\documentclass{article}
\newtheorem{axiom}{Axiom}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t19\_funcsdom (TMZGEd8Uq1xBSsXwRAetoxYubGu5A2oVGAD)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k9\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k1\_funcsdom : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k5\_funcsdom : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_funcsdom : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k7\_funcsdom : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k8\_funcsdom : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (\preoh v1\_xboole\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m2\_funct\_2~X3~X2~k1\_numbers~(k9\_funct\_2~X2~k1\_numbers)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m2\_funct\_2~X4~X2~k1\_numbers~(k9\_funct\_2~X2~k1\_numbers)){\unicdbdjdcd}(((X0 \in \\
X2){\unicdcdcdhd}((X1 \in X2){\unicdcdcdhd}(({\unicdcdadad} X5 .  (X5 \in X2){\unicdbdjdcd}(((X5=X0){\unicdbdjdcd}(k1\_funct\_1~X3~\\
X5=np\_\_1)){\unicdcdcdhd}((X5{\unicdcdgdad}X0){\unicdbdjdcd}(k1\_funct\_1~X3~X5=k6\_numbers)))){\unicdcdcdhd}({\unicdcdadad} X5 .  \\
(X5 \in X2){\unicdbdjdcd}(((X5=X0){\unicdbdjdcd}(k1\_funct\_1~X4~X5=k6\_numbers)){\unicdcdcdhd}((X5{\unicdcdgdad}X0){\unicdbdjdcd}\\
(k1\_funct\_1~X4~X5=np\_\_1))))))){\unicdbdjdcd}((X0=X1){\unicdcdcdid}({\unicdcdadad} X5 .  (m1\_subset\_1~\\
X5~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~k1\_numbers){\unicdbdjdcd}((r2\_funct\_2~\\
X2~k1\_numbers~(k1\_funcsdom~X2~k1\_numbers~(k5\_funcsdom~X2)~(k2\_funcsdom~\\
X2~k1\_numbers~k1\_numbers~(k9\_funct\_2~X2~k1\_numbers)~(k7\_funcsdom~\\
X2)~(k1\_domain\_1~k1\_numbers~(k9\_funct\_2~X2~k1\_numbers)~X5~X3))~\\
(k2\_funcsdom~X2~k1\_numbers~k1\_numbers~(k9\_funct\_2~X2~k1\_numbers)~\\
(k7\_funcsdom~X2)~(k1\_domain\_1~k1\_numbers~(k9\_funct\_2~X2~k1\_numbers)~\\
X6~X4)))~(k8\_funcsdom~X2)){\unicdbdjdcd}((X5=k6\_numbers){\unicdcdcdhd}(X6=k6\_numbers)))))))))\end{array}
\label{hyp:ehbdidpfggfhogdgdhegpgng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}({\unicdcdaddd} X2 .  (m2\_funct\_2~\\
X2~X1~k1\_numbers~(k9\_funct\_2~X1~k1\_numbers)){\unicdcdcdhd}({\unicdcdaddd} X3 .  (m2\_funct\_2~\\
X3~X1~k1\_numbers~(k9\_funct\_2~X1~k1\_numbers)){\unicdcdcdhd}(({\unicdcdadad} X4 .  (X4 \in \\
X1){\unicdbdjdcd}(((X4=X0){\unicdbdjdcd}(k1\_funct\_1~X2~X4=np\_\_1)){\unicdcdcdhd}((X4{\unicdcdgdad}X0){\unicdbdjdcd}(k1\_funct\_1~\\
X2~X4=k6\_numbers)))){\unicdcdcdhd}({\unicdcdadad} X4 .  (X4 \in X1){\unicdbdjdcd}(((X4=X0){\unicdbdjdcd}(k1\_funct\_1~\\
X3~X4=k6\_numbers)){\unicdcdcdhd}((X4{\unicdcdgdad}X0){\unicdbdjdcd}(k1\_funct\_1~X3~X4=np\_\_1)))))))\end{array}
\label{hyp:ehbdhdpfggfhogdgdhegpgng}
\end{equation}
\begin{theorem}\label{thm:ehbdjdpfggfhogdgdhegpgng}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (\preoh v1\_xboole\_0~X2){\unicdbdjdcd}(\preoh (X0 \in X2){\unicdcdcdhd}\\
((X1 \in X2){\unicdcdcdhd}((X0{\unicdcdgdad}X1){\unicdcdcdhd}({\unicdcdadad} X3 .  (m2\_funct\_2~X3~X2~k1\_numbers~(\\
k9\_funct\_2~X2~k1\_numbers)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_funct\_2~X4~X2~k1\_numbers~\\
(k9\_funct\_2~X2~k1\_numbers)){\unicdbdjdcd}({\unicdcdaddd} X5 .  (m1\_subset\_1~X5~k1\_numbers){\unicdcdcdhd}\\
({\unicdcdaddd} X6 .  (m1\_subset\_1~X6~k1\_numbers){\unicdcdcdhd}((r2\_funct\_2~X2~k1\_numbers~\\
(k1\_funcsdom~X2~k1\_numbers~(k5\_funcsdom~X2)~(k2\_funcsdom~X2~k1\_numbers~\\
k1\_numbers~(k9\_funct\_2~X2~k1\_numbers)~(k7\_funcsdom~X2)~(k1\_domain\_1~\\
k1\_numbers~(k9\_funct\_2~X2~k1\_numbers)~X5~X3))~(k2\_funcsdom~X2~k1\_numbers~\\
k1\_numbers~(k9\_funct\_2~X2~k1\_numbers)~(k7\_funcsdom~X2)~(k1\_domain\_1~\\
k1\_numbers~(k9\_funct\_2~X2~k1\_numbers)~X6~X4)))~(k8\_funcsdom~X2)){\unicdcdcdhd}\\
(\preoh (X5=k6\_numbers){\unicdcdcdhd}(X6=k6\_numbers))))))))))\end{array}$$
\end{theorem}
\end{document}
