\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{t7\_partfun2 (TMXqNh4w4WQxyXyP5Y1EGiswansdH83tA8d)}
\maketitle
Let $ v1\_xboole\_0 : {{\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 $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k1\_partfun2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k3\_xboole\_0 : {{\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 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0)))){\unicdbdjdcd}((r2\_relset\_1~X0~X0~X2~(k1\_partfun2~X0~X1)){\unicdbdjded}\\
((k1\_relset\_1~X0~X2=X1){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~X0){\unicdbdjdcd}((X3 \in \\
X1){\unicdbdjdcd}(k7\_partfun1~X0~X2~X3=X3)))))))\end{array}
\label{hyp:ehgdpfahbgchehggfhogcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X0 \in X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X2))){\unicdbdjdcd}(m1\_subset\_1~X0~X2)\end{array}
\label{hyp:ehedpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (\preoh v1\_xboole\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}\\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X2~X0)))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~\\
X1)))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_funct\_1~X5){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X2~X1)))){\unicdbdjdcd}((r2\_relset\_1~X2~X1~X5~(k1\_partfun1~X2~X0~\\
X0~X1~X3~X4)){\unicdbdjded}(({\unicdcdadad} X6 .  (m1\_subset\_1~X6~X2){\unicdbdjdcd}((X6 \in k1\_relset\_1~\\
X2~X5){\unicdbdjded}((X6 \in k1\_relset\_1~X2~X3){\unicdcdcdhd}(k7\_partfun1~X0~X3~X6 \in k1\_relset\_1~\\
X0~X4)))){\unicdcdcdhd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~X2){\unicdbdjdcd}((X6 \in k1\_relset\_1~X2~\\
X5){\unicdbdjdcd}(k7\_partfun1~X1~X5~X6=k7\_partfun1~X1~X4~(k7\_partfun1~X0~X3~X6)))))))))))\end{array}
\label{hyp:ehddpfahbgchehggfhogcd}
\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~X2)\end{array}
\label{hyp:chfgggmgfgihjgghjgehjhpfchcdpfchfgmgdhfgehpfbd}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0))){\unicdbdjdcd}((v1\_funct\_1~(k1\_partfun2~X0~X1)){\unicdcdcdhd}(m1\_subset\_1~(k1\_partfun2~\\
X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0))))\end{array}
\label{hyp:egehpflgbdpfahbgchehggfhogcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
(((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1)))){\unicdcdcdhd}((v1\_funct\_1~X5){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X2~X3))))){\unicdbdjdcd}((v1\_funct\_1~(k1\_partfun1~X0~X1~X2~X3~X4~X5)){\unicdcdcdhd}(m1\_subset\_1~\\
(k1\_partfun1~X0~X1~X2~X3~X4~X5)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X3))))\end{array}
\label{hyp:egehpflgbdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X2=k3\_xboole\_0~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(X3 \in X2){\unicdbdjded}((X3 \in X0){\unicdcdcdhd}(X3 \in X1)))\end{array}
\label{hyp:egedpfihcgpgpgmgfgpfad}
\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}
\begin{theorem}\label{thm:ehhdpfahbgchehggfhogcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~\\
X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)))){\unicdbdjdcd}((X2 \in \\
k9\_subset\_1~X0~(k1\_relset\_1~X0~X3)~X1){\unicdbdjdcd}(k7\_partfun1~X0~X3~X2=k7\_partfun1~\\
X0~(k1\_partfun1~X0~X0~X0~X0~(k1\_partfun2~X0~X1)~X3)~X2)))))\end{array}$$
\end{theorem}
\end{document}
