\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{t48\_interva1 (TMYTX2t9guTR6q1uyR8xJCBA88XTkjbwbQn)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_interva1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k10\_interva1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_interva1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_subset\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_subset\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_interva1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k1\_interva1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_interva1~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~X0)){\unicdbdjdcd}(((X1=k2\_interva1~\\
X0~X2~X3){\unicdcdcdhd}(r1\_tarski~X2~X3)){\unicdbdjdcd}(k10\_interva1~X0~X1=k2\_interva1~X0~\\
(k3\_subset\_1~X0~X3)~(k3\_subset\_1~X0~X2))))))\end{array}
\label{hyp:ehedgdpfjgogehfgchghbgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (k4\_xboole\_0~X0~X1=k1\_xboole\_0){\unicdbdjded}(r1\_tarski~\\
X0~X1)\end{array}
\label{hyp:ehddhdpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{r1\_tarski}~{X0}}~{X0}}}}\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(((\preoh v1\_xboole\_0~\\
X1){\unicdcdcdhd}(m1\_interva1~X1~X0)){\unicdcdcdhd}((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m1\_interva1~X2~\\
X0)))){\unicdbdjdcd}((r1\_interva1~X0~X1~X2){\unicdbdjded}(X1=X2))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchbdpfjgogehfgchghbgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~X0))){\unicdbdjdcd}(k2\_interva1~X0~X1~X2=\\
k1\_interva1~X0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfjgogehfgchghbgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}(\preoh v1\_xboole\_0~(k1\_interva1~X0~(\\
k1\_subset\_1~X0)~(k1\_subset\_1~X0)))\end{array}
\label{hyp:ggdgfdpfjgogehfgchghbgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}(\preoh v1\_xboole\_0~(k1\_interva1~X0~(\\
k2\_subset\_1~X0)~(k2\_subset\_1~X0)))\end{array}
\label{hyp:ggdgedpfjgogehfgchghbgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{m1\_subset\_1}~{({{k2\_subset\_1}~{X0}})}}~{({{k1\_zfmisc\_1}~{X0}})}}}\label{hyp:egehpflgcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~X0))){\unicdbdjdcd}(m1\_interva1~(k2\_interva1~\\
X0~X1~X2)~X0)\end{array}
\label{hyp:egehpflgcdpfjgogehfgchghbgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{m1\_subset\_1}~{({{k1\_subset\_1}~{X0}})}}~{({{k1\_zfmisc\_1}~{X0}})}}}\label{hyp:egehpflgbdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)){\unicdbdjdcd}(k3\_subset\_1~\\
X0~X1=k4\_xboole\_0~X0~X1)\end{array}
\label{hyp:egedpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k2\_subset\_1}~{X0}}={X0}}}\label{hyp:egddpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k1\_subset\_1}~{X0}}={k1\_xboole\_0}}}\label{hyp:egcdpfdhfhcgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedidpfjgogehfgchghbgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}(r1\_interva1~X0~(k10\_interva1~X0~\\
(k2\_interva1~X0~(k2\_subset\_1~X0)~(k2\_subset\_1~X0)))~(k2\_interva1~\\
X0~(k1\_subset\_1~X0)~(k1\_subset\_1~X0)))\end{array}$$
\end{theorem}
\end{document}
