\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{t72\_xxreal\_3 (TMX5ByYxt1bn1ZWKpsp51XvkKtUbBPrpuFm)}
\maketitle
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_xxreal\_0 : {\iota}$ be given.
Let $ k4\_xxreal\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_xxreal\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_xxreal\_0 : {\iota}$ be given.
Let $ k1\_numbers : {\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}(\preoh (\preoh \\
r1\_xxreal\_0~X0~X1){\unicdcdcdhd}((\preoh v3\_xxreal\_0~X1){\unicdcdcdhd}(\preoh v2\_xxreal\_0~X0))))\end{array}
\label{hyp:ehidpfchfgbgmg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  \preoh (v1\_xboole\_0~X0){\unicdcdcdhd}((X0{\unicdcdgdad}X1){\unicdcdcdhd}(v1\_xboole\_0~\\
X1))\end{array}
\label{hyp:ehidpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xxreal\_0~X2){\unicdbdjdcd}(((r1\_xxreal\_0~X0~X1){\unicdcdcdhd}(r1\_xxreal\_0~k6\_numbers~\\
X2)){\unicdbdjdcd}(r1\_xxreal\_0~(k4\_xxreal\_3~X0~X2)~(k4\_xxreal\_3~X1~X2)))))\end{array}
\label{hyp:ehhdbdpfihihchfgbgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xxreal\_0~X2){\unicdbdjdcd}((k4\_xxreal\_3~X0~X1=k4\_xxreal\_3~X0~X2){\unicdbdjdcd}((X0=\\
k6\_numbers){\unicdcdcdid}(X1=X2)))))\end{array}
\label{hyp:ehgdidpfihihchfgbgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xxreal\_0~X2){\unicdbdjdcd}(k4\_xxreal\_3~X0~(k4\_xxreal\_3~X1~X2)=k4\_xxreal\_3~\\
(k4\_xxreal\_3~X0~X1)~X2)))\end{array}
\label{hyp:ehgdgdpfihihchfgbgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xxreal\_0}~{X0}})}{\unicdbdjdcd}{({{{r1\_xxreal\_0}~{X0}}~{k1\_xxreal\_0}})}}}\label{hyp:ehddpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xxreal\_0~X2){\unicdbdjdcd}((X0 \in k3\_xxreal\_1~X1~X2){\unicdbdjded}((\preoh r1\_xxreal\_0~X0~X1){\unicdcdcdhd}\\
(r1\_xxreal\_0~X0~X2)))))\end{array}
\label{hyp:ehcdpfihihchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}((X1 \in \\
k3\_xxreal\_1~k2\_xxreal\_0~X0){\unicdbdjded}(r1\_xxreal\_0~X1~X0)))\end{array}
\label{hyp:ehcdddedpfihihchfgbgmgpfbd}
\end{equation}
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}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}(\preoh (\preoh X0 \in k1\_numbers){\unicdcdcdhd}((X0{\unicdcdgdad}k1\_xxreal\_0){\unicdcdcdhd}\\
(X0{\unicdcdgdad}k2\_xxreal\_0)))\end{array}
\label{hyp:ehbdedpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdaddd} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdcdcdhd}{({{v1\_xxreal\_0}~{X0}})}}}\label{hyp:chdgedpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdaddd} X0 .  {{({{v1\_xxreal\_0}~{X0}})}{\unicdcdcdhd}{({{({{v3\_xxreal\_0}~{X0}})}{\unicdcdcdhd}{({\preoh{{{v1\_xreal\_0}~{X0}}}})}})}}}\label{hyp:chdgcdpfihihchfgbgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdaddd} X0 .  {{({{v1\_xxreal\_0}~{X0}})}{\unicdcdcdhd}{({{({{v2\_xxreal\_0}~{X0}})}{\unicdcdcdhd}{({\preoh{{{v1\_xreal\_0}~{X0}}}})}})}}}\label{hyp:chdgbdpfihihchfgbgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}(\preoh \\
(k4\_xxreal\_3~X0~X1 \in k1\_numbers){\unicdcdcdhd}((\preoh (X0 \in k1\_numbers){\unicdcdcdhd}(X1 \in k1\_numbers)){\unicdcdcdhd}\\
(k4\_xxreal\_3~X0~X1{\unicdcdgdad}k6\_numbers))))\end{array}
\label{hyp:mgjdjdpfihihchfgbgmgpfdd}
\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}
{{v2\_xxreal\_0}~{k1\_xxreal\_0}}\label{hyp:ggdgddpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_xxreal\_0~X0)){\unicdcdcdhd}\\
(v1\_xxreal\_0~X1)){\unicdbdjdcd}((v1\_xboole\_0~(k4\_xxreal\_3~X0~X1)){\unicdcdcdhd}(v1\_xxreal\_0~\\
(k4\_xxreal\_3~X0~X1)))\end{array}
\label{hyp:ggdgddhdpfihihchfgbgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xxreal\_0}~{k2\_xxreal\_0}}\label{hyp:ggdgcdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_xxreal\_0~X0){\unicdcdcdhd}(\preoh v3\_xxreal\_0~X0)){\unicdcdcdhd}\\
((v1\_xxreal\_0~X1){\unicdcdcdhd}(\preoh v3\_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:ggdgcdjdpfihihchfgbgmgpfdd}
\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 v3\_xxreal\_0~X1))){\unicdbdjdcd}((v1\_xxreal\_0~(k4\_xxreal\_3~\\
X0~X1)){\unicdcdcdhd}(\preoh v2\_xxreal\_0~(k4\_xxreal\_3~X0~X1)))\end{array}
\label{hyp:ggdgcdhdpfihihchfgbgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xxreal\_0}~{k1\_xxreal\_0}}\label{hyp:ggdgbdpfihihchfgbgmgpfad}
\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}
{{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}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xxreal\_0~X0){\unicdcdcdhd}(v1\_xxreal\_0~X1)){\unicdbdjdcd}(\\
(r1\_xxreal\_0~X0~X1){\unicdcdcdid}(r1\_xxreal\_0~X1~X0))\end{array}
\label{hyp:dgpgogogfgdgehfgegogfgdhdhpfchbdpfihihchfgbgmgpfad}
\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\_xboole\_0~X0){\unicdcdcdhd}(v1\_xxreal\_0~X0)){\unicdbdjdcd}((v1\_xxreal\_0~\\
X0){\unicdcdcdhd}((\preoh v2\_xxreal\_0~X0){\unicdcdcdhd}(\preoh v3\_xxreal\_0~X0)))\end{array}
\label{hyp:dgdghdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{X0}})}}}\label{hyp:dgdgedpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_xxreal\_0~X0){\unicdcdcdhd}(v2\_xxreal\_0~X0)){\unicdbdjdcd}((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((v1\_xxreal\_0~X0){\unicdcdcdhd}(\preoh v3\_xxreal\_0~X0)))\end{array}
\label{hyp:dgdgddpfihihchfgbgmgpfad}
\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:ehhdcdpfihihchfgbgmgpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xxreal\_0~X2){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~X1~X0){\unicdcdcdhd}((\preoh r1\_xxreal\_0~X2~k6\_numbers){\unicdcdcdhd}\\
((X2{\unicdcdgdad}k1\_xxreal\_0){\unicdcdcdhd}(r1\_xxreal\_0~(k4\_xxreal\_3~X1~X2)~(k4\_xxreal\_3~\\
X0~X2)))))))\end{array}$$
\end{theorem}
\end{document}
