\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{t52\_modelc\_1 (TMFA76n7U9gFsqEvAg5aLXAPW7Lt5ypwjwS)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k30\_modelc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k48\_modelc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k61\_modelc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k4\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k51\_modelc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k9\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k50\_modelc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k58\_modelc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k3\_robbins1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k28\_modelc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v6\_cohsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k53\_modelc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k52\_modelc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k60\_modelc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k59\_modelc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k54\_modelc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k25\_modelc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_partfun1~X1~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k30\_modelc\_1~\\
X0)))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~(k48\_modelc\_1~\\
X0~X1~X2))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k1\_zfmisc\_1~X0)){\unicdbdjdcd}(k3\_funct\_2~\\
(k1\_zfmisc\_1~X0)~(k1\_zfmisc\_1~X0)~(k58\_modelc\_1~X0~X1~X2~X3)~X4=\\
k9\_subset\_1~X0~(k51\_modelc\_1~X0~X1~X2~X3)~(k50\_modelc\_1~X0~X1~X4))))))\end{array}
\label{hyp:ehfdbdpfngpgegfgmgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_partfun1~X1~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k30\_modelc\_1~\\
X0)))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~(k48\_modelc\_1~\\
X0~X1~X2))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~(k48\_modelc\_1~\\
X0~X1~X2))){\unicdbdjdcd}((k51\_modelc\_1~X0~X1~X2~(k3\_robbins1~(k48\_modelc\_1~\\
X0~X1~X2)~X3)=k6\_subset\_1~X0~(k51\_modelc\_1~X0~X1~X2~X3)){\unicdcdcdhd}((k51\_modelc\_1~\\
X0~X1~X2~(k2\_lattices~(k48\_modelc\_1~X0~X1~X2)~X3~X4)=k9\_subset\_1~\\
X0~(k51\_modelc\_1~X0~X1~X2~X3)~(k51\_modelc\_1~X0~X1~X2~X4)){\unicdcdcdhd}(k51\_modelc\_1~\\
X0~X1~X2~(k28\_modelc\_1~(k48\_modelc\_1~X0~X1~X2)~X3~X4)=k4\_subset\_1~\\
X0~(k51\_modelc\_1~X0~X1~X2~X3)~(k51\_modelc\_1~X0~X1~X2~X4))))))))\end{array}
\label{hyp:ehddddpfngpgegfgmgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}(((v1\_partfun1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0)))){\unicdcdcdhd}(((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(\\
k30\_modelc\_1~X0)))){\unicdcdcdhd}((m1\_subset\_1~X3~(u1\_struct\_0~(k48\_modelc\_1~\\
X0~X1~X2))){\unicdcdcdhd}(m1\_subset\_1~X4~(u1\_struct\_0~(k48\_modelc\_1~X0~X1~X2))))))){\unicdbdjdcd}\\
((v1\_funct\_1~(k61\_modelc\_1~X0~X1~X2~X3~X4)){\unicdcdcdhd}((v1\_funct\_2~(k61\_modelc\_1~\\
X0~X1~X2~X3~X4)~(k1\_zfmisc\_1~X0)~(k1\_zfmisc\_1~X0)){\unicdcdcdhd}((v6\_cohsp\_1~\\
(k61\_modelc\_1~X0~X1~X2~X3~X4)){\unicdcdcdhd}(m1\_subset\_1~(k61\_modelc\_1~X0~X1~\\
X2~X3~X4)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_zfmisc\_1~X0)~(k1\_zfmisc\_1~\\
X0)))))))\end{array}
\label{hyp:egehpflggdbdpfngpgegfgmgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
(((v1\_partfun1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0)))){\unicdcdcdhd}(((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(\\
k30\_modelc\_1~X0)))){\unicdcdcdhd}(m1\_subset\_1~X3~(u1\_struct\_0~(k48\_modelc\_1~\\
X0~X1~X2)))))){\unicdbdjdcd}((v1\_funct\_1~(k58\_modelc\_1~X0~X1~X2~X3)){\unicdcdcdhd}((v1\_funct\_2~\\
(k58\_modelc\_1~X0~X1~X2~X3)~(k1\_zfmisc\_1~X0)~(k1\_zfmisc\_1~X0)){\unicdcdcdhd}(\\
(v6\_cohsp\_1~(k58\_modelc\_1~X0~X1~X2~X3)){\unicdcdcdhd}(m1\_subset\_1~(k58\_modelc\_1~\\
X0~X1~X2~X3)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_zfmisc\_1~X0)~(k1\_zfmisc\_1~\\
X0)))))))\end{array}
\label{hyp:egehpflgfdidpfngpgegfgmgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}(((v1\_partfun1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0)))){\unicdcdcdhd}(((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(\\
k30\_modelc\_1~X0)))){\unicdcdcdhd}((m1\_subset\_1~X3~(u1\_struct\_0~(k48\_modelc\_1~\\
X0~X1~X2))){\unicdcdcdhd}(m1\_subset\_1~X4~(u1\_struct\_0~(k48\_modelc\_1~X0~X1~X2))))))){\unicdbdjdcd}\\
(m1\_subset\_1~(k53\_modelc\_1~X0~X1~X2~X3~X4)~(u1\_struct\_0~(k48\_modelc\_1~\\
X0~X1~X2)))\end{array}
\label{hyp:egehpflgfdddpfngpgegfgmgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
(((v1\_partfun1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0)))){\unicdcdcdhd}(((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(\\
k30\_modelc\_1~X0)))){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~X0))))){\unicdbdjdcd}(m1\_subset\_1~\\
(k52\_modelc\_1~X0~X1~X2~X3)~(u1\_struct\_0~(k48\_modelc\_1~X0~X1~X2)))\end{array}
\label{hyp:egehpflgfdcdpfngpgegfgmgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_partfun1~X1~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k30\_modelc\_1~\\
X0)))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~(k48\_modelc\_1~\\
X0~X1~X2))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~(k48\_modelc\_1~\\
X0~X1~X2))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_funct\_1~X5){\unicdcdcdhd}((v1\_funct\_2~X5~(k1\_zfmisc\_1~\\
X0)~(k1\_zfmisc\_1~X0)){\unicdcdcdhd}((v6\_cohsp\_1~X5){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k1\_zfmisc\_1~X0)~(k1\_zfmisc\_1~X0))))))){\unicdbdjdcd}((X5=k61\_modelc\_1~\\
X0~X1~X2~X3~X4){\unicdbdjded}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(k1\_zfmisc\_1~X0)){\unicdbdjdcd}(\\
k3\_funct\_2~(k1\_zfmisc\_1~X0)~(k1\_zfmisc\_1~X0)~X5~X6=k60\_modelc\_1~\\
X0~X1~X2~X3~X4~X6))))))))\end{array}
\label{hyp:eghdddpfngpgegfgmgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_partfun1~X1~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k30\_modelc\_1~\\
X0)))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~(k48\_modelc\_1~\\
X0~X1~X2))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~(k48\_modelc\_1~\\
X0~X1~X2))){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(k1\_zfmisc\_1~X0)){\unicdbdjdcd}(k60\_modelc\_1~\\
X0~X1~X2~X3~X4~X5=k51\_modelc\_1~X0~X1~X2~(k59\_modelc\_1~X0~X1~X2~X3~X4~(\\
k52\_modelc\_1~X0~X1~X2~X5))))))))\end{array}
\label{hyp:eghdcdpfngpgegfgmgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_partfun1~X1~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k30\_modelc\_1~\\
X0)))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~(k48\_modelc\_1~\\
X0~X1~X2))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~(k48\_modelc\_1~\\
X0~X1~X2))){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~(k48\_modelc\_1~\\
X0~X1~X2))){\unicdbdjdcd}(k59\_modelc\_1~X0~X1~X2~X3~X4~X5=k28\_modelc\_1~(k48\_modelc\_1~\\
X0~X1~X2)~X4~(k53\_modelc\_1~X0~X1~X2~X3~X5)))))))\end{array}
\label{hyp:eghdbdpfngpgegfgmgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_partfun1~X1~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k30\_modelc\_1~\\
X0)))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~(k48\_modelc\_1~\\
X0~X1~X2))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~(k1\_zfmisc\_1~\\
X0)~(k1\_zfmisc\_1~X0)){\unicdcdcdhd}((v6\_cohsp\_1~X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k1\_zfmisc\_1~X0)~(k1\_zfmisc\_1~X0))))))){\unicdbdjdcd}((X4=k58\_modelc\_1~\\
X0~X1~X2~X3){\unicdbdjded}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(k1\_zfmisc\_1~X0)){\unicdbdjdcd}(k3\_funct\_2~\\
(k1\_zfmisc\_1~X0)~(k1\_zfmisc\_1~X0)~X4~X5=k54\_modelc\_1~X0~X1~X2~X3~\\
X5)))))))\end{array}
\label{hyp:eghdadpfngpgegfgmgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_partfun1~X1~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k30\_modelc\_1~\\
X0)))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~(k48\_modelc\_1~\\
X0~X1~X2))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k1\_zfmisc\_1~X0)){\unicdbdjdcd}(k54\_modelc\_1~\\
X0~X1~X2~X3~X4=k51\_modelc\_1~X0~X1~X2~(k53\_modelc\_1~X0~X1~X2~X3~(k52\_modelc\_1~\\
X0~X1~X2~X4)))))))\end{array}
\label{hyp:eggdgdpfngpgegfgmgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_partfun1~X1~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k30\_modelc\_1~\\
X0)))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~(k48\_modelc\_1~\\
X0~X1~X2))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~(k48\_modelc\_1~\\
X0~X1~X2))){\unicdbdjdcd}(k53\_modelc\_1~X0~X1~X2~X3~X4=k2\_lattices~(k48\_modelc\_1~\\
X0~X1~X2)~X3~(k25\_modelc\_1~(k48\_modelc\_1~X0~X1~X2)~X4))))))\end{array}
\label{hyp:eggdfdpfngpgegfgmgdgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehfdcdpfngpgegfgmgdgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_partfun1~X1~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k30\_modelc\_1~\\
X0)))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~(k48\_modelc\_1~\\
X0~X1~X2))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~(k48\_modelc\_1~\\
X0~X1~X2))){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(k1\_zfmisc\_1~X0)){\unicdbdjdcd}(k3\_funct\_2~\\
(k1\_zfmisc\_1~X0)~(k1\_zfmisc\_1~X0)~(k61\_modelc\_1~X0~X1~X2~X3~X4)~X5=\\
k4\_subset\_1~X0~(k51\_modelc\_1~X0~X1~X2~X4)~(k9\_subset\_1~X0~(k51\_modelc\_1~\\
X0~X1~X2~X3)~(k50\_modelc\_1~X0~X1~X5))))))))\end{array}$$
\end{theorem}
\end{document}
