\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{t160\_zf\_lang1 (TMPNbnEsmstqMTacBYMC3QFyDpFXG5bjit7)}
\maketitle
Let $ v1\_zf\_lang : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_zf\_lang : {\iota}$ be given.
Let $ k8\_zf\_lang : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_zf\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_zf\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ 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\_finseq\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_1~\\
X1~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~X2~k5\_numbers~k1\_zf\_lang){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m2\_subset\_1~X3~k5\_numbers~k1\_zf\_lang){\unicdbdjdcd}((k8\_zf\_lang~\\
X2~X0=k8\_zf\_lang~X3~X1){\unicdbdjdcd}((X2=X3){\unicdcdcdhd}(X0=X1))))))\end{array}
\label{hyp:ehddpfkhggpfmgbgoghg}
\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}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m2\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjded}{({{{m1\_finseq\_1}~{X1}}~{X0}})}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_zf\_lang~X0){\unicdcdcdhd}(m1\_finseq\_1~\\
X0~k5\_numbers)){\unicdcdcdhd}((m1\_subset\_1~X1~k1\_zf\_lang){\unicdcdcdhd}(m1\_subset\_1~X2~\\
k1\_zf\_lang))){\unicdbdjdcd}(k6\_zf\_lang1~X0~X1~X2=k5\_zf\_lang1~X0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfkhggpfmgbgoghgbd}
\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\_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}({\unicdcdadad} X2 .  (\\
m2\_subset\_1~X2~k5\_numbers~k1\_zf\_lang){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_subset\_1~\\
X3~k5\_numbers~k1\_zf\_lang){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_subset\_1~X4~k5\_numbers~\\
k1\_zf\_lang){\unicdbdjdcd}({\unicdcdadad} X5 .  (m2\_subset\_1~X5~k5\_numbers~k1\_zf\_lang){\unicdbdjdcd}\\
((X0=k5\_zf\_lang1~X1~X2~X3){\unicdbdjdcd}(((\preoh (X4=X5){\unicdcdcdhd}(X5{\unicdcdgdad}X2)){\unicdcdcdhd}(\preoh (X4=X3){\unicdcdcdhd}\\
(X5=X2))){\unicdcdcdid}(k8\_zf\_lang~X4~X0=k5\_zf\_lang1~(k8\_zf\_lang~X5~X1)~X2~\\
X3))))))))\end{array}
\label{hyp:mgbdgdbdpfkhggpfmgbgoghgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k1\_zf\_lang){\unicdcdcdhd}((v1\_zf\_lang~\\
X1){\unicdcdcdhd}(m1\_finseq\_1~X1~k5\_numbers))){\unicdbdjdcd}(v1\_zf\_lang~(k8\_zf\_lang~X0~\\
X1))\end{array}
\label{hyp:ggdggdpfkhggpfmgbgoghg}
\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\_finseq\_1~\\
X1~k5\_numbers)){\unicdbdjdcd}(m2\_finseq\_1~(k8\_zf\_lang~X0~X1)~k5\_numbers)\end{array}
\label{hyp:egehpflgidpfkhggpfmgbgoghg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_zf\_lang~X0){\unicdcdcdhd}(m1\_finseq\_1~\\
X0~k5\_numbers)){\unicdcdcdhd}((m1\_subset\_1~X1~k1\_zf\_lang){\unicdcdcdhd}(m1\_subset\_1~X2~\\
k1\_zf\_lang))){\unicdbdjdcd}((v1\_zf\_lang~(k6\_zf\_lang1~X0~X1~X2)){\unicdcdcdhd}(m2\_finseq\_1~\\
(k6\_zf\_lang1~X0~X1~X2)~k5\_numbers))\end{array}
\label{hyp:egehpflggdpfkhggpfmgbgoghgbd}
\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}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}
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:ehbdgdadpfkhggpfmgbgoghgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_zf\_lang~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_zf\_lang~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~k5\_numbers)){\unicdbdjdcd}({\unicdcdadad} X2 .  (\\
m2\_subset\_1~X2~k5\_numbers~k1\_zf\_lang){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_subset\_1~\\
X3~k5\_numbers~k1\_zf\_lang){\unicdbdjdcd}((k8\_zf\_lang~X2~X0=k6\_zf\_lang1~(k8\_zf\_lang~\\
X3~X1)~X3~X2){\unicdbdjded}(X0=k6\_zf\_lang1~X1~X3~X2)))))\end{array}$$
\end{theorem}
\end{document}
