\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{l5\_metric\_1 (TMNbGvs43hAzZ41JngFxGGq6QB3A6xfZMFq)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k9\_funct\_5 : {\iota}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k7\_funct\_5 : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k12\_arytm\_3 : {\iota}$ be given.
Let $ k1\_arytm\_3 : {\iota}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_arytm\_3 : {\iota}$ be given.
Let $ c1\_\_xreal\_0 : {\iota}$ be given.
Assume the following.
\begin{equation}
{{np\_\_1}={{k1\_tarski}~{k1\_xboole\_0}}}\label{hyp:ehedjdpfdgbgchegpfbd}
\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 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}(r1\_xxreal\_0~\\
X0~(k2\_xcmplx\_0~X0~X1)))\end{array}
\label{hyp:ehbdbdpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k9\_funct\_5}={k7\_funct\_5}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfggfhogdgehpffd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{k12\_arytm\_3}={k1\_arytm\_3}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdcdpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~np\_\_1){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~\\
np\_\_1){\unicdbdjdcd}((k5\_binop\_1~np\_\_1~k9\_funct\_5~X0~X1=k6\_numbers){\unicdbdjded}(X0=\\
X1)))\end{array}
\label{hyp:mgddpfngfgehchjgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{k1\_xboole\_0}}\label{hyp:ggdgbdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(\preoh v1\_xboole\_0~k12\_arytm\_3){\unicdcdcdhd}((v3\_ordinal1~k12\_arytm\_3){\unicdcdcdhd}(m1\_subset\_1~\\
k12\_arytm\_3~k5\_arytm\_3))\end{array}
\label{hyp:egehpflgbdcdpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{c1\_\_xreal\_0}={k6\_numbers}}\label{hyp:egfgpfdgbdpfpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{k1\_xboole\_0}={{the}~{({{\uniddcgcg} X0 : {\iota} .  {{v1\_xboole\_0}~{X0}}})}}}\label{hyp:egcdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (X1=k1\_tarski~X0){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X1){\unicdbdjded}\\
(X2=X0))\end{array}
\label{hyp:egbdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
{{k1\_arytm\_3}={np\_\_1}}\label{hyp:egbdpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdghdpfpgchegjgogbgmgbd}
\end{equation}
\begin{theorem}\label{thm:mgfdpfngfgehchjgdgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~np\_\_1){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~\\
np\_\_1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~np\_\_1){\unicdbdjdcd}(r1\_xxreal\_0~(k5\_binop\_1~\\
np\_\_1~k9\_funct\_5~X0~X2)~(k2\_xcmplx\_0~(k5\_binop\_1~np\_\_1~k9\_funct\_5~\\
X0~X1)~(k5\_binop\_1~np\_\_1~k9\_funct\_5~X1~X2)))))\end{array}$$
\end{theorem}
\end{document}
