\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{t42\_ltlaxio1 (TMEp8sm79HnqphBebKRK1Eb54xADQABpzfG)}
\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 $ k13\_ltlaxio1 : {\iota}$ be given.
Let $ r8\_ltlaxio1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_xxreal\_0 : {{\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 $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ 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 $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r7\_ltlaxio1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r5\_ltlaxio1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k7\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r6\_ltlaxio1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r4\_ltlaxio1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}(k2\_finseq\_1~np\_\_1=k1\_tarski~np\_\_1){\unicdcdcdhd}(k2\_finseq\_1~np\_\_2=k2\_tarski~\\
np\_\_1~np\_\_2)\end{array}
\label{hyp:ehcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}((\\
(r1\_xxreal\_0~X0~X1){\unicdcdcdhd}(r1\_xxreal\_0~X1~X0)){\unicdbdjdcd}(X0=X1)))\end{array}
\label{hyp:ehbdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_1){\unicdcdcdhd}(m2\_subset\_1~np\_\_1~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_1~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_1~k1\_numbers))\end{array}
\label{hyp:dhahdgbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 : \iota{\unicdbdjdcd}\iota{\unicdbdjdcd}o .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ({\unicdcdadad} X3 .  (\\
v7\_ordinal1~X3){\unicdbdjdcd}(\preoh (X3 \in k2\_finseq\_1~X2){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~X1){\unicdbdjdcd}(\preoh X0~X3~X4)))){\unicdbdjdcd}({\unicdcdaddd} X3 .  (m2\_finseq\_1~X3~X1){\unicdcdcdhd}((k4\_finseq\_1~\\
X3=k2\_finseq\_1~X2){\unicdcdcdhd}({\unicdcdadad} X4 .  (v7\_ordinal1~X4){\unicdbdjdcd}((X4 \in k2\_finseq\_1~\\
X2){\unicdbdjdcd}(X0~X4~(k1\_funct\_1~X3~X4))))))\end{array}
\label{hyp:dhfdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{{r1\_xxreal\_0}~{np\_\_1}}~{np\_\_1}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdpfchbd}
\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 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finseq\_1~X0))){\unicdbdjdcd}\\
(k4\_finseq\_1~X0=k9\_xtuple\_0~X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m2\_finseq\_1~X1~X0){\unicdbdjdcd}((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_finseq\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~\\
X0)))))\end{array}
\label{hyp:egehpfngcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finseq\_1~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m2\_subset\_1~X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}((X1=k3\_finseq\_1~\\
X0){\unicdbdjded}(k2\_finseq\_1~X1=k9\_xtuple\_0~X0)))\end{array}
\label{hyp:egddpfggjgogdhfgbhpfbd}
\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}((r8\_ltlaxio1~X0~X1){\unicdbdjded}({\unicdcdaddd} X2 .  \\
(m2\_finseq\_1~X2~k1\_hilbert1){\unicdcdcdhd}((k1\_funct\_1~X2~(k3\_finseq\_1~X2)=\\
X1){\unicdcdcdhd}((r1\_xxreal\_0~np\_\_1~(k3\_finseq\_1~X2)){\unicdcdcdhd}({\unicdcdadad} X3 .  (v7\_ordinal1~\\
X3){\unicdbdjdcd}(((r1\_xxreal\_0~np\_\_1~X3){\unicdcdcdhd}(r1\_xxreal\_0~X3~(k3\_finseq\_1~X2))){\unicdbdjdcd}\\
(r7\_ltlaxio1~X3~X2~X0))))))))\end{array}
\label{hyp:egddadpfmgehmgbgihjgpgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_1~X1~k1\_hilbert1){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~k1\_hilbert1)){\unicdbdjdcd}((r7\_ltlaxio1~\\
X0~X1~X2){\unicdbdjded}(\preoh (\preoh k1\_funct\_1~X1~X0 \in k13\_ltlaxio1){\unicdcdcdhd}((\preoh k1\_funct\_1~X1~\\
X0 \in X2){\unicdcdcdhd}(({\unicdcdadad} X3 .  (v7\_ordinal1~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (v7\_ordinal1~\\
X4){\unicdbdjdcd}(\preoh (r1\_xxreal\_0~np\_\_1~X3){\unicdcdcdhd}((\preoh r1\_xxreal\_0~X0~X3){\unicdcdcdhd}((r1\_xxreal\_0~\\
np\_\_1~X4){\unicdcdcdhd}((\preoh r1\_xxreal\_0~X0~X4){\unicdcdcdhd}((r5\_ltlaxio1~(k7\_partfun1~k1\_hilbert1~\\
X1~X3)~(k7\_partfun1~k1\_hilbert1~X1~X4)~(k7\_partfun1~k1\_hilbert1~\\
X1~X0)){\unicdcdcdid}(r6\_ltlaxio1~(k7\_partfun1~k1\_hilbert1~X1~X3)~(k7\_partfun1~\\
k1\_hilbert1~X1~X4)~(k7\_partfun1~k1\_hilbert1~X1~X0))))))))){\unicdcdcdhd}({\unicdcdadad} X3 .  \\
(v7\_ordinal1~X3){\unicdbdjdcd}(\preoh (r1\_xxreal\_0~np\_\_1~X3){\unicdcdcdhd}((\preoh r1\_xxreal\_0~X0~\\
X3){\unicdcdcdhd}(r4\_ltlaxio1~(k7\_partfun1~k1\_hilbert1~X1~X3)~(k7\_partfun1~\\
k1\_hilbert1~X1~X0)))))))))))\end{array}
\label{hyp:egcdjdpfmgehmgbgihjgpgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (X1=k1\_tarski~X0){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X1){\unicdbdjded}\\
(X2=X0))\end{array}
\label{hyp:egbdpfehbgchdhlgjg}
\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 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{X0}})}}}\label{hyp:dgdgcdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(v1\_relat\_1~X2)\end{array}
\label{hyp:dgdgbdpfchfgmgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedcdpfmgehmgbgihjgpgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~k1\_hilbert1)){\unicdbdjdcd}(((X0 \in k13\_ltlaxio1){\unicdcdcdid}(X0 \in X1)){\unicdbdjdcd}\\
(r8\_ltlaxio1~X1~X0)))\end{array}$$
\end{theorem}
\end{document}
