\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{t41\_jordan15 (TMdbPhPFwFKreYzzepThy3JxmCK65USxJWk)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_topreal2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_zfmisc\_1 : {{\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 $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_jordan8 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_matrix\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k3\_matrix\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k8\_jordan6 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_topreal1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_jordan9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_jordan6 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_rltopsp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v2\_connsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_compts\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_sppol\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_sppol\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_jordan1e : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_jordan1e : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_connsp\_1~X0~(k15\_euclid~np\_\_2)){\unicdcdcdhd}((v2\_compts\_1~\\
X0~(k15\_euclid~np\_\_2)){\unicdcdcdhd}((\preoh v1\_sppol\_1~X0){\unicdcdcdhd}((\preoh v2\_sppol\_1~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2)))))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k5\_numbers){\unicdbdjdcd}((\preoh r1\_xxreal\_0~X1~k6\_numbers){\unicdbdjdcd}\\
(k3\_topreal1~np\_\_2~(k2\_jordan1e~X0~X1)=k9\_jordan6~(k3\_topreal1~\\
np\_\_2~(k1\_jordan9~X0~X1)))))\end{array}
\label{hyp:ehfdgdpfkgpgchegbgogbdhg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_connsp\_1~X0~(k15\_euclid~np\_\_2)){\unicdcdcdhd}((v2\_compts\_1~\\
X0~(k15\_euclid~np\_\_2)){\unicdcdcdhd}((\preoh v1\_sppol\_1~X0){\unicdcdcdhd}((\preoh v2\_sppol\_1~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2)))))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k5\_numbers){\unicdbdjdcd}((\preoh r1\_xxreal\_0~X1~k6\_numbers){\unicdbdjdcd}\\
(k3\_topreal1~np\_\_2~(k1\_jordan1e~X0~X1)=k8\_jordan6~(k3\_topreal1~\\
np\_\_2~(k1\_jordan9~X0~X1)))))\end{array}
\label{hyp:ehfdfdpfkgpgchegbgogbdhg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_topreal2~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))))){\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}(\preoh (\preoh \\
r1\_xxreal\_0~X3~np\_\_1){\unicdcdcdhd}((r1\_xxreal\_0~X3~X4){\unicdcdcdhd}((\preoh r1\_xxreal\_0~(k3\_finseq\_1~\\
(k1\_jordan8~X1~X0))~X4){\unicdcdcdhd}((r1\_xxreal\_0~np\_\_1~X2){\unicdcdcdhd}((r1\_xxreal\_0~\\
X2~(k1\_matrix\_1~(k1\_jordan8~X1~X0))){\unicdcdcdhd}((k3\_matrix\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~(k1\_jordan8~X1~X0)~X3~X2 \in k3\_topreal1~np\_\_2~\\
(k1\_jordan1e~X1~X0)){\unicdcdcdhd}((k3\_matrix\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~(k1\_jordan8~X1~X0)~X4~X2 \in k3\_topreal1~np\_\_2~(k2\_jordan1e~\\
X1~X0)){\unicdcdcdhd}(r2\_subset\_1~(k1\_rltopsp1~(k15\_euclid~np\_\_2)~(k3\_matrix\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~(k1\_jordan8~X1~X0)~X3~X2)~(k3\_matrix\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~(k1\_jordan8~X1~X0)~X4~X2))~(k8\_jordan6~\\
X1)))))))))))))\end{array}
\label{hyp:ehddjdpfkgpgchegbgogbdfd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2)))){\unicdbdjdcd}((v1\_topreal2~X0){\unicdbdjdcd}(v2\_connsp\_1~X0~(k15\_euclid~np\_\_2)))\end{array}
\label{hyp:dgdgidpfehpgahchfgbgmggd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2)))){\unicdbdjdcd}((v1\_topreal2~X0){\unicdbdjdcd}((v1\_topreal2~X0){\unicdcdcdhd}((\preoh v1\_sppol\_1~\\
X0){\unicdcdcdhd}(\preoh v2\_sppol\_1~X0))))\end{array}
\label{hyp:dgdgbdpfehpgahchfgbgmgfd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2)))){\unicdbdjdcd}((v1\_topreal2~X0){\unicdbdjdcd}((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v2\_compts\_1~\\
X0~(k15\_euclid~np\_\_2))))\end{array}
\label{hyp:dgdgbdpfehpgahchfgbgmgcd}
\end{equation}
\begin{theorem}\label{thm:ehedbdpfkgpgchegbgogbdfd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_topreal2~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k5\_numbers){\unicdbdjdcd}(\preoh (\preoh \\
r1\_xxreal\_0~X3~np\_\_1){\unicdcdcdhd}((r1\_xxreal\_0~X3~X4){\unicdcdcdhd}((\preoh r1\_xxreal\_0~(k3\_finseq\_1~\\
(k1\_jordan8~X1~X0))~X4){\unicdcdcdhd}((r1\_xxreal\_0~np\_\_1~X2){\unicdcdcdhd}((r1\_xxreal\_0~\\
X2~(k1\_matrix\_1~(k1\_jordan8~X1~X0))){\unicdcdcdhd}((\preoh r1\_xxreal\_0~X0~k6\_numbers){\unicdcdcdhd}\\
((k3\_matrix\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~(k1\_jordan8~X1~\\
X0)~X3~X2 \in k8\_jordan6~(k3\_topreal1~np\_\_2~(k1\_jordan9~X1~X0))){\unicdcdcdhd}(\\
(k3\_matrix\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~(k1\_jordan8~X1~\\
X0)~X4~X2 \in k9\_jordan6~(k3\_topreal1~np\_\_2~(k1\_jordan9~X1~X0))){\unicdcdcdhd}(\\
r2\_subset\_1~(k1\_rltopsp1~(k15\_euclid~np\_\_2)~(k3\_matrix\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~(k1\_jordan8~X1~X0)~X3~X2)~(k3\_matrix\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~(k1\_jordan8~X1~X0)~X4~X2))~(k8\_jordan6~X1))))))))))))))\end{array}$$
\end{theorem}
\end{document}
