\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}
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\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{t1\_zf\_model (TMc1ZK4A8nv5XfAn7228t42ZJ86e6nKEUwD)}
\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 $ v2\_zf\_lang : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_zf\_model : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k18\_zf\_lang : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k19\_zf\_lang : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_zf\_lang : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_zf\_lang : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k20\_zf\_lang : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v5\_zf\_lang : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_zf\_lang : {\iota}$ be given.
Let $ k21\_zf\_lang : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k22\_zf\_lang : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v6\_zf\_lang : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k7\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k24\_zf\_lang : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k23\_zf\_lang : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ k4\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ k1\_zf\_model : {{\iota}{\unicdbdjdcd}{\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}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{k3\_tarski}~{({{{k2\_tarski}~{X0}}~{X1}})}}={{{k2\_xboole\_0}~{X0}}~{X1}}}}}\label{hyp:ehhdfdpfkhggngjgdhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k3\_tarski}~{({{k1\_tarski}~{X0}})}}={X0}}}\label{hyp:ehcdfdpfkhggngjgdhdgpfbd}
\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 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(k7\_subset\_1~X0~X1~X2=k4\_xboole\_0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflghdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k6\_subset\_1}~{X0}}~{X1}}={{{k4\_xboole\_0}~{X0}}~{X1}}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfdhfhcgdhfgehpfbd}
\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 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~X0))){\unicdbdjdcd}(k4\_subset\_1~X0~X1~X2=\\
k2\_xboole\_0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_zf\_lang~X0){\unicdcdcdhd}(m1\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(k2\_zf\_model~\\
X0=k1\_zf\_model~X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfkhggpfngpgegfgmg}
\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\_zf\_model~X0=k2\_tarski~(k18\_zf\_lang~X0)~(\\
k19\_zf\_lang~X0))){\unicdcdcdhd}(((v3\_zf\_lang~X0){\unicdbdjdcd}(k1\_zf\_model~X0=k2\_tarski~\\
(k18\_zf\_lang~X0)~(k19\_zf\_lang~X0))){\unicdcdcdhd}(((v4\_zf\_lang~X0){\unicdbdjdcd}(k1\_zf\_model~\\
X0=k1\_zf\_model~(k20\_zf\_lang~X0))){\unicdcdcdhd}(((v5\_zf\_lang~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
{\unicdcdadad} X2 .  ((X1=k1\_zf\_model~(k21\_zf\_lang~X0)){\unicdcdcdhd}(X2=k1\_zf\_model~\\
(k22\_zf\_lang~X0))){\unicdbdjdcd}(k1\_zf\_model~X0=k3\_tarski~(k2\_tarski~X1~X2)))){\unicdcdcdhd}\\
((v6\_zf\_lang~X0){\unicdbdjdcd}(k1\_zf\_model~X0=k6\_subset\_1~(k3\_tarski~(k1\_tarski~\\
(k1\_zf\_model~(k24\_zf\_lang~X0))))~(k1\_tarski~(k23\_zf\_lang~X0))))))))\end{array}
\label{hyp:mgddpfkhggpfngpgegfgmg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_zf\_lang~X0){\unicdcdcdhd}(m1\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(m1\_subset\_1~\\
(k2\_zf\_model~X0)~(k1\_zfmisc\_1~k1\_zf\_lang))\end{array}
\label{hyp:egehpflgcdpfkhggpfngpgegfgmg}
\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}((\\
v1\_zf\_lang~(k22\_zf\_lang~X0)){\unicdcdcdhd}(m2\_finseq\_1~(k22\_zf\_lang~X0)~k5\_numbers))\end{array}
\label{hyp:egehpflgcdcdpfkhggpfmgbgoghg}
\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~(k21\_zf\_lang~X0)){\unicdcdcdhd}(m2\_finseq\_1~(k21\_zf\_lang~X0)~k5\_numbers))\end{array}
\label{hyp:egehpflgcdbdpfkhggpfmgbgoghg}
\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}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:ehbdpfkhggpfngpgegfgmg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_zf\_lang~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}((\\
(v2\_zf\_lang~X0){\unicdbdjdcd}(k2\_zf\_model~X0=k2\_tarski~(k18\_zf\_lang~X0)~(\\
k19\_zf\_lang~X0))){\unicdcdcdhd}(((v3\_zf\_lang~X0){\unicdbdjdcd}(k2\_zf\_model~X0=k2\_tarski~\\
(k18\_zf\_lang~X0)~(k19\_zf\_lang~X0))){\unicdcdcdhd}(((v4\_zf\_lang~X0){\unicdbdjdcd}(k2\_zf\_model~\\
X0=k2\_zf\_model~(k20\_zf\_lang~X0))){\unicdcdcdhd}(((v5\_zf\_lang~X0){\unicdbdjdcd}(k2\_zf\_model~\\
X0=k4\_subset\_1~k1\_zf\_lang~(k2\_zf\_model~(k21\_zf\_lang~X0))~(k2\_zf\_model~\\
(k22\_zf\_lang~X0)))){\unicdcdcdhd}((v6\_zf\_lang~X0){\unicdbdjdcd}(k2\_zf\_model~X0=k7\_subset\_1~\\
k1\_zf\_lang~(k2\_zf\_model~(k24\_zf\_lang~X0))~(k1\_tarski~(k23\_zf\_lang~\\
X0))))))))\end{array}$$
\end{theorem}
\end{document}
