\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{t8\_zf\_lang1 (TMS8ut8TsfiZpzH4tLxkoAed88iwnp19mx8)}
\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 $ k23\_zf\_lang : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_zf\_lang : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k24\_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.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v6\_zf\_lang : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_zf\_lang : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k13\_zf\_lang : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
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 .  (m2\_subset\_1~X0~k5\_numbers~k1\_zf\_lang){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_zf\_lang~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~k5\_numbers)){\unicdbdjdcd}((r2\_relset\_1~\\
k5\_numbers~k5\_numbers~(k24\_zf\_lang~(k8\_zf\_lang~X0~X1))~X1){\unicdcdcdhd}(k23\_zf\_lang~\\
(k8\_zf\_lang~X0~X1)=X0)))\end{array}
\label{hyp:mgbdcdpfkhggngpgegfgmgbd}
\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}
{{{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\_zf\_lang~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}((\\
(v6\_zf\_lang~X0){\unicdcdcdid}(v11\_zf\_lang~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_zf\_lang~\\
X1){\unicdcdcdhd}(m2\_finseq\_1~X1~k5\_numbers)){\unicdbdjdcd}(((v6\_zf\_lang~X0){\unicdbdjdcd}((X1=k24\_zf\_lang~\\
X0){\unicdbdjded}({\unicdcdaddd} X2 .  (m2\_subset\_1~X2~k5\_numbers~k1\_zf\_lang){\unicdcdcdhd}(k8\_zf\_lang~\\
X2~X1=X0)))){\unicdcdcdhd}((\preoh v6\_zf\_lang~X0){\unicdbdjdcd}((X1=k24\_zf\_lang~X0){\unicdbdjded}({\unicdcdaddd} X2 .  \\
(m2\_subset\_1~X2~k5\_numbers~k1\_zf\_lang){\unicdcdcdhd}(k13\_zf\_lang~X2~X1=X0)))))))\end{array}
\label{hyp:egddedpfkhggpfmgbgoghg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_zf\_lang~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}((\\
v6\_zf\_lang~X0){\unicdbdjded}({\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))))\end{array}
\label{hyp:egbdedpfkhggpfmgbgoghg}
\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:ehidpfkhggpfmgbgoghgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_zf\_lang~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m2\_subset\_1~X1~k5\_numbers~k1\_zf\_lang){\unicdbdjdcd}((k23\_zf\_lang~(k8\_zf\_lang~\\
X1~X0)=X1){\unicdcdcdhd}(k24\_zf\_lang~(k8\_zf\_lang~X1~X0)=X0)))\end{array}$$
\end{theorem}
\end{document}
