\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{t21\_jordan14 (TMd7FTx1UHvkFc67uspFXayNEcU4VDSiP2R)}
\maketitle
Let $ v1\_topreal2 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ k15\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_2 : {\iota}$ 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 $ r1\_jordan1h : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_topreal1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_jordan13 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_jordan2c : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_connsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_jordan2c : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_topreal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_topreal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_goboard5 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_goboard5 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_sppol\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_sppol\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_sprect\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_compts\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_topreal2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_subset\_1~X1~k1\_numbers~\\
k5\_numbers){\unicdbdjdcd}((r1\_jordan1h~X0~X1){\unicdbdjdcd}(r1\_subset\_1~X0~(k3\_topreal1~\\
np\_\_2~(k1\_jordan13~X0~X1)))))\end{array}
\label{hyp:ehidpfkgpgchegbgogbded}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((r1\_tarski~X0~X1){\unicdcdcdhd}(r1\_xboole\_0~\\
X1~X2)){\unicdbdjdcd}(r1\_xboole\_0~X0~X2)\end{array}
\label{hyp:ehgdddpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (\preoh (\preoh r1\_xboole\_0~X0~X1){\unicdcdcdhd}({\unicdcdadad} X2 .  \preoh (X2 \in \\
X0){\unicdcdcdhd}(X2 \in X1))){\unicdcdcdhd}(\preoh ({\unicdcdaddd} X2 .  (X2 \in X0){\unicdcdcdhd}(X2 \in X1)){\unicdcdcdhd}(r1\_xboole\_0~\\
X0~X1))\end{array}
\label{hyp:ehddpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v2\_connsp\_1~\\
X1~(k15\_euclid~X0)){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
(k15\_euclid~X0))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k15\_euclid~X0)))){\unicdbdjdcd}(\preoh (r1\_xboole\_0~X1~X2){\unicdcdcdhd}((\preoh r1\_tarski~\\
X1~(k2\_jordan2c~X0~X2)){\unicdcdcdhd}(\preoh r1\_tarski~X1~(k1\_jordan2c~X0~X2))))))\end{array}
\label{hyp:ehbdjdpfkgpgchegbgogbdlg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_topreal2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_subset\_1~X1~k1\_numbers~\\
k5\_numbers){\unicdbdjdcd}((r1\_jordan1h~X0~X1){\unicdbdjdcd}(r1\_tarski~(k2\_jordan2c~np\_\_2~\\
X0)~(k2\_jordan2c~np\_\_2~(k3\_topreal1~np\_\_2~(k1\_jordan13~X0~X1))))))\end{array}
\label{hyp:ehbdedpfkgpgchegbgogbded}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2)))){\unicdbdjdcd}(r1\_xboole\_0~(k2\_jordan2c~np\_\_2~X0)~X0)\end{array}
\label{hyp:ehbdadpfkgpgchegbgogcdbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{r1\_xboole\_0}~{X0}}~{X1}})}{\unicdbdjdcd}{({{{r1\_xboole\_0}~{X1}}~{X0}})}}}}\label{hyp:dhjhngngfgehchjhpfchbdpfihcgpgpgmgfgpfad}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(\preoh v1\_xboole\_0~X1)){\unicdbdjdcd}\\
((r1\_subset\_1~X0~X1){\unicdbdjded}(r1\_xboole\_0~X0~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchbdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~X0~X1){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m2\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjded}{({{{m1\_finseq\_1}~{X1}}~{X0}})}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k4\_ordinal1}}}})}{\unicdcdcdhd}{({{v3\_ordinal1}~{k4\_ordinal1}})}}\label{hyp:ggdggdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v3\_funct\_1~X0){\unicdcdcdhd}((v1\_finseq\_6~\\
X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdcdcdhd}((v1\_topreal1~X0){\unicdcdcdhd}((v2\_topreal1~\\
X0){\unicdcdcdhd}((v1\_goboard5~X0){\unicdcdcdhd}((v2\_goboard5~X0){\unicdcdcdhd}(m1\_finseq\_1~X0~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2)))))))))){\unicdbdjdcd}(v1\_topreal2~(k3\_topreal1~np\_\_2~\\
X0))\end{array}
\label{hyp:ggdgddpfdhahchfgdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k5\_numbers}}~{({{k1\_zfmisc\_1}~{k1\_numbers}})}}\label{hyp:egehpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(m1\_finseq\_1~X1~(u1\_struct\_0~\\
(k15\_euclid~X0)))){\unicdbdjdcd}(m1\_subset\_1~(k3\_topreal1~X0~X1)~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k15\_euclid~X0))))\end{array}
\label{hyp:egehpflgddpfehpgahchfgbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_sppol\_1~X0){\unicdcdcdhd}\\
((\preoh v2\_sppol\_1~X0){\unicdcdcdhd}((v1\_topreal2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2)))))))){\unicdcdcdhd}(m1\_subset\_1~X1~k5\_numbers)){\unicdbdjdcd}\\
((\preoh v1\_xboole\_0~(k1\_jordan13~X0~X1)){\unicdcdcdhd}((\preoh v3\_funct\_1~(k1\_jordan13~\\
X0~X1)){\unicdcdcdhd}((v1\_finseq\_6~(k1\_jordan13~X0~X1)~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))){\unicdcdcdhd}((v1\_topreal1~(k1\_jordan13~X0~X1)){\unicdcdcdhd}((v2\_topreal1~(\\
k1\_jordan13~X0~X1)){\unicdcdcdhd}((v1\_goboard5~(k1\_jordan13~X0~X1)){\unicdcdcdhd}((v2\_goboard5~\\
(k1\_jordan13~X0~X1)){\unicdcdcdhd}((v1\_sprect\_2~(k1\_jordan13~X0~X1)){\unicdcdcdhd}(m2\_finseq\_1~\\
(k1\_jordan13~X0~X1)~(u1\_struct\_0~(k15\_euclid~np\_\_2)))))))))))\end{array}
\label{hyp:egehpflgbdpfkgpgchegbgogbddd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjded}{({{\unicdcdadad} X1 .  {\preoh{{{X1} \in {X0}}}}})}}}\label{hyp:egbdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2)))){\unicdbdjdcd}((v1\_topreal2~X0){\unicdbdjdcd}(v2\_connsp\_1~X0~(k15\_euclid~np\_\_2)))\end{array}
\label{hyp:dgdgidpfehpgahchfgbgmggd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgidpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2)))){\unicdbdjdcd}((v1\_topreal2~X0){\unicdbdjdcd}((v1\_topreal2~X0){\unicdcdcdhd}((\preoh v1\_sppol\_1~\\
X0){\unicdcdcdhd}(\preoh v2\_sppol\_1~X0))))\end{array}
\label{hyp:dgdgbdpfehpgahchfgbgmgfd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2)))){\unicdbdjdcd}((v1\_topreal2~X0){\unicdbdjdcd}((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v2\_compts\_1~\\
X0~(k15\_euclid~np\_\_2))))\end{array}
\label{hyp:dgdgbdpfehpgahchfgbgmgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v1\_xboole\_0~X1))\end{array}
\label{hyp:dgdgbdpfdhfhcgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdbdpfkgpgchegbgogbded}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_topreal2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_subset\_1~X1~k1\_numbers~\\
k5\_numbers){\unicdbdjdcd}((r1\_jordan1h~X0~X1){\unicdbdjdcd}(r1\_tarski~(k3\_topreal1~np\_\_2~\\
(k1\_jordan13~X0~X1))~(k1\_jordan2c~np\_\_2~X0))))\end{array}$$
\end{theorem}
\end{document}
