\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{t6\_ltlaxio1 (TMKVQ4BF1jtgTJ1WSaVXFn9XQ3ZiXgcXwia)}
\maketitle
Let $ m1\_subset\_1 : {{\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 $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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 $ k1\_hilbert1 : {\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\_ltlaxio1 : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k1\_ltlaxio1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k2\_hilbert1 : {\iota}$ be given.
Let $ k1\_hilbert2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_hilbert1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_xboolean : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_hilbert1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ 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~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~(k1\_ltlaxio1~\\
X0))=np\_\_1){\unicdbdjded}(k3\_funct\_2~(k2\_zfmisc\_1~k5\_numbers~k1\_hilbert1)~\\
k6\_margrel1~(k11\_ltlaxio1~X2)~(k1\_domain\_1~k5\_numbers~k1\_hilbert1~\\
X1~X0)=k6\_numbers))))\end{array}
\label{hyp:ehfdpfmgehmgbgihjgpgbd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k2\_hilbert1}}~{k1\_hilbert1}}\label{hyp:egehpflgcdpfigjgmgcgfgchehbd}
\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}((v1\_funct\_1~(k11\_ltlaxio1~\\
X0)){\unicdcdcdhd}((v1\_funct\_2~(k11\_ltlaxio1~X0)~(k2\_zfmisc\_1~k5\_numbers~\\
k1\_hilbert1)~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~(k11\_ltlaxio1~X0)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_hilbert1)~k6\_margrel1)))))\end{array}
\label{hyp:egehpflgbdbdpfmgehmgbgihjgpgbd}
\end{equation}
Assume the following.
\begin{equation}
{{k3\_ltlaxio1}={{k1\_ltlaxio1}~{k2\_hilbert1}}}\label{hyp:egddpfmgehmgbgihjgpgbd}
\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 .  ((v1\_funct\_1~X1){\unicdcdcdhd}\\
((v1\_funct\_2~X1~(k2\_zfmisc\_1~k5\_numbers~k1\_hilbert1)~k6\_margrel1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~\\
k1\_hilbert1)~k6\_margrel1))))){\unicdbdjdcd}((X1=k11\_ltlaxio1~X0){\unicdbdjded}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~k5\_numbers){\unicdbdjdcd}((k3\_funct\_2~(k2\_zfmisc\_1~k5\_numbers~\\
k1\_hilbert1)~k6\_margrel1~X1~(k1\_domain\_1~k5\_numbers~k1\_hilbert1~\\
X2~k2\_hilbert1)=k6\_numbers){\unicdcdcdhd}(({\unicdcdadad} X3 .  (m1\_subset\_1~X3~k5\_numbers){\unicdbdjdcd}\\
((k3\_funct\_2~(k2\_zfmisc\_1~k5\_numbers~k1\_hilbert1)~k6\_margrel1~\\
X1~(k1\_domain\_1~k5\_numbers~k1\_hilbert1~X2~(k1\_hilbert2~X3))=np\_\_1){\unicdbdjded}\\
(k1\_hilbert2~X3 \in k3\_funct\_2~k5\_numbers~(k1\_zfmisc\_1~k10\_ltlaxio1)~\\
X0~X2))){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~k1\_hilbert1){\unicdbdjdcd}((k3\_funct\_2~(k2\_zfmisc\_1~k5\_numbers~\\
k1\_hilbert1)~k6\_margrel1~X1~(k1\_domain\_1~k5\_numbers~k1\_hilbert1~\\
X2~(k3\_hilbert1~X3~X4))=k6\_xboolean~(k3\_funct\_2~(k2\_zfmisc\_1~\\
k5\_numbers~k1\_hilbert1)~k6\_margrel1~X1~(k1\_domain\_1~k5\_numbers~\\
k1\_hilbert1~X2~X3))~(k3\_funct\_2~(k2\_zfmisc\_1~k5\_numbers~k1\_hilbert1)~\\
k6\_margrel1~X1~(k1\_domain\_1~k5\_numbers~k1\_hilbert1~X2~X4))){\unicdcdcdhd}(\\
(\preoh (k3\_funct\_2~(k2\_zfmisc\_1~k5\_numbers~k1\_hilbert1)~k6\_margrel1~\\
X1~(k1\_domain\_1~k5\_numbers~k1\_hilbert1~X2~(k4\_hilbert1~X3~X4))=\\
np\_\_1){\unicdcdcdhd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~k5\_numbers){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~\\
X5~k6\_numbers){\unicdcdcdhd}((k3\_funct\_2~(k2\_zfmisc\_1~k5\_numbers~k1\_hilbert1)~\\
k6\_margrel1~X1~(k1\_domain\_1~k5\_numbers~k1\_hilbert1~(k2\_nat\_1~\\
X2~X5)~X4)=np\_\_1){\unicdcdcdhd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~k5\_numbers){\unicdbdjdcd}((\\
r1\_xxreal\_0~np\_\_1~X6){\unicdbdjdcd}((r1\_xxreal\_0~X5~X6){\unicdcdcdid}(k3\_funct\_2~(k2\_zfmisc\_1~\\
k5\_numbers~k1\_hilbert1)~k6\_margrel1~X1~(k1\_domain\_1~k5\_numbers~\\
k1\_hilbert1~(k2\_nat\_1~X2~X6)~X3)=np\_\_1)))))))){\unicdcdcdhd}(({\unicdcdaddd} X5 .  \\
(m1\_subset\_1~X5~k5\_numbers){\unicdcdcdhd}((\preoh r1\_xxreal\_0~X5~k6\_numbers){\unicdcdcdhd}(\\
(k3\_funct\_2~(k2\_zfmisc\_1~k5\_numbers~k1\_hilbert1)~k6\_margrel1~\\
X1~(k1\_domain\_1~k5\_numbers~k1\_hilbert1~(k2\_nat\_1~X2~X5)~X4)=np\_\_1){\unicdcdcdhd}\\
({\unicdcdadad} X6 .  (m1\_subset\_1~X6~k5\_numbers){\unicdbdjdcd}((r1\_xxreal\_0~np\_\_1~\\
X6){\unicdbdjdcd}((r1\_xxreal\_0~X5~X6){\unicdcdcdid}(k3\_funct\_2~(k2\_zfmisc\_1~k5\_numbers~\\
k1\_hilbert1)~k6\_margrel1~X1~(k1\_domain\_1~k5\_numbers~k1\_hilbert1~\\
(k2\_nat\_1~X2~X6)~X3)=np\_\_1))))))){\unicdbdjdcd}(k3\_funct\_2~(k2\_zfmisc\_1~k5\_numbers~\\
k1\_hilbert1)~k6\_margrel1~X1~(k1\_domain\_1~k5\_numbers~k1\_hilbert1~\\
X2~(k4\_hilbert1~X3~X4))=np\_\_1)))))))))))\end{array}
\label{hyp:egbdbdpfmgehmgbgihjgpgbd}
\end{equation}
\begin{theorem}\label{thm:ehgdpfmgehmgbgihjgpgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~\\
X1){\unicdcdcdhd}((v1\_funct\_2~X1~k5\_numbers~(k1\_zfmisc\_1~k10\_ltlaxio1)){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k1\_zfmisc\_1~\\
k10\_ltlaxio1)))))){\unicdbdjdcd}(k3\_funct\_2~(k2\_zfmisc\_1~k5\_numbers~k1\_hilbert1)~\\
k6\_margrel1~(k11\_ltlaxio1~X1)~(k1\_domain\_1~k5\_numbers~k1\_hilbert1~\\
X0~k3\_ltlaxio1)=np\_\_1))\end{array}$$
\end{theorem}
\end{document}
