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\begin{document}
\title{t29\_bagorder (TMd4nkeFpHnz5ArmWgiBHJqTTu16E8xgAuY)}
\maketitle
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_bagorder : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k7\_bagorder : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k15\_pre\_poly : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_relat\_2 : {{\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 $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_pre\_poly : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k11\_pre\_poly : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r7\_relat\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_bagorder : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_bagorder : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k16\_pre\_poly : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_partfun1~X1~(k15\_pre\_poly~\\
X0)){\unicdcdcdhd}((v1\_relat\_2~X1){\unicdcdcdhd}((v4\_relat\_2~X1){\unicdcdcdhd}((v8\_relat\_2~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k15\_pre\_poly~X0)~(k15\_pre\_poly~\\
X0)))))))){\unicdbdjdcd}((({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}\\
((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_partfun1~X2~X0){\unicdcdcdhd}((v4\_valued\_0~X2){\unicdcdcdhd}(v2\_pre\_poly~\\
X2)))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}((v4\_relat\_1~X3~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X3){\unicdcdcdhd}((v1\_partfun1~X3~X0){\unicdcdcdhd}((v4\_valued\_0~X3){\unicdcdcdhd}(v2\_pre\_poly~\\
X3)))))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_relat\_1~X4){\unicdcdcdhd}((v4\_relat\_1~X4~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X4){\unicdcdcdhd}((v1\_partfun1~X4~X0){\unicdcdcdhd}((v4\_valued\_0~X4){\unicdcdcdhd}(v2\_pre\_poly~\\
X4)))))){\unicdbdjdcd}((k4\_tarski~X2~X3 \in X1){\unicdbdjdcd}(k4\_tarski~(k11\_pre\_poly~X0~X2~\\
X4)~(k11\_pre\_poly~X0~X3~X4) \in X1))))){\unicdcdcdhd}(r7\_relat\_2~X1~(k15\_pre\_poly~\\
X0))){\unicdbdjdcd}(v2\_bagorder~(k5\_bagorder~X0~X1)~X0)))\end{array}
\label{hyp:ehcdgdpfcgbghgpgchegfgch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}((v1\_partfun1~(k4\_bagorder~X0)~(\\
k15\_pre\_poly~X0)){\unicdcdcdhd}((v1\_relat\_2~(k4\_bagorder~X0)){\unicdcdcdhd}((v4\_relat\_2~\\
(k4\_bagorder~X0)){\unicdcdcdhd}((v8\_relat\_2~(k4\_bagorder~X0)){\unicdcdcdhd}(v2\_bagorder~\\
(k4\_bagorder~X0)~X0)))))\end{array}
\label{hyp:ggdggdpfcgbghgpgchegfgch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}((v1\_partfun1~(k4\_bagorder~X0)~(\\
k15\_pre\_poly~X0)){\unicdcdcdhd}((v1\_relat\_2~(k4\_bagorder~X0)){\unicdcdcdhd}((v4\_relat\_2~\\
(k4\_bagorder~X0)){\unicdcdcdhd}((v8\_relat\_2~(k4\_bagorder~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
(k4\_bagorder~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k15\_pre\_poly~X0)~\\
(k15\_pre\_poly~X0))))))))\end{array}
\label{hyp:egehpflgedpfcgbghgpgchegfgch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}(k7\_bagorder~X0=k5\_bagorder~X0~(\\
k4\_bagorder~X0))\end{array}
\label{hyp:egjdpfcgbghgpgchegfgch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_partfun1~X1~(k15\_pre\_poly~\\
X0)){\unicdcdcdhd}((v1\_relat\_2~X1){\unicdcdcdhd}((v4\_relat\_2~X1){\unicdcdcdhd}((v8\_relat\_2~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k15\_pre\_poly~X0)~(k15\_pre\_poly~\\
X0)))))))){\unicdbdjdcd}((v2\_bagorder~X1~X0){\unicdbdjded}((r7\_relat\_2~X1~(k15\_pre\_poly~\\
X0)){\unicdcdcdhd}(({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}((v1\_funct\_1~\\
X2){\unicdcdcdhd}((v1\_partfun1~X2~X0){\unicdcdcdhd}((v4\_valued\_0~X2){\unicdcdcdhd}(v2\_pre\_poly~X2)))))){\unicdbdjdcd}\\
(k4\_tarski~(k16\_pre\_poly~X0)~X2 \in X1)){\unicdcdcdhd}({\unicdcdadad} X2 .  ((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_partfun1~X2~X0){\unicdcdcdhd}\\
((v4\_valued\_0~X2){\unicdcdcdhd}(v2\_pre\_poly~X2)))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_relat\_1~\\
X3){\unicdcdcdhd}((v4\_relat\_1~X3~X0){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_partfun1~X3~X0){\unicdcdcdhd}\\
((v4\_valued\_0~X3){\unicdcdcdhd}(v2\_pre\_poly~X3)))))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_relat\_1~\\
X4){\unicdcdcdhd}((v4\_relat\_1~X4~X0){\unicdcdcdhd}((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_partfun1~X4~X0){\unicdcdcdhd}\\
((v4\_valued\_0~X4){\unicdcdcdhd}(v2\_pre\_poly~X4)))))){\unicdbdjdcd}((k4\_tarski~X2~X3 \in X1){\unicdbdjdcd}\\
(k4\_tarski~(k11\_pre\_poly~X0~X2~X4)~(k11\_pre\_poly~X0~X3~X4) \in X1)))))))))\end{array}
\label{hyp:egfdpfcgbghgpgchegfgch}
\end{equation}
\begin{theorem}\label{thm:ehcdjdpfcgbghgpgchegfgch}
${{\unicdcdadad} X0 .  {{({{v3\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{{v2\_bagorder}~{({{k7\_bagorder}~{X0}})}}~{X0}})}}}$.
\end{theorem}
\end{document}
