\documentclass{article}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t24\_jordan4 (TMQELeoPdonh6TB4LE7GrveqVRs5Gv73d51)}
\maketitle
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 $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ r3\_jordan4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_jordan4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_nat\_d : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ r1\_jordan4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ r2\_jordan4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\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}((r3\_jordan4~X0~X1~X2~\\
X3){\unicdbdjded}((r1\_jordan4~X0~X1~X2~X3){\unicdcdcdid}(r2\_jordan4~X0~X1~X2~X3))))))\end{array}
\label{hyp:egedpfkgpgchegbgoged}
\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}((r2\_jordan4~X0~X1~X2~\\
X3){\unicdbdjded}((r1\_xxreal\_0~np\_\_1~X2){\unicdcdcdhd}((r1\_xxreal\_0~(k2\_nat\_1~X2~np\_\_1)~\\
(k3\_finseq\_1~X0)){\unicdcdcdhd}((r1\_xxreal\_0~np\_\_1~X3){\unicdcdcdhd}((r1\_xxreal\_0~(k2\_nat\_1~\\
X3~np\_\_1)~(k3\_finseq\_1~X0)){\unicdcdcdhd}((k1\_funct\_1~X1~(k3\_finseq\_1~X1)=\\
k1\_funct\_1~X0~X3){\unicdcdcdhd}((r1\_xxreal\_0~np\_\_1~(k3\_finseq\_1~X1)){\unicdcdcdhd}((\preoh r1\_xxreal\_0~\\
(k3\_finseq\_1~X0)~(k3\_finseq\_1~X1)){\unicdcdcdhd}({\unicdcdadad} X4 .  (v7\_ordinal1~\\
X4){\unicdbdjdcd}(((r1\_xxreal\_0~np\_\_1~X4){\unicdcdcdhd}(r1\_xxreal\_0~X4~(k3\_finseq\_1~X1))){\unicdbdjdcd}\\
(k1\_funct\_1~X1~X4=k1\_funct\_1~X0~(k1\_jordan4~(k7\_nat\_d~(k2\_nat\_1~\\
(k3\_finseq\_1~X0)~X2)~X4)~X0)))))))))))))))\end{array}
\label{hyp:egddpfkgpgchegbgoged}
\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){\unicdbdjded}((r1\_xxreal\_0~np\_\_1~X2){\unicdcdcdhd}((r1\_xxreal\_0~(k2\_nat\_1~X2~np\_\_1)~\\
(k3\_finseq\_1~X0)){\unicdcdcdhd}((r1\_xxreal\_0~np\_\_1~X3){\unicdcdcdhd}((r1\_xxreal\_0~(k2\_nat\_1~\\
X3~np\_\_1)~(k3\_finseq\_1~X0)){\unicdcdcdhd}((k1\_funct\_1~X1~(k3\_finseq\_1~X1)=\\
k1\_funct\_1~X0~X3){\unicdcdcdhd}((r1\_xxreal\_0~np\_\_1~(k3\_finseq\_1~X1)){\unicdcdcdhd}((\preoh r1\_xxreal\_0~\\
(k3\_finseq\_1~X0)~(k3\_finseq\_1~X1)){\unicdcdcdhd}({\unicdcdadad} X4 .  (v7\_ordinal1~\\
X4){\unicdbdjdcd}(((r1\_xxreal\_0~np\_\_1~X4){\unicdcdcdhd}(r1\_xxreal\_0~X4~(k3\_finseq\_1~X1))){\unicdbdjdcd}\\
(k1\_funct\_1~X1~X4=k1\_funct\_1~X0~(k1\_jordan4~(k7\_nat\_d~(k2\_nat\_1~\\
X2~X4)~np\_\_1)~X0)))))))))))))))\end{array}
\label{hyp:egcdpfkgpgchegbgoged}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgidpfpgchegjgogbgmgbd}
\end{equation}
\begin{theorem}\label{thm:ehcdedpfkgpgchegbgoged}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v3\_funct\_1~X0){\unicdcdcdhd}((v1\_finseq\_6~\\
X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdcdcdhd}((v1\_topreal1~X0){\unicdcdcdhd}((v2\_topreal1~\\
X0){\unicdcdcdhd}((v1\_goboard5~X0){\unicdcdcdhd}((v2\_goboard5~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_1~X1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k5\_numbers){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~k5\_numbers){\unicdbdjdcd}((r3\_jordan4~X0~X1~X2~\\
X3){\unicdbdjdcd}((r1\_xxreal\_0~np\_\_1~X2){\unicdcdcdhd}((r1\_xxreal\_0~(k2\_nat\_1~X2~np\_\_1)~\\
(k3\_finseq\_1~X0)){\unicdcdcdhd}((r1\_xxreal\_0~np\_\_1~X3){\unicdcdcdhd}((r1\_xxreal\_0~(k2\_nat\_1~\\
X3~np\_\_1)~(k3\_finseq\_1~X0)){\unicdcdcdhd}((k1\_funct\_1~X1~(k3\_finseq\_1~X1)=\\
k1\_funct\_1~X0~X3){\unicdcdcdhd}((r1\_xxreal\_0~np\_\_1~(k3\_finseq\_1~X1)){\unicdcdcdhd}((\preoh r1\_xxreal\_0~\\
(k3\_finseq\_1~X0)~(k3\_finseq\_1~X1)){\unicdcdcdhd}(({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~k5\_numbers){\unicdbdjdcd}(((r1\_xxreal\_0~np\_\_1~X4){\unicdcdcdhd}(r1\_xxreal\_0~X4~(k3\_finseq\_1~\\
X1))){\unicdbdjdcd}(k1\_funct\_1~X1~X4=k1\_funct\_1~X0~(k1\_jordan4~(k7\_nat\_d~(\\
k2\_nat\_1~X2~X4)~np\_\_1)~X0)))){\unicdcdcdid}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k5\_numbers){\unicdbdjdcd}\\
(((r1\_xxreal\_0~np\_\_1~X4){\unicdcdcdhd}(r1\_xxreal\_0~X4~(k3\_finseq\_1~X1))){\unicdbdjdcd}\\
(k1\_funct\_1~X1~X4=k1\_funct\_1~X0~(k1\_jordan4~(k7\_nat\_d~(k2\_nat\_1~\\
(k3\_finseq\_1~X0)~X2)~X4)~X0))))))))))))))))\end{array}$$
\end{theorem}
\end{document}
