\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{t20\_jordan1j (TMHCd2NJHNF1cxT6kmrxzHUrdM6mZ3Ld9W2)}
\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 $ k24\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k17\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k18\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k17\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k25\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k19\_euclid : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k2\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_pscomp\_1 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
(((k17\_euclid~X0=k17\_euclid~X1){\unicdcdcdhd}(k18\_euclid~X0=k18\_euclid~X1)){\unicdbdjdcd}\\
(X0=X1)))\end{array}
\label{hyp:ehgdpfehpgahchfgbgmgdd}
\end{equation}
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 .  ((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}(r1\_xxreal\_0~(k9\_pscomp\_1~\\
X1)~(k9\_pscomp\_1~X0))))\end{array}
\label{hyp:ehgdidpfahdhdgpgngahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))))){\unicdbdjdcd}((X0 \in k17\_pscomp\_1~X1){\unicdbdjdcd}\\
((k18\_euclid~X0=k18\_euclid~(k25\_pscomp\_1~X1)){\unicdcdcdhd}((v2\_compts\_1~\\
X1~(k15\_euclid~np\_\_2)){\unicdbdjdcd}((r1\_xxreal\_0~(k17\_euclid~(k25\_pscomp\_1~\\
X1))~(k17\_euclid~X0)){\unicdcdcdhd}(r1\_xxreal\_0~(k17\_euclid~X0)~(k17\_euclid~\\
(k24\_pscomp\_1~X1))))))))\end{array}
\label{hyp:ehfdfdpfahdhdgpgngahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}((k17\_euclid~\\
(k19\_euclid~X0~X1)=X0){\unicdcdcdhd}(k18\_euclid~(k19\_euclid~X0~X1)=X1)))\end{array}
\label{hyp:ehfdcdpffgfhdgmgjgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X0 \in X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X2))){\unicdbdjdcd}(m1\_subset\_1~X0~X2)\end{array}
\label{hyp:ehedpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~X1)){\unicdbdjded}(r1\_tarski~\\
X0~X1)\end{array}
\label{hyp:ehddpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~X1){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}\\
(X0 \in X1))\end{array}
\label{hyp:ehcdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(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}((X0 \in X1){\unicdbdjdcd}((r1\_xxreal\_0~(k6\_pscomp\_1~X1)~(k17\_euclid~\\
X0)){\unicdcdcdhd}((r1\_xxreal\_0~(k17\_euclid~X0)~(k8\_pscomp\_1~X1)){\unicdcdcdhd}((r1\_xxreal\_0~\\
(k9\_pscomp\_1~X1)~(k18\_euclid~X0)){\unicdcdcdhd}(r1\_xxreal\_0~(k18\_euclid~X0)~\\
(k7\_pscomp\_1~X1)))))))\end{array}
\label{hyp:ehcdedpfahdhdgpgngahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}((\\
(r1\_xxreal\_0~X0~X1){\unicdcdcdhd}(r1\_xxreal\_0~X1~X0)){\unicdbdjdcd}(X0=X1)))\end{array}
\label{hyp:ehbdpfihihchfgbgmgpfad}
\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 X0){\unicdcdcdhd}(k24\_pscomp\_1~X0 \in X0))\end{array}
\label{hyp:ehbdcdpfdhahchfgdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((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}(((X1 \in X0){\unicdcdcdhd}\\
(k18\_euclid~X1=k9\_pscomp\_1~X0)){\unicdbdjdcd}(X1 \in k17\_pscomp\_1~X0)))\end{array}
\label{hyp:ehbdbdpfdhahchfgdgehpfcd}
\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~(k9\_pscomp\_1~X0)~k1\_numbers)\end{array}
\label{hyp:egehpflgjdpfahdhdgpgngahpfbd}
\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~(k8\_pscomp\_1~X0)~k1\_numbers)\end{array}
\label{hyp:egehpflgidpfahdhdgpgngahpfbd}
\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}
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~(k17\_pscomp\_1~X0)~(k1\_zfmisc\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))))\end{array}
\label{hyp:egehpflgbdhdpfahdhdgpgngahpfbd}
\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}(k8\_pscomp\_1~X0=k2\_pscomp\_1~(k1\_pre\_topc~(k15\_euclid~\\
np\_\_2)~X0)~(k3\_pscomp\_1~(k15\_euclid~np\_\_2)~k4\_pscomp\_1~X0))\end{array}
\label{hyp:egjdpfahdhdgpgngahpfbd}
\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}(k24\_pscomp\_1~X0=k19\_euclid~(k2\_pscomp\_1~(k1\_pre\_topc~\\
(k15\_euclid~np\_\_2)~(k17\_pscomp\_1~X0))~(k3\_pscomp\_1~(k15\_euclid~\\
np\_\_2)~k4\_pscomp\_1~(k17\_pscomp\_1~X0)))~(k9\_pscomp\_1~X0))\end{array}
\label{hyp:egcdfdpfahdhdgpgngahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{X0}})}}}\label{hyp:dgdgedpfihchfgbgmgpfad}
\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:ehcdadpfkgpgchegbgogbdkg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v2\_compts\_1~X0~(k15\_euclid~np\_\_2)){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v2\_compts\_1~X1~(k15\_euclid~\\
np\_\_2)){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2)))))){\unicdbdjdcd}(((r1\_tarski~X0~X1){\unicdcdcdhd}(k24\_pscomp\_1~X1 \in X0)){\unicdbdjdcd}(k24\_pscomp\_1~\\
X0=k24\_pscomp\_1~X1)))\end{array}$$
\end{theorem}
\end{document}
