\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{t25\_jordan1h (TMMgaoaAfhVL5AkqHiRm5wpYasjc2P9qGJa)}
\maketitle
Let $ v3\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_matrix\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_goboard1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_goboard1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_goboard1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_goboard1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_finseq\_2 : {{\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 $ v1\_xboole\_0 : {{\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 $ r1\_goboard1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_tops\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_gobrd13 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_goboard9 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_gobrd13 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_goboard9 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k7\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_topreal1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_rltopsp1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_rltopsp1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((r1\_tarski~X0~X1){\unicdcdcdhd}(r1\_xboole\_0~\\
X0~X2)){\unicdbdjdcd}(r1\_tarski~X0~(k4\_xboole\_0~X1~X2))\end{array}
\label{hyp:ehidgdpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v3\_relat\_1~X0){\unicdcdcdhd}((v1\_matrix\_1~X0){\unicdcdcdhd}((v2\_goboard1~\\
X0){\unicdcdcdhd}((v3\_goboard1~X0){\unicdcdcdhd}((v4\_goboard1~X0){\unicdcdcdhd}((v5\_goboard1~X0){\unicdcdcdhd}\\
(m2\_finseq\_1~X0~(k3\_finseq\_2~(u1\_struct\_0~(k15\_euclid~np\_\_2)))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((\preoh v3\_funct\_1~X1){\unicdcdcdhd}((v1\_finseq\_6~\\
X1~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdcdcdhd}((v1\_topreal1~X1){\unicdcdcdhd}((v2\_topreal1~\\
X1){\unicdcdcdhd}((v1\_goboard5~X1){\unicdcdcdhd}((v2\_goboard5~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2)))))))))){\unicdbdjdcd}((r1\_goboard1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k5\_numbers){\unicdbdjdcd}(((r1\_xxreal\_0~\\
np\_\_1~X2){\unicdcdcdhd}(r1\_xxreal\_0~(k2\_nat\_1~X2~np\_\_1)~(k3\_finseq\_1~X1))){\unicdbdjdcd}\\
((r1\_tarski~(k7\_subset\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~(k2\_gobrd13~\\
X1~X0~X2)~(k3\_topreal1~np\_\_2~X1))~(k3\_goboard9~X1)){\unicdcdcdhd}(r1\_tarski~\\
(k7\_subset\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~(k3\_gobrd13~X1~\\
X0~X2)~(k3\_topreal1~np\_\_2~X1))~(k2\_goboard9~X1)))))))\end{array}
\label{hyp:ehcdhdpfkgpgchegbgogjd}
\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 .  (l1\_pre\_topc~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))){\unicdbdjdcd}(r1\_tarski~(k1\_tops\_1~X0~X1)~X1))\end{array}
\label{hyp:ehbdgdpfehpgahdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v3\_relat\_1~\\
X1){\unicdcdcdhd}((v1\_matrix\_1~X1){\unicdcdcdhd}((v2\_goboard1~X1){\unicdcdcdhd}((v3\_goboard1~X1){\unicdcdcdhd}\\
((v4\_goboard1~X1){\unicdcdcdhd}((v5\_goboard1~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~(k3\_finseq\_2~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2)))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_1~\\
X2~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}(((r1\_goboard1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~X2~X1){\unicdcdcdhd}((v1\_topreal1~X2){\unicdcdcdhd}((r1\_xxreal\_0~np\_\_1~\\
X0){\unicdcdcdhd}(r1\_xxreal\_0~(k2\_nat\_1~X0~np\_\_1)~(k3\_finseq\_1~X2))))){\unicdbdjdcd}((\\
r1\_xboole\_0~(k1\_tops\_1~(k15\_euclid~np\_\_2)~(k3\_gobrd13~X2~X1~X0))~\\
(k3\_topreal1~np\_\_2~X2)){\unicdcdcdhd}(r1\_xboole\_0~(k1\_tops\_1~(k15\_euclid~\\
np\_\_2)~(k2\_gobrd13~X2~X1~X0))~(k3\_topreal1~np\_\_2~X2))))))\end{array}
\label{hyp:ehbdfdpfkgpgchegbgogjd}
\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){\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}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(k7\_subset\_1~X0~X1~X2=k4\_xboole\_0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflghdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_finset\_1}~{k4\_ordinal1}}}}\label{hyp:ggdghdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{v6\_membered}~{k4\_ordinal1}}\label{hyp:ggdggdpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k1\_numbers}}}}\label{hyp:ggdgbdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_rltopsp1}~{X0}})}{\unicdbdjdcd}{({{({{l1\_rlvect\_1}~{X0}})}{\unicdcdcdhd}{({{l1\_pre\_topc}~{X0}})}})}}}\label{hyp:egehpfmgbdpfchmgehpgahdhahbd}
\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 .  {\unicdcdadad} X2 .  ((m1\_finseq\_1~X0~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))){\unicdcdcdhd}(((\preoh v3\_relat\_1~X1){\unicdcdcdhd}((v1\_matrix\_1~X1){\unicdcdcdhd}\\
((v2\_goboard1~X1){\unicdcdcdhd}((v3\_goboard1~X1){\unicdcdcdhd}((v4\_goboard1~X1){\unicdcdcdhd}((v5\_goboard1~\\
X1){\unicdcdcdhd}(m1\_finseq\_1~X1~(k3\_finseq\_2~(u1\_struct\_0~(k15\_euclid~np\_\_2)))))))))){\unicdcdcdhd}\\
(m1\_subset\_1~X2~k5\_numbers))){\unicdbdjdcd}(m1\_subset\_1~(k3\_gobrd13~X0~X1~\\
X2)~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))))\end{array}
\label{hyp:egehpflgddpfhgpgcgchegbddd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_finseq\_1~X0~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))){\unicdcdcdhd}(((\preoh v3\_relat\_1~X1){\unicdcdcdhd}((v1\_matrix\_1~X1){\unicdcdcdhd}\\
((v2\_goboard1~X1){\unicdcdcdhd}((v3\_goboard1~X1){\unicdcdcdhd}((v4\_goboard1~X1){\unicdcdcdhd}((v5\_goboard1~\\
X1){\unicdcdcdhd}(m1\_finseq\_1~X1~(k3\_finseq\_2~(u1\_struct\_0~(k15\_euclid~np\_\_2)))))))))){\unicdcdcdhd}\\
(m1\_subset\_1~X2~k5\_numbers))){\unicdbdjdcd}(m1\_subset\_1~(k2\_gobrd13~X0~X1~\\
X2)~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))))\end{array}
\label{hyp:egehpflgcdpfhgpgcgchegbddd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}((v5\_rltopsp1~(k15\_euclid~X0)){\unicdcdcdhd}\\
(l1\_rltopsp1~(k15\_euclid~X0)))\end{array}
\label{hyp:egehpflgbdfdpffgfhdgmgjgeg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_finset\_1}~{X0}})}}}\label{hyp:dgdgbdpfggjgogdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v6\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
(v7\_ordinal1~X1))\end{array}
\label{hyp:dgdgbdhdpfngfgngcgfgchfgeg}
\end{equation}
\begin{theorem}\label{thm:ehcdfdpfkgpgchegbgogbdig}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v3\_relat\_1~X0){\unicdcdcdhd}((v1\_matrix\_1~X0){\unicdcdcdhd}((v2\_goboard1~\\
X0){\unicdcdcdhd}((v3\_goboard1~X0){\unicdcdcdhd}((v4\_goboard1~X0){\unicdcdcdhd}((v5\_goboard1~X0){\unicdcdcdhd}\\
(m2\_finseq\_1~X0~(k3\_finseq\_2~(u1\_struct\_0~(k15\_euclid~np\_\_2)))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((\preoh v3\_funct\_1~X1){\unicdcdcdhd}((v1\_finseq\_6~\\
X1~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdcdcdhd}((v1\_topreal1~X1){\unicdcdcdhd}((v2\_topreal1~\\
X1){\unicdcdcdhd}((v1\_goboard5~X1){\unicdcdcdhd}((v2\_goboard5~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2)))))))))){\unicdbdjdcd}((r1\_goboard1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~X2~k1\_numbers~k5\_numbers){\unicdbdjdcd}\\
(((r1\_xxreal\_0~np\_\_1~X2){\unicdcdcdhd}(r1\_xxreal\_0~(k2\_nat\_1~X2~np\_\_1)~(k3\_finseq\_1~\\
X1))){\unicdbdjdcd}((r1\_tarski~(k1\_tops\_1~(k15\_euclid~np\_\_2)~(k2\_gobrd13~\\
X1~X0~X2))~(k3\_goboard9~X1)){\unicdcdcdhd}(r1\_tarski~(k1\_tops\_1~(k15\_euclid~\\
np\_\_2)~(k3\_gobrd13~X1~X0~X2))~(k2\_goboard9~X1)))))))\end{array}$$
\end{theorem}
\end{document}
