\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{l103\_fomodel4 (TMFydN3hweRdTg5tUuNTNNSgcNVmfLVQkJH)}
\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 $ v10\_fomodel1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_fomodel1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_setfam\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_fomodel4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k7\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k22\_fomodel4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k25\_fomodel4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k27\_fomodel4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k24\_fomodel4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k26\_fomodel4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k28\_fomodel4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v10\_fomodel4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v2\_fomodel3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ k4\_fomodel3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k35\_fomodel1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_fomodel4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k3\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v7\_fomodel1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v5\_fomodel1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v8\_fomodel1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_fomodel1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k11\_fomodel0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v9\_fomodel1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~X1)){\unicdbdjded}(r1\_tarski~\\
X0~X1)\end{array}
\label{hyp:ehddpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k2\_tarski~X0~X1=k2\_xboole\_0~(k1\_tarski~\\
X0)~(k1\_tarski~X1)\end{array}
\label{hyp:ehbdpffgogfhngdhfgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m1\_funct\_2~\\
X2~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_funct\_2~X3~X0~X1~X2){\unicdbdjded}(m1\_subset\_1~X3~\\
X2))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(k9\_subset\_1~X0~X1~X2=k3\_xboole\_0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k9\_setfam\_1}~{X0}}={{k1\_zfmisc\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfdhfgehggbgngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X1~X0){\unicdcdcdhd}(m1\_subset\_1~X2~X0))){\unicdbdjdcd}(k7\_domain\_1~X0~X1~X2=k2\_tarski~X1~\\
X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflghdpfegpgngbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~X0)){\unicdbdjdcd}\\
(k6\_domain\_1~X0~X1=k1\_tarski~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfegpgngbgjgogpfbd}
\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 .  {\unicdcdadad} X1 .  ((\preoh v6\_struct\_0~X1){\unicdcdcdhd}((v11\_fomodel1~X1){\unicdcdcdhd}\\
(l1\_fomodel1~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v7\_fomodel1~X2~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_fomodel1~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k9\_funct\_2~(k9\_setfam\_1~(k1\_fomodel4~X1))~(k9\_setfam\_1~(k1\_fomodel4~\\
X1))))){\unicdbdjdcd}(((k9\_subset\_1~(k9\_funct\_2~(k9\_setfam\_1~(k1\_fomodel4~\\
X1))~(k9\_setfam\_1~(k1\_fomodel4~X1)))~(k6\_domain\_1~(k9\_funct\_2~\\
(k9\_setfam\_1~(k1\_fomodel4~X1))~(k9\_setfam\_1~(k1\_fomodel4~X1)))~\\
(k24\_fomodel4~X1))~X3=k6\_domain\_1~(k9\_funct\_2~(k9\_setfam\_1~(\\
k1\_fomodel4~X1))~(k9\_setfam\_1~(k1\_fomodel4~X1)))~(k24\_fomodel4~\\
X1)){\unicdcdcdhd}((k9\_subset\_1~(k9\_funct\_2~(k9\_setfam\_1~(k1\_fomodel4~X1))~\\
(k9\_setfam\_1~(k1\_fomodel4~X1)))~(k6\_domain\_1~(k9\_funct\_2~(k9\_setfam\_1~\\
(k1\_fomodel4~X1))~(k9\_setfam\_1~(k1\_fomodel4~X1)))~(k26\_fomodel4~\\
X1))~X3=k6\_domain\_1~(k9\_funct\_2~(k9\_setfam\_1~(k1\_fomodel4~X1))~\\
(k9\_setfam\_1~(k1\_fomodel4~X1)))~(k26\_fomodel4~X1)){\unicdcdcdhd}((k9\_subset\_1~\\
(k9\_funct\_2~(k9\_setfam\_1~(k1\_fomodel4~X1))~(k9\_setfam\_1~(k1\_fomodel4~\\
X1)))~X3~(k6\_domain\_1~(k9\_funct\_2~(k9\_setfam\_1~(k1\_fomodel4~X1))~\\
(k9\_setfam\_1~(k1\_fomodel4~X1)))~(k28\_fomodel4~X1))=k6\_domain\_1~\\
(k9\_funct\_2~(k9\_setfam\_1~(k1\_fomodel4~X1))~(k9\_setfam\_1~(k1\_fomodel4~\\
X1)))~(k28\_fomodel4~X1)){\unicdcdcdhd}(v10\_fomodel4~X0~X1~X3)))){\unicdbdjdcd}(v2\_fomodel3~\\
(k4\_fomodel3~X1~X2~X0)~X1~(k35\_fomodel1~X1)~X2~(k6\_fomodel4~X1~X3~\\
X0)))))\end{array}
\label{hyp:mgjdjdpfggpgngpgegfgmged}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v6\_struct\_0~X1){\unicdcdcdhd}((v11\_fomodel1~X1){\unicdcdcdhd}\\
(l1\_fomodel1~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k9\_funct\_2~(k9\_setfam\_1~(k1\_fomodel4~X1))~(k9\_setfam\_1~(k1\_fomodel4~\\
X1))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v5\_fomodel1~X3~X1){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_fomodel1~\\
X1))){\unicdbdjdcd}(((r1\_tarski~(k6\_domain\_1~(k9\_funct\_2~(k9\_setfam\_1~(k1\_fomodel4~\\
X1))~(k9\_setfam\_1~(k1\_fomodel4~X1)))~(k27\_fomodel4~X1))~X2){\unicdcdcdhd}(\\
(v10\_fomodel4~X0~X1~X2){\unicdcdcdhd}(v8\_fomodel1~X3~X1))){\unicdbdjdcd}(v2\_fomodel3~(k4\_fomodel3~\\
X1~X3~X0)~X1~(k35\_fomodel1~X1)~X3~(k6\_fomodel4~X1~X2~X0)))))\end{array}
\label{hyp:mgjdfdpfggpgngpgegfgmged}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v6\_struct\_0~X1){\unicdcdcdhd}((v11\_fomodel1~X1){\unicdcdcdhd}\\
(l1\_fomodel1~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v4\_fomodel1~X2~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_fomodel1~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k9\_funct\_2~(k9\_setfam\_1~(k1\_fomodel4~X1))~(k9\_setfam\_1~(k1\_fomodel4~\\
X1))))){\unicdbdjdcd}(((r1\_tarski~(k7\_domain\_1~(k9\_funct\_2~(k9\_setfam\_1~\\
(k1\_fomodel4~X1))~(k9\_setfam\_1~(k1\_fomodel4~X1)))~(k22\_fomodel4~\\
X1)~(k25\_fomodel4~X1))~X3){\unicdcdcdhd}((r1\_tarski~(k7\_domain\_1~(k9\_funct\_2~\\
(k9\_setfam\_1~(k1\_fomodel4~X1))~(k9\_setfam\_1~(k1\_fomodel4~X1)))~\\
(k24\_fomodel4~X1)~(k26\_fomodel4~X1))~X3){\unicdcdcdhd}(v10\_fomodel4~X0~X1~X3))){\unicdbdjdcd}\\
(v2\_fomodel3~(k4\_fomodel3~X1~X2~X0)~X1~(k35\_fomodel1~X1)~X2~(k6\_fomodel4~\\
X1~X3~X0)))))\end{array}
\label{hyp:mgbdadcdpfggpgngpgegfgmged}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {\preoh{{{v1\_xboole\_0}~{({{{k2\_tarski}~{X0}}~{X1}})}}}}}}\label{hyp:ggdgddpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {\preoh{{{v1\_xboole\_0}~{({{k1\_zfmisc\_1}~{X0}})}}}}}\label{hyp:ggdgbdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_funct\_2~X2~X0~X1){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
X2)\end{array}
\label{hyp:egehpfngbdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}(m1\_funct\_2~(k9\_funct\_2~\\
X0~X1)~X0~X1)\end{array}
\label{hyp:egehpflgjdpfggfhogdgehpfcd}
\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}(m1\_subset\_1~(k4\_subset\_1~\\
X0~X1~X2)~(k1\_zfmisc\_1~X0))\end{array}
\label{hyp:egehpflgedpfdhfhcgdhfgehpfbd}
\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}(m2\_funct\_2~(k26\_fomodel4~X0)~(k9\_setfam\_1~(k1\_fomodel4~\\
X0))~(k9\_setfam\_1~(k1\_fomodel4~X0))~(k9\_funct\_2~(k9\_setfam\_1~\\
(k1\_fomodel4~X0))~(k9\_setfam\_1~(k1\_fomodel4~X0))))\end{array}
\label{hyp:egehpflgcdgdpfggpgngpgegfgmged}
\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}(m2\_funct\_2~(k24\_fomodel4~X0)~(k9\_setfam\_1~(k1\_fomodel4~\\
X0))~(k9\_setfam\_1~(k1\_fomodel4~X0))~(k9\_funct\_2~(k9\_setfam\_1~\\
(k1\_fomodel4~X0))~(k9\_setfam\_1~(k1\_fomodel4~X0))))\end{array}
\label{hyp:egehpflgcdedpfggpgngpgegfgmged}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  m1\_subset\_1~(k11\_fomodel0~X0~X1)~(k1\_zfmisc\_1~\\
X0)\end{array}
\label{hyp:egehpflgbdbdpfggpgngpgegfgmgad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k11\_fomodel0}~{X0}}~{X1}}={{{k3\_xboole\_0}~{X0}}~{X1}}}}}\label{hyp:egbdedpfggpgngpgegfgmgad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(k9\_subset\_1~X0~X1~X2=k9\_subset\_1~X0~X2~X1)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgjdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k3\_xboole\_0}~{X0}}~{X1}}={{{k3\_xboole\_0}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgddpfihcgpgpgmgfgpfad}
\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}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_fomodel1~X0)){\unicdbdjdcd}((v8\_fomodel1~\\
X1~X0){\unicdbdjdcd}(v9\_fomodel1~X1~X0)))\end{array}
\label{hyp:dgdggdpfggpgngpgegfgmgbd}
\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}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_fomodel1~X0)){\unicdbdjdcd}(((\preoh v5\_fomodel1~\\
X1~X0){\unicdcdcdhd}(v9\_fomodel1~X1~X0)){\unicdbdjdcd}((v4\_fomodel1~X1~X0){\unicdcdcdhd}(v9\_fomodel1~\\
X1~X0))))\end{array}
\label{hyp:dgdgcdhdpfggpgngpgegfgmgbd}
\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}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_fomodel1~X0)){\unicdbdjdcd}(((\preoh v7\_fomodel1~\\
X1~X0){\unicdcdcdhd}(v10\_fomodel1~X1~X0)){\unicdbdjdcd}((v8\_fomodel1~X1~X0){\unicdcdcdhd}(v10\_fomodel1~\\
X1~X0))))\end{array}
\label{hyp:dgdgcdddpfggpgngpgegfgmgbd}
\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:mgbdadddpfggpgngpgegfgmged}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v6\_struct\_0~X1){\unicdcdcdhd}((v11\_fomodel1~X1){\unicdcdcdhd}\\
(l1\_fomodel1~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v10\_fomodel1~X2~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_fomodel1~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k9\_funct\_2~(k9\_setfam\_1~(k1\_fomodel4~X1))~(k9\_setfam\_1~(k1\_fomodel4~\\
X1))))){\unicdbdjdcd}(((r1\_tarski~(k7\_domain\_1~(k9\_funct\_2~(k9\_setfam\_1~\\
(k1\_fomodel4~X1))~(k9\_setfam\_1~(k1\_fomodel4~X1)))~(k22\_fomodel4~\\
X1)~(k25\_fomodel4~X1))~X3){\unicdcdcdhd}((k9\_subset\_1~(k9\_funct\_2~(k9\_setfam\_1~\\
(k1\_fomodel4~X1))~(k9\_setfam\_1~(k1\_fomodel4~X1)))~X3~(k6\_domain\_1~\\
(k9\_funct\_2~(k9\_setfam\_1~(k1\_fomodel4~X1))~(k9\_setfam\_1~(k1\_fomodel4~\\
X1)))~(k27\_fomodel4~X1))=k6\_domain\_1~(k9\_funct\_2~(k9\_setfam\_1~\\
(k1\_fomodel4~X1))~(k9\_setfam\_1~(k1\_fomodel4~X1)))~(k27\_fomodel4~\\
X1)){\unicdcdcdhd}((k9\_subset\_1~(k9\_funct\_2~(k9\_setfam\_1~(k1\_fomodel4~X1))~\\
(k9\_setfam\_1~(k1\_fomodel4~X1)))~(k6\_domain\_1~(k9\_funct\_2~(k9\_setfam\_1~\\
(k1\_fomodel4~X1))~(k9\_setfam\_1~(k1\_fomodel4~X1)))~(k24\_fomodel4~\\
X1))~X3=k6\_domain\_1~(k9\_funct\_2~(k9\_setfam\_1~(k1\_fomodel4~X1))~\\
(k9\_setfam\_1~(k1\_fomodel4~X1)))~(k24\_fomodel4~X1)){\unicdcdcdhd}((k9\_subset\_1~\\
(k9\_funct\_2~(k9\_setfam\_1~(k1\_fomodel4~X1))~(k9\_setfam\_1~(k1\_fomodel4~\\
X1)))~(k6\_domain\_1~(k9\_funct\_2~(k9\_setfam\_1~(k1\_fomodel4~X1))~\\
(k9\_setfam\_1~(k1\_fomodel4~X1)))~(k26\_fomodel4~X1))~X3=k6\_domain\_1~\\
(k9\_funct\_2~(k9\_setfam\_1~(k1\_fomodel4~X1))~(k9\_setfam\_1~(k1\_fomodel4~\\
X1)))~(k26\_fomodel4~X1)){\unicdcdcdhd}((k9\_subset\_1~(k9\_funct\_2~(k9\_setfam\_1~\\
(k1\_fomodel4~X1))~(k9\_setfam\_1~(k1\_fomodel4~X1)))~X3~(k6\_domain\_1~\\
(k9\_funct\_2~(k9\_setfam\_1~(k1\_fomodel4~X1))~(k9\_setfam\_1~(k1\_fomodel4~\\
X1)))~(k28\_fomodel4~X1))=k6\_domain\_1~(k9\_funct\_2~(k9\_setfam\_1~\\
(k1\_fomodel4~X1))~(k9\_setfam\_1~(k1\_fomodel4~X1)))~(k28\_fomodel4~\\
X1)){\unicdcdcdhd}(v10\_fomodel4~X0~X1~X3)))))){\unicdbdjdcd}(v2\_fomodel3~(k4\_fomodel3~\\
X1~X2~X0)~X1~(k35\_fomodel1~X1)~X2~(k6\_fomodel4~X1~X3~X0)))))\end{array}$$
\end{theorem}
\end{document}
