\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\_simplex1 (TMcX6fdM6yAL7nhDwBMfzex9eNHbak5Dg98)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_pencil\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_matroid0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_matroid0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_simplex1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_simplex0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_simplex1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_simplex0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_simplex1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_simplex1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ m1\_simplex1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ 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 $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v5\_rlvect\_1~X0){\unicdcdcdhd}\\
((v6\_rlvect\_1~X0){\unicdcdcdhd}((v7\_rlvect\_1~X0){\unicdcdcdhd}((v8\_rlvect\_1~X0){\unicdcdcdhd}(l1\_rlvect\_1~\\
X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v3\_pencil\_1~X1){\unicdcdcdhd}((v1\_matroid0~\\
X1){\unicdcdcdhd}((v3\_matroid0~X1){\unicdcdcdhd}((v1\_simplex1~X1~X0){\unicdcdcdhd}(m1\_simplex0~X1~(\\
u1\_struct\_0~X0)))))){\unicdbdjdcd}((r1\_tarski~(k3\_simplex1~X0~X1)~(k2\_struct\_0~\\
X1)){\unicdbdjdcd}(k6\_simplex0~X1=k6\_simplex0~(k4\_simplex1~X0~X1))))\end{array}
\label{hyp:ehddbdpfdhjgngahmgfgihbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v5\_rlvect\_1~X0){\unicdcdcdhd}\\
((v6\_rlvect\_1~X0){\unicdcdcdhd}((v7\_rlvect\_1~X0){\unicdcdcdhd}((v8\_rlvect\_1~X0){\unicdcdcdhd}(l1\_rlvect\_1~\\
X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v3\_pencil\_1~X1){\unicdcdcdhd}((v1\_matroid0~\\
X1){\unicdcdcdhd}((v3\_matroid0~X1){\unicdcdcdhd}((v1\_simplex1~X1~X0){\unicdcdcdhd}(m1\_simplex0~X1~(\\
u1\_struct\_0~X0)))))){\unicdbdjdcd}((r1\_tarski~(k3\_simplex1~X0~X1)~(k2\_struct\_0~\\
X1)){\unicdbdjdcd}(v1\_simplex1~(k4\_simplex1~X0~X1)~X0)))\end{array}
\label{hyp:ehcdidpfdhjgngahmgfgihbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((v13\_algstr\_0~X1){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~\\
X1){\unicdcdcdhd}((v5\_rlvect\_1~X1){\unicdcdcdhd}((v6\_rlvect\_1~X1){\unicdcdcdhd}((v7\_rlvect\_1~X1){\unicdcdcdhd}\\
((v8\_rlvect\_1~X1){\unicdcdcdhd}(l1\_rlvect\_1~X1)))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\\
\preoh v3\_pencil\_1~X2){\unicdcdcdhd}((v1\_matroid0~X2){\unicdcdcdhd}((v3\_matroid0~X2){\unicdcdcdhd}(m1\_simplex0~\\
X2~(u1\_struct\_0~X1))))){\unicdbdjdcd}((r1\_tarski~(k3\_simplex1~X1~X2)~(k2\_struct\_0~\\
X2)){\unicdbdjdcd}(k5\_simplex1~(k3\_real\_1~X0~np\_\_1)~X1~X2=k4\_simplex1~X1~(k5\_simplex1~\\
X0~X1~X2)))))\end{array}
\label{hyp:ehcdadpfdhjgngahmgfgihbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((v13\_algstr\_0~X1){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~\\
X1){\unicdcdcdhd}((v5\_rlvect\_1~X1){\unicdcdcdhd}((v6\_rlvect\_1~X1){\unicdcdcdhd}((v7\_rlvect\_1~X1){\unicdcdcdhd}\\
((v8\_rlvect\_1~X1){\unicdcdcdhd}(l1\_rlvect\_1~X1)))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\\
\preoh v3\_pencil\_1~X2){\unicdcdcdhd}((v1\_matroid0~X2){\unicdcdcdhd}((v3\_matroid0~X2){\unicdcdcdhd}(m1\_simplex0~\\
X2~(u1\_struct\_0~X1))))){\unicdbdjdcd}((r1\_tarski~(k3\_simplex1~X1~X2)~(k2\_struct\_0~\\
X2)){\unicdbdjdcd}(k2\_struct\_0~(k5\_simplex1~X0~X1~X2)=k2\_struct\_0~X2))))\end{array}
\label{hyp:ehbdidpfdhjgngahmgfgihbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v5\_rlvect\_1~X0){\unicdcdcdhd}\\
((v6\_rlvect\_1~X0){\unicdcdcdhd}((v7\_rlvect\_1~X0){\unicdcdcdhd}((v8\_rlvect\_1~X0){\unicdcdcdhd}(l1\_rlvect\_1~\\
X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v3\_pencil\_1~X1){\unicdcdcdhd}((v1\_matroid0~\\
X1){\unicdcdcdhd}((v3\_matroid0~X1){\unicdcdcdhd}(m1\_simplex0~X1~(u1\_struct\_0~X0))))){\unicdbdjdcd}\\
((r1\_tarski~(k3\_simplex1~X0~X1)~(k2\_struct\_0~X1)){\unicdbdjdcd}(k5\_simplex1~\\
k1\_xboole\_0~X0~X1=X1)))\end{array}
\label{hyp:ehbdgdpfdhjgngahmgfgihbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_rlvect\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_simplex0~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_simplex1~X2~\\
X0~X1){\unicdbdjdcd}(k3\_simplex1~X0~X1=k3\_simplex1~X0~X2)))\end{array}
\label{hyp:ehbdadpfdhjgngahmgfgihbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_1){\unicdcdcdhd}(m2\_subset\_1~np\_\_1~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_1~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_1~k1\_numbers))\end{array}
\label{hyp:dhahdgbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 : \iota{\unicdbdjdcd}o .  ((X0~k6\_numbers){\unicdcdcdhd}({\unicdcdadad} X1 .  (v7\_ordinal1~\\
X1){\unicdbdjdcd}((X0~X1){\unicdbdjdcd}(X0~(k1\_nat\_1~X1~np\_\_1))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~\\
X1){\unicdbdjdcd}(X0~X1))\end{array}
\label{hyp:dhcdpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xreal\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~k1\_numbers)){\unicdbdjdcd}\\
(k3\_real\_1~X0~X1=k2\_xcmplx\_0~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~k5\_numbers)){\unicdbdjdcd}\\
(k1\_nat\_1~X0~X1=k2\_xcmplx\_0~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_rlvect\_1~X0)){\unicdcdcdhd}\\
(m1\_simplex0~X1~(u1\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_simplex1~\\
X2~X0~X1){\unicdbdjdcd}(m1\_simplex0~X2~(u1\_struct\_0~X0)))\end{array}
\label{hyp:egehpfngbdpfdhjgngahmgfgihbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(((\preoh v2\_struct\_0~\\
X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}\\
((v4\_rlvect\_1~X1){\unicdcdcdhd}((v5\_rlvect\_1~X1){\unicdcdcdhd}((v6\_rlvect\_1~X1){\unicdcdcdhd}((v7\_rlvect\_1~\\
X1){\unicdcdcdhd}((v8\_rlvect\_1~X1){\unicdcdcdhd}(l1\_rlvect\_1~X1)))))))))){\unicdcdcdhd}((\preoh v3\_pencil\_1~\\
X2){\unicdcdcdhd}((v1\_matroid0~X2){\unicdcdcdhd}((v3\_matroid0~X2){\unicdcdcdhd}(m1\_simplex0~X2~(u1\_struct\_0~\\
X1))))))){\unicdbdjdcd}((\preoh v3\_pencil\_1~(k5\_simplex1~X0~X1~X2)){\unicdcdcdhd}((v1\_matroid0~\\
(k5\_simplex1~X0~X1~X2)){\unicdcdcdhd}((v3\_matroid0~(k5\_simplex1~X0~X1~X2)){\unicdcdcdhd}\\
(m1\_simplex1~(k5\_simplex1~X0~X1~X2)~X1~X2))))\end{array}
\label{hyp:egehpflgfdpfdhjgngahmgfgihbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}\\
((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v5\_rlvect\_1~\\
X0){\unicdcdcdhd}((v6\_rlvect\_1~X0){\unicdcdcdhd}((v7\_rlvect\_1~X0){\unicdcdcdhd}((v8\_rlvect\_1~X0){\unicdcdcdhd}\\
(l1\_rlvect\_1~X0)))))))))){\unicdcdcdhd}((\preoh v3\_pencil\_1~X1){\unicdcdcdhd}((v1\_matroid0~\\
X1){\unicdcdcdhd}((v3\_matroid0~X1){\unicdcdcdhd}(m1\_simplex0~X1~(u1\_struct\_0~X0)))))){\unicdbdjdcd}\\
((\preoh v3\_pencil\_1~(k4\_simplex1~X0~X1)){\unicdcdcdhd}((v1\_matroid0~(k4\_simplex1~\\
X0~X1)){\unicdcdcdhd}((v3\_matroid0~(k4\_simplex1~X0~X1)){\unicdcdcdhd}(m1\_simplex1~(k4\_simplex1~\\
X0~X1)~X0~X1))))\end{array}
\label{hyp:egehpflgedpfdhjgngahmgfgihbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgcdpfihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehddcdpfdhjgngahmgfgihbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((v13\_algstr\_0~X1){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~\\
X1){\unicdcdcdhd}((v5\_rlvect\_1~X1){\unicdcdcdhd}((v6\_rlvect\_1~X1){\unicdcdcdhd}((v7\_rlvect\_1~X1){\unicdcdcdhd}\\
((v8\_rlvect\_1~X1){\unicdcdcdhd}(l1\_rlvect\_1~X1)))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\\
\preoh v3\_pencil\_1~X2){\unicdcdcdhd}((v1\_matroid0~X2){\unicdcdcdhd}((v3\_matroid0~X2){\unicdcdcdhd}((v1\_simplex1~\\
X2~X1){\unicdcdcdhd}(m1\_simplex0~X2~(u1\_struct\_0~X1)))))){\unicdbdjdcd}((r1\_tarski~(k3\_simplex1~\\
X1~X2)~(k2\_struct\_0~X2)){\unicdbdjdcd}(k6\_simplex0~X2=k6\_simplex0~(k5\_simplex1~\\
X0~X1~X2)))))\end{array}$$
\end{theorem}
\end{document}
