\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{t28\_partit1 (TMd4coTozkrZeTwLsNrpfbAafVVmF8urEc2)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_eqrel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_partit1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_partit1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_partit1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_eqrel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_eqrel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v3\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_relat\_2 : {{\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 $ r2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_eqrel\_1~X1~X0){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_eqrel\_1~X2~X0){\unicdbdjdcd}((k4\_partit1~X0~X1=k4\_partit1~\\
X0~X2){\unicdbdjdcd}(X1=X2))))\end{array}
\label{hyp:ehcdfdpfahbgchehjgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_eqrel\_1~X1~X0){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_eqrel\_1~X2~X0){\unicdbdjdcd}(k4\_partit1~X0~(k2\_partit1~X0~X1~\\
X2)=k4\_eqrel\_1~X0~(k4\_partit1~X0~X1)~(k4\_partit1~X0~X2))))\end{array}
\label{hyp:ehcdedpfahbgchehjgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_eqrel\_1~X1~X0){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_eqrel\_1~X2~X0){\unicdbdjdcd}(k4\_partit1~X0~(k3\_partit1~X0~X1~\\
X2)=k5\_eqrel\_1~X0~(k4\_partit1~X0~X1)~(k4\_partit1~X0~X2))))\end{array}
\label{hyp:ehcdddpfahbgchehjgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v3\_relat\_2~X1){\unicdcdcdhd}((v8\_relat\_2~X1){\unicdcdcdhd}((v1\_partfun1~\\
X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v3\_relat\_2~X2){\unicdcdcdhd}((v8\_relat\_2~X2){\unicdcdcdhd}((v1\_partfun1~\\
X2~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)))))){\unicdbdjdcd}\\
(r2\_relset\_1~X0~X0~(k5\_eqrel\_1~X0~X1~(k4\_eqrel\_1~X0~X1~X2))~X1))\end{array}
\label{hyp:ehbdhdpffgbhchfgmgpfbd}
\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))){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}((r2\_relset\_1~X0~X1~X2~X3){\unicdbdjded}(X2=X3))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchcdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_eqrel\_1~X1~X0)){\unicdbdjdcd}\\
((v1\_partfun1~(k4\_partit1~X0~X1)~X0){\unicdcdcdhd}((v3\_relat\_2~(k4\_partit1~\\
X0~X1)){\unicdcdcdhd}((v8\_relat\_2~(k4\_partit1~X0~X1)){\unicdcdcdhd}(m1\_subset\_1~(k4\_partit1~\\
X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0))))))\end{array}
\label{hyp:egehpflgedpfahbgchehjgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((m1\_eqrel\_1~\\
X1~X0){\unicdcdcdhd}(m1\_eqrel\_1~X2~X0))){\unicdbdjdcd}(m1\_eqrel\_1~(k3\_partit1~X0~X1~X2)~X0)\end{array}
\label{hyp:egehpflgddpfahbgchehjgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((m1\_eqrel\_1~\\
X1~X0){\unicdcdcdhd}(m1\_eqrel\_1~X2~X0))){\unicdbdjdcd}(m1\_eqrel\_1~(k2\_partit1~X0~X1~X2)~X0)\end{array}
\label{hyp:egehpflgcdpfahbgchehjgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((m1\_eqrel\_1~\\
X1~X0){\unicdcdcdhd}(m1\_eqrel\_1~X2~X0))){\unicdbdjdcd}(k3\_partit1~X0~X1~X2=k3\_partit1~X0~\\
X2~X1)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgddpfahbgchehjgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((m1\_eqrel\_1~\\
X1~X0){\unicdcdcdhd}(m1\_eqrel\_1~X2~X0))){\unicdbdjdcd}(k2\_partit1~X0~X1~X2=k2\_partit1~X0~\\
X2~X1)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfahbgchehjgehbd}
\end{equation}
\begin{theorem}\label{thm:ehcdidpfahbgchehjgehbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_eqrel\_1~X1~X0){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_eqrel\_1~X2~X0){\unicdbdjdcd}(k3\_partit1~X0~X1~(k2\_partit1~X0~\\
X1~X2)=X1)))\end{array}$$
\end{theorem}
\end{document}
