\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{t52\_jordan4 (TMdLtbQbFFw8FKFNFgbUYAdN8BddyKQQTcf)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_6 : {{\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 $ v1\_topreal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_topreal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_goboard5 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_goboard5 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_jordan4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_nat\_d : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_finseq\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k17\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v3\_funct\_1~X0){\unicdcdcdhd}((v1\_finseq\_6~\\
X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdcdcdhd}((v1\_topreal1~X0){\unicdcdcdhd}((v2\_topreal1~\\
X0){\unicdcdcdhd}((v1\_goboard5~X0){\unicdcdcdhd}((v2\_goboard5~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_1~X1~(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}((r1\_jordan4~X0~X1~X2~\\
X3){\unicdbdjdcd}((r1\_xxreal\_0~X2~X3){\unicdcdcdid}((k3\_finseq\_1~X1=k7\_nat\_d~(k2\_nat\_1~\\
(k3\_finseq\_1~X0)~X3)~X2){\unicdcdcdhd}((X1=k8\_finseq\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~(k3\_finseq\_6~(u1\_struct\_0~(k15\_euclid~np\_\_2))~X0~X2~(k7\_nat\_d~\\
(k3\_finseq\_1~X0)~np\_\_1))~(k17\_finseq\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~X3~X0)){\unicdcdcdhd}(X1=k8\_finseq\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~\\
(k3\_finseq\_6~(u1\_struct\_0~(k15\_euclid~np\_\_2))~X0~X2~(k7\_nat\_d~\\
(k3\_finseq\_1~X0)~np\_\_1))~(k3\_finseq\_6~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~X0~np\_\_1~X3)))))))))\end{array}
\label{hyp:ehcdgdpfkgpgchegbgoged}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v3\_funct\_1~X0){\unicdcdcdhd}((v1\_finseq\_6~\\
X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdcdcdhd}((v1\_topreal1~X0){\unicdcdcdhd}((v2\_topreal1~\\
X0){\unicdcdcdhd}((v1\_goboard5~X0){\unicdcdcdhd}((v2\_goboard5~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_1~X1~(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}(((r1\_jordan4~X0~X1~X2~\\
X3){\unicdcdcdhd}(r1\_xxreal\_0~X2~X3)){\unicdbdjdcd}((k3\_finseq\_1~X1=k2\_nat\_1~(k7\_nat\_d~\\
X3~X2)~np\_\_1){\unicdcdcdhd}(X1=k3\_finseq\_6~(u1\_struct\_0~(k15\_euclid~np\_\_2))~\\
X0~X2~X3))))))\end{array}
\label{hyp:ehcdfdpfkgpgchegbgoged}
\end{equation}
\begin{theorem}\label{thm:ehfdcdpfkgpgchegbgoged}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((\preoh v3\_funct\_1~\\
X2){\unicdcdcdhd}((v1\_finseq\_6~X2~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdcdcdhd}((v1\_topreal1~\\
X2){\unicdcdcdhd}((v2\_topreal1~X2){\unicdcdcdhd}((v1\_goboard5~X2){\unicdcdcdhd}((v2\_goboard5~X2){\unicdcdcdhd}\\
(m2\_finseq\_1~X2~(u1\_struct\_0~(k15\_euclid~np\_\_2)))))))))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m2\_finseq\_1~X3~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m2\_finseq\_1~X4~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}(((r1\_jordan4~\\
X2~X3~X0~X1){\unicdcdcdhd}(r1\_jordan4~X2~X4~X0~X1)){\unicdbdjdcd}(X3=X4))))))\end{array}$$
\end{theorem}
\end{document}
