\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{t37\_ltlaxio1 (TMRxNL6SuDmGAcxt4cgqedX8fSjRwqNfjkQ)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_hilbert1 : {\iota}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_ltlaxio1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_ltlaxio1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_ltlaxio1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_ltlaxio1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ltlaxio1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_ltlaxio1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v9\_ltlaxio1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r3\_ltlaxio1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\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 $ k10\_ltlaxio1 : {\iota}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k6\_margrel1 : {\iota}$ be given.
Let $ k11\_ltlaxio1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k3\_hilbert1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_hilbert1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_ltlaxio1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_ltlaxio1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k5\_ltlaxio1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_ltlaxio1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_ltlaxio1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_ltlaxio1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r2\_ltlaxio1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_ltlaxio1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~k5\_numbers~(k1\_zfmisc\_1~k10\_ltlaxio1)){\unicdcdcdhd}\\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k1\_zfmisc\_1~\\
k10\_ltlaxio1)))))){\unicdbdjdcd}(k3\_funct\_2~(k2\_zfmisc\_1~k5\_numbers~k1\_hilbert1)~\\
k6\_margrel1~(k11\_ltlaxio1~X3)~(k1\_domain\_1~k5\_numbers~k1\_hilbert1~\\
X2~(k3\_hilbert1~(k4\_hilbert1~X0~X1)~(k2\_ltlaxio1~(k7\_ltlaxio1~\\
X1))))=np\_\_1))))\end{array}
\label{hyp:ehcdbdpfmgehmgbgihjgpgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~k5\_numbers~(k1\_zfmisc\_1~k10\_ltlaxio1)){\unicdcdcdhd}\\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k1\_zfmisc\_1~\\
k10\_ltlaxio1)))))){\unicdbdjdcd}(k3\_funct\_2~(k2\_zfmisc\_1~k5\_numbers~k1\_hilbert1)~\\
k6\_margrel1~(k11\_ltlaxio1~X3)~(k1\_domain\_1~k5\_numbers~k1\_hilbert1~\\
X2~(k3\_hilbert1~(k5\_ltlaxio1~(k2\_ltlaxio1~X0)~(k2\_ltlaxio1~(k4\_ltlaxio1~\\
X1~(k4\_hilbert1~X1~X0))))~(k4\_hilbert1~X1~X0)))=np\_\_1))))\end{array}
\label{hyp:ehcdadpfmgehmgbgihjgpgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~k5\_numbers~(k1\_zfmisc\_1~k10\_ltlaxio1)){\unicdcdcdhd}\\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k1\_zfmisc\_1~\\
k10\_ltlaxio1)))))){\unicdbdjdcd}(k3\_funct\_2~(k2\_zfmisc\_1~k5\_numbers~k1\_hilbert1)~\\
k6\_margrel1~(k11\_ltlaxio1~X3)~(k1\_domain\_1~k5\_numbers~k1\_hilbert1~\\
X2~(k3\_hilbert1~(k4\_hilbert1~X0~X1)~(k5\_ltlaxio1~(k2\_ltlaxio1~\\
X1)~(k2\_ltlaxio1~(k4\_ltlaxio1~X0~(k4\_hilbert1~X0~X1))))))=np\_\_1))))\end{array}
\label{hyp:ehbdjdpfmgehmgbgihjgpgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~\\
k5\_numbers~(k1\_zfmisc\_1~k10\_ltlaxio1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k5\_numbers~(k1\_zfmisc\_1~k10\_ltlaxio1)))))){\unicdbdjdcd}(k3\_funct\_2~\\
(k2\_zfmisc\_1~k5\_numbers~k1\_hilbert1)~k6\_margrel1~(k11\_ltlaxio1~\\
X2)~(k1\_domain\_1~k5\_numbers~k1\_hilbert1~X1~(k3\_hilbert1~(k6\_ltlaxio1~\\
X0)~(k4\_ltlaxio1~X0~(k2\_ltlaxio1~(k6\_ltlaxio1~X0)))))=np\_\_1)))\end{array}
\label{hyp:ehbdidpfmgehmgbgihjgpgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~k5\_numbers~(k1\_zfmisc\_1~k10\_ltlaxio1)){\unicdcdcdhd}\\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k1\_zfmisc\_1~\\
k10\_ltlaxio1)))))){\unicdbdjdcd}(k3\_funct\_2~(k2\_zfmisc\_1~k5\_numbers~k1\_hilbert1)~\\
k6\_margrel1~(k11\_ltlaxio1~X3)~(k1\_domain\_1~k5\_numbers~k1\_hilbert1~\\
X2~(k3\_hilbert1~(k2\_ltlaxio1~(k3\_hilbert1~X0~X1))~(k3\_hilbert1~\\
(k2\_ltlaxio1~X0)~(k2\_ltlaxio1~X1))))=np\_\_1))))\end{array}
\label{hyp:ehbdhdpfmgehmgbgihjgpgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~\\
k5\_numbers~(k1\_zfmisc\_1~k10\_ltlaxio1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k5\_numbers~(k1\_zfmisc\_1~k10\_ltlaxio1)))))){\unicdbdjdcd}(k3\_funct\_2~\\
(k2\_zfmisc\_1~k5\_numbers~k1\_hilbert1)~k6\_margrel1~(k11\_ltlaxio1~\\
X2)~(k1\_domain\_1~k5\_numbers~k1\_hilbert1~X1~(k3\_hilbert1~(k2\_ltlaxio1~\\
(k1\_ltlaxio1~X0))~(k1\_ltlaxio1~(k2\_ltlaxio1~X0))))=np\_\_1)))\end{array}
\label{hyp:ehbdgdpfmgehmgbgihjgpgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~\\
k5\_numbers~(k1\_zfmisc\_1~k10\_ltlaxio1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k5\_numbers~(k1\_zfmisc\_1~k10\_ltlaxio1)))))){\unicdbdjdcd}(k3\_funct\_2~\\
(k2\_zfmisc\_1~k5\_numbers~k1\_hilbert1)~k6\_margrel1~(k11\_ltlaxio1~\\
X2)~(k1\_domain\_1~k5\_numbers~k1\_hilbert1~X1~(k3\_hilbert1~(k1\_ltlaxio1~\\
(k2\_ltlaxio1~X0))~(k2\_ltlaxio1~(k1\_ltlaxio1~X0))))=np\_\_1)))\end{array}
\label{hyp:ehbdfdpfmgehmgbgihjgpgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_hilbert1){\unicdbdjdcd}((v9\_ltlaxio1~X0){\unicdbdjded}(\\
{\unicdcdaddd} X1 .  (m1\_subset\_1~X1~k1\_hilbert1){\unicdcdcdhd}({\unicdcdaddd} X2 .  (m1\_subset\_1~\\
X2~k1\_hilbert1){\unicdcdcdhd}(X0=k3\_hilbert1~(k4\_hilbert1~X1~X2)~(k2\_ltlaxio1~\\
(k7\_ltlaxio1~X2))))))\end{array}
\label{hyp:egcdidpfmgehmgbgihjgpgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_hilbert1){\unicdbdjdcd}((v8\_ltlaxio1~X0){\unicdbdjded}(\\
{\unicdcdaddd} X1 .  (m1\_subset\_1~X1~k1\_hilbert1){\unicdcdcdhd}({\unicdcdaddd} X2 .  (m1\_subset\_1~\\
X2~k1\_hilbert1){\unicdcdcdhd}(X0=k3\_hilbert1~(k5\_ltlaxio1~(k2\_ltlaxio1~X2)~\\
(k2\_ltlaxio1~(k4\_ltlaxio1~X1~(k4\_hilbert1~X1~X2))))~(k4\_hilbert1~\\
X1~X2)))))\end{array}
\label{hyp:egcdhdpfmgehmgbgihjgpgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_hilbert1){\unicdbdjdcd}((v7\_ltlaxio1~X0){\unicdbdjded}(\\
{\unicdcdaddd} X1 .  (m1\_subset\_1~X1~k1\_hilbert1){\unicdcdcdhd}({\unicdcdaddd} X2 .  (m1\_subset\_1~\\
X2~k1\_hilbert1){\unicdcdcdhd}(X0=k3\_hilbert1~(k4\_hilbert1~X1~X2)~(k5\_ltlaxio1~\\
(k2\_ltlaxio1~X2)~(k2\_ltlaxio1~(k4\_ltlaxio1~X1~(k4\_hilbert1~X1~\\
X2))))))))\end{array}
\label{hyp:egcdgdpfmgehmgbgihjgpgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_hilbert1){\unicdbdjdcd}((v6\_ltlaxio1~X0){\unicdbdjded}(\\
{\unicdcdaddd} X1 .  (m1\_subset\_1~X1~k1\_hilbert1){\unicdcdcdhd}(X0=k3\_hilbert1~(k6\_ltlaxio1~\\
X1)~(k4\_ltlaxio1~X1~(k2\_ltlaxio1~(k6\_ltlaxio1~X1))))))\end{array}
\label{hyp:egcdfdpfmgehmgbgihjgpgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_hilbert1){\unicdbdjdcd}((v5\_ltlaxio1~X0){\unicdbdjded}(\\
{\unicdcdaddd} X1 .  (m1\_subset\_1~X1~k1\_hilbert1){\unicdcdcdhd}({\unicdcdaddd} X2 .  (m1\_subset\_1~\\
X2~k1\_hilbert1){\unicdcdcdhd}(X0=k3\_hilbert1~(k2\_ltlaxio1~(k3\_hilbert1~X1~\\
X2))~(k3\_hilbert1~(k2\_ltlaxio1~X1)~(k2\_ltlaxio1~X2))))))\end{array}
\label{hyp:egcdedpfmgehmgbgihjgpgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_hilbert1){\unicdbdjdcd}((v4\_ltlaxio1~X0){\unicdbdjded}(\\
{\unicdcdaddd} X1 .  (m1\_subset\_1~X1~k1\_hilbert1){\unicdcdcdhd}(X0=k3\_hilbert1~(k2\_ltlaxio1~\\
(k1\_ltlaxio1~X1))~(k1\_ltlaxio1~(k2\_ltlaxio1~X1)))))\end{array}
\label{hyp:egcdddpfmgehmgbgihjgpgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_hilbert1){\unicdbdjdcd}((v3\_ltlaxio1~X0){\unicdbdjded}(\\
{\unicdcdaddd} X1 .  (m1\_subset\_1~X1~k1\_hilbert1){\unicdcdcdhd}(X0=k3\_hilbert1~(k1\_ltlaxio1~\\
(k2\_ltlaxio1~X1))~(k2\_ltlaxio1~(k1\_ltlaxio1~X1)))))\end{array}
\label{hyp:egcdcdpfmgehmgbgihjgpgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_hilbert1)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~k1\_hilbert1){\unicdbdjdcd}((r3\_ltlaxio1~X0~X1){\unicdbdjded}({\unicdcdadad} X2 .  \\
((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~k5\_numbers~(k1\_zfmisc\_1~k10\_ltlaxio1)){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k1\_zfmisc\_1~\\
k10\_ltlaxio1)))))){\unicdbdjdcd}((r2\_ltlaxio1~X2~X0){\unicdbdjdcd}(r1\_ltlaxio1~X2~X1)))))\end{array}
\label{hyp:egbdedpfmgehmgbgihjgpgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~(k1\_zfmisc\_1~\\
k10\_ltlaxio1)){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~\\
(k1\_zfmisc\_1~k10\_ltlaxio1)))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~\\
k1\_hilbert1){\unicdbdjdcd}((r1\_ltlaxio1~X0~X1){\unicdbdjded}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~k5\_numbers){\unicdbdjdcd}(k3\_funct\_2~(k2\_zfmisc\_1~k5\_numbers~k1\_hilbert1)~\\
k6\_margrel1~(k11\_ltlaxio1~X0)~(k1\_domain\_1~k5\_numbers~k1\_hilbert1~\\
X2~X1)=np\_\_1))))\end{array}
\label{hyp:egbdcdpfmgehmgbgihjgpgbd}
\end{equation}
\begin{theorem}\label{thm:ehddhdpfmgehmgbgihjgpgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~k1\_hilbert1)){\unicdbdjdcd}((\preoh (\preoh v3\_ltlaxio1~X0){\unicdcdcdhd}((\preoh v4\_ltlaxio1~\\
X0){\unicdcdcdhd}((\preoh v5\_ltlaxio1~X0){\unicdcdcdhd}((\preoh v6\_ltlaxio1~X0){\unicdcdcdhd}((\preoh v7\_ltlaxio1~X0){\unicdcdcdhd}\\
((\preoh v8\_ltlaxio1~X0){\unicdcdcdhd}(\preoh v9\_ltlaxio1~X0))))))){\unicdbdjdcd}(r3\_ltlaxio1~X1~\\
X0)))\end{array}$$
\end{theorem}
\end{document}
