\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{t6\_jordan7 (TMJpHpHnaKGmppg3kdajGiu9oHg6Zziv3i6)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_compts\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k15\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_2 : {\iota}$ 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 $ v1\_topreal2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_jordan6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_jordan7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k18\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v2\_compts\_1~X0~(k15\_euclid~np\_\_2)){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
(((v1\_topreal2~X0){\unicdcdcdhd}(r1\_jordan6~X0~X1~X2)){\unicdbdjdcd}((X1 \in X0){\unicdcdcdhd}(X2 \in X0)))))\end{array}
\label{hyp:ehfdpfkgpgchegbgoghd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))){\unicdbdjdcd}(((v1\_topreal2~X0){\unicdcdcdhd}(X1 \in X0)){\unicdbdjdcd}(r1\_jordan6~X0~X1~X1)))\end{array}
\label{hyp:ehfdgdpfkgpgchegbgoggd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2)))){\unicdbdjdcd}(m1\_subset\_1~(k18\_pscomp\_1~X0)~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2)))\end{array}
\label{hyp:egehpflgbdidpfahdhdgpgngahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v2\_compts\_1~X0~(k15\_euclid~np\_\_2)){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
(((X2{\unicdcdgdad}k18\_pscomp\_1~X0){\unicdbdjdcd}(k1\_jordan7~X0~X1~X2=ReplSep~(toset~({\uniddcgcg} X3 : \\
\iota .  m1\_subset\_1~X3~(u1\_struct\_0~(k15\_euclid~np\_\_2))))~({\uniddcgcg} X3 : \\
\iota .  (r1\_jordan6~X0~X1~X3){\unicdcdcdhd}(r1\_jordan6~X0~X3~X2))~({\uniddcgcg} X3 : \iota .  X3))){\unicdcdcdhd}\\
((X2=k18\_pscomp\_1~X0){\unicdbdjdcd}(k1\_jordan7~X0~X1~X2=ReplSep~(toset~({\uniddcgcg} X3 : \\
\iota .  m1\_subset\_1~X3~(u1\_struct\_0~(k15\_euclid~np\_\_2))))~({\uniddcgcg} X3 : \\
\iota .  (r1\_jordan6~X0~X1~X3){\unicdcdcdid}((X1 \in X0){\unicdcdcdhd}(X3=k18\_pscomp\_1~X0)))~({\uniddcgcg} X3 : \\
\iota .  X3))))))\end{array}
\label{hyp:egbdpfkgpgchegbgoghd}
\end{equation}
\begin{theorem}\label{thm:ehgdpfkgpgchegbgoghd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v2\_compts\_1~X0~(k15\_euclid~np\_\_2)){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
(((v1\_topreal2~X0){\unicdcdcdhd}(r1\_jordan6~X0~X1~X2)){\unicdbdjdcd}((X1 \in k1\_jordan7~X0~\\
X1~X2){\unicdcdcdhd}(X2 \in k1\_jordan7~X0~X1~X2)))))\end{array}$$
\end{theorem}
\end{document}
