\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{t68\_chain\_1 (TMY97Adin3qqUxFucBDS5XR5yDFFBfB4P8d)}
\maketitle
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 $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_chain\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ k4\_chain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k15\_chain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ k1\_chain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k11\_chain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k7\_chain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
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}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)){\unicdbdjdcd}(k1\_chain\_1~\\
X0~X1=k1\_zfmisc\_1~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfdgigbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_finset\_1}~{k4\_ordinal1}}}}\label{hyp:ggdghdpfdgbgchegpfbd}
\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 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~k5\_numbers)){\unicdcdcdhd}((m1\_chain\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X2~k5\_numbers))){\unicdbdjdcd}\\
((\preoh v1\_xboole\_0~(k4\_chain\_1~X0~X1~X2)){\unicdcdcdhd}((v1\_finset\_1~(k4\_chain\_1~\\
X0~X1~X2)){\unicdcdcdhd}(m1\_subset\_1~(k4\_chain\_1~X0~X1~X2)~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
(k1\_euclid~X0))))))\end{array}
\label{hyp:egehpflgedpfdgigbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~k5\_numbers)){\unicdcdcdhd}((m1\_chain\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X2~k5\_numbers))){\unicdbdjdcd}\\
((\preoh v2\_struct\_0~(k15\_chain\_1~X0~X1~X2)){\unicdcdcdhd}((v8\_algstr\_0~(k15\_chain\_1~\\
X0~X1~X2)){\unicdcdcdhd}((v13\_algstr\_0~(k15\_chain\_1~X0~X1~X2)){\unicdcdcdhd}((v2\_rlvect\_1~\\
(k15\_chain\_1~X0~X1~X2)){\unicdcdcdhd}((v3\_rlvect\_1~(k15\_chain\_1~X0~X1~X2)){\unicdcdcdhd}\\
((v4\_rlvect\_1~(k15\_chain\_1~X0~X1~X2)){\unicdcdcdhd}(l2\_algstr\_0~(k15\_chain\_1~\\
X0~X1~X2))))))))\end{array}
\label{hyp:egehpflgbdfdpfdgigbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m2\_subset\_1~X0~k1\_numbers~k5\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_chain\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~X2~k1\_numbers~\\
k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  ((\preoh v2\_struct\_0~X3){\unicdcdcdhd}((v8\_algstr\_0~X3){\unicdcdcdhd}\\
((v13\_algstr\_0~X3){\unicdcdcdhd}((v2\_rlvect\_1~X3){\unicdcdcdhd}((v3\_rlvect\_1~X3){\unicdcdcdhd}((v4\_rlvect\_1~\\
X3){\unicdcdcdhd}(l2\_algstr\_0~X3))))))){\unicdbdjdcd}((X3=k15\_chain\_1~X0~X1~X2){\unicdbdjded}((u1\_struct\_0~\\
X3=k1\_chain\_1~(k1\_zfmisc\_1~(k1\_euclid~X0))~(k4\_chain\_1~X0~X1~X2)){\unicdcdcdhd}\\
((k4\_struct\_0~X3=k11\_chain\_1~X0~X1~X2){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~X3)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~\\
X3)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(k1\_zfmisc\_1~(k4\_chain\_1~X0~\\
X1~X2))){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~(k1\_zfmisc\_1~(k4\_chain\_1~\\
X0~X1~X2))){\unicdbdjdcd}(((X4=X6){\unicdcdcdhd}(X5=X7)){\unicdbdjdcd}(k3\_rlvect\_1~X3~X4~X5=k7\_chain\_1~\\
X0~X1~X2~X6~X7))))))))))))\end{array}
\label{hyp:egbdgdpfdgigbgjgogpfbd}
\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}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_finset\_1}~{X0}})}}}\label{hyp:dgdgbdpfggjgogdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehgdidpfdgigbgjgogpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m2\_subset\_1~X1~k1\_numbers~k5\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_chain\_1~X2~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k4\_chain\_1~X1~X2~X0))){\unicdbdjded}(m1\_subset\_1~X3~(u1\_struct\_0~(k15\_chain\_1~\\
X1~X2~X0))))))\end{array}$$
\end{theorem}
\end{document}
