\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{t82\_jordan2c (TMVvH4PwSd426qLaHfSQL38B7GZdzDangNx)}
\maketitle
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k15\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k12\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_connsp\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
(k15\_euclid~X0))))){\unicdbdjdcd}((v3\_pre\_topc~X1~(k15\_euclid~X0)){\unicdbdjdcd}(v1\_connsp\_2~\\
(k1\_pre\_topc~(k15\_euclid~X0)~X1))))\end{array}
\label{hyp:ehidbdpfkgpgchegbgogcddg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~X0)))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (v1\_xreal\_0~X2){\unicdbdjdcd}((X1=ReplSep~(toset~({\uniddcgcg} X3 : \iota .  \\
m1\_subset\_1~X3~(u1\_struct\_0~(k15\_euclid~X0))))~({\uniddcgcg} X3 : \iota .  k12\_euclid~\\
X3=X2)~({\uniddcgcg} X3 : \iota .  X3)){\unicdbdjdcd}((v3\_pre\_topc~(k3\_subset\_1~(u1\_struct\_0~\\
(k15\_euclid~X0))~X1)~(k15\_euclid~X0)){\unicdcdcdhd}(v4\_pre\_topc~X1~(k15\_euclid~\\
X0))))))\end{array}
\label{hyp:ehidadpfkgpgchegbgogcddg}
\end{equation}
\begin{theorem}\label{thm:ehidcdpfkgpgchegbgogcddg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
(k15\_euclid~X0))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k15\_euclid~X0)))){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_xreal\_0~X3){\unicdbdjdcd}\\
(((X2=ReplSep~(toset~({\uniddcgcg} X4 : \iota .  m1\_subset\_1~X4~(u1\_struct\_0~\\
(k15\_euclid~X0))))~({\uniddcgcg} X4 : \iota .  k12\_euclid~X4=X3)~({\uniddcgcg} X4 : \iota .  \\
X4)){\unicdcdcdhd}(k3\_subset\_1~(u1\_struct\_0~(k15\_euclid~X0))~X2=X1)){\unicdbdjdcd}(v1\_connsp\_2~\\
(k1\_pre\_topc~(k15\_euclid~X0)~X1))))))\end{array}$$
\end{theorem}
\end{document}
