\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{t77\_zf\_lang (TMTT8yn2Pc5UtkBUeFpyQJ9Kq9dwLvZ8PKM)}
\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 $ v1\_zf\_lang : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r2\_zf\_lang : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_zf\_lang : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r3\_zf\_lang : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_zf\_lang : {\iota}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_zf\_lang : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_zf\_lang : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_zf\_lang : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_zf\_lang : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_5 : {\iota}$ be given.
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}({\unicdcdadad} X2 .  ((v1\_zf\_lang~\\
X2){\unicdcdcdhd}(m2\_finseq\_1~X2~k5\_numbers)){\unicdbdjdcd}(\preoh r3\_zf\_lang~X2~(k5\_zf\_lang~\\
X0~X1))))\end{array}
\label{hyp:ehgdidpfkhggpfmgbgoghg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_zf\_lang~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(r2\_zf\_lang~\\
X0~X0)\end{array}
\label{hyp:ehfdjdpfkhggpfmgbgoghg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_zf\_lang~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjded}(X0 \in \\
k9\_zf\_lang)\end{array}
\label{hyp:ehedpfkhggpfmgbgoghg}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k9\_zf\_lang}}}}\label{hyp:egehpflgjdpfkhggpfmgbgoghg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((X0=k9\_zf\_lang){\unicdbdjded}(({\unicdcdadad} X1 .  \\
(X1 \in X0){\unicdbdjdcd}(m2\_finseq\_1~X1~k5\_numbers)){\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}((k4\_zf\_lang~X1~X2 \in X0){\unicdcdcdhd}(k5\_zf\_lang~X1~X2 \in X0)))){\unicdcdcdhd}\\
(({\unicdcdadad} X1 .  (m2\_finseq\_1~X1~k5\_numbers){\unicdbdjdcd}((X1 \in X0){\unicdbdjdcd}(k6\_zf\_lang~\\
X1 \in X0))){\unicdcdcdhd}(({\unicdcdadad} X1 .  (m2\_finseq\_1~X1~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m2\_finseq\_1~X2~k5\_numbers){\unicdbdjdcd}(((X1 \in X0){\unicdcdcdhd}(X2 \in X0)){\unicdbdjdcd}(k7\_zf\_lang~\\
X1~X2 \in X0)))){\unicdcdcdhd}(({\unicdcdadad} X1 .  (m2\_subset\_1~X1~k5\_numbers~k1\_zf\_lang){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m2\_finseq\_1~X2~k5\_numbers){\unicdbdjdcd}((X2 \in X0){\unicdbdjdcd}(k8\_zf\_lang~\\
X1~X2 \in X0)))){\unicdcdcdhd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}((({\unicdcdadad} X2 .  (X2 \in \\
X1){\unicdbdjdcd}(m2\_finseq\_1~X2~k5\_numbers)){\unicdcdcdhd}(({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~k5\_numbers~k1\_zf\_lang){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_subset\_1~X3~k5\_numbers~\\
k1\_zf\_lang){\unicdbdjdcd}((k4\_zf\_lang~X2~X3 \in X1){\unicdcdcdhd}(k5\_zf\_lang~X2~X3 \in X1)))){\unicdcdcdhd}\\
(({\unicdcdadad} X2 .  (m2\_finseq\_1~X2~k5\_numbers){\unicdbdjdcd}((X2 \in X1){\unicdbdjdcd}(k6\_zf\_lang~\\
X2 \in X1))){\unicdcdcdhd}(({\unicdcdadad} X2 .  (m2\_finseq\_1~X2~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m2\_finseq\_1~X3~k5\_numbers){\unicdbdjdcd}(((X2 \in X1){\unicdcdcdhd}(X3 \in X1)){\unicdbdjdcd}(k7\_zf\_lang~\\
X2~X3 \in X1)))){\unicdcdcdhd}({\unicdcdadad} X2 .  (m2\_subset\_1~X2~k5\_numbers~k1\_zf\_lang){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m2\_finseq\_1~X3~k5\_numbers){\unicdbdjdcd}((X3 \in X1){\unicdbdjdcd}(k8\_zf\_lang~\\
X2~X3 \in X1)))))))){\unicdbdjdcd}(r1\_tarski~X0~X1)))))))))\end{array}
\label{hyp:egidpfkhggpfmgbgoghg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_zf\_lang~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_zf\_lang~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~k5\_numbers)){\unicdbdjdcd}((r3\_zf\_lang~\\
X0~X1){\unicdbdjded}((r2\_zf\_lang~X0~X1){\unicdcdcdhd}(X0{\unicdcdgdad}X1))))\end{array}
\label{hyp:egedbdpfkhggpfmgbgoghg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}k1\_zf\_lang=ReplSep~(toset~({\uniddcgcg} X0 : \iota .  m1\_subset\_1~X0~k5\_numbers))~\\
({\uniddcgcg} X0 : \iota .  r1\_xxreal\_0~np\_\_5~X0)~({\uniddcgcg} X0 : \iota .  X0)\end{array}
\label{hyp:egbdpfkhggpfmgbgoghg}
\end{equation}
\begin{theorem}\label{thm:ehhdhdpfkhggpfmgbgoghg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k5\_numbers~k1\_zf\_lang){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m2\_subset\_1~X1~k5\_numbers~k1\_zf\_lang){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_zf\_lang~\\
X2){\unicdcdcdhd}(m2\_finseq\_1~X2~k5\_numbers)){\unicdbdjdcd}((r2\_zf\_lang~X2~(k5\_zf\_lang~\\
X0~X1)){\unicdbdjded}(X2=k5\_zf\_lang~X0~X1))))\end{array}$$
\end{theorem}
\end{document}
