\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{t53\_setwiseo (TMMLhxRRfFf6dJi6jkRzQt43tpAJ45ax7aQ)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ k2\_zfmisc\_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 $ v1\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_setwiseo : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_finsub\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_setwiseo : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_setwiseo : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k10\_setwiseo : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k7\_setwiseo : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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\_xboole\_0 : {\iota}$ be given.
Let $ k8\_setwiseo : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k7\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_finsub\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\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 .  {\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(k2\_zfmisc\_1~\\
X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0)~X0))))){\unicdbdjdcd}(((v1\_binop\_1~X3~X0){\unicdcdcdhd}((v2\_binop\_1~X3~X0){\unicdcdcdhd}(v3\_binop\_1~\\
X3~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k5\_finsub\_1~X1)){\unicdbdjdcd}((X4{\unicdcdgdad}\\
k1\_xboole\_0){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_funct\_1~X5){\unicdcdcdhd}((v1\_funct\_2~X5~X1~\\
(k5\_finsub\_1~X2)){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X1~(k5\_finsub\_1~X2)))))){\unicdbdjdcd}({\unicdcdadad} X6 .  ((v1\_funct\_1~X6){\unicdcdcdhd}((v1\_funct\_2~\\
X6~(k5\_finsub\_1~X2)~X0){\unicdcdcdhd}(m1\_subset\_1~X6~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k5\_finsub\_1~X2)~X0))))){\unicdbdjdcd}(({\unicdcdadad} X7 .  (m1\_subset\_1~X7~(k5\_finsub\_1~\\
X2)){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_subset\_1~X8~(k5\_finsub\_1~X2)){\unicdbdjdcd}(k3\_funct\_2~\\
(k5\_finsub\_1~X2)~X0~X6~(k5\_setwiseo~X2~X7~X8)=k5\_binop\_1~X0~X3~(k3\_funct\_2~\\
(k5\_finsub\_1~X2)~X0~X6~X7)~(k3\_funct\_2~(k5\_finsub\_1~X2)~X0~X6~X8)))){\unicdbdjdcd}\\
(k3\_funct\_2~(k5\_finsub\_1~X2)~X0~X6~(k10\_setwiseo~X1~X2~X4~X5)=k7\_setwiseo~\\
X1~X0~X3~X4~(k1\_partfun1~X1~(k5\_finsub\_1~X2)~(k5\_finsub\_1~X2)~X0~X5~\\
X6))))))))))\end{array}
\label{hyp:ehfdcdpfdhfgehhhjgdhfgpg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_funct\_1~\\
X2){\unicdcdcdhd}((v1\_funct\_2~X2~X0~(k5\_finsub\_1~X1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~(k5\_finsub\_1~X1)))))){\unicdbdjdcd}(k10\_setwiseo~X0~X1~(k1\_setwiseo~\\
X0)~X2=k1\_xboole\_0))\end{array}
\label{hyp:ehedhdpfdhfgehhhjgdhfgpg}
\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}\\
((v1\_funct\_2~X3~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~X0))))){\unicdbdjdcd}(((v3\_binop\_1~X3~X0){\unicdcdcdhd}\\
((v1\_binop\_1~X3~X0){\unicdcdcdhd}((v2\_binop\_1~X3~X0){\unicdcdcdhd}(v1\_setwiseo~X3~X0)))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k5\_finsub\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X5 .  ((\\
v1\_funct\_1~X5){\unicdcdcdhd}((v1\_funct\_2~X5~X1~X2){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X1~X2))))){\unicdbdjdcd}({\unicdcdadad} X6 .  ((v1\_funct\_1~X6){\unicdcdcdhd}((v1\_funct\_2~\\
X6~X2~X0){\unicdcdcdhd}(m1\_subset\_1~X6~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X2~X0))))){\unicdbdjdcd}\\
(k7\_setwiseo~X2~X0~X3~(k8\_setwiseo~X1~X2~X5~X4)~X6=k7\_setwiseo~X1~\\
X0~X3~X4~(k1\_partfun1~X1~X2~X2~X0~X5~X6)))))))))\end{array}
\label{hyp:ehddfdpfdhfgehhhjgdhfgpg}
\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 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(k2\_zfmisc\_1~X0~\\
X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0)~X0))))){\unicdbdjdcd}(((v1\_binop\_1~X2~X0){\unicdcdcdhd}((v2\_binop\_1~X2~X0){\unicdcdcdhd}(v1\_setwiseo~\\
X2~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~X1~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~X0))))){\unicdbdjdcd}(k7\_setwiseo~\\
X1~X0~X2~(k1\_setwiseo~X1)~X3=k4\_binop\_1~X0~X2)))))\end{array}
\label{hyp:ehddbdpfdhfgehhhjgdhfgpg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~X0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))))){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k5\_finsub\_1~X0))))){\unicdbdjdcd}(k8\_setwiseo~X0~X1~X2~X3=k7\_relat\_1~X2~\\
X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgidpfdhfgehhhjgdhfgpg}
\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 .  (\preoh v1\_xboole\_0~(k5\_finsub\_1~X0)){\unicdcdcdhd}(v4\_finsub\_1~(k5\_finsub\_1~\\
X0))\end{array}
\label{hyp:ggdgcdpfggjgogdhfhcgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{k1\_xboole\_0}}\label{hyp:ggdgbdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_xboole\_0~X1)){\unicdbdjdcd}(v1\_xboole\_0~\\
(k7\_relat\_1~X0~X1))\end{array}
\label{hyp:ggdgbdjdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k1\_setwiseo}~{X0}}={k1\_xboole\_0}}}\label{hyp:egbdpfdhfgehhhjgdhfgpg}
\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:ehfdddpfdhfgehhhjgdhfgpg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(k2\_zfmisc\_1~\\
X1~X1)~X1){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~\\
X1~X1)~X1))))){\unicdbdjdcd}(((v1\_binop\_1~X3~X1){\unicdcdcdhd}((v2\_binop\_1~X3~X1){\unicdcdcdhd}((v3\_binop\_1~\\
X3~X1){\unicdcdcdhd}(v1\_setwiseo~X3~X1)))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}(\\
(v1\_funct\_2~X4~X0~(k5\_finsub\_1~X2)){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~(k5\_finsub\_1~X2)))))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_funct\_1~\\
X5){\unicdcdcdhd}((v1\_funct\_2~X5~(k5\_finsub\_1~X2)~X1){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k5\_finsub\_1~X2)~X1))))){\unicdbdjdcd}(((k3\_funct\_2~(k5\_finsub\_1~\\
X2)~X1~X5~(k1\_setwiseo~X2)=k4\_binop\_1~X1~X3){\unicdcdcdhd}({\unicdcdadad} X6 .  (m1\_subset\_1~\\
X6~(k5\_finsub\_1~X2)){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~(k5\_finsub\_1~\\
X2)){\unicdbdjdcd}(k3\_funct\_2~(k5\_finsub\_1~X2)~X1~X5~(k5\_setwiseo~X2~X6~X7)=\\
k5\_binop\_1~X1~X3~(k3\_funct\_2~(k5\_finsub\_1~X2)~X1~X5~X6)~(k3\_funct\_2~\\
(k5\_finsub\_1~X2)~X1~X5~X7))))){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(k5\_finsub\_1~\\
X0)){\unicdbdjdcd}(k3\_funct\_2~(k5\_finsub\_1~X2)~X1~X5~(k10\_setwiseo~X0~X2~X6~X4)=\\
k7\_setwiseo~X0~X1~X3~X6~(k1\_partfun1~X0~(k5\_finsub\_1~X2)~(k5\_finsub\_1~\\
X2)~X1~X4~X5)))))))))\end{array}$$
\end{theorem}
\end{document}
