\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{t170\_zf\_lang1 (TMUSTs242U6CWcXZbYRia4nFHhQTHuUPNhS)}
\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 $ v6\_zf\_lang : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_zf\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v2\_zf\_lang : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_zf\_lang : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_zf\_lang : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_zf\_lang : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ np\_\_4 : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ k8\_zf\_lang : {{\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.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_zf\_lang~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\preoh \\
(\preoh v2\_zf\_lang~X0){\unicdcdcdhd}((\preoh v3\_zf\_lang~X0){\unicdcdcdhd}((\preoh v4\_zf\_lang~X0){\unicdcdcdhd}((\preoh v5\_zf\_lang~\\
X0){\unicdcdcdhd}(\preoh v6\_zf\_lang~X0)))))\end{array}
\label{hyp:ehjdpfkhggpfmgbgoghg}
\end{equation}
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}(\preoh (\preoh v3\_zf\_lang~X0){\unicdcdcdhd}((\preoh v4\_zf\_lang~X0){\unicdcdcdhd}((\preoh v5\_zf\_lang~\\
X0){\unicdcdcdhd}(\preoh v6\_zf\_lang~X0))))){\unicdcdcdhd}((\preoh (v3\_zf\_lang~X0){\unicdcdcdhd}(\preoh (\preoh v4\_zf\_lang~\\
X0){\unicdcdcdhd}((\preoh v5\_zf\_lang~X0){\unicdcdcdhd}(\preoh v6\_zf\_lang~X0)))){\unicdcdcdhd}((\preoh (v4\_zf\_lang~X0){\unicdcdcdhd}\\
((v5\_zf\_lang~X0){\unicdcdcdid}(v6\_zf\_lang~X0))){\unicdcdcdhd}(\preoh (v5\_zf\_lang~X0){\unicdcdcdhd}(v6\_zf\_lang~\\
X0)))))\end{array}
\label{hyp:ehddidpfkhggpfmgbgoghgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_zf\_lang~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}((\\
k1\_funct\_1~X0~np\_\_1=np\_\_4){\unicdbdjdcd}(v6\_zf\_lang~X0))\end{array}
\label{hyp:ehcdidpfkhggpfmgbgoghg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_zf\_lang~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}((\\
k1\_funct\_1~X0~np\_\_1=np\_\_1){\unicdbdjdcd}(v3\_zf\_lang~X0))\end{array}
\label{hyp:ehcdfdpfkhggpfmgbgoghg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_zf\_lang~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}((\\
k1\_funct\_1~X0~np\_\_1=k6\_numbers){\unicdbdjdcd}(v2\_zf\_lang~X0))\end{array}
\label{hyp:ehcdedpfkhggpfmgbgoghg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_zf\_lang~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\preoh \\
(\preoh (v2\_zf\_lang~X0){\unicdcdcdhd}(k1\_funct\_1~X0~np\_\_1=k6\_numbers)){\unicdcdcdhd}((\preoh (v3\_zf\_lang~\\
X0){\unicdcdcdhd}(k1\_funct\_1~X0~np\_\_1=np\_\_1)){\unicdcdcdhd}((\preoh (v4\_zf\_lang~X0){\unicdcdcdhd}(k1\_funct\_1~\\
X0~np\_\_1=np\_\_2)){\unicdcdcdhd}((\preoh (v5\_zf\_lang~X0){\unicdcdcdhd}(k1\_funct\_1~X0~np\_\_1=np\_\_3)){\unicdcdcdhd}\\
(\preoh (v6\_zf\_lang~X0){\unicdcdcdhd}(k1\_funct\_1~X0~np\_\_1=np\_\_4))))))\end{array}
\label{hyp:ehcdddpfkhggpfmgbgoghg}
\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){\unicdbdjdcd}(k1\_funct\_1~X0~np\_\_1=np\_\_4))\end{array}
\label{hyp:ehcdcdpfkhggpfmgbgoghg}
\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}(k1\_funct\_1~X0~np\_\_1=k6\_numbers))\end{array}
\label{hyp:ehbdidpfkhggpfmgbgoghg}
\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}(k1\_funct\_1~(\\
k8\_zf\_lang~X0~X1)~np\_\_1=np\_\_4))\end{array}
\label{hyp:ehbdhdpfkhggpfmgbgoghg}
\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 .  \\
(m2\_subset\_1~X1~k5\_numbers~k1\_zf\_lang){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~k5\_numbers~k1\_zf\_lang){\unicdbdjdcd}((v5\_zf\_lang~X0){\unicdbdjded}(v5\_zf\_lang~(k6\_zf\_lang1~\\
X0~X1~X2)))))\end{array}
\label{hyp:ehbdgdjdpfkhggpfmgbgoghgbd}
\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 .  \\
(m2\_subset\_1~X1~k5\_numbers~k1\_zf\_lang){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~k5\_numbers~k1\_zf\_lang){\unicdbdjdcd}((v4\_zf\_lang~X0){\unicdbdjded}(v4\_zf\_lang~(k6\_zf\_lang1~\\
X0~X1~X2)))))\end{array}
\label{hyp:ehbdgdidpfkhggpfmgbgoghgbd}
\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 .  \\
(m2\_subset\_1~X1~k5\_numbers~k1\_zf\_lang){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~k5\_numbers~k1\_zf\_lang){\unicdbdjdcd}((v3\_zf\_lang~X0){\unicdbdjded}(v3\_zf\_lang~(k6\_zf\_lang1~\\
X0~X1~X2)))))\end{array}
\label{hyp:ehbdgdhdpfkhggpfmgbgoghgbd}
\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 .  \\
(m2\_subset\_1~X1~k5\_numbers~k1\_zf\_lang){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~k5\_numbers~k1\_zf\_lang){\unicdbdjdcd}((v2\_zf\_lang~X0){\unicdbdjded}(v2\_zf\_lang~(k6\_zf\_lang1~\\
X0~X1~X2)))))\end{array}
\label{hyp:ehbdgdgdpfkhggpfmgbgoghgbd}
\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 .  ((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}{\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:ehbdhdadpfkhggpfmgbgoghgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_zf\_lang~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m2\_subset\_1~X1~k5\_numbers~k1\_zf\_lang){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~k5\_numbers~k1\_zf\_lang){\unicdbdjdcd}((v6\_zf\_lang~X0){\unicdbdjded}(v6\_zf\_lang~(k6\_zf\_lang1~\\
X0~X1~X2)))))\end{array}$$
\end{theorem}
\end{document}
