\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{l27\_jordan5b (TMQdrDiLRgBfWg7tVWpySnJPeD3PA3wF5nk)}
\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 $ k1\_jordan3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r2\_jordan3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k7\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_jordan3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_jordan3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_jordan3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_finseq\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ 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\_tarski~(k3\_topreal1~np\_\_2~(k2\_jordan3~\\
X0~X1))~(k3\_topreal1~np\_\_2~X0))))\end{array}
\label{hyp:ehedcdpfkgpgchegbgogdd}
\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}(r1\_tarski~(k3\_topreal1~np\_\_2~(k3\_jordan3~\\
X0~X1))~(k3\_topreal1~np\_\_2~X0))))\end{array}
\label{hyp:ehedbdpfkgpgchegbgogdd}
\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}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
(((X1 \in k3\_topreal1~np\_\_2~X0){\unicdcdcdhd}((X2 \in k3\_topreal1~np\_\_2~X0){\unicdcdcdhd}((k1\_jordan3~\\
X0~X1=k1\_jordan3~X0~X2){\unicdcdcdhd}(r2\_jordan3~(k7\_partfun1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~X0~(k1\_jordan3~X0~X1))~(k7\_partfun1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~X0~(k2\_nat\_1~(k1\_jordan3~X0~X1)~np\_\_1))~X1~X2)))){\unicdbdjdcd}\\
((X1=X2){\unicdcdcdid}(X2 \in k3\_topreal1~np\_\_2~(k2\_jordan3~X0~X1))))))\end{array}
\label{hyp:ehddbdpfkgpgchegbgogdd}
\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}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
(((X1 \in k3\_topreal1~np\_\_2~X0){\unicdcdcdhd}(X2 \in k3\_topreal1~np\_\_2~X0)){\unicdbdjdcd}((r1\_xxreal\_0~\\
(k1\_jordan3~X0~X2)~(k1\_jordan3~X0~X1)){\unicdcdcdid}(X2 \in k3\_topreal1~np\_\_2~(\\
k2\_jordan3~X0~X1))))))\end{array}
\label{hyp:ehcdjdpfkgpgchegbgogdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((r1\_tarski~X0~X1){\unicdcdcdhd}(r1\_tarski~\\
X1~X2)){\unicdbdjdcd}(r1\_tarski~X0~X2)\end{array}
\label{hyp:ehbdpfihcgpgpgmgfgpfbd}
\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~(k2\_jordan3~X0~X1)~(u1\_struct\_0~(k15\_euclid~np\_\_2)))\end{array}
\label{hyp:egehpflgcdpfkgpgchegbgogdd}
\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}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
(((((X1 \in k3\_topreal1~np\_\_2~X0){\unicdcdcdhd}((X2 \in k3\_topreal1~np\_\_2~X0){\unicdcdcdhd}(\preoh \\
r1\_xxreal\_0~(k1\_jordan3~X0~X2)~(k1\_jordan3~X0~X1)))){\unicdcdcdid}((k1\_jordan3~\\
X0~X1=k1\_jordan3~X0~X2){\unicdcdcdhd}(r2\_jordan3~(k7\_partfun1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~X0~(k1\_jordan3~X0~X1))~(k7\_partfun1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~X0~(k2\_nat\_1~(k1\_jordan3~X0~X1)~np\_\_1))~X1~X2))){\unicdbdjdcd}\\
(k4\_jordan3~X0~X1~X2=k3\_jordan3~(k2\_jordan3~X0~X1)~X2)){\unicdcdcdhd}(\preoh (\preoh (X1 \in \\
k3\_topreal1~np\_\_2~X0){\unicdcdcdhd}((X2 \in k3\_topreal1~np\_\_2~X0){\unicdcdcdhd}(\preoh r1\_xxreal\_0~\\
(k1\_jordan3~X0~X2)~(k1\_jordan3~X0~X1)))){\unicdcdcdhd}((\preoh (k1\_jordan3~X0~X1=\\
k1\_jordan3~X0~X2){\unicdcdcdhd}(r2\_jordan3~(k7\_partfun1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~X0~(k1\_jordan3~X0~X1))~(k7\_partfun1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~X0~(k2\_nat\_1~(k1\_jordan3~X0~X1)~np\_\_1))~X1~X2)){\unicdcdcdhd}(k4\_jordan3~\\
X0~X1~X2{\unicdcdgdad}k4\_finseq\_5~(u1\_struct\_0~(k15\_euclid~np\_\_2))~(k3\_jordan3~\\
(k2\_jordan3~X0~X2)~X1)))))))\end{array}
\label{hyp:eghdpfkgpgchegbgogdd}
\end{equation}
\begin{theorem}\label{thm:mgcdhdpfkgpgchegbgogfdcg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m2\_finseq\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
(((X1 \in k3\_topreal1~np\_\_2~X0){\unicdcdcdhd}(X2 \in k3\_topreal1~np\_\_2~X0)){\unicdbdjdcd}(((r1\_xxreal\_0~\\
(k1\_jordan3~X0~X2)~(k1\_jordan3~X0~X1)){\unicdcdcdhd}(\preoh (k1\_jordan3~X0~X1=k1\_jordan3~\\
X0~X2){\unicdcdcdhd}(r2\_jordan3~(k7\_partfun1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~\\
X0~(k1\_jordan3~X0~X1))~(k7\_partfun1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~\\
X0~(k2\_nat\_1~(k1\_jordan3~X0~X1)~np\_\_1))~X1~X2))){\unicdcdcdid}((X1=X2){\unicdcdcdid}(r1\_tarski~\\
(k3\_topreal1~np\_\_2~(k4\_jordan3~X0~X1~X2))~(k3\_topreal1~np\_\_2~X0)))))))\end{array}$$
\end{theorem}
\end{document}
