\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{t22\_jordan1k (TMWWU7nwzxs6bP5WrgvW7W28nuNcEyQfv21)}
\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 $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_topreal6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_numbers : {\iota}$ 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 $ k4\_metric\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v6\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_metric\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k14\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((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}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}(\preoh (X1{\unicdcdgdad}X2){\unicdcdcdhd}(r1\_xxreal\_0~(k4\_metric\_1~X0~X1~X2)~k6\_numbers))))\end{array}
\label{hyp:ehhdpfngfgehchjgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_2){\unicdcdcdhd}(m2\_subset\_1~np\_\_2~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_2~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_2~k1\_numbers))\end{array}
\label{hyp:dhahdgcdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{v6\_membered}~{k4\_ordinal1}}\label{hyp:ggdggdpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_subset\_1~X0~k5\_numbers){\unicdcdcdhd}\\
((m1\_subset\_1~X1~(u1\_struct\_0~(k15\_euclid~X0))){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(u1\_struct\_0~(k15\_euclid~X0))))){\unicdbdjdcd}(m1\_subset\_1~(k1\_topreal6~\\
X0~X1~X2)~k1\_numbers)\end{array}
\label{hyp:egehpflgbdpfehpgahchfgbgmggd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}((v1\_metric\_1~(k14\_euclid~X0)){\unicdcdcdhd}\\
((v6\_metric\_1~(k14\_euclid~X0)){\unicdcdcdhd}((v7\_metric\_1~(k14\_euclid~X0)){\unicdcdcdhd}\\
((v8\_metric\_1~(k14\_euclid~X0)){\unicdcdcdhd}((v9\_metric\_1~(k14\_euclid~X0)){\unicdcdcdhd}\\
(l1\_metric\_1~(k14\_euclid~X0)))))))\end{array}
\label{hyp:egehpflgbdedpffgfhdgmgjgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~(k15\_euclid~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (\\
m1\_subset\_1~X2~(u1\_struct\_0~(k15\_euclid~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~k1\_numbers){\unicdbdjdcd}((X3=k1\_topreal6~X0~X1~X2){\unicdbdjded}({\unicdcdaddd} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~(k14\_euclid~X0))){\unicdcdcdhd}({\unicdcdaddd} X5 .  (m1\_subset\_1~X5~\\
(u1\_struct\_0~(k14\_euclid~X0))){\unicdcdcdhd}((X4=X1){\unicdcdcdhd}((X5=X2){\unicdcdcdhd}(X3=k4\_metric\_1~\\
(k14\_euclid~X0)~X4~X5)))))))))\end{array}
\label{hyp:egbdpfehpgahchfgbgmggd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v6\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
(v7\_ordinal1~X1))\end{array}
\label{hyp:dgdgbdhdpfngfgngcgfgchfgeg}
\end{equation}
\begin{theorem}\label{thm:ehcdcdpfkgpgchegbgogbdlg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
(\preoh (X0{\unicdcdgdad}X1){\unicdcdcdhd}(r1\_xxreal\_0~(k1\_topreal6~np\_\_2~X0~X1)~k6\_numbers)))\end{array}$$
\end{theorem}
\end{document}
