\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{t32\_simplex0 (TMacu5xgSZWsci8Bj5srDYR8Cratdhor8Kj)}
\maketitle
Let $ m1\_simplex0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_simplex0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_simplex0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xxreal\_0 : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_int\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_pencil\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_xxreal\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v3\_matroid0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xxreal\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_matroid0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_matroid0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_pre\_topc : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k1\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xxreal\_0}~{X0}})}{\unicdbdjdcd}{({{{r1\_xxreal\_0}~{X0}}~{k1\_xxreal\_0}})}}}\label{hyp:ehddpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~X1)){\unicdbdjded}(r1\_tarski~\\
X0~X1)\end{array}
\label{hyp:ehddpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_int\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_pre\_topc~X1){\unicdbdjdcd}((\preoh (v3\_pencil\_1~\\
X1){\unicdcdcdhd}(\preoh r1\_xxreal\_0~(k2\_xxreal\_3~np\_\_1)~X0)){\unicdbdjdcd}((r1\_xxreal\_0~(k6\_simplex0~\\
X1)~X0){\unicdbdjded}((v3\_matroid0~X1){\unicdcdcdhd}({\unicdcdadad} X2 .  ((v1\_finset\_1~X2){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(u1\_struct\_0~X1)))){\unicdbdjdcd}((v3\_pre\_topc~X2~X1){\unicdbdjdcd}(r1\_xxreal\_0~\\
(k5\_card\_1~X2)~(k1\_xxreal\_3~X0~np\_\_1))))))))\end{array}
\label{hyp:ehcdfdpfdhjgngahmgfgihad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_finset\_1~X1){\unicdcdcdhd}(\\
m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}((v3\_pre\_topc~\\
X1~X0){\unicdbdjdcd}(r1\_xxreal\_0~(k5\_card\_1~X1)~(k1\_xxreal\_3~(k6\_simplex0~\\
X0)~np\_\_1))))\end{array}
\label{hyp:ehcdedpfdhjgngahmgfgihad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}(r1\_xxreal\_0~(k2\_xxreal\_3~np\_\_1)~\\
(k6\_simplex0~X0))\end{array}
\label{hyp:ehcdddpfdhjgngahmgfgihad}
\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 .  (m1\_simplex0~X1~X0){\unicdbdjdcd}({\unicdcdaddd} X2 .  (m2\_simplex0~\\
X2~X0~X1){\unicdcdcdhd}((v2\_struct\_0~X2){\unicdcdcdhd}((v1\_pre\_topc~X2){\unicdcdcdhd}((v3\_pencil\_1~\\
X2){\unicdcdcdhd}((v1\_matroid0~X2){\unicdcdcdhd}(v3\_matroid0~X2))))))\end{array}
\label{hyp:chdgjdpfdhjgngahmgfgihad}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xxreal\_0}~{k1\_xxreal\_0}}\label{hyp:ggdgbdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v4\_matroid0~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdbdjdcd}((v1\_xxreal\_0~\\
(k6\_simplex0~X0)){\unicdcdcdhd}(v1\_int\_1~(k6\_simplex0~X0)))\end{array}
\label{hyp:ggdgbdjdpfdhjgngahmgfgihad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_simplex0~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_simplex0~\\
X2~X0~X1){\unicdbdjdcd}((v1\_matroid0~X2){\unicdcdcdhd}((v3\_matroid0~X2){\unicdcdcdhd}(m1\_simplex0~X2~\\
X0))))\end{array}
\label{hyp:egehpfngcdpfdhjgngahmgfgihad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m1\_simplex0}~{X1}}~{X0}})}{\unicdbdjdcd}{({{l1\_pre\_topc}~{X1}})}}}}\label{hyp:egehpfngbdpfdhjgngahmgfgihad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_pre\_topc}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfahchfgpfehpgahdg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_pre\_topc}~{X0}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{({{k6\_simplex0}~{X0}})}})}}}\label{hyp:egehpflggdpfdhjgngahmgfgihad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}((v3\_pencil\_1~X0){\unicdbdjded}(v1\_xboole\_0~\\
(u1\_pre\_topc~X0)))\end{array}
\label{hyp:egedpfahfgogdgjgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (r1\_tarski~X0~X1){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X0){\unicdbdjdcd}\\
(X2 \in X1))\end{array}
\label{hyp:egddpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{{k2\_struct\_0}~{X0}}={{u1\_struct\_0}~{X0}}})}}}\label{hyp:egddpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
{{k1\_xxreal\_0}={k1\_numbers}}\label{hyp:egcdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))){\unicdbdjdcd}((v3\_pre\_topc~X1~X0){\unicdbdjded}(X1 \in u1\_pre\_topc~X0)))\end{array}
\label{hyp:egcdpfahchfgpfehpgahdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_simplex0~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_matroid0~\\
X2){\unicdcdcdhd}((v3\_matroid0~X2){\unicdcdcdhd}(m1\_simplex0~X2~X0))){\unicdbdjdcd}((m2\_simplex0~X2~\\
X0~X1){\unicdbdjded}((r1\_tarski~(k2\_struct\_0~X2)~(k2\_struct\_0~X1)){\unicdcdcdhd}(r1\_tarski~\\
(u1\_pre\_topc~X2)~(u1\_pre\_topc~X1)))))\end{array}
\label{hyp:egbdddpfdhjgngahmgfgihad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}((\\
(v4\_matroid0~X0){\unicdbdjdcd}((v3\_pencil\_1~X0){\unicdcdcdid}((X1=k6\_simplex0~X0){\unicdbdjded}((\\
{\unicdcdadad} X2 .  ((v1\_finset\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0)))){\unicdbdjdcd}((v3\_pre\_topc~X2~X0){\unicdbdjdcd}(r1\_xxreal\_0~(k5\_card\_1~X2)~(k1\_xxreal\_3~\\
X1~np\_\_1)))){\unicdcdcdhd}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))){\unicdcdcdhd}((v3\_pre\_topc~X2~X0){\unicdcdcdhd}(k1\_card\_1~X2=k1\_xxreal\_3~X1~np\_\_1))))))){\unicdcdcdhd}\\
(((v3\_pencil\_1~X0){\unicdbdjdcd}((X1=k6\_simplex0~X0){\unicdbdjded}(X1=k2\_xxreal\_3~np\_\_1))){\unicdcdcdhd}\\
(\preoh (\preoh (\preoh v3\_pencil\_1~X0){\unicdcdcdhd}(v4\_matroid0~X0)){\unicdcdcdhd}((\preoh v3\_pencil\_1~X0){\unicdcdcdhd}\\
(\preoh (X1=k6\_simplex0~X0){\unicdbdjded}(X1=k1\_xxreal\_0)))))))\end{array}
\label{hyp:egbdcdpfdhjgngahmgfgihad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v3\_pencil\_1~X1){\unicdcdcdhd}(m1\_simplex0~X1~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m2\_simplex0~X2~X0~X1){\unicdbdjdcd}(v3\_pencil\_1~X2))\end{array}
\label{hyp:dgdgbdedpfdhjgngahmgfgihad}
\end{equation}
\begin{theorem}\label{thm:ehddcdpfdhjgngahmgfgihad}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_simplex0~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_simplex0~\\
X2~X0~X1){\unicdbdjdcd}(r1\_xxreal\_0~(k6\_simplex0~X2)~(k6\_simplex0~X1)))\end{array}$$
\end{theorem}
\end{document}
