\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{t14\_borsuk\_5 (TMbWURfFTh2kf6EvEXqDnsyr6J9Vgu6UkrX)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_metric\_1 : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_metric\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k18\_complex1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k16\_complex1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_metric\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_topmetr : {{\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\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_metric\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}((r1\_xxreal\_0~\\
X0~X1){\unicdbdjdcd}(r1\_xxreal\_0~k6\_numbers~(k6\_xcmplx\_0~X1~X0))))\end{array}
\label{hyp:ehedidpfihchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~k8\_metric\_1)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~k8\_metric\_1)){\unicdbdjdcd}({\unicdcdadad} X2 .  (v1\_xreal\_0~\\
X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_xreal\_0~X3){\unicdbdjdcd}(((X2=X0){\unicdcdcdhd}(X3=X1)){\unicdbdjdcd}(k4\_metric\_1~\\
k8\_metric\_1~X0~X1=k18\_complex1~(k6\_xcmplx\_0~X2~X3))))))\end{array}
\label{hyp:ehbdbdpfehpgahngfgehch}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xcmplx\_0}~{X0}})}{\unicdbdjdcd}{({{{k18\_complex1}~{X0}}={{k16\_complex1}~{X0}}})}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdidpfdgpgngahmgfgihbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xreal\_0~X0){\unicdcdcdhd}(v1\_xreal\_0~X1)){\unicdbdjdcd}(v1\_xreal\_0~\\
(k6\_xcmplx\_0~X0~X1))\end{array}
\label{hyp:ggdghdpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{({{v1\_metric\_1}~{k8\_metric\_1}})}{\unicdcdcdhd}{({{v3\_topmetr}~{k8\_metric\_1}})}}\label{hyp:ggdggdpfehpgahngfgehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_metric\_1~k8\_metric\_1){\unicdcdcdhd}((v6\_metric\_1~k8\_metric\_1){\unicdcdcdhd}((v7\_metric\_1~\\
k8\_metric\_1){\unicdcdcdhd}((v8\_metric\_1~k8\_metric\_1){\unicdcdcdhd}(v9\_metric\_1~k8\_metric\_1))))\end{array}
\label{hyp:ggdggdpfngfgehchjgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_topmetr~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}(v3\_membered~\\
(u1\_struct\_0~X0))\end{array}
\label{hyp:ggdgedpfehpgahngfgehch}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_metric\_1}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfngfgehchjgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{({{v1\_metric\_1}~{k8\_metric\_1}})}{\unicdcdcdhd}{({{l1\_metric\_1}~{k8\_metric\_1}})}}\label{hyp:egehpflgidpfngfgehchjgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}(((r1\_xxreal\_0~k6\_numbers~X0){\unicdbdjdcd}(k16\_complex1~\\
X0=X0)){\unicdcdcdhd}((\preoh r1\_xxreal\_0~k6\_numbers~X0){\unicdbdjdcd}(k16\_complex1~X0=k4\_xcmplx\_0~\\
X0)))\end{array}
\label{hyp:egbdpfbgcgdhghbgmgfhfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v8\_metric\_1~X0){\unicdcdcdhd}(l1\_metric\_1~\\
X0)){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)))){\unicdbdjdcd}(k4\_metric\_1~X0~X1~X2=k4\_metric\_1~X0~X2~X1)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgedpfngfgehchjgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xcmplx\_0}~{X0}})}}}\label{hyp:dgdgddpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
(v1\_xreal\_0~X1))\end{array}
\label{hyp:dgdgbdedpfngfgngcgfgchfgeg}
\end{equation}
\begin{theorem}\label{thm:ehbdedpfcgpgchdhfhlgpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~k8\_metric\_1)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~k8\_metric\_1)){\unicdbdjdcd}((r1\_xxreal\_0~X0~\\
X1){\unicdbdjdcd}(k4\_metric\_1~k8\_metric\_1~X0~X1=k6\_xcmplx\_0~X1~X0)))\end{array}$$
\end{theorem}
\end{document}
