\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{t27\_jordan15 (TMW29FSQbhgkAr7xfVGf19eXTAXVQVqCS61)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v2\_connsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k15\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_2 : {\iota}$ 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 $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\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 $ k3\_matrix\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k3\_topreal1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_jordan1e : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_jordan1e : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v2\_connsp\_1~\\
X1~(k15\_euclid~np\_\_2)){\unicdcdcdhd}((v2\_compts\_1~X1~(k15\_euclid~np\_\_2)){\unicdcdcdhd}\\
((\preoh v1\_sppol\_1~X1){\unicdcdcdhd}((\preoh v2\_sppol\_1~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~X2~np\_\_1){\unicdcdcdhd}((\preoh r1\_xxreal\_0~\\
(k3\_finseq\_1~(k1\_jordan8~X1~X0))~X2){\unicdcdcdhd}((r1\_xxreal\_0~np\_\_1~X3){\unicdcdcdhd}\\
((r1\_xxreal\_0~X4~(k1\_matrix\_1~(k1\_jordan8~X1~X0))){\unicdcdcdhd}((k3\_matrix\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~(k1\_jordan8~X1~X0)~X2~X4 \in k3\_topreal1~\\
np\_\_2~(k1\_jordan1e~X1~X0)){\unicdcdcdhd}((k3\_matrix\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~(k1\_jordan8~X1~X0)~X2~X3 \in k3\_topreal1~np\_\_2~(k2\_jordan1e~\\
X1~X0)){\unicdcdcdhd}(X3=X4)))))))))))\end{array}
\label{hyp:ehfdhdpfkgpgchegbgogbdkg}
\end{equation}
\begin{theorem}\label{thm:ehcdhdpfkgpgchegbgogbdfd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v2\_connsp\_1~\\
X1~(k15\_euclid~np\_\_2)){\unicdcdcdhd}((v2\_compts\_1~X1~(k15\_euclid~np\_\_2)){\unicdcdcdhd}\\
((\preoh v1\_sppol\_1~X1){\unicdcdcdhd}((\preoh v2\_sppol\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2)))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~k5\_numbers){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~X3~np\_\_1){\unicdcdcdhd}((\preoh r1\_xxreal\_0~\\
(k3\_finseq\_1~(k1\_jordan8~X1~X0))~X4){\unicdcdcdhd}((r1\_xxreal\_0~np\_\_1~X2){\unicdcdcdhd}\\
((r1\_xxreal\_0~X2~(k1\_matrix\_1~(k1\_jordan8~X1~X0))){\unicdcdcdhd}((k3\_matrix\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~(k1\_jordan8~X1~X0)~X4~X2 \in k3\_topreal1~\\
np\_\_2~(k1\_jordan1e~X1~X0)){\unicdcdcdhd}((k3\_matrix\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~(k1\_jordan8~X1~X0)~X3~X2 \in k3\_topreal1~np\_\_2~(k2\_jordan1e~\\
X1~X0)){\unicdcdcdhd}(X3=X4)))))))))))\end{array}$$
\end{theorem}
\end{document}
