\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{t30\_jordan1 (TMHjG2qLVLReBDeaw3qDuLDmiC6R2jAEtKy)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k15\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k17\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k18\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k19\_euclid : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~k1\_numbers){\unicdbdjdcd}(ReplSep~(toset~({\uniddcgcg} X4 : \iota .  m1\_subset\_1~\\
X4~(u1\_struct\_0~(k15\_euclid~np\_\_2))))~({\uniddcgcg} X4 : \iota .  \preoh (r1\_xxreal\_0~\\
X0~(k17\_euclid~X4)){\unicdcdcdhd}((r1\_xxreal\_0~(k17\_euclid~X4)~X1){\unicdcdcdhd}((r1\_xxreal\_0~\\
X2~(k18\_euclid~X4)){\unicdcdcdhd}(r1\_xxreal\_0~(k18\_euclid~X4)~X3))))~({\uniddcgcg} X4 : \\
\iota .  X4)=ReplSep2~(toset~({\uniddcgcg} X4 : \iota .  m1\_subset\_1~X4~k1\_numbers))~\\
({\uniddcgcg} X4 : \iota .  toset~({\uniddcgcg} X5 : \iota .  m1\_subset\_1~X5~k1\_numbers))~(\\
{\uniddcgcg} X4 : \iota .  {\uniddcgcg} X5 : \iota .  \preoh (r1\_xxreal\_0~X0~X4){\unicdcdcdhd}((r1\_xxreal\_0~X4~\\
X1){\unicdcdcdhd}((r1\_xxreal\_0~X2~X5){\unicdcdcdhd}(r1\_xxreal\_0~X5~X3))))~({\uniddcgcg} X4 : \iota .  \\
{\uniddcgcg} X5 : \iota .  k19\_euclid~X4~X5)))))\end{array}
\label{hyp:ehcdidpfkgpgchegbgogbd}
\end{equation}
Assume the following.
\begin{equation}
{{{u1\_struct\_0}~{({{k15\_euclid}~{np\_\_2}})}}={{k1\_euclid}~{np\_\_2}}}\label{hyp:mgidpfkgpgchegbgogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~k1\_numbers){\unicdbdjdcd}(m1\_subset\_1~(ReplSep2~(toset~({\uniddcgcg} X4 : \\
\iota .  m1\_subset\_1~X4~k1\_numbers))~({\uniddcgcg} X4 : \iota .  toset~({\uniddcgcg} X5 : \iota .  \\
m1\_subset\_1~X5~k1\_numbers))~({\uniddcgcg} X4 : \iota .  {\uniddcgcg} X5 : \iota .  \preoh (r1\_xxreal\_0~\\
X0~X4){\unicdcdcdhd}((r1\_xxreal\_0~X4~X1){\unicdcdcdhd}((r1\_xxreal\_0~X2~X5){\unicdcdcdhd}(r1\_xxreal\_0~\\
X5~X3))))~({\uniddcgcg} X4 : \iota .  {\uniddcgcg} X5 : \iota .  k19\_euclid~X4~X5))~(k1\_zfmisc\_1~\\
(k1\_euclid~np\_\_2))))))\end{array}
\label{hyp:mgbdedpfkgpgchegbgogbd}
\end{equation}
\begin{theorem}\label{thm:ehddadpfkgpgchegbgogbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~k1\_numbers){\unicdbdjdcd}(m1\_subset\_1~(ReplSep~(toset~({\uniddcgcg} X4 : \\
\iota .  m1\_subset\_1~X4~(u1\_struct\_0~(k15\_euclid~np\_\_2))))~({\uniddcgcg} X4 : \\
\iota .  \preoh (r1\_xxreal\_0~X0~(k17\_euclid~X4)){\unicdcdcdhd}((r1\_xxreal\_0~(k17\_euclid~\\
X4)~X1){\unicdcdcdhd}((r1\_xxreal\_0~X2~(k18\_euclid~X4)){\unicdcdcdhd}(r1\_xxreal\_0~(k18\_euclid~\\
X4)~X3))))~({\uniddcgcg} X4 : \iota .  X4))~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2)))))))\end{array}$$
\end{theorem}
\end{document}
