\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{l30\_jordan12 (TMGZTZ5ytofrudMfBjEmeNhkpNTBsEN3BWb)}
\maketitle
Let $ m1\_subset\_1 : {{\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\_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 $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_rltopsp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k9\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_topreal1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r3\_connsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((\preoh v3\_funct\_1~X2){\unicdcdcdhd}((v1\_finseq\_6~\\
X2~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdcdcdhd}((v1\_topreal1~X2){\unicdcdcdhd}((v2\_topreal1~\\
X2){\unicdcdcdhd}((v1\_goboard5~X2){\unicdcdcdhd}((v2\_goboard5~X2){\unicdcdcdhd}(m2\_finseq\_1~X2~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2)))))))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))){\unicdbdjdcd}(\preoh (X3 \in k1\_rltopsp1~(k15\_euclid~np\_\_2)~X0~\\
X1){\unicdcdcdhd}(({\unicdcdaddd} X4 .  k9\_subset\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~\\
(k3\_topreal1~np\_\_2~X2)~(k1\_rltopsp1~(k15\_euclid~np\_\_2)~X0~X1)=\\
k1\_tarski~X4){\unicdcdcdhd}((\preoh X3 \in k3\_topreal1~np\_\_2~X2){\unicdcdcdhd}((\preoh r1\_xboole\_0~(k3\_topreal1~\\
np\_\_2~X2)~(k1\_rltopsp1~(k15\_euclid~np\_\_2)~X0~X3)){\unicdcdcdhd}(\preoh r1\_xboole\_0~\\
(k3\_topreal1~np\_\_2~X2)~(k1\_rltopsp1~(k15\_euclid~np\_\_2)~X3~X1)))))))))\end{array}
\label{hyp:ehcdddpfkgpgchegbgogbdcd}
\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~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))){\unicdbdjdcd}(\preoh (r1\_xboole\_0~(k1\_rltopsp1~(k15\_euclid~\\
np\_\_2)~X1~X2)~(k3\_topreal1~np\_\_2~X0)){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2)))){\unicdbdjdcd}(\preoh (r3\_connsp\_1~\\
(k15\_euclid~np\_\_2)~(k3\_subset\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~\\
(k3\_topreal1~np\_\_2~X0))~X3){\unicdcdcdhd}((X1 \in X3){\unicdcdcdhd}(X2 \in X3)))))))\end{array}
\label{hyp:ehbdddpfkgpgchegbgogbdcd}
\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}
\begin{theorem}\label{thm:mgddadpfkgpgchegbgogbdcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((\preoh v3\_funct\_1~X2){\unicdcdcdhd}((v1\_finseq\_6~\\
X2~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdcdcdhd}((v1\_topreal1~X2){\unicdcdcdhd}((v2\_topreal1~\\
X2){\unicdcdcdhd}((v1\_goboard5~X2){\unicdcdcdhd}((v2\_goboard5~X2){\unicdcdcdhd}(m2\_finseq\_1~X2~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2)))))))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))){\unicdbdjdcd}(\preoh (X3 \in k1\_rltopsp1~(k15\_euclid~np\_\_2)~X0~\\
X1){\unicdcdcdhd}(({\unicdcdaddd} X4 .  k9\_subset\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~\\
(k3\_topreal1~np\_\_2~X2)~(k1\_rltopsp1~(k15\_euclid~np\_\_2)~X0~X1)=\\
k1\_tarski~X4){\unicdcdcdhd}((\preoh X3 \in k3\_topreal1~np\_\_2~X2){\unicdcdcdhd}(({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2)))){\unicdbdjdcd}(\preoh (r3\_connsp\_1~\\
(k15\_euclid~np\_\_2)~(k3\_subset\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~\\
(k3\_topreal1~np\_\_2~X2))~X4){\unicdcdcdhd}((X3 \in X4){\unicdcdcdhd}(X0 \in X4)))){\unicdcdcdhd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2)))){\unicdbdjdcd}\\
(\preoh (r3\_connsp\_1~(k15\_euclid~np\_\_2)~(k3\_subset\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~(k3\_topreal1~np\_\_2~X2))~X4){\unicdcdcdhd}((X3 \in X4){\unicdcdcdhd}(X1 \in \\
X4)))))))))))\end{array}$$
\end{theorem}
\end{document}
