\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{t37\_setwop\_2 (TMSviXxEvp8p6SfJwuFSZBsqNVT2BEm6DB6)}
\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 $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k4\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\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 $ v1\_setwiseo : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_finseqop : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r8\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ k7\_finseqop : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k6\_partfun1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_finseqop : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_finsop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_finseqop : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k4\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_relat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_partfun1 : {{\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 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~X0))))){\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~X1~X0){\unicdcdcdhd}\\
((v2\_binop\_1~X1~X0){\unicdcdcdhd}((v1\_setwiseo~X1~X0){\unicdcdcdhd}((v1\_finseqop~X1~X0){\unicdcdcdhd}\\
(r8\_binop\_1~X0~X0~X0~X2~(k7\_finseqop~X0~X1~(k6\_partfun1~X0)~(k5\_finseqop~\\
X0~X1))))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~X0){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~X0){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~X0){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~\\
X6~X0){\unicdbdjdcd}(k5\_binop\_1~X0~X1~(k5\_binop\_1~X0~X2~X3~X4)~(k5\_binop\_1~X0~X2~\\
X5~X6)=k5\_binop\_1~X0~X2~(k5\_binop\_1~X0~X1~X3~X5)~(k5\_binop\_1~X0~X1~\\
X4~X6)))))))))\end{array}
\label{hyp:ehidjdpfggjgogdhfgbhpgah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\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}(((v2\_binop\_1~X2~X0){\unicdcdcdhd}((v1\_setwiseo~X2~X0){\unicdcdcdhd}(v1\_finseqop~\\
X2~X0))){\unicdbdjdcd}(k5\_binop\_1~X0~(k7\_finseqop~X0~X2~(k6\_partfun1~X0)~(k5\_finseqop~\\
X0~X2))~X1~X1=k4\_binop\_1~X0~X2))))\end{array}
\label{hyp:ehidgdpfggjgogdhfgbhpgah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\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}({\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}({\unicdcdadad} X4 .  (v7\_ordinal1~X4){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
(m2\_finseq\_2~X5~X0~(k4\_finseq\_2~X4~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m2\_finseq\_2~\\
X6~X0~(k4\_finseq\_2~X4~X0)){\unicdbdjdcd}(((v1\_binop\_1~X2~X0){\unicdcdcdhd}((v2\_binop\_1~X2~\\
X0){\unicdcdcdhd}((v1\_setwiseo~X2~X0){\unicdcdcdhd}((X1=k4\_binop\_1~X0~X2){\unicdcdcdhd}((k5\_binop\_1~\\
X0~X3~X1~X1=X1){\unicdcdcdhd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~X0){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_subset\_1~\\
X8~X0){\unicdbdjdcd}({\unicdcdadad} X9 .  (m1\_subset\_1~X9~X0){\unicdbdjdcd}({\unicdcdadad} X10 .  (m1\_subset\_1~\\
X10~X0){\unicdbdjdcd}(k5\_binop\_1~X0~X2~(k5\_binop\_1~X0~X3~X7~X8)~(k5\_binop\_1~X0~\\
X3~X9~X10)=k5\_binop\_1~X0~X3~(k5\_binop\_1~X0~X2~X7~X9)~(k5\_binop\_1~X0~\\
X2~X8~X10))))))))))){\unicdbdjdcd}(k5\_binop\_1~X0~X3~(k1\_finsop\_1~X0~X5~X2)~(k1\_finsop\_1~\\
X0~X6~X2)=k1\_finsop\_1~X0~(k1\_finseqop~X0~X0~X0~X3~X5~X6)~X2))))))))\end{array}
\label{hyp:ehddddpfdhfgehhhpgahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (((v1\_funct\_1~\\
X3){\unicdcdcdhd}((v1\_funct\_2~X3~(k2\_zfmisc\_1~X0~X1)~X2){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)~X2))))){\unicdcdcdhd}((v1\_funct\_1~X4){\unicdcdcdhd}((\\
v1\_funct\_2~X4~(k2\_zfmisc\_1~X0~X1)~X2){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)~X2)))))){\unicdbdjdcd}((r8\_binop\_1~X0~X1~X2~\\
X3~X4){\unicdbdjded}(X3=X4))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchidpfcgjgogpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k6\_partfun1}~{X0}}={{k4\_relat\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~(k4\_relat\_1~X0)){\unicdcdcdhd}((v4\_relat\_1~(k4\_relat\_1~\\
X0)~X0){\unicdcdcdhd}((v1\_funct\_1~(k4\_relat\_1~X0)){\unicdcdcdhd}(v1\_partfun1~(k4\_relat\_1~\\
X0)~X0)))\end{array}
\label{hyp:ggdgbdbdpfggfhogdgehpfcd}
\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\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~X0))))){\unicdcdcdhd}(((v1\_funct\_1~\\
X2){\unicdcdcdhd}((v1\_funct\_2~X2~X0~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0))))){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~X0~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)))))))){\unicdbdjdcd}((v1\_funct\_1~(k7\_finseqop~\\
X0~X1~X2~X3)){\unicdcdcdhd}((v1\_funct\_2~(k7\_finseqop~X0~X1~X2~X3)~(k2\_zfmisc\_1~\\
X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~(k7\_finseqop~X0~X1~X2~X3)~(k1\_zfmisc\_1~(\\
k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~X0)))))\end{array}
\label{hyp:egehpflghdpfggjgogdhfgbhpgah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_partfun1~(k6\_partfun1~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~(k6\_partfun1~\\
X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)))\end{array}
\label{hyp:egehpflggdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~X0)))))){\unicdbdjdcd}((v1\_funct\_1~(k5\_finseqop~\\
X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(k5\_finseqop~X0~X1)~X0~X0){\unicdcdcdhd}(m1\_subset\_1~(\\
k5\_finseqop~X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)))))\end{array}
\label{hyp:egehpflgfdpfggjgogdhfgbhpgah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k2\_zfmisc\_1~\\
X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0)~X0))))){\unicdbdjdcd}(m1\_subset\_1~(k4\_binop\_1~X0~X1)~X0)\end{array}
\label{hyp:egehpflgedpfcgjgogpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}((v1\_partfun1~X2~X0){\unicdbdjdcd}(v1\_funct\_2~X2~X0~X1))\end{array}
\label{hyp:dgdgbdpfggfhogdgehpfcd}
\end{equation}
\begin{theorem}\label{thm:ehddhdpfdhfgehhhpgahpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~X0))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~\\
X2){\unicdcdcdhd}((v1\_funct\_2~X2~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~X0))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (v7\_ordinal1~\\
X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_finseq\_2~X4~X0~(k4\_finseq\_2~X3~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
(m2\_finseq\_2~X5~X0~(k4\_finseq\_2~X3~X0)){\unicdbdjdcd}(((v1\_binop\_1~X1~X0){\unicdcdcdhd}(\\
(v2\_binop\_1~X1~X0){\unicdcdcdhd}((v1\_setwiseo~X1~X0){\unicdcdcdhd}((v1\_finseqop~X1~X0){\unicdcdcdhd}\\
(r8\_binop\_1~X0~X0~X0~X2~(k7\_finseqop~X0~X1~(k6\_partfun1~X0)~(k5\_finseqop~\\
X0~X1))))))){\unicdbdjdcd}(k5\_binop\_1~X0~X2~(k1\_finsop\_1~X0~X4~X1)~(k1\_finsop\_1~\\
X0~X5~X1)=k1\_finsop\_1~X0~(k1\_finseqop~X0~X0~X0~X2~X4~X5)~X1)))))))\end{array}$$
\end{theorem}
\end{document}
