\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\_metric\_2 (TMZ2KE5KdLHrtfXh1AqjFhXHKS57LtsbxYR)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_metric\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_metric\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_metric\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v9\_metric\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_metric\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_metric\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_metric\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_metric\_1~X1)){\unicdbdjdcd}\\
((X0 \in k2\_metric\_2~X1){\unicdbdjded}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X1)){\unicdcdcdhd}(X0=k1\_metric\_2~X1~X2)))\end{array}
\label{hyp:ehbdfdpfngfgehchjgdgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v6\_metric\_1~X0){\unicdcdcdhd}((v7\_metric\_1~\\
X0){\unicdcdcdhd}((v8\_metric\_1~X0){\unicdcdcdhd}((v9\_metric\_1~X0){\unicdcdcdhd}(l1\_metric\_1~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(k1\_metric\_2~X0~\\
X1=k6\_domain\_1~(u1\_struct\_0~X0)~X1))\end{array}
\label{hyp:ehbdddpfngfgehchjgdgpfcd}
\end{equation}
\begin{theorem}\label{thm:ehbdjdpfngfgehchjgdgpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v6\_metric\_1~X1){\unicdcdcdhd}\\
((v7\_metric\_1~X1){\unicdcdcdhd}((v8\_metric\_1~X1){\unicdcdcdhd}((v9\_metric\_1~X1){\unicdcdcdhd}(l1\_metric\_1~\\
X1)))))){\unicdbdjdcd}((X0 \in k2\_metric\_2~X1){\unicdbdjded}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~(\\
u1\_struct\_0~X1)){\unicdcdcdhd}(X0=k6\_domain\_1~(u1\_struct\_0~X1)~X2)))\end{array}$$
\end{theorem}
\end{document}
