\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{t19\_metrizts (TMX3UaqyZDsHruJqwthN1vD1rNA8th9BBhw)}
\maketitle
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_pcomps\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_card\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_ordinal1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_waybel23 : {{\iota}{\unicdbdjdcd}{\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 $ v4\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_tex\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_tops\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_setfam\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k4\_topgen\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
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 .  ((v2\_pre\_topc~X0){\unicdcdcdhd}((v3\_pcomps\_1~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_finset\_1~X1){\unicdcdcdhd}(v1\_card\_1~X1)){\unicdbdjdcd}((r1\_ordinal1~\\
(k2\_waybel23~X0)~X1){\unicdbdjded}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}(\preoh (v1\_tops\_2~X2~X0){\unicdcdcdhd}((m1\_setfam\_1~\\
X2~(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}(\preoh (r1\_tarski~X3~X2){\unicdcdcdhd}((m1\_setfam\_1~\\
X3~(u1\_struct\_0~X0)){\unicdcdcdhd}(r1\_ordinal1~(k1\_card\_1~X3)~X1)))))))))\end{array}
\label{hyp:ehbdidpfngfgehchjgkhehdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_card\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~\\
X1)){\unicdbdjdcd}(({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X1))){\unicdbdjdcd}((v2\_tex\_2~X2~X1){\unicdbdjdcd}(r1\_ordinal1~(k1\_card\_1~X2)~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~X1)))){\unicdbdjdcd}\\
(((v1\_tops\_2~X2~X1){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X1))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X1))){\unicdbdjdcd}(((X3 \in X2){\unicdcdcdhd}(X4 \in X2)){\unicdbdjdcd}((X3=X4){\unicdcdcdid}(r1\_xboole\_0~\\
X3~X4)))))){\unicdbdjdcd}((k1\_xboole\_0 \in X2){\unicdcdcdid}(r1\_ordinal1~(k1\_card\_1~X2)~X0))))))\end{array}
\label{hyp:ehbdfdpfngfgehchjgkhehdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_finset\_1~X0){\unicdcdcdhd}(v1\_card\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (\\
(v2\_pre\_topc~X1){\unicdcdcdhd}((v3\_pcomps\_1~X1){\unicdcdcdhd}(l1\_pre\_topc~X1))){\unicdbdjdcd}(({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~X1))){\unicdbdjdcd}(((v4\_pre\_topc~\\
X2~X1){\unicdcdcdhd}(v2\_tex\_2~X2~X1)){\unicdbdjdcd}(r1\_ordinal1~(k1\_card\_1~X2)~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~X1))){\unicdbdjdcd}((v2\_tex\_2~X2~\\
X1){\unicdbdjdcd}(r1\_ordinal1~(k1\_card\_1~X2)~X0)))))\end{array}
\label{hyp:ehbdedpfngfgehchjgkhehdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_card\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~\\
X1)){\unicdbdjdcd}(({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X1)))){\unicdbdjdcd}(\preoh (v1\_tops\_2~X2~X1){\unicdcdcdhd}((m1\_setfam\_1~X2~(u1\_struct\_0~\\
X1)){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~(k1\_zfmisc\_1~(\\
u1\_struct\_0~X1)))){\unicdbdjdcd}(\preoh (r1\_tarski~X3~X2){\unicdcdcdhd}((m1\_setfam\_1~X3~(u1\_struct\_0~\\
X1)){\unicdcdcdhd}(r1\_ordinal1~(k1\_card\_1~X3)~X0))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(u1\_struct\_0~X1))){\unicdbdjdcd}(((v4\_pre\_topc~X2~X1){\unicdcdcdhd}(v2\_tex\_2~\\
X2~X1)){\unicdbdjdcd}(r1\_ordinal1~(k1\_card\_1~X2)~X0)))))\end{array}
\label{hyp:ehbdddpfngfgehchjgkhehdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_pre\_topc~X0){\unicdcdcdhd}((v3\_pcomps\_1~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_finset\_1~X1){\unicdcdcdhd}(v1\_card\_1~X1)){\unicdbdjdcd}((r1\_ordinal1~\\
(k4\_topgen\_1~X0)~X1){\unicdbdjdcd}(r1\_ordinal1~(k2\_waybel23~X0)~X1)))\end{array}
\label{hyp:mgcdfdpfngfgehchjgkhehdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_pre\_topc~X0){\unicdcdcdhd}((v3\_pcomps\_1~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_finset\_1~X1){\unicdcdcdhd}(v1\_card\_1~X1)){\unicdbdjdcd}(({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}\\
(((v1\_tops\_2~X2~X0){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))){\unicdbdjdcd}(((X3 \in X2){\unicdcdcdhd}(X4 \in X2)){\unicdbdjdcd}((X3=X4){\unicdcdcdid}(r1\_xboole\_0~\\
X3~X4)))))){\unicdbdjdcd}((k1\_xboole\_0 \in X2){\unicdcdcdid}(r1\_ordinal1~(k1\_card\_1~X2)~X1)))){\unicdbdjdcd}\\
(r1\_ordinal1~(k4\_topgen\_1~X0)~X1)))\end{array}
\label{hyp:mgcdddpfngfgehchjgkhehdh}
\end{equation}
\begin{theorem}\label{thm:ehbdjdpfngfgehchjgkhehdh}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_pre\_topc~X0){\unicdcdcdhd}((v3\_pcomps\_1~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_finset\_1~X1){\unicdcdcdhd}(v1\_card\_1~X1)){\unicdbdjdcd}((r1\_ordinal1~\\
(k2\_waybel23~X0)~X1){\unicdbdjded}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))){\unicdbdjdcd}(((v4\_pre\_topc~X2~X0){\unicdcdcdhd}(v2\_tex\_2~X2~X0)){\unicdbdjdcd}(\\
r1\_ordinal1~(k1\_card\_1~X2)~X1)))))\end{array}$$
\end{theorem}
\end{document}
