))))))\end{array}
\label{hyp:egddpfihihchfgbgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{k1\_xxreal\_0}={k1\_numbers}}\label{hyp:egcdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}((\\
((X0 \in k1\_numbers){\unicdcdcdhd}(X1 \in k1\_numbers)){\unicdbdjdcd}((r1\_xxreal\_0~X0~X1){\unicdbdjded}({\unicdcdaddd} X2 .  \\
(m1\_subset\_1~X2~k1\_numbers){\unicdcdcdhd}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~k1\_numbers){\unicdcdcdhd}\\
((X2=X0){\unicdcdcdhd}((X3=X1){\unicdcdcdhd}(r1\_xxreal\_0~X2~X3))))))){\unicdcdcdhd}((\preoh (X0 \in k1\_numbers){\unicdcdcdhd}\\
(X1 \in k1\_numbers)){\unicdbdjdcd}((r1\_xxreal\_0~X0~X1){\unicdbdjded}((X0=k2\_xxreal\_0){\unicdcdcdid}(\\
X1=k1\_xxreal\_0))))))\end{array}
\label{hyp:egbdpfihihchfgbgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjded}{({{X0} \in {k1\_numbers}})}}}\label{hyp:egbdpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{X0}})}}}\label{hyp:dgdgedpfihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:mgfdddpfihihchfgbgmgpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}((\\
r1\_xxreal\_0~X0~X1){\unicdbdjdcd}(r1\_xxreal\_0~(k2\_xxreal\_3~X1)~(k2\_xxreal\_3~\\
X0))))\end{array}$$
\end{theorem}
\end{document}
