\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{t58\_zf\_lang1 (TMbD7QeqeRMxXdnYXoCEj5VswAUc5rEfmPu)}
\maketitle
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k1\_zf\_lang : {\iota}$ be given.
Let $ k2\_zf\_model : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_zf\_lang : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_zf\_lang : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_zf\_lang : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_zf\_lang : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_zf\_lang : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v4\_zf\_lang : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_zf\_lang : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v5\_zf\_lang : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k7\_zf\_lang : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v6\_zf\_lang : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k8\_zf\_lang : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k18\_zf\_lang : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k19\_zf\_lang : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k20\_zf\_lang : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k21\_zf\_lang : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k22\_zf\_lang : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k24\_zf\_lang : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k23\_zf\_lang : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\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.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_zf\_lang~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}((\\
\preoh (v2\_zf\_lang~X0){\unicdcdcdhd}({\unicdcdadad} X1 .  (m2\_subset\_1~X1~k5\_numbers~k1\_zf\_lang){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m2\_subset\_1~X2~k5\_numbers~k1\_zf\_lang){\unicdbdjdcd}(X0{\unicdcdgdad}k4\_zf\_lang~\\
X1~X2)))){\unicdcdcdhd}((({\unicdcdaddd} X1 .  (m2\_subset\_1~X1~k5\_numbers~k1\_zf\_lang){\unicdcdcdhd}\\
({\unicdcdaddd} X2 .  (m2\_subset\_1~X2~k5\_numbers~k1\_zf\_lang){\unicdcdcdhd}(X0=k4\_zf\_lang~\\
X1~X2))){\unicdbdjdcd}(v2\_zf\_lang~X0)){\unicdcdcdhd}((\preoh (v3\_zf\_lang~X0){\unicdcdcdhd}({\unicdcdadad} X1 .  (m2\_subset\_1~\\
X1~k5\_numbers~k1\_zf\_lang){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~X2~k5\_numbers~\\
k1\_zf\_lang){\unicdbdjdcd}(X0{\unicdcdgdad}k5\_zf\_lang~X1~X2)))){\unicdcdcdhd}((({\unicdcdaddd} X1 .  (m2\_subset\_1~\\
X1~k5\_numbers~k1\_zf\_lang){\unicdcdcdhd}({\unicdcdaddd} X2 .  (m2\_subset\_1~X2~k5\_numbers~\\
k1\_zf\_lang){\unicdcdcdhd}(X0=k5\_zf\_lang~X1~X2))){\unicdbdjdcd}(v3\_zf\_lang~X0)){\unicdcdcdhd}((\preoh (v4\_zf\_lang~\\
X0){\unicdcdcdhd}({\unicdcdadad} X1 .  ((v1\_zf\_lang~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~k5\_numbers)){\unicdbdjdcd}\\
(X0{\unicdcdgdad}k6\_zf\_lang~X1))){\unicdcdcdhd}((({\unicdcdaddd} X1 .  ((v1\_zf\_lang~X1){\unicdcdcdhd}(m2\_finseq\_1~\\
X1~k5\_numbers)){\unicdcdcdhd}(X0=k6\_zf\_lang~X1)){\unicdbdjdcd}(v4\_zf\_lang~X0)){\unicdcdcdhd}((\preoh (v5\_zf\_lang~\\
X0){\unicdcdcdhd}({\unicdcdadad} X1 .  ((v1\_zf\_lang~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~k5\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_zf\_lang~X2){\unicdcdcdhd}(m2\_finseq\_1~X2~k5\_numbers)){\unicdbdjdcd}(\\
X0{\unicdcdgdad}k7\_zf\_lang~X1~X2)))){\unicdcdcdhd}((({\unicdcdaddd} X1 .  ((v1\_zf\_lang~X1){\unicdcdcdhd}(m2\_finseq\_1~\\
X1~k5\_numbers)){\unicdcdcdhd}({\unicdcdaddd} X2 .  ((v1\_zf\_lang~X2){\unicdcdcdhd}(m2\_finseq\_1~X2~\\
k5\_numbers)){\unicdcdcdhd}(X0=k7\_zf\_lang~X1~X2))){\unicdbdjdcd}(v5\_zf\_lang~X0)){\unicdcdcdhd}((\preoh (\\
v6\_zf\_lang~X0){\unicdcdcdhd}({\unicdcdadad} X1 .  (m2\_subset\_1~X1~k5\_numbers~k1\_zf\_lang){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_zf\_lang~X2){\unicdcdcdhd}(m2\_finseq\_1~X2~k5\_numbers)){\unicdbdjdcd}(\\
X0{\unicdcdgdad}k8\_zf\_lang~X1~X2)))){\unicdcdcdhd}(({\unicdcdaddd} X1 .  (m2\_subset\_1~X1~k5\_numbers~\\
k1\_zf\_lang){\unicdcdcdhd}({\unicdcdaddd} X2 .  ((v1\_zf\_lang~X2){\unicdcdcdhd}(m2\_finseq\_1~X2~k5\_numbers)){\unicdcdcdhd}\\
(X0=k8\_zf\_lang~X1~X2))){\unicdbdjdcd}(v6\_zf\_lang~X0)))))))))))\end{array}
\label{hyp:ehfdpfkhggpfmgbgoghg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_zf\_lang~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}((\\
(v2\_zf\_lang~X0){\unicdbdjdcd}(k2\_zf\_model~X0=k2\_tarski~(k18\_zf\_lang~X0)~(\\
k19\_zf\_lang~X0))){\unicdcdcdhd}(((v3\_zf\_lang~X0){\unicdbdjdcd}(k2\_zf\_model~X0=k2\_tarski~\\
(k18\_zf\_lang~X0)~(k19\_zf\_lang~X0))){\unicdcdcdhd}(((v4\_zf\_lang~X0){\unicdbdjdcd}(k2\_zf\_model~\\
X0=k2\_zf\_model~(k20\_zf\_lang~X0))){\unicdcdcdhd}(((v5\_zf\_lang~X0){\unicdbdjdcd}(k2\_zf\_model~\\
X0=k4\_subset\_1~k1\_zf\_lang~(k2\_zf\_model~(k21\_zf\_lang~X0))~(k2\_zf\_model~\\
(k22\_zf\_lang~X0)))){\unicdcdcdhd}((v6\_zf\_lang~X0){\unicdbdjdcd}(k2\_zf\_model~X0=k7\_subset\_1~\\
k1\_zf\_lang~(k2\_zf\_model~(k24\_zf\_lang~X0))~(k1\_tarski~(k23\_zf\_lang~\\
X0))))))))\end{array}
\label{hyp:ehbdpfkhggpfngpgegfgmg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k5\_numbers~k1\_zf\_lang){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m2\_subset\_1~X1~k5\_numbers~k1\_zf\_lang){\unicdbdjdcd}((k18\_zf\_lang~(k4\_zf\_lang~\\
X0~X1)=X0){\unicdcdcdhd}(k19\_zf\_lang~(k4\_zf\_lang~X0~X1)=X1)))\end{array}
\label{hyp:ehbdpfkhggpfmgbgoghgbd}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k1\_zf\_lang){\unicdcdcdhd}(m1\_subset\_1~\\
X1~k1\_zf\_lang)){\unicdbdjdcd}(v1\_zf\_lang~(k4\_zf\_lang~X0~X1))\end{array}
\label{hyp:ggdgcdpfkhggpfmgbgoghg}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k1\_zf\_lang}}}}\label{hyp:ggdgbdpfkhggpfmgbgoghg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k1\_zf\_lang){\unicdcdcdhd}(m1\_subset\_1~\\
X1~k1\_zf\_lang)){\unicdbdjdcd}(m2\_finseq\_1~(k4\_zf\_lang~X0~X1)~k5\_numbers)\end{array}
\label{hyp:egehpflgedpfkhggpfmgbgoghg}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k1\_zf\_lang}}~{({{k1\_zfmisc\_1}~{k5\_numbers}})}}\label{hyp:egehpflgbdpfkhggpfmgbgoghg}
\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:ehfdidpfkhggpfmgbgoghgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k5\_numbers~k1\_zf\_lang){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m2\_subset\_1~X1~k5\_numbers~k1\_zf\_lang){\unicdbdjdcd}(k2\_zf\_model~(k4\_zf\_lang~\\
X0~X1)=k2\_tarski~X0~X1))\end{array}$$
\end{theorem}
\end{document}
