\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{t34\_jordan1h (TMcLYszvX4NAwYYdJ8QF4Q5zVpQzzatFbic)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
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 $ v3\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_matrix\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_goboard1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_goboard1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_goboard1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_goboard1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_finseq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_goboard1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ k5\_numbers : {\iota}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k2\_matrix\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_matrix\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_matrix\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_goboard2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k4\_pscomp\_1 : {\iota}$ be given.
Let $ k2\_jordan1h : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_pscomp\_1 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~(u1\_struct\_0~(\\
k15\_euclid~np\_\_2)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v3\_relat\_1~X1){\unicdcdcdhd}((v1\_matrix\_1~\\
X1){\unicdcdcdhd}((v2\_goboard1~X1){\unicdcdcdhd}((v3\_goboard1~X1){\unicdcdcdhd}((v4\_goboard1~X1){\unicdcdcdhd}\\
((v5\_goboard1~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~(k3\_finseq\_2~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2)))))))))){\unicdbdjdcd}(((k7\_relset\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~k1\_numbers~k4\_pscomp\_1~(k2\_relset\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~X0)=k7\_relset\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~k1\_numbers~\\
k4\_pscomp\_1~(k2\_jordan1h~(u1\_struct\_0~(k15\_euclid~np\_\_2))~X1)){\unicdcdcdhd}\\
(k7\_relset\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~k1\_numbers~k5\_pscomp\_1~\\
(k2\_relset\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~X0)=k7\_relset\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~k1\_numbers~k5\_pscomp\_1~(k2\_jordan1h~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~X1))){\unicdbdjdcd}(X1=k2\_goboard2~X0)))\end{array}
\label{hyp:ehddddpfkgpgchegbgogbdig}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~(u1\_struct\_0~(\\
k15\_euclid~np\_\_2)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v3\_relat\_1~X1){\unicdcdcdhd}((v1\_matrix\_1~\\
X1){\unicdcdcdhd}((v2\_goboard1~X1){\unicdcdcdhd}((v3\_goboard1~X1){\unicdcdcdhd}((v4\_goboard1~X1){\unicdcdcdhd}\\
((v5\_goboard1~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~(k3\_finseq\_2~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2)))))))))){\unicdbdjdcd}((r1\_goboard1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~X0~X1){\unicdbdjdcd}(({\unicdcdadad} X2 .  (m2\_subset\_1~X2~k1\_numbers~k5\_numbers){\unicdbdjdcd}\\
(\preoh (k4\_tarski~X2~np\_\_1 \in k2\_matrix\_1~X1){\unicdcdcdhd}(k3\_matrix\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~X1~X2~np\_\_1 \in k2\_relset\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~X0))){\unicdcdcdid}(({\unicdcdadad} X2 .  (m2\_subset\_1~X2~k1\_numbers~k5\_numbers){\unicdbdjdcd}\\
(\preoh (k4\_tarski~X2~(k1\_matrix\_1~X1) \in k2\_matrix\_1~X1){\unicdcdcdhd}(k3\_matrix\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~X1~X2~(k1\_matrix\_1~X1) \in k2\_relset\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~X0))){\unicdcdcdid}(k7\_relset\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~k1\_numbers~k5\_pscomp\_1~(k2\_relset\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~X0)=k7\_relset\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~k1\_numbers~k5\_pscomp\_1~(k2\_jordan1h~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~X1))))))\end{array}
\label{hyp:ehddbdpfkgpgchegbgogbdig}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~(u1\_struct\_0~(\\
k15\_euclid~np\_\_2)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v3\_relat\_1~X1){\unicdcdcdhd}((v1\_matrix\_1~\\
X1){\unicdcdcdhd}((v2\_goboard1~X1){\unicdcdcdhd}((v3\_goboard1~X1){\unicdcdcdhd}((v4\_goboard1~X1){\unicdcdcdhd}\\
((v5\_goboard1~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~(k3\_finseq\_2~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2)))))))))){\unicdbdjdcd}((r1\_goboard1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~X0~X1){\unicdbdjdcd}(({\unicdcdadad} X2 .  (m2\_subset\_1~X2~k1\_numbers~k5\_numbers){\unicdbdjdcd}\\
(\preoh (k4\_tarski~np\_\_1~X2 \in k2\_matrix\_1~X1){\unicdcdcdhd}(k3\_matrix\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~X1~np\_\_1~X2 \in k2\_relset\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~X0))){\unicdcdcdid}(({\unicdcdadad} X2 .  (m2\_subset\_1~X2~k1\_numbers~k5\_numbers){\unicdbdjdcd}\\
(\preoh (k4\_tarski~(k3\_finseq\_1~X1)~X2 \in k2\_matrix\_1~X1){\unicdcdcdhd}(k3\_matrix\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~X1~(k3\_finseq\_1~X1)~X2 \in k2\_relset\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~X0))){\unicdcdcdid}(k7\_relset\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~k1\_numbers~k4\_pscomp\_1~(k2\_relset\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~X0)=k7\_relset\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~k1\_numbers~k4\_pscomp\_1~(k2\_jordan1h~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~X1))))))\end{array}
\label{hyp:ehddadpfkgpgchegbgogbdig}
\end{equation}
\begin{theorem}\label{thm:ehddedpfkgpgchegbgogbdig}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~(u1\_struct\_0~(\\
k15\_euclid~np\_\_2)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v3\_relat\_1~X1){\unicdcdcdhd}((v1\_matrix\_1~\\
X1){\unicdcdcdhd}((v2\_goboard1~X1){\unicdcdcdhd}((v3\_goboard1~X1){\unicdcdcdhd}((v4\_goboard1~X1){\unicdcdcdhd}\\
((v5\_goboard1~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~(k3\_finseq\_2~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2)))))))))){\unicdbdjdcd}((r1\_goboard1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~X0~X1){\unicdbdjdcd}(({\unicdcdadad} X2 .  (m2\_subset\_1~X2~k1\_numbers~k5\_numbers){\unicdbdjdcd}\\
(\preoh (k4\_tarski~np\_\_1~X2 \in k2\_matrix\_1~X1){\unicdcdcdhd}(k3\_matrix\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~X1~np\_\_1~X2 \in k2\_relset\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~X0))){\unicdcdcdid}(({\unicdcdadad} X2 .  (m2\_subset\_1~X2~k1\_numbers~k5\_numbers){\unicdbdjdcd}\\
(\preoh (k4\_tarski~X2~np\_\_1 \in k2\_matrix\_1~X1){\unicdcdcdhd}(k3\_matrix\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~X1~X2~np\_\_1 \in k2\_relset\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~X0))){\unicdcdcdid}(({\unicdcdadad} X2 .  (m2\_subset\_1~X2~k1\_numbers~k5\_numbers){\unicdbdjdcd}\\
(\preoh (k4\_tarski~(k3\_finseq\_1~X1)~X2 \in k2\_matrix\_1~X1){\unicdcdcdhd}(k3\_matrix\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~X1~(k3\_finseq\_1~X1)~X2 \in k2\_relset\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~X0))){\unicdcdcdid}(({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~k1\_numbers~k5\_numbers){\unicdbdjdcd}(\preoh (k4\_tarski~X2~(k1\_matrix\_1~X1) \in k2\_matrix\_1~\\
X1){\unicdcdcdhd}(k3\_matrix\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~X1~X2~(k1\_matrix\_1~\\
X1) \in k2\_relset\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~X0))){\unicdcdcdid}(X1=\\
k2\_goboard2~X0)))))))\end{array}$$
\end{theorem}
\end{document}
