\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{l89\_xxreal\_3 (TMaBdojvXYcvdaNbPMarsvG27Nf1ij32RQY)}
\maketitle
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_xxreal\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}((\\
(r1\_xxreal\_0~X0~X1){\unicdcdcdhd}(r1\_xxreal\_0~X1~X0)){\unicdbdjdcd}(X0=X1)))\end{array}
\label{hyp:ehbdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xxreal\_0}~{X0}})}{\unicdbdjdcd}{({{{{k4\_xxreal\_3}~{X0}}~{k6\_numbers}}={k6\_numbers}})}}}\label{hyp:mgididpfihihchfgbgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_xxreal\_0~X0){\unicdcdcdhd}(\preoh v2\_xxreal\_0~X0)){\unicdcdcdhd}\\
((v1\_xxreal\_0~X1){\unicdcdcdhd}(\preoh v2\_xxreal\_0~X1))){\unicdbdjdcd}((v1\_xxreal\_0~(k4\_xxreal\_3~\\
X0~X1)){\unicdcdcdhd}(\preoh v3\_xxreal\_0~(k4\_xxreal\_3~X0~X1)))\end{array}
\label{hyp:ggdgcdidpfihihchfgbgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_xxreal\_0~X0){\unicdcdcdhd}(v2\_xxreal\_0~X0)){\unicdcdcdhd}\\
((v1\_xxreal\_0~X1){\unicdcdcdhd}(v2\_xxreal\_0~X1))){\unicdbdjdcd}((v1\_xxreal\_0~(k4\_xxreal\_3~\\
X0~X1)){\unicdcdcdhd}(v2\_xxreal\_0~(k4\_xxreal\_3~X0~X1)))\end{array}
\label{hyp:ggdgcdgdpfihihchfgbgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_xxreal\_0~X0){\unicdcdcdhd}(v3\_xxreal\_0~X0)){\unicdcdcdhd}\\
((v1\_xxreal\_0~X1){\unicdcdcdhd}(v3\_xxreal\_0~X1))){\unicdbdjdcd}((v1\_xxreal\_0~(k4\_xxreal\_3~\\
X0~X1)){\unicdcdcdhd}(v2\_xxreal\_0~(k4\_xxreal\_3~X0~X1)))\end{array}
\label{hyp:ggdgcdfdpfihihchfgbgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_xxreal\_0~X0){\unicdcdcdhd}(v2\_xxreal\_0~X0)){\unicdcdcdhd}\\
((v1\_xxreal\_0~X1){\unicdcdcdhd}(v3\_xxreal\_0~X1))){\unicdbdjdcd}((v1\_xxreal\_0~(k4\_xxreal\_3~\\
X0~X1)){\unicdcdcdhd}(v3\_xxreal\_0~(k4\_xxreal\_3~X0~X1)))\end{array}
\label{hyp:ggdgcdedpfihihchfgbgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xxreal\_0~X0){\unicdcdcdhd}(v1\_xxreal\_0~X1)){\unicdbdjdcd}(\\
v1\_xxreal\_0~(k4\_xxreal\_3~X0~X1))\end{array}
\label{hyp:egehpflgedpfihihchfgbgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}((v3\_xxreal\_0~X0){\unicdbdjded}(\preoh r1\_xxreal\_0~\\
k6\_numbers~X0))\end{array}
\label{hyp:eghdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}((v2\_xxreal\_0~X0){\unicdbdjded}(\preoh r1\_xxreal\_0~\\
X0~k6\_numbers))\end{array}
\label{hyp:eggdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xxreal\_0~X0){\unicdcdcdhd}(v1\_xxreal\_0~X1)){\unicdbdjdcd}(\\
k4\_xxreal\_3~X0~X1=k4\_xxreal\_3~X1~X0)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgedpfihihchfgbgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_xxreal\_0~X0){\unicdcdcdhd}(v3\_xxreal\_0~X0)){\unicdbdjdcd}((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((v1\_xxreal\_0~X0){\unicdcdcdhd}(\preoh v2\_xxreal\_0~X0)))\end{array}
\label{hyp:dgdgfdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_xxreal\_0~X0){\unicdcdcdhd}((\preoh v3\_xxreal\_0~X0){\unicdcdcdhd}(\preoh v1\_xreal\_0~\\
X0))){\unicdbdjdcd}((v1\_xxreal\_0~X0){\unicdcdcdhd}(v2\_xxreal\_0~X0))\end{array}
\label{hyp:dgdgbdpfihihchfgbgmgpfdd}
\end{equation}
\begin{theorem}\label{thm:mgidjdpfihihchfgbgmgpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}((\\
k4\_xxreal\_3~X0~X1=k6\_numbers){\unicdbdjdcd}((v1\_xreal\_0~X0){\unicdcdcdid}(X1=k6\_numbers))))\end{array}$$
\end{theorem}
\end{document}
