\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{t22\_jordan\_a (TMLw7M5v944cTYojWfvFgJJpbPe2nGnRXoY)}
\maketitle
Let $ v1\_topreal2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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 $ 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 $ m1\_jordan\_a : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_jordan\_a : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_jordan7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k7\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_topreal2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))){\unicdbdjdcd}(r1\_tarski~(k1\_jordan7~X0~X1~X2)~X0)))\end{array}
\label{hyp:ehgdpfkgpgchegbgogbdgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~X0~X1){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m2\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjded}{({{{m1\_finseq\_1}~{X1}}~{X0}})}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k4\_ordinal1}}}})}{\unicdcdcdhd}{({{v3\_ordinal1}~{k4\_ordinal1}})}}\label{hyp:ggdggdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_topreal2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_jordan\_a~X1~X0){\unicdbdjdcd}(m2\_finseq\_1~\\
X1~(u1\_struct\_0~(k15\_euclid~np\_\_2))))\end{array}
\label{hyp:egehpfngbdpfkgpgchegbgogpfbg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_finseq\_1~X1~X0){\unicdbdjdcd}((v1\_relat\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~X1)))\end{array}
\label{hyp:egehpfngbdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v5\_relat\_1~\\
X1~X0){\unicdcdcdhd}(v1\_funct\_1~X1))){\unicdbdjdcd}(m1\_subset\_1~(k7\_partfun1~X0~X1~X2)~X0)\end{array}
\label{hyp:egehpflghdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k5\_numbers}}~{({{k1\_zfmisc\_1}~{k1\_numbers}})}}\label{hyp:egehpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_topreal2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_jordan\_a~X2~X0){\unicdbdjdcd}(((r1\_xxreal\_0~np\_\_1~X1){\unicdbdjdcd}((r1\_xxreal\_0~(\\
k3\_finseq\_1~X2)~X1){\unicdcdcdid}(k2\_jordan\_a~X0~X1~X2=k1\_jordan7~X0~(k7\_partfun1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~X2~X1)~(k7\_partfun1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~X2~(k1\_nat\_1~X1~np\_\_1))))){\unicdcdcdhd}((\preoh (r1\_xxreal\_0~\\
np\_\_1~X1){\unicdcdcdhd}(\preoh r1\_xxreal\_0~(k3\_finseq\_1~X2)~X1)){\unicdbdjdcd}(k2\_jordan\_a~X0~\\
X1~X2=k1\_jordan7~X0~(k7\_partfun1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~\\
X2~(k3\_finseq\_1~X2))~(k7\_partfun1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~\\
X2~np\_\_1))))))\end{array}
\label{hyp:egedpfkgpgchegbgogpfbg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgidpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m1\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjdcd}{({{{v5\_relat\_1}~{X1}}~{X0}})}}}}\label{hyp:dgdgddpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v1\_xboole\_0~X1))\end{array}
\label{hyp:dgdgbdpfdhfhcgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdcdpfkgpgchegbgogpfbg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_topreal2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_subset\_1~X1~k1\_numbers~\\
k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_jordan\_a~X2~X0){\unicdbdjdcd}((X1 \in k4\_finseq\_1~\\
X2){\unicdbdjdcd}(r1\_tarski~(k2\_jordan\_a~X0~X1~X2)~X0))))\end{array}$$
\end{theorem}
\end{document}
