\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{t30\_goboard6 (TMRiuzhJxRYbfDh5uQ57qQi8b2ij1eppQK7)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\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 $ 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 $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_tops\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_goboard5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k17\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_matrix\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k19\_euclid : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k18\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_numbers : {\iota}$ 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 $ np\_\_0 : {\iota}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v6\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}((k17\_euclid~\\
(k19\_euclid~X0~X1)=X0){\unicdcdcdhd}(k18\_euclid~(k19\_euclid~X0~X1)=X1)))\end{array}
\label{hyp:ehfdcdpffgfhdgmgjgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}((\preoh r1\_xxreal\_0~np\_\_1~X0){\unicdbdjdcd}(X0=k6\_numbers))\end{array}
\label{hyp:ehbdedpfogbgehpfbd}
\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}((r1\_xxreal\_0~np\_\_1~\\
X0){\unicdbdjdcd}((r1\_xxreal\_0~(k3\_finseq\_1~X1)~X0){\unicdcdcdid}(k1\_tops\_1~(k15\_euclid~\\
np\_\_2)~(k1\_goboard5~X1~X0)=ReplSep2~(toset~({\uniddcgcg} X2 : \iota .  m1\_subset\_1~\\
X2~k1\_numbers))~({\uniddcgcg} X2 : \iota .  toset~({\uniddcgcg} X3 : \iota .  m1\_subset\_1~X3~\\
k1\_numbers))~({\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \iota .  (\preoh r1\_xxreal\_0~X2~(k17\_euclid~\\
(k3\_matrix\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~X1~X0~np\_\_1))){\unicdcdcdhd}\\
(\preoh r1\_xxreal\_0~(k17\_euclid~(k3\_matrix\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~X1~(k2\_nat\_1~X0~np\_\_1)~np\_\_1))~X2))~({\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \\
\iota .  k19\_euclid~X2~X3)))))\end{array}
\label{hyp:ehbdedpfhgpgcgpgbgcheggd}
\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}\\
(k1\_tops\_1~(k15\_euclid~np\_\_2)~(k1\_goboard5~X0~k6\_numbers)=ReplSep2~\\
(toset~({\uniddcgcg} X1 : \iota .  m1\_subset\_1~X1~k1\_numbers))~({\uniddcgcg} X1 : \iota .  \\
toset~({\uniddcgcg} X2 : \iota .  m1\_subset\_1~X2~k1\_numbers))~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \\
\iota .  \preoh r1\_xxreal\_0~(k17\_euclid~(k3\_matrix\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~X0~np\_\_1~np\_\_1))~X1)~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  k19\_euclid~\\
X1~X2))\end{array}
\label{hyp:ehbdcdpfhgpgcgpgbgcheggd}
\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}
{{v1\_xboole\_0}~{np\_\_0}}\label{hyp:dhahdgadpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{{{{k2\_xcmplx\_0}~{np\_\_1}}~{np\_\_0}}={np\_\_1}}\label{hyp:chbhcffgbgmgbeegegpfpflgcdpfihdgngahmgihpfadpfpfchbdpfchadpfchbd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k5\_numbers){\unicdcdcdhd}(v7\_ordinal1~\\
X1)){\unicdbdjdcd}(k2\_nat\_1~X0~X1=k2\_xcmplx\_0~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{v6\_membered}~{k4\_ordinal1}}\label{hyp:ggdggdpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k5\_numbers){\unicdcdcdhd}(v7\_ordinal1~\\
X1)){\unicdbdjdcd}(k2\_nat\_1~X0~X1=k2\_nat\_1~X1~X0)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgbdpfihchfgbgmgpfad}
\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:ehddadpfhgpgcgpgbgcheggd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v3\_relat\_1~\\
X2){\unicdcdcdhd}((v1\_matrix\_1~X2){\unicdcdcdhd}((v2\_goboard1~X2){\unicdcdcdhd}((v3\_goboard1~X2){\unicdcdcdhd}\\
((v4\_goboard1~X2){\unicdcdcdhd}((v5\_goboard1~X2){\unicdcdcdhd}(m2\_finseq\_1~X2~(k3\_finseq\_2~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2)))))))))){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~(\\
k3\_finseq\_1~X2)~X0){\unicdcdcdhd}((X1 \in k1\_tops\_1~(k15\_euclid~np\_\_2)~(k1\_goboard5~\\
X2~X0)){\unicdcdcdhd}(r1\_xxreal\_0~(k17\_euclid~(k3\_matrix\_1~(u1\_struct\_0~(\\
k15\_euclid~np\_\_2))~X2~(k2\_nat\_1~X0~np\_\_1)~np\_\_1))~(k17\_euclid~X1))))))\end{array}$$
\end{theorem}
\end{document}
