\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{t32\_jordan1k (TMJq26YV2skVytR331vaxZFsqK687FFNecT)}
\maketitle
Let $ m1\_subset\_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 $ k1\_numbers : {\iota}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_jgraph\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k19\_euclid : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k17\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k18\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))){\unicdbdjdcd}(k1\_rlvect\_1~(k15\_euclid~np\_\_2)~X1~X0=k19\_euclid~\\
(k4\_real\_1~X0~(k17\_euclid~X1))~(k4\_real\_1~X0~(k18\_euclid~X1))))\end{array}
\label{hyp:ehfdhdpffgfhdgmgjgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
(k3\_rlvect\_1~(k15\_euclid~np\_\_2)~X0~X1=k19\_euclid~(k7\_real\_1~(\\
k17\_euclid~X0)~(k17\_euclid~X1))~(k7\_real\_1~(k18\_euclid~X0)~(k18\_euclid~\\
X1))))\end{array}
\label{hyp:ehfdfdpffgfhdgmgjgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}((k17\_euclid~\\
(k19\_euclid~X0~X1)=X0){\unicdcdcdhd}(k18\_euclid~(k19\_euclid~X0~X1)=X1)))\end{array}
\label{hyp:ehfdcdpffgfhdgmgjgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}((k17\_euclid~(k1\_rlvect\_1~(k15\_euclid~\\
np\_\_2)~X0~X1)=k4\_real\_1~X1~(k17\_euclid~X0)){\unicdcdcdhd}(k18\_euclid~(k1\_rlvect\_1~\\
(k15\_euclid~np\_\_2)~X0~X1)=k4\_real\_1~X1~(k18\_euclid~X0))))\end{array}
\label{hyp:ehedpfehpgahchfgbgmgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xreal\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~k1\_numbers)){\unicdbdjdcd}\\
(m1\_subset\_1~(k4\_real\_1~X0~X1)~k1\_numbers)\end{array}
\label{hyp:egehpflgedpfchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_xreal\_0~X0){\unicdcdcdhd}\\
((v1\_xreal\_0~X1){\unicdcdcdhd}((v1\_xreal\_0~X2){\unicdcdcdhd}(v1\_xreal\_0~X3)))){\unicdbdjdcd}((v1\_funct\_1~\\
(k2\_jgraph\_2~X0~X1~X2~X3)){\unicdcdcdhd}((v1\_funct\_2~(k2\_jgraph\_2~X0~X1~X2~X3)~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdcdcdhd}\\
(m1\_subset\_1~(k2\_jgraph\_2~X0~X1~X2~X3)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~(u1\_struct\_0~(k15\_euclid~np\_\_2)))))))\end{array}
\label{hyp:egehpflgcdpfkghgchbgahigpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xreal\_0~X0){\unicdcdcdhd}(v1\_xreal\_0~X1)){\unicdbdjdcd}(m1\_subset\_1~\\
(k19\_euclid~X0~X1)~(u1\_struct\_0~(k15\_euclid~np\_\_2)))\end{array}
\label{hyp:egehpflgbdjdpffgfhdgmgjgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
(m1\_subset\_1~(k18\_euclid~X0)~k1\_numbers)\end{array}
\label{hyp:egehpflgbdidpffgfhdgmgjgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
(m1\_subset\_1~(k17\_euclid~X0)~k1\_numbers)\end{array}
\label{hyp:egehpflgbdhdpffgfhdgmgjgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xreal\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_xreal\_0~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~\\
X4){\unicdcdcdhd}((v1\_funct\_2~X4~(u1\_struct\_0~(k15\_euclid~np\_\_2))~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~(u1\_struct\_0~(k15\_euclid~np\_\_2))))))){\unicdbdjdcd}\\
((X4=k2\_jgraph\_2~X0~X1~X2~X3){\unicdbdjded}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))){\unicdbdjdcd}(k3\_funct\_2~(u1\_struct\_0~(k15\_euclid~np\_\_2))~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~X4~X5=k19\_euclid~(k7\_real\_1~\\
(k4\_real\_1~X0~(k17\_euclid~X5))~X1)~(k7\_real\_1~(k4\_real\_1~X2~(k18\_euclid~\\
X5))~X3))))))))\end{array}
\label{hyp:egcdpfkghgchbgahigpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xreal\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~k1\_numbers)){\unicdbdjdcd}\\
(k4\_real\_1~X0~X1=k4\_real\_1~X1~X0)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgedpfchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgbdpfihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehddcdpfkgpgchegbgogbdlg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~k1\_numbers){\unicdbdjdcd}(k3\_funct\_2~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~(u1\_struct\_0~(k15\_euclid~np\_\_2))~\\
(k2\_jgraph\_2~X1~X2~X1~X3)~X0=k3\_rlvect\_1~(k15\_euclid~np\_\_2)~(k1\_rlvect\_1~\\
(k15\_euclid~np\_\_2)~X0~X1)~(k19\_euclid~X2~X3)))))\end{array}$$
\end{theorem}
\end{document}
