\documentclass{article}
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\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdcdadjd{\notin}
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\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t19\_setwop\_2 (TMYE3EK3JEXEEHDmzLLwUoMb12vwnq1pjBV)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_finsub\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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 $ 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 $ v1\_setwiseo : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_finseqop : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k5\_finseqop : {{\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 $ r7\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k4\_binop\_1 : {{\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 .  ((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){\unicdcdcdhd}\\
((v2\_binop\_1~X1~X0){\unicdcdcdhd}((v1\_binop\_1~X1~X0){\unicdcdcdhd}(v1\_finseqop~X1~X0)))){\unicdbdjdcd}\\
(r7\_binop\_1~X0~(k5\_finseqop~X0~X1)~X1)))\end{array}
\label{hyp:ehgdddpfggjgogdhfgbhpgah}
\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){\unicdcdcdhd}\\
((v2\_binop\_1~X1~X0){\unicdcdcdhd}(v1\_finseqop~X1~X0))){\unicdbdjdcd}(k3\_funct\_2~X0~X0~(k5\_finseqop~\\
X0~X1)~(k4\_binop\_1~X0~X1)=k4\_binop\_1~X0~X1)))\end{array}
\label{hyp:ehgdbdpfggjgogdhfgbhpgah}
\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 .  (m1\_subset\_1~X2~(k5\_finsub\_1~X0)){\unicdbdjdcd}({\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}({\unicdcdadad} X4 .  \\
((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~X1~X1){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X1~X1))))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_funct\_1~X5){\unicdcdcdhd}((v1\_funct\_2~\\
X5~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))))){\unicdbdjdcd}\\
(((v1\_binop\_1~X3~X1){\unicdcdcdhd}((v2\_binop\_1~X3~X1){\unicdcdcdhd}((v1\_setwiseo~X3~X1){\unicdcdcdhd}\\
((k3\_funct\_2~X1~X1~X4~(k4\_binop\_1~X1~X3)=k4\_binop\_1~X1~X3){\unicdcdcdhd}(r7\_binop\_1~\\
X1~X4~X3))))){\unicdbdjdcd}(k3\_funct\_2~X1~X1~X4~(k7\_setwiseo~X0~X1~X3~X2~X5)=k7\_setwiseo~\\
X0~X1~X3~X2~(k1\_partfun1~X0~X1~X1~X1~X5~X4))))))))\end{array}
\label{hyp:ehbdhdpfdhfgehhhpgahpfcd}
\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}
\begin{theorem}\label{thm:ehbdjdpfdhfgehhhpgahpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k5\_finsub\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((\\
v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(k2\_zfmisc\_1~X1~X1)~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X1~X1)~X1))))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))))){\unicdbdjdcd}(((v1\_binop\_1~X3~X1){\unicdcdcdhd}((v2\_binop\_1~X3~\\
X1){\unicdcdcdhd}((v1\_setwiseo~X3~X1){\unicdcdcdhd}(v1\_finseqop~X3~X1)))){\unicdbdjdcd}(k3\_funct\_2~\\
X1~X1~(k5\_finseqop~X1~X3)~(k7\_setwiseo~X0~X1~X3~X2~X4)=k7\_setwiseo~\\
X0~X1~X3~X2~(k1\_partfun1~X0~X1~X1~X1~X4~(k5\_finseqop~X1~X3))))))))\end{array}$$
\end{theorem}
\end{document}
