\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{t68\_jordan1j (TMVQhtaHMMSSqqdZnTT1nVeHBeTyfNnjbtR)}
\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 $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k25\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k24\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k17\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k18\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k13\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\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}((X1 \in k17\_pscomp\_1~X0){\unicdbdjdcd}\\
(k18\_euclid~X1=k9\_pscomp\_1~X0)))\end{array}
\label{hyp:ehfdpfkgpgchegbgogbdbg}
\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}\\
((k25\_pscomp\_1~X0 \in k17\_pscomp\_1~X0){\unicdcdcdhd}(k24\_pscomp\_1~X0 \in k17\_pscomp\_1~\\
X0))\end{array}
\label{hyp:ehfdidpfahdhdgpgngahpfbd}
\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}((k18\_euclid~(k10\_pscomp\_1~X0)=k18\_euclid~(k25\_pscomp\_1~\\
X0)){\unicdcdcdhd}((k18\_euclid~(k10\_pscomp\_1~X0)=k18\_euclid~(k24\_pscomp\_1~\\
X0)){\unicdcdcdhd}((k18\_euclid~(k25\_pscomp\_1~X0)=k18\_euclid~(k24\_pscomp\_1~\\
X0)){\unicdcdcdhd}((k18\_euclid~(k25\_pscomp\_1~X0)=k18\_euclid~(k13\_pscomp\_1~\\
X0)){\unicdcdcdhd}(k18\_euclid~(k24\_pscomp\_1~X0)=k18\_euclid~(k13\_pscomp\_1~\\
X0))))))\end{array}
\label{hyp:ehfdddpfahdhdgpgngahpfbd}
\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 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v2\_compts\_1~X1~(k15\_euclid~\\
np\_\_2)){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2)))))){\unicdbdjdcd}(((r1\_tarski~X0~X1){\unicdcdcdhd}(k24\_pscomp\_1~X1 \in X0)){\unicdbdjdcd}(k24\_pscomp\_1~\\
X0=k24\_pscomp\_1~X1)))\end{array}
\label{hyp:ehcdadpfkgpgchegbgogbdkg}
\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 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v2\_compts\_1~X1~(k15\_euclid~\\
np\_\_2)){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2)))))){\unicdbdjdcd}(((r1\_tarski~X0~X1){\unicdcdcdhd}(k25\_pscomp\_1~X1 \in X0)){\unicdbdjdcd}(k25\_pscomp\_1~\\
X0=k25\_pscomp\_1~X1)))\end{array}
\label{hyp:ehbdjdpfkgpgchegbgogbdkg}
\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~(k25\_pscomp\_1~X0)~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2)))\end{array}
\label{hyp:egehpflgcdfdpfahdhdgpgngahpfbd}
\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~(k24\_pscomp\_1~X0)~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2)))\end{array}
\label{hyp:egehpflgcdedpfahdhdgpgngahpfbd}
\end{equation}
\begin{theorem}\label{thm:ehgdidpfkgpgchegbgogbdkg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v2\_compts\_1~X0~(k15\_euclid~np\_\_2)){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v2\_compts\_1~X1~(k15\_euclid~\\
np\_\_2)){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2)))))){\unicdbdjdcd}((r1\_tarski~X0~X1){\unicdbdjdcd}(((\preoh k25\_pscomp\_1~X1 \in X0){\unicdcdcdhd}(\preoh k24\_pscomp\_1~\\
X1 \in X0)){\unicdcdcdid}(k9\_pscomp\_1~X0=k9\_pscomp\_1~X1))))\end{array}$$
\end{theorem}
\end{document}
