\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{t103\_jordan2c (TMYLAAsxuNJKhEFXfEtva9QLukcZaysNUtH)}
\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 $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k14\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k15\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_metric\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k12\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_xreal\_0 : {{\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 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~(k14\_euclid~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (\\
m1\_subset\_1~X2~(u1\_struct\_0~(k15\_euclid~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_xreal\_0~\\
X3){\unicdbdjdcd}((X2=X1){\unicdbdjdcd}(k9\_metric\_1~(k14\_euclid~X0)~X1~X3=ReplSep~(toset~\\
({\uniddcgcg} X4 : \iota .  m1\_subset\_1~X4~(u1\_struct\_0~(k15\_euclid~X0))))~(\\
{\uniddcgcg} X4 : \iota .  \preoh r1\_xxreal\_0~X3~(k12\_euclid~(k5\_algstr\_0~(k15\_euclid~\\
X0)~X2~X4)))~({\uniddcgcg} X4 : \iota .  X4))))))\end{array}
\label{hyp:ehcdpfkghgchbgahigpfcd}
\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~(u1\_struct\_0~(k15\_euclid~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (\\
m1\_subset\_1~X2~(u1\_struct\_0~(k15\_euclid~X0))){\unicdbdjdcd}(k12\_euclid~(k5\_algstr\_0~\\
(k15\_euclid~X0)~X1~X2)=k12\_euclid~(k5\_algstr\_0~(k15\_euclid~X0)~\\
X2~X1))))\end{array}
\label{hyp:ehcdhdpfehpgahchogdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgbdpfihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehbdadddpfkgpgchegbgogcddg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
(k14\_euclid~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~(\\
k15\_euclid~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~(k15\_euclid~\\
X0))){\unicdbdjdcd}(((X3=X2){\unicdcdcdhd}(X4 \in k9\_metric\_1~(k14\_euclid~X0)~X2~X1)){\unicdbdjdcd}((\preoh \\
r1\_xxreal\_0~X1~(k12\_euclid~(k5\_algstr\_0~(k15\_euclid~X0)~X3~X4))){\unicdcdcdhd}\\
(\preoh r1\_xxreal\_0~X1~(k12\_euclid~(k5\_algstr\_0~(k15\_euclid~X0)~X4~X3)))))))))\end{array}$$
\end{theorem}
\end{document}
