\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{l31\_jordan5c (TMLsdDien8EJu2vUgpNXmVPSB2V3LmBcyS8)}
\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 $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v4\_topreal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_jordan5c : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k3\_topreal1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_topreal1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r2\_jordan3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (\preoh (\preoh r1\_xboole\_0~X0~X1){\unicdcdcdhd}({\unicdcdadad} X2 .  \preoh (X2 \in \\
X0){\unicdcdcdhd}(X2 \in X1))){\unicdcdcdhd}(\preoh ({\unicdcdaddd} X2 .  (X2 \in X0){\unicdcdcdhd}(X2 \in X1)){\unicdcdcdhd}(r1\_xboole\_0~\\
X0~X1))\end{array}
\label{hyp:ehddpfihcgpgpgmgfgpfad}
\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~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k5\_numbers){\unicdbdjdcd}(((v4\_pre\_topc~\\
X1~(k15\_euclid~np\_\_2)){\unicdcdcdhd}((v4\_topreal1~X0){\unicdcdcdhd}((r1\_xxreal\_0~np\_\_1~\\
X2){\unicdcdcdhd}((r1\_xxreal\_0~(k2\_nat\_1~X2~np\_\_1)~(k3\_finseq\_1~X0)){\unicdcdcdhd}(k2\_jordan5c~\\
(k3\_topreal1~np\_\_2~X0)~X1~(k7\_partfun1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~X0~np\_\_1)~(k7\_partfun1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~\\
X0~(k3\_finseq\_1~X0)) \in k2\_topreal1~np\_\_2~X0~X2))))){\unicdbdjdcd}((r1\_xboole\_0~\\
(k3\_topreal1~np\_\_2~X0)~X1){\unicdcdcdid}(k2\_jordan5c~(k3\_topreal1~np\_\_2~X0)~\\
X1~(k7\_partfun1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~X0~np\_\_1)~(k7\_partfun1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~X0~(k3\_finseq\_1~X0))=k2\_jordan5c~\\
(k2\_topreal1~np\_\_2~X0~X2)~X1~(k7\_partfun1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~X0~X2)~(k7\_partfun1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~X0~\\
(k2\_nat\_1~X2~np\_\_1)))))))\end{array}
\label{hyp:ehcdadpfkgpgchegbgogfddg}
\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~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~k5\_numbers){\unicdbdjdcd}(((v4\_topreal1~\\
X0){\unicdcdcdhd}((v4\_pre\_topc~X1~(k15\_euclid~np\_\_2)){\unicdcdcdhd}((r1\_xxreal\_0~np\_\_1~\\
X3){\unicdcdcdhd}((r1\_xxreal\_0~(k2\_nat\_1~X3~np\_\_1)~(k3\_finseq\_1~X0)){\unicdcdcdhd}((X2 \in \\
k2\_topreal1~np\_\_2~X0~X3){\unicdcdcdhd}(X2 \in X1)))))){\unicdbdjdcd}((r1\_xboole\_0~(k2\_topreal1~\\
np\_\_2~X0~X3)~X1){\unicdcdcdid}(r2\_jordan3~(k7\_partfun1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~X0~X3)~(k7\_partfun1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~X0~\\
(k2\_nat\_1~X3~np\_\_1))~X2~(k2\_jordan5c~(k2\_topreal1~np\_\_2~X0~X3)~X1~\\
(k7\_partfun1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~X0~X3)~(k7\_partfun1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~X0~(k2\_nat\_1~X3~np\_\_1)))))))))\end{array}
\label{hyp:mgddadpfkgpgchegbgogfddg}
\end{equation}
\begin{theorem}\label{thm:mgddbdpfkgpgchegbgogfddg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m2\_finseq\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~k5\_numbers){\unicdbdjdcd}(((v4\_topreal1~\\
X0){\unicdcdcdhd}((v4\_pre\_topc~X1~(k15\_euclid~np\_\_2)){\unicdcdcdhd}((k2\_jordan5c~(k3\_topreal1~\\
np\_\_2~X0)~X1~(k7\_partfun1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~X0~np\_\_1)~\\
(k7\_partfun1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~X0~(k3\_finseq\_1~\\
X0)) \in k2\_topreal1~np\_\_2~X0~X3){\unicdcdcdhd}((r1\_xxreal\_0~np\_\_1~X3){\unicdcdcdhd}((r1\_xxreal\_0~\\
(k2\_nat\_1~X3~np\_\_1)~(k3\_finseq\_1~X0)){\unicdcdcdhd}((X2 \in k2\_topreal1~np\_\_2~\\
X0~X3){\unicdcdcdhd}(X2 \in X1))))))){\unicdbdjdcd}((r1\_xboole\_0~(k3\_topreal1~np\_\_2~X0)~X1){\unicdcdcdid}\\
(r2\_jordan3~(k7\_partfun1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~X0~\\
X3)~(k7\_partfun1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~X0~(k2\_nat\_1~\\
X3~np\_\_1))~X2~(k2\_jordan5c~(k3\_topreal1~np\_\_2~X0)~X1~(k7\_partfun1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~X0~np\_\_1)~(k7\_partfun1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~X0~(k3\_finseq\_1~X0)))))))))\end{array}$$
\end{theorem}
\end{document}
