\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{t32\_pscomp\_1 (TMYB1VUpjqZcndT7CVkddBS56PEbNrMmuzK)}
\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 $ k14\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_rltopsp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k18\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k19\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k17\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k18\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k11\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{\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}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
(((k17\_euclid~X0=k17\_euclid~X1){\unicdcdcdhd}((k17\_euclid~X1=k17\_euclid~\\
X2){\unicdcdcdhd}((r1\_xxreal\_0~(k18\_euclid~X0)~(k18\_euclid~X1)){\unicdcdcdhd}(r1\_xxreal\_0~\\
(k18\_euclid~X1)~(k18\_euclid~X2))))){\unicdbdjdcd}(X1 \in k1\_rltopsp1~(k15\_euclid~\\
np\_\_2)~X0~X2))))\end{array}
\label{hyp:ehhdpfhgpgcgpgbgcheghd}
\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 .  (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 k14\_pscomp\_1~X1){\unicdbdjdcd}\\
((k17\_euclid~X0=k17\_euclid~(k18\_pscomp\_1~X1)){\unicdcdcdhd}((v2\_compts\_1~\\
X1~(k15\_euclid~np\_\_2)){\unicdbdjdcd}((r1\_xxreal\_0~(k18\_euclid~(k18\_pscomp\_1~\\
X1))~(k18\_euclid~X0)){\unicdcdcdhd}(r1\_xxreal\_0~(k18\_euclid~X0)~(k18\_euclid~\\
(k19\_pscomp\_1~X1))))))))\end{array}
\label{hyp:ehddbdpfahdhdgpgngahpfbd}
\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}((k17\_euclid~(k10\_pscomp\_1~X0)=k17\_euclid~(k18\_pscomp\_1~\\
X0)){\unicdcdcdhd}((k17\_euclid~(k10\_pscomp\_1~X0)=k17\_euclid~(k19\_pscomp\_1~\\
X0)){\unicdcdcdhd}((k17\_euclid~(k18\_pscomp\_1~X0)=k17\_euclid~(k19\_pscomp\_1~\\
X0)){\unicdcdcdhd}((k17\_euclid~(k18\_pscomp\_1~X0)=k17\_euclid~(k11\_pscomp\_1~\\
X0)){\unicdcdcdhd}(k17\_euclid~(k19\_pscomp\_1~X0)=k17\_euclid~(k11\_pscomp\_1~\\
X0))))))\end{array}
\label{hyp:ehcdjdpfahdhdgpgngahpfbd}
\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~(k19\_pscomp\_1~X0)~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2)))\end{array}
\label{hyp:egehpflgbdjdpfahdhdgpgngahpfbd}
\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 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2)))){\unicdbdjdcd}(m1\_subset\_1~(k14\_pscomp\_1~X0)~(k1\_zfmisc\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))))\end{array}
\label{hyp:egehpflgbdedpfahdhdgpgngahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (r1\_tarski~X0~X1){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X0){\unicdbdjdcd}\\
(X2 \in X1))\end{array}
\label{hyp:egddpfehbgchdhlgjg}
\end{equation}
\begin{theorem}\label{thm:ehddcdpfahdhdgpgngahpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v2\_compts\_1~X0~(k15\_euclid~np\_\_2)){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2)))))){\unicdbdjdcd}\\
(r1\_tarski~(k14\_pscomp\_1~X0)~(k1\_rltopsp1~(k15\_euclid~np\_\_2)~\\
(k18\_pscomp\_1~X0)~(k19\_pscomp\_1~X0)))\end{array}$$
\end{theorem}
\end{document}
