\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{t6\_gobrd12 (TMX7n2s1x2QGRbyad9RFuU4PahzvCPzSUxm)}
\maketitle
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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k15\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_2 : {\iota}$ 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 $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_goboard2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_matrix\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r2\_gobrd10 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_tops\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_goboard5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_goboard9 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_goboard9 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ r1\_gobrd10 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
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}(m2\_finseq\_1~X0~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k5\_numbers){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k5\_numbers){\unicdbdjdcd}(((r1\_xxreal\_0~\\
X1~(k3\_finseq\_1~(k2\_goboard2~X0))){\unicdcdcdhd}((r1\_xxreal\_0~X2~(k1\_matrix\_1~\\
(k2\_goboard2~X0))){\unicdcdcdhd}((r1\_xxreal\_0~X3~(k3\_finseq\_1~(k2\_goboard2~\\
X0))){\unicdcdcdhd}((r1\_xxreal\_0~X4~(k1\_matrix\_1~(k2\_goboard2~X0))){\unicdcdcdhd}((X1=\\
X3){\unicdcdcdhd}(r1\_tarski~(k1\_tops\_1~(k15\_euclid~np\_\_2)~(k3\_goboard5~(k2\_goboard2~\\
X0)~X1~X2))~(k4\_subset\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~(k2\_goboard9~\\
X0)~(k3\_goboard9~X0)))))))){\unicdbdjdcd}(((X4{\unicdcdgdad}k2\_nat\_1~X2~np\_\_1){\unicdcdcdhd}(X2{\unicdcdgdad}k2\_nat\_1~\\
X4~np\_\_1)){\unicdcdcdid}(r1\_tarski~(k1\_tops\_1~(k15\_euclid~np\_\_2)~(k3\_goboard5~\\
(k2\_goboard2~X0)~X3~X4))~(k4\_subset\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~(k2\_goboard9~X0)~(k3\_goboard9~X0)))))))))\end{array}
\label{hyp:mgbdbdpfhgpgcgchegbdcd}
\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}(m2\_finseq\_1~X0~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k5\_numbers){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k5\_numbers){\unicdbdjdcd}(((r1\_xxreal\_0~\\
X1~(k3\_finseq\_1~(k2\_goboard2~X0))){\unicdcdcdhd}((r1\_xxreal\_0~X2~(k1\_matrix\_1~\\
(k2\_goboard2~X0))){\unicdcdcdhd}((r1\_xxreal\_0~X3~(k3\_finseq\_1~(k2\_goboard2~\\
X0))){\unicdcdcdhd}((r1\_xxreal\_0~X4~(k1\_matrix\_1~(k2\_goboard2~X0))){\unicdcdcdhd}((X2=\\
X4){\unicdcdcdhd}(r1\_tarski~(k1\_tops\_1~(k15\_euclid~np\_\_2)~(k3\_goboard5~(k2\_goboard2~\\
X0)~X1~X2))~(k4\_subset\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~(k2\_goboard9~\\
X0)~(k3\_goboard9~X0)))))))){\unicdbdjdcd}(((X3{\unicdcdgdad}k2\_nat\_1~X1~np\_\_1){\unicdcdcdhd}(X1{\unicdcdgdad}k2\_nat\_1~\\
X3~np\_\_1)){\unicdcdcdid}(r1\_tarski~(k1\_tops\_1~(k15\_euclid~np\_\_2)~(k3\_goboard5~\\
(k2\_goboard2~X0)~X3~X4))~(k4\_subset\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~(k2\_goboard9~X0)~(k3\_goboard9~X0)))))))))\end{array}
\label{hyp:mgbdadpfhgpgcgchegbdcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~k5\_numbers){\unicdbdjdcd}((r2\_gobrd10~X0~X1~X2~X3){\unicdbdjded}(((r1\_gobrd10~\\
X0~X2){\unicdcdcdhd}(X1=X3)){\unicdcdcdid}((X0=X2){\unicdcdcdhd}(r1\_gobrd10~X1~X3)))))))\end{array}
\label{hyp:egcdpfhgpgcgchegbdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k5\_numbers){\unicdbdjdcd}((r1\_gobrd10~X0~X1){\unicdbdjded}((X1=k2\_nat\_1~X0~np\_\_1){\unicdcdcdid}(\\
X0=k2\_nat\_1~X1~np\_\_1))))\end{array}
\label{hyp:egbdpfhgpgcgchegbdad}
\end{equation}
\begin{theorem}\label{thm:ehgdpfhgpgcgchegbdcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v3\_funct\_1~X0){\unicdcdcdhd}((v1\_finseq\_6~\\
X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdcdcdhd}((v1\_topreal1~X0){\unicdcdcdhd}((v2\_topreal1~\\
X0){\unicdcdcdhd}((v1\_goboard5~X0){\unicdcdcdhd}((v2\_goboard5~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k5\_numbers){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k5\_numbers){\unicdbdjdcd}(((r1\_xxreal\_0~\\
X1~(k3\_finseq\_1~(k2\_goboard2~X0))){\unicdcdcdhd}((r1\_xxreal\_0~X2~(k1\_matrix\_1~\\
(k2\_goboard2~X0))){\unicdcdcdhd}((r1\_xxreal\_0~X3~(k3\_finseq\_1~(k2\_goboard2~\\
X0))){\unicdcdcdhd}((r1\_xxreal\_0~X4~(k1\_matrix\_1~(k2\_goboard2~X0))){\unicdcdcdhd}(r2\_gobrd10~\\
X1~X2~X3~X4))))){\unicdbdjdcd}((r1\_tarski~(k1\_tops\_1~(k15\_euclid~np\_\_2)~(k3\_goboard5~\\
(k2\_goboard2~X0)~X1~X2))~(k4\_subset\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~(k2\_goboard9~X0)~(k3\_goboard9~X0))){\unicdbdjded}(r1\_tarski~(k1\_tops\_1~\\
(k15\_euclid~np\_\_2)~(k3\_goboard5~(k2\_goboard2~X0)~X3~X4))~(k4\_subset\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~(k2\_goboard9~X0)~(k3\_goboard9~\\
X0)))))))))\end{array}$$
\end{theorem}
\end{document}
