\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{t2\_simplex2 (TMZGkt7cncGdr4HrnW2LTFENvK4EyfqQHok)}
\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 $ v1\_tops\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_pcomps\_1 : {{\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 $ m1\_simplex2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_compts\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_setfam\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_setfam\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_setfam\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k9\_metric\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
X0))){\unicdbdjdcd}((m1\_setfam\_1~X1~X0){\unicdbdjded}(k5\_setfam\_1~X0~X1=X0))\end{array}
\label{hyp:ehedfdpfdhfgehggbgngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((r1\_tarski~X0~X1){\unicdcdcdhd}(r1\_tarski~\\
X1~X2)){\unicdbdjdcd}(r1\_tarski~X0~X2)\end{array}
\label{hyp:ehbdpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (r1\_setfam\_1~X0~X1){\unicdbdjdcd}(r1\_tarski~(k3\_tarski~\\
X0)~(k3\_tarski~X1))\end{array}
\label{hyp:ehbdddpfdhfgehggbgngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
X0))){\unicdbdjdcd}(k5\_setfam\_1~X0~X1=k3\_tarski~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfdhfgehggbgngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\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)))))){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
(k3\_pcomps\_1~X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_simplex2~X2~X0~X1){\unicdbdjdcd}((v2\_xxreal\_0~\\
X2){\unicdcdcdhd}(m1\_subset\_1~X2~k1\_numbers)))\end{array}
\label{hyp:egehpfngbdpfdhjgngahmgfgihcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (r1\_setfam\_1~X0~X1){\unicdbdjded}({\unicdcdadad} X2 .  \preoh (X2 \in X0){\unicdcdcdhd}\\
({\unicdcdadad} X3 .  \preoh (X3 \in X1){\unicdcdcdhd}(r1\_tarski~X2~X3)))\end{array}
\label{hyp:egcdpfdhfgehggbgngpfbd}
\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}\\
((v1\_compts\_1~(k3\_pcomps\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~\\
(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~(k3\_pcomps\_1~X0))))){\unicdbdjdcd}\\
(((v1\_tops\_2~X1~(k3\_pcomps\_1~X0)){\unicdcdcdhd}(m1\_setfam\_1~X1~(u1\_struct\_0~\\
(k3\_pcomps\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v2\_xxreal\_0~X2){\unicdcdcdhd}(m1\_subset\_1~\\
X2~k1\_numbers)){\unicdbdjdcd}((m1\_simplex2~X2~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdaddd} X4 .  (m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k3\_pcomps\_1~X0)))){\unicdcdcdhd}((X4 \in X1){\unicdcdcdhd}(r1\_tarski~(k9\_metric\_1~\\
X0~X3~X2)~X4)))))))))\end{array}
\label{hyp:egbdpfdhjgngahmgfgihcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_setfam\_1~X1~X0){\unicdbdjded}(r1\_tarski~X0~(k3\_tarski~\\
X1))\end{array}
\label{hyp:egbdbdpfdhfgehggbgngpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdpfdhjgngahmgfgihcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v6\_metric\_1~X0){\unicdcdcdhd}((v7\_metric\_1~\\
X0){\unicdcdcdhd}((v8\_metric\_1~X0){\unicdcdcdhd}((v9\_metric\_1~X0){\unicdcdcdhd}(l1\_metric\_1~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_tops\_2~X1~(k3\_pcomps\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~X1~\\
(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~(k3\_pcomps\_1~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_tops\_2~X2~(k3\_pcomps\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~(k3\_pcomps\_1~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_simplex2~X3~X0~X1){\unicdbdjdcd}(((v1\_compts\_1~(k3\_pcomps\_1~\\
X0)){\unicdcdcdhd}((m1\_setfam\_1~X1~(u1\_struct\_0~(k3\_pcomps\_1~X0))){\unicdcdcdhd}(r1\_setfam\_1~\\
X1~X2))){\unicdbdjdcd}(m1\_simplex2~X3~X0~X2)))))\end{array}$$
\end{theorem}
\end{document}
