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\newtheorem{conjecture}{Conjecture}
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\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t18\_rfunct\_3 (TMYTdV9vEbEfHWkb8YDd1S2D8Bfj51mJwmJ)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_setwiseo : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k13\_rfunct\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_rfunct\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k4\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_rfunct\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_subset\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ r3\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ k4\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}(k4\_binop\_1~(k3\_rfunct\_3~X0~k1\_numbers)~\\
(k13\_rfunct\_3~X0)=k4\_rfunct\_3~X0~k1\_numbers~(k2\_subset\_1~X0)~\\
k6\_numbers)\end{array}
\label{hyp:ehbdhdpfchggfhogdgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}(r3\_binop\_1~(k3\_rfunct\_3~X0~k1\_numbers)~\\
(k4\_rfunct\_3~X0~k1\_numbers~(k2\_subset\_1~X0)~k6\_numbers)~(k13\_rfunct\_3~\\
X0))\end{array}
\label{hyp:ehbdgdpfchggfhogdgehpfdd}
\end{equation}
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}((v1\_setwiseo~X1~X0){\unicdbdjded}\\
(r3\_binop\_1~X0~(k4\_binop\_1~X0~X1)~X1)))\end{array}
\label{hyp:ehbdedpfdhfgehhhjgdhfgpg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k3\_rfunct\_3}~{X0}}~{X1}}={{{k4\_partfun1}~{X0}}~{X1}}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfchggfhogdgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {\preoh{{{v1\_xboole\_0}~{({{{k4\_partfun1}~{X0}}~{X1}})}}}}}}\label{hyp:ggdgbdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((v1\_funct\_1~(k13\_rfunct\_3~X0)){\unicdcdcdhd}\\
((v1\_funct\_2~(k13\_rfunct\_3~X0)~(k2\_zfmisc\_1~(k3\_rfunct\_3~X0~k1\_numbers)~\\
(k3\_rfunct\_3~X0~k1\_numbers))~(k3\_rfunct\_3~X0~k1\_numbers)){\unicdcdcdhd}(m1\_subset\_1~\\
(k13\_rfunct\_3~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k3\_rfunct\_3~\\
X0~k1\_numbers)~(k3\_rfunct\_3~X0~k1\_numbers))~(k3\_rfunct\_3~X0~k1\_numbers))))))\end{array}
\label{hyp:egehpflgbdddpfchggfhogdgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k2\_subset\_1}~{X0}}={X0}}}\label{hyp:egddpfdhfhcgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdidpfchggfhogdgehpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}(v1\_setwiseo~(k13\_rfunct\_3~X0)~\\
(k3\_rfunct\_3~X0~k1\_numbers))\end{array}$$
\end{theorem}
\end{document}
