\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{t10\_fomodel1 (TMWwbzFDfAZuqe2BSNdrfvgKY4vFF7bzxUy)}
\maketitle
Let $ v6\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_fomodel1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_fomodel1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_fomodel1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k16\_fomodel1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_fomodel1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k8\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k7\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_fomodel1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_fomodel1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u3\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k6\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~\\
X2)){\unicdbdjdcd}(k8\_relat\_1~X2~(k6\_subset\_1~X0~X1)=k6\_subset\_1~(k8\_relat\_1~\\
X2~X0)~(k8\_relat\_1~X2~X1))\end{array}
\label{hyp:ehgdjdpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (m1\_subset\_1~X2~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(k8\_relset\_1~X0~X1~X2~X3=k8\_relat\_1~\\
X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgidpfchfgmgdhfgehpfbd}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v6\_struct\_0~X0){\unicdcdcdhd}((v11\_fomodel1~X0){\unicdcdcdhd}(l1\_fomodel1~\\
X0))){\unicdbdjdcd}(k16\_fomodel1~X0=k2\_fomodel1~X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdgdpfggpgngpgegfgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{v1\_relat\_1}~{({{{k2\_zfmisc\_1}~{X0}}~{X1}})}}}}\label{hyp:ggdggdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_fomodel1~X0){\unicdbdjdcd}((v1\_funct\_1~(u1\_fomodel1~X0)){\unicdcdcdhd}\\
((v1\_funct\_2~(u1\_fomodel1~X0)~(k6\_subset\_1~(u1\_struct\_0~X0)~(\\
k1\_tarski~(u3\_struct\_0~X0)))~k4\_numbers){\unicdcdcdhd}(m1\_subset\_1~(u1\_fomodel1~\\
X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k6\_subset\_1~(u1\_struct\_0~X0)~(\\
k1\_tarski~(u3\_struct\_0~X0)))~k4\_numbers)))))\end{array}
\label{hyp:egehpffhbdpfggpgngpgegfgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k5\_numbers}}~{({{k1\_zfmisc\_1}~{k1\_numbers}})}}\label{hyp:egehpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_fomodel1~X0){\unicdbdjdcd}(k5\_fomodel1~X0=k8\_relset\_1~(k6\_subset\_1~\\
(u1\_struct\_0~X0)~(k1\_tarski~(u3\_struct\_0~X0)))~k4\_numbers~(u1\_fomodel1~\\
X0)~k5\_numbers)\end{array}
\label{hyp:egfdpfggpgngpgegfgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_fomodel1~X0){\unicdbdjdcd}(k3\_fomodel1~X0=k8\_relset\_1~(k6\_subset\_1~\\
(u1\_struct\_0~X0)~(k1\_tarski~(u3\_struct\_0~X0)))~k4\_numbers~(u1\_fomodel1~\\
X0)~(k7\_subset\_1~k1\_numbers~k5\_numbers~(k6\_domain\_1~k5\_numbers~\\
k6\_numbers)))\end{array}
\label{hyp:egddpfggpgngpgegfgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_fomodel1~X0){\unicdbdjdcd}(k2\_fomodel1~X0=k8\_relset\_1~(k6\_subset\_1~\\
(u1\_struct\_0~X0)~(k1\_tarski~(u3\_struct\_0~X0)))~k4\_numbers~(u1\_fomodel1~\\
X0)~(k6\_domain\_1~k5\_numbers~k6\_numbers))\end{array}
\label{hyp:egcdpfggpgngpgegfgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v1\_relat\_1~X1))\end{array}
\label{hyp:dgdgcdpfchfgmgbgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdadpfggpgngpgegfgmgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v6\_struct\_0~X0){\unicdcdcdhd}((v11\_fomodel1~X0){\unicdcdcdhd}(l1\_fomodel1~\\
X0))){\unicdbdjdcd}(k6\_subset\_1~(k5\_fomodel1~X0)~(k16\_fomodel1~X0)=k3\_fomodel1~\\
X0)\end{array}$$
\end{theorem}
\end{document}
