\documentclass{article}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t25\_rfunct\_4 (TMbrbH2akF1j97kZwYiTBcrXYgnhqrX7WTX)}
\maketitle
Let $ v1\_funct\_1 : {{\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 $ k1\_numbers : {\iota}$ be given.
Let $ r4\_rfunct\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r3\_rfunct\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k9\_binop\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k11\_binop\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_binop\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (r4\_rfunct\_4~X0~X1){\unicdbdjded}(\\
(r1\_tarski~X1~(k9\_xtuple\_0~X0)){\unicdcdcdhd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}\\
(\preoh (\preoh r1\_xxreal\_0~X2~k6\_numbers){\unicdcdcdhd}((\preoh r1\_xxreal\_0~np\_\_1~X2){\unicdcdcdhd}({\unicdcdaddd} X3 .  \\
(m1\_subset\_1~X3~k1\_numbers){\unicdcdcdhd}({\unicdcdaddd} X4 .  (m1\_subset\_1~X4~k1\_numbers){\unicdcdcdhd}\\
((X3 \in X1){\unicdcdcdhd}((X4 \in X1){\unicdcdcdhd}((k9\_binop\_2~(k11\_binop\_2~X2~X3)~(k11\_binop\_2~\\
(k10\_binop\_2~np\_\_1~X2)~X4) \in X1){\unicdcdcdhd}((X3{\unicdcdgdad}X4){\unicdcdcdhd}(r1\_xxreal\_0~(k4\_xxreal\_0~\\
(k1\_seq\_1~X0~X3)~(k1\_seq\_1~X0~X4))~(k1\_seq\_1~X0~(k9\_binop\_2~(k11\_binop\_2~\\
X2~X3)~(k11\_binop\_2~(k10\_binop\_2~np\_\_1~X2)~X4)))))))))))))))\end{array}
\label{hyp:egedpfchggfhogdgehpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (r3\_rfunct\_4~X0~X1){\unicdbdjded}(\\
(r1\_tarski~X1~(k9\_xtuple\_0~X0)){\unicdcdcdhd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}\\
(\preoh (\preoh r1\_xxreal\_0~X2~k6\_numbers){\unicdcdcdhd}((\preoh r1\_xxreal\_0~np\_\_1~X2){\unicdcdcdhd}({\unicdcdaddd} X3 .  \\
(m1\_subset\_1~X3~k1\_numbers){\unicdcdcdhd}({\unicdcdaddd} X4 .  (m1\_subset\_1~X4~k1\_numbers){\unicdcdcdhd}\\
((X3 \in X1){\unicdcdcdhd}((X4 \in X1){\unicdcdcdhd}((k9\_binop\_2~(k11\_binop\_2~X2~X3)~(k11\_binop\_2~\\
(k10\_binop\_2~np\_\_1~X2)~X4) \in X1){\unicdcdcdhd}((k1\_seq\_1~X0~X3{\unicdcdgdad}k1\_seq\_1~X0~X4){\unicdcdcdhd}\\
(r1\_xxreal\_0~(k4\_xxreal\_0~(k1\_seq\_1~X0~X3)~(k1\_seq\_1~X0~X4))~(k1\_seq\_1~\\
X0~(k9\_binop\_2~(k11\_binop\_2~X2~X3)~(k11\_binop\_2~(k10\_binop\_2~np\_\_1~\\
X2)~X4)))))))))))))))\end{array}
\label{hyp:egddpfchggfhogdgehpfed}
\end{equation}
\begin{theorem}\label{thm:ehcdfdpfchggfhogdgehpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}((r4\_rfunct\_4~X1~X0){\unicdbdjdcd}\\
(r3\_rfunct\_4~X1~X0))\end{array}$$
\end{theorem}
\end{document}
