\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{t17\_goboard1 (TMUT9Fv96hL6kBLDAMD27rZDzG2yTBydQEd)}
\maketitle
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 $ 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 $ k1\_matrix\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k9\_matrix\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_goboard1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}((\preoh (\preoh r1\_xxreal\_0~\\
X0~np\_\_1){\unicdcdcdhd}({\unicdcdadad} X1 .  (m2\_subset\_1~X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}\\
(\preoh (X0=k2\_nat\_1~X1~np\_\_1){\unicdcdcdhd}(\preoh r1\_xxreal\_0~X1~k6\_numbers)))){\unicdcdcdhd}(\preoh \\
({\unicdcdaddd} X1 .  (m2\_subset\_1~X1~k1\_numbers~k5\_numbers){\unicdcdcdhd}((X0=k2\_nat\_1~\\
X1~np\_\_1){\unicdcdcdhd}(\preoh r1\_xxreal\_0~X1~k6\_numbers))){\unicdcdcdhd}(r1\_xxreal\_0~X0~np\_\_1)))\end{array}
\label{hyp:ehedddpfdhfgbhngpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}((\\
X0 \in k2\_finseq\_1~X1){\unicdbdjded}((r1\_xxreal\_0~np\_\_1~X0){\unicdcdcdhd}(r1\_xxreal\_0~X0~X1))))\end{array}
\label{hyp:ehbdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m2\_subset\_1~X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  ((\preoh v3\_relat\_1~X3){\unicdcdcdhd}((v1\_matrix\_1~\\
X3){\unicdcdcdhd}((v2\_goboard1~X3){\unicdcdcdhd}((v3\_goboard1~X3){\unicdcdcdhd}((v4\_goboard1~X3){\unicdcdcdhd}\\
((v5\_goboard1~X3){\unicdcdcdhd}(m2\_finseq\_1~X3~(k3\_finseq\_2~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2)))))))))){\unicdbdjdcd}(((X0 \in k2\_finseq\_1~(k1\_matrix\_1~\\
X3)){\unicdcdcdhd}((k1\_matrix\_1~X3=k2\_nat\_1~X1~np\_\_1){\unicdcdcdhd}((r1\_xxreal\_0~X0~X2){\unicdcdcdhd}\\
(r1\_xxreal\_0~X2~X1)))){\unicdbdjdcd}((r1\_xxreal\_0~X1~k6\_numbers){\unicdcdcdid}((k9\_matrix\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~(k3\_goboard1~X3~X0)~X2=k9\_matrix\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~X3~(k2\_nat\_1~X2~np\_\_1)){\unicdcdcdhd}((X2 \in \\
k2\_finseq\_1~(k1\_matrix\_1~(k3\_goboard1~X3~X0))){\unicdcdcdhd}(k2\_nat\_1~X2~np\_\_1 \in \\
k2\_finseq\_1~(k1\_matrix\_1~X3)))))))))\end{array}
\label{hyp:ehbdedpfhgpgcgpgbgchegbd}
\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}
{{{r1\_xxreal\_0}~{np\_\_1}}~{np\_\_1}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdpfchbd}
\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}
{{v3\_membered}~{k1\_numbers}}\label{hyp:ggdgddpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k1\_numbers}}}}\label{hyp:ggdgbdpfogfhngcgfgchdh}
\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){\unicdbdjdcd}(m1\_subset\_1~X2~X0))\end{array}
\label{hyp:egehpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_finseq\_1~X1~X0){\unicdbdjdcd}((v1\_relat\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~X1)))\end{array}
\label{hyp:egehpfngbdpfggjgogdhfgbhpfbd}
\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 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_finseq\_1~\\
X0){\unicdcdcdhd}(v1\_matrix\_1~X0)))){\unicdbdjdcd}(m1\_subset\_1~(k1\_matrix\_1~X0)~k5\_numbers)\end{array}
\label{hyp:egehpflgbdpfngbgehchjgihpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xxreal\_0~X0){\unicdcdcdhd}(v1\_xxreal\_0~X1)){\unicdbdjdcd}(\\
(r1\_xxreal\_0~X0~X1){\unicdcdcdid}(r1\_xxreal\_0~X1~X0))\end{array}
\label{hyp:dgpgogogfgdgehfgegogfgdhdhpfchbdpfihihchfgbgmgpfad}
\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}
{{\unicdcdadad} X0 .  {{({{v3\_membered}~{X0}})}{\unicdbdjdcd}{({{v2\_membered}~{X0}})}}}\label{hyp:dgdgedpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v2\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
(v1\_xxreal\_0~X1))\end{array}
\label{hyp:dgdgbdddpfngfgngcgfgchfgeg}
\end{equation}
\begin{theorem}\label{thm:ehbdhdpfhgpgcgpgbgchegbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m2\_subset\_1~X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v3\_relat\_1~\\
X2){\unicdcdcdhd}((v1\_matrix\_1~X2){\unicdcdcdhd}((v2\_goboard1~X2){\unicdcdcdhd}((v3\_goboard1~X2){\unicdcdcdhd}\\
((v4\_goboard1~X2){\unicdcdcdhd}((v5\_goboard1~X2){\unicdcdcdhd}(m2\_finseq\_1~X2~(k3\_finseq\_2~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2)))))))))){\unicdbdjdcd}(((k1\_matrix\_1~X2=\\
k2\_nat\_1~X0~np\_\_1){\unicdcdcdhd}(X1 \in k2\_finseq\_1~X0)){\unicdbdjdcd}((r1\_xxreal\_0~X0~k6\_numbers){\unicdcdcdid}\\
((k9\_matrix\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~(k3\_goboard1~\\
X2~np\_\_1)~X1=k9\_matrix\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~X2~(\\
k2\_nat\_1~X1~np\_\_1)){\unicdcdcdhd}((X1 \in k2\_finseq\_1~(k1\_matrix\_1~(k3\_goboard1~\\
X2~np\_\_1))){\unicdcdcdhd}(k2\_nat\_1~X1~np\_\_1 \in k2\_finseq\_1~(k1\_matrix\_1~X2))))))))\end{array}$$
\end{theorem}
\end{document}
