\documentclass{article}
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\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{t57\_interva1 (TMPGpFnJkALuQRnBYa5yJFSizXDiPZC18z1)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_roughs\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_interva1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k15\_interva1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k16\_interva1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u1\_struct\_0 : {{\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 $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k14\_interva1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
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}(k4\_subset\_1~X0~X1~X2=\\
k2\_xboole\_0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{k2\_xtuple\_0}~{({{{k4\_tarski}~{X0}}~{X1}})}}={X1}}}}\label{hyp:chegcdpfihehfhahmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_roughs\_1~\\
X0){\unicdcdcdhd}(l1\_orders\_2~X0))){\unicdcdcdhd}((m2\_interva1~X1~X0){\unicdcdcdhd}(m2\_interva1~X2~\\
X0))){\unicdbdjdcd}(m2\_interva1~(k16\_interva1~X0~X1~X2)~X0)\end{array}
\label{hyp:egehpflgbdgdpfjgogehfgchghbgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_roughs\_1~X0){\unicdcdcdhd}\\
(l1\_orders\_2~X0))){\unicdcdcdhd}(m2\_interva1~X1~X0)){\unicdbdjdcd}(m1\_subset\_1~(k15\_interva1~\\
X0~X1)~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))\end{array}
\label{hyp:egehpflgbdfdpfjgogehfgchghbgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_roughs\_1~X0){\unicdcdcdhd}(l1\_orders\_2~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_interva1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_interva1~\\
X2~X0){\unicdbdjdcd}(k16\_interva1~X0~X1~X2=k4\_tarski~(k4\_subset\_1~(u1\_struct\_0~\\
X0)~(k14\_interva1~X0~X1)~(k14\_interva1~X0~X2))~(k4\_subset\_1~(u1\_struct\_0~\\
X0)~(k15\_interva1~X0~X1)~(k15\_interva1~X0~X2)))))\end{array}
\label{hyp:egbdidpfjgogehfgchghbgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_roughs\_1~X0){\unicdcdcdhd}(l1\_orders\_2~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_interva1~X1~X0){\unicdbdjdcd}(k15\_interva1~X0~X1=k2\_xtuple\_0~\\
X1))\end{array}
\label{hyp:egbdgdpfjgogehfgchghbgbd}
\end{equation}
\begin{theorem}\label{thm:ehfdhdpfjgogehfgchghbgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_roughs\_1~X0){\unicdcdcdhd}(l1\_orders\_2~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_interva1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_interva1~\\
X2~X0){\unicdbdjdcd}(k15\_interva1~X0~(k16\_interva1~X0~X1~X2)=k4\_subset\_1~(u1\_struct\_0~\\
X0)~(k15\_interva1~X0~X1)~(k15\_interva1~X0~X2))))\end{array}$$
\end{theorem}
\end{document}
