\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}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t14\_interva1 (TMZvVhf85xbLu65VX2CYkgnGwW8Kb9ECKNU)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_interva1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_interva1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_interva1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_interva1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_interva1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (X3 \in k1\_interva1~\\
X0~X1~X2){\unicdbdjded}((r1\_tarski~X1~X3){\unicdcdcdhd}(r1\_tarski~X3~X2))))\end{array}
\label{hyp:ehbdpfjgogehfgchghbgbd}
\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 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_interva1~X1~X0))){\unicdbdjdcd}(m1\_subset\_1~(k6\_interva1~X0~X1)~(k1\_zfmisc\_1~\\
X0))\end{array}
\label{hyp:egehpflggdpfjgogehfgchghbgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_interva1~X1~X0))){\unicdbdjdcd}(m1\_subset\_1~(k5\_interva1~X0~X1)~(k1\_zfmisc\_1~\\
X0))\end{array}
\label{hyp:egehpflgfdpfjgogehfgchghbgbd}
\end{equation}
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}((X2=k6\_interva1~X0~X1){\unicdbdjded}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
X0)){\unicdcdcdhd}(X1=k2\_interva1~X0~X3~X2)))))\end{array}
\label{hyp:eggdpfjgogehfgchghbgbd}
\end{equation}
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}((X2=k5\_interva1~X0~X1){\unicdbdjded}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
X0)){\unicdcdcdhd}(X1=k2\_interva1~X0~X2~X3)))))\end{array}
\label{hyp:egfdpfjgogehfgchghbgbd}
\end{equation}
\begin{theorem}\label{thm:ehbdedpfjgogehfgchghbgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_interva1~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (X2 \in X1){\unicdbdjded}((r1\_tarski~(k5\_interva1~\\
X0~X1)~X2){\unicdcdcdhd}(r1\_tarski~X2~(k6\_interva1~X0~X1)))))\end{array}$$
\end{theorem}
\end{document}
