\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=}
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\newcommand\unicdcdbdgd{\setminus}
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\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t37\_zf\_lang1 (TMLAuco4aCRGsvdDz1iQLHR7kNuvSxL9NYK)}
\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 $ v11\_zf\_lang : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_zf\_lang : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_zf\_lang : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k20\_zf\_lang : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k24\_zf\_lang : {{\iota}{\unicdbdjdcd}{\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 $ k13\_zf\_lang : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_zf\_lang : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_zf\_lang : {{\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}({\unicdcdadad} X1 .  \\
(m2\_subset\_1~X1~k5\_numbers~k1\_zf\_lang){\unicdbdjdcd}((k23\_zf\_lang~(k13\_zf\_lang~\\
X1~X0)=X1){\unicdcdcdhd}(k24\_zf\_lang~(k13\_zf\_lang~X1~X0)=X0)))\end{array}
\label{hyp:ehjdpfkhggpfmgbgoghgbd}
\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}((k23\_zf\_lang~(k8\_zf\_lang~\\
X1~X0)=X1){\unicdcdcdhd}(k24\_zf\_lang~(k8\_zf\_lang~X1~X0)=X0)))\end{array}
\label{hyp:ehidpfkhggpfmgbgoghgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_zf\_lang~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}((\\
v11\_zf\_lang~X0){\unicdbdjdcd}(X0=k13\_zf\_lang~(k23\_zf\_lang~X0)~(k24\_zf\_lang~\\
X0)))\end{array}
\label{hyp:ehedfdpfkhggpfmgbgoghg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_zf\_lang~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(k20\_zf\_lang~\\
(k6\_zf\_lang~X0)=X0)\end{array}
\label{hyp:ehddpfkhggpfmgbgoghgbd}
\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}(k20\_zf\_lang~(k13\_zf\_lang~\\
X1~X0)=k8\_zf\_lang~X1~(k6\_zf\_lang~X0)))\end{array}
\label{hyp:ehddddpfkhggpfmgbgoghgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_zf\_lang~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}((\\
v11\_zf\_lang~X0){\unicdbdjdcd}((k23\_zf\_lang~X0=k23\_zf\_lang~(k20\_zf\_lang~X0)){\unicdcdcdhd}\\
(k24\_zf\_lang~X0=k20\_zf\_lang~(k24\_zf\_lang~(k20\_zf\_lang~X0)))))\end{array}
\label{hyp:ehcdjdpfkhggpfmgbgoghgbd}
\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 .  ((v1\_zf\_lang~X0){\unicdcdcdhd}(m1\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(v1\_zf\_lang~\\
(k6\_zf\_lang~X0))\end{array}
\label{hyp:ggdgedpfkhggpfmgbgoghg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_finseq\_1~X0~k5\_numbers){\unicdbdjdcd}(m2\_finseq\_1~(k6\_zf\_lang~\\
X0)~k5\_numbers)\end{array}
\label{hyp:egehpflggdpfkhggpfmgbgoghg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_zf\_lang~X0){\unicdcdcdhd}(m1\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}((\\
v1\_zf\_lang~(k24\_zf\_lang~X0)){\unicdcdcdhd}(m2\_finseq\_1~(k24\_zf\_lang~X0)~k5\_numbers))\end{array}
\label{hyp:egehpflgcdedpfkhggpfmgbgoghg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_zf\_lang~X0){\unicdcdcdhd}(m1\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(m2\_subset\_1~\\
(k23\_zf\_lang~X0)~k5\_numbers~k1\_zf\_lang)\end{array}
\label{hyp:egehpflgcdddpfkhggpfmgbgoghg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_zf\_lang~X0){\unicdcdcdhd}(m1\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}((\\
v1\_zf\_lang~(k20\_zf\_lang~X0)){\unicdcdcdhd}(m2\_finseq\_1~(k20\_zf\_lang~X0)~k5\_numbers))\end{array}
\label{hyp:egehpflgcdadpfkhggpfmgbgoghg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_zf\_lang~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}((\\
v11\_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=k13\_zf\_lang~X1~X2))))\end{array}
\label{hyp:egcdddpfkhggpfmgbgoghg}
\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}(k13\_zf\_lang~\\
X0~X1=k6\_zf\_lang~(k8\_zf\_lang~X0~(k6\_zf\_lang~X1))))\end{array}
\label{hyp:egbdjdpfkhggpfmgbgoghg}
\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\_zf\_lang~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}((\\
v4\_zf\_lang~X0){\unicdbdjded}({\unicdcdaddd} X1 .  ((v1\_zf\_lang~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~\\
k5\_numbers)){\unicdcdcdhd}(X0=k6\_zf\_lang~X1)))\end{array}
\label{hyp:egbdcdpfkhggpfmgbgoghg}
\end{equation}
\begin{theorem}\label{thm:ehddhdpfkhggpfmgbgoghgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_zf\_lang~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}((\\
v11\_zf\_lang~X0){\unicdbdjdcd}((v4\_zf\_lang~X0){\unicdcdcdhd}((v6\_zf\_lang~(k20\_zf\_lang~\\
X0)){\unicdcdcdhd}(v4\_zf\_lang~(k24\_zf\_lang~(k20\_zf\_lang~X0))))))\end{array}$$
\end{theorem}
\end{document}
