\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{t47\_pscomp\_1 (TMXKaVCSNQEJRAHSdYq7R2Z3LSe7oGb3gSw)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ 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 $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k16\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k17\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k23\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_compts\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k18\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k22\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_rltopsp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ k9\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_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.
Let $ k2\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_pscomp\_1 : {\iota}$ be given.
Let $ k9\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k8\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k13\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k12\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{\preoh{{({{X0} \in {X1}})}}}{\unicdcdcdhd}{({{v1\_xboole\_0}~{X1}})}}}}\label{hyp:ehhdpfcgpgpgmgfg}
\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 .  (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}\\
(((X0 \in k1\_rltopsp1~(k15\_euclid~np\_\_2)~X1~X2){\unicdcdcdhd}(k17\_euclid~X1=k17\_euclid~\\
X2)){\unicdbdjdcd}(k17\_euclid~X0=k17\_euclid~X2))))\end{array}
\label{hyp:ehfdpfhgpgcgpgbgcheghd}
\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 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(k9\_subset\_1~X0~X1~X2=k3\_xboole\_0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfdhfhcgdhfgehpfbd}
\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~(k1\_pscomp\_1~(k1\_pre\_topc~\\
(k15\_euclid~np\_\_2)~X1)~(k3\_pscomp\_1~(k15\_euclid~np\_\_2)~k4\_pscomp\_1~\\
X1))~(k17\_euclid~X0)){\unicdcdcdhd}((r1\_xxreal\_0~(k17\_euclid~X0)~(k2\_pscomp\_1~\\
(k1\_pre\_topc~(k15\_euclid~np\_\_2)~X1)~(k3\_pscomp\_1~(k15\_euclid~\\
np\_\_2)~k4\_pscomp\_1~X1))){\unicdcdcdhd}((r1\_xxreal\_0~(k1\_pscomp\_1~(k1\_pre\_topc~\\
(k15\_euclid~np\_\_2)~X1)~(k3\_pscomp\_1~(k15\_euclid~np\_\_2)~k5\_pscomp\_1~\\
X1))~(k18\_euclid~X0)){\unicdcdcdhd}(r1\_xxreal\_0~(k18\_euclid~X0)~(k2\_pscomp\_1~\\
(k1\_pre\_topc~(k15\_euclid~np\_\_2)~X1)~(k3\_pscomp\_1~(k15\_euclid~\\
np\_\_2)~k5\_pscomp\_1~X1))))))))\end{array}
\label{hyp:mgddgdpfahdhdgpgngahpfbd}
\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}\\
((\preoh v1\_xboole\_0~(k16\_pscomp\_1~X0)){\unicdcdcdhd}(v2\_compts\_1~(k16\_pscomp\_1~\\
X0)~(k15\_euclid~np\_\_2)))\end{array}
\label{hyp:ggdgidpfahdhdgpgngahpfbd}
\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~(k7\_pscomp\_1~X0)~k1\_numbers)\end{array}
\label{hyp:egehpflghdpfahdhdgpgngahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xreal\_0~X0){\unicdcdcdhd}(v1\_xreal\_0~X1)){\unicdbdjdcd}(m1\_subset\_1~\\
(k19\_euclid~X0~X1)~(u1\_struct\_0~(k15\_euclid~np\_\_2)))\end{array}
\label{hyp:egehpflgbdjdpffgfhdgmgjgeg}
\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~(k16\_pscomp\_1~X0)~(k1\_zfmisc\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))))\end{array}
\label{hyp:egehpflgbdgdpfahdhdgpgngahpfbd}
\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}(k7\_pscomp\_1~X0=k2\_pscomp\_1~(k1\_pre\_topc~(k15\_euclid~\\
np\_\_2)~X0)~(k3\_pscomp\_1~(k15\_euclid~np\_\_2)~k5\_pscomp\_1~X0))\end{array}
\label{hyp:egidpfahdhdgpgngahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X2=k3\_xboole\_0~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(X3 \in X2){\unicdbdjded}((X3 \in X0){\unicdcdcdhd}(X3 \in X1)))\end{array}
\label{hyp:egedpfihcgpgpgmgfgpfad}
\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}(k23\_pscomp\_1~X0=k19\_euclid~(k8\_pscomp\_1~X0)~(k1\_pscomp\_1~\\
(k1\_pre\_topc~(k15\_euclid~np\_\_2)~(k16\_pscomp\_1~X0))~(k3\_pscomp\_1~\\
(k15\_euclid~np\_\_2)~k5\_pscomp\_1~(k16\_pscomp\_1~X0))))\end{array}
\label{hyp:egcdedpfahdhdgpgngahpfbd}
\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}(k22\_pscomp\_1~X0=k19\_euclid~(k8\_pscomp\_1~X0)~(k2\_pscomp\_1~\\
(k1\_pre\_topc~(k15\_euclid~np\_\_2)~(k16\_pscomp\_1~X0))~(k3\_pscomp\_1~\\
(k15\_euclid~np\_\_2)~k5\_pscomp\_1~(k16\_pscomp\_1~X0))))\end{array}
\label{hyp:egcdddpfahdhdgpgngahpfbd}
\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}(k16\_pscomp\_1~X0=k9\_subset\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~(k1\_rltopsp1~(k15\_euclid~np\_\_2)~(k13\_pscomp\_1~X0)~(k12\_pscomp\_1~\\
X0))~X0)\end{array}
\label{hyp:egbdhdpfahdhdgpgngahpfbd}
\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}(k13\_pscomp\_1~X0=k19\_euclid~(k8\_pscomp\_1~X0)~(k9\_pscomp\_1~\\
X0))\end{array}
\label{hyp:egbdedpfahdhdgpgngahpfbd}
\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}(k12\_pscomp\_1~X0=k19\_euclid~(k8\_pscomp\_1~X0)~(k7\_pscomp\_1~\\
X0))\end{array}
\label{hyp:egbdddpfahdhdgpgngahpfbd}
\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}(k9\_pscomp\_1~X0=k1\_pscomp\_1~(k1\_pre\_topc~(k15\_euclid~\\
np\_\_2)~X0)~(k3\_pscomp\_1~(k15\_euclid~np\_\_2)~k5\_pscomp\_1~X0))\end{array}
\label{hyp:egbdadpfahdhdgpgngahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k3\_xboole\_0}~{X0}}~{X1}}={{{k3\_xboole\_0}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgddpfihcgpgpgmgfgpfad}
\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:ehedhdpfahdhdgpgngahpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))))){\unicdbdjdcd}((X0 \in k16\_pscomp\_1~X1){\unicdbdjdcd}\\
((k17\_euclid~X0=k17\_euclid~(k23\_pscomp\_1~X1)){\unicdcdcdhd}((v2\_compts\_1~\\
X1~(k15\_euclid~np\_\_2)){\unicdbdjdcd}((r1\_xxreal\_0~(k18\_euclid~(k23\_pscomp\_1~\\
X1))~(k18\_euclid~X0)){\unicdcdcdhd}(r1\_xxreal\_0~(k18\_euclid~X0)~(k18\_euclid~\\
(k22\_pscomp\_1~X1))))))))\end{array}$$
\end{theorem}
\end{document}
