\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{t4\_jordan1e (TMVwpRGDKUcF3UquAMNJp8hW4WPf9PFo2AA)}
\maketitle
Let $ m2\_finseq\_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 $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_topreal1 : {{\iota}{\unicdbdjdcd}{{\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 $ k3\_jordan3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k1\_jordan3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k7\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\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 $ k1\_numbers : {\iota}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (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}\\
((X1 \in k3\_topreal1~np\_\_2~X0){\unicdbdjdcd}((r1\_xxreal\_0~np\_\_1~(k1\_jordan3~X0~\\
X1)){\unicdcdcdhd}(\preoh r1\_xxreal\_0~(k3\_finseq\_1~X0)~(k1\_jordan3~X0~X1)))))\end{array}
\label{hyp:ehidpfkgpgchegbgogdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (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}\\
((X1 \in k3\_topreal1~np\_\_2~X0){\unicdbdjdcd}((k1\_funct\_1~(k3\_jordan3~X0~X1)~(k3\_finseq\_1~\\
(k3\_jordan3~X0~X1))=X1){\unicdcdcdhd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k5\_numbers){\unicdbdjdcd}\\
(((r1\_xxreal\_0~np\_\_1~X2){\unicdcdcdhd}(r1\_xxreal\_0~X2~(k1\_jordan3~X0~X1))){\unicdbdjdcd}\\
(k1\_funct\_1~(k3\_jordan3~X0~X1)~X2=k1\_funct\_1~X0~X2))))))\end{array}
\label{hyp:ehcdedpfkgpgchegbgogdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_1~\\
X1~(u1\_struct\_0~(k15\_euclid~X0))){\unicdbdjdcd}((r1\_xxreal\_0~np\_\_2~(k3\_finseq\_1~\\
X1)){\unicdbdjdcd}((k1\_funct\_1~X1~np\_\_1 \in k3\_topreal1~X0~X1){\unicdcdcdhd}((k7\_partfun1~\\
(u1\_struct\_0~(k15\_euclid~X0))~X1~np\_\_1 \in k3\_topreal1~X0~X1){\unicdcdcdhd}((k1\_funct\_1~\\
X1~(k3\_finseq\_1~X1) \in k3\_topreal1~X0~X1){\unicdcdcdhd}(k7\_partfun1~(u1\_struct\_0~\\
(k15\_euclid~X0))~X1~(k3\_finseq\_1~X1) \in k3\_topreal1~X0~X1))))))\end{array}
\label{hyp:ehbdpfkgpgchegbgogdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_2){\unicdcdcdhd}(m2\_subset\_1~np\_\_2~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_2~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_2~k1\_numbers))\end{array}
\label{hyp:dhahdgcdpfogfhngfgchbgmgdh}
\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}
{{{r1\_xxreal\_0}~{np\_\_1}}~{np\_\_1}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdpfchbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m2\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjded}{({{{m1\_finseq\_1}~{X1}}~{X0}})}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_finseq\_1~X0~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~(k15\_euclid~np\_\_2)))){\unicdbdjdcd}\\
(m2\_finseq\_1~(k3\_jordan3~X0~X1)~(u1\_struct\_0~(k15\_euclid~np\_\_2)))\end{array}
\label{hyp:egehpflgddpfkgpgchegbgogdd}
\end{equation}
\begin{theorem}\label{thm:ehedpfkgpgchegbgogbdfg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m2\_finseq\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
(((X1 \in k3\_topreal1~np\_\_2~X0){\unicdcdcdhd}(r1\_xxreal\_0~np\_\_2~(k3\_finseq\_1~\\
(k3\_jordan3~X0~X1)))){\unicdbdjdcd}(k1\_funct\_1~X0~np\_\_1 \in k3\_topreal1~np\_\_2~\\
(k3\_jordan3~X0~X1))))\end{array}$$
\end{theorem}
\end{document}
