\documentclass{article}
\newtheorem{axiom}{Axiom}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
\newcommand\unicdcdadad{\forall}
\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
\newcommand\uniddcgcg{\lambda}
\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t14\_anproj\_2 (TMHQZ9dK7bC7SKQGVFWZ6tgcMUG7AFQuxY4)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k8\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ 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 $ 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 $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_funct\_2~X1~X0~k1\_numbers~\\
(k9\_funct\_2~X0~k1\_numbers)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_funct\_2~X2~X0~k1\_numbers~\\
(k9\_funct\_2~X0~k1\_numbers)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_funct\_2~X3~X0~k1\_numbers~\\
(k9\_funct\_2~X0~k1\_numbers)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~X0){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  (m1\_subset\_1~X5~X0){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~X0){\unicdbdjdcd}\\
(((X0=k8\_domain\_1~X0~X4~X5~X6){\unicdcdcdhd}((k3\_funct\_2~X0~k1\_numbers~X1~X4=\\
np\_\_1){\unicdcdcdhd}(({\unicdcdadad} X7 .  (X7 \in X0){\unicdbdjdcd}((X7=X4){\unicdcdcdid}(k1\_funct\_1~X1~X7=k6\_numbers))){\unicdcdcdhd}\\
((k3\_funct\_2~X0~k1\_numbers~X2~X5=np\_\_1){\unicdcdcdhd}(({\unicdcdadad} X7 .  (X7 \in X0){\unicdbdjdcd}\\
((X7=X5){\unicdcdcdid}(k1\_funct\_1~X2~X7=k6\_numbers))){\unicdcdcdhd}((k3\_funct\_2~X0~k1\_numbers~\\
X3~X6=np\_\_1){\unicdcdcdhd}({\unicdcdadad} X7 .  (X7 \in X0){\unicdbdjdcd}((X7=X6){\unicdcdcdid}(k1\_funct\_1~X3~X7=\\
k6\_numbers))))))))){\unicdbdjdcd}((X4=X5){\unicdcdcdid}((X4=X6){\unicdcdcdid}((X5=X6){\unicdcdcdid}({\unicdcdadad} X7 .  \\
(m2\_funct\_2~X7~X0~k1\_numbers~(k9\_funct\_2~X0~k1\_numbers)){\unicdbdjdcd}({\unicdcdaddd} X8 .  \\
(m1\_subset\_1~X8~k1\_numbers){\unicdcdcdhd}({\unicdcdaddd} X9 .  (m1\_subset\_1~X9~k1\_numbers){\unicdcdcdhd}\\
({\unicdcdaddd} X10 .  (m1\_subset\_1~X10~k1\_numbers){\unicdcdcdhd}(r2\_funct\_2~X0~k1\_numbers~\\
X7~(k1\_funcsdom~X0~k1\_numbers~(k5\_funcsdom~X0)~(k1\_funcsdom~X0~\\
k1\_numbers~(k5\_funcsdom~X0)~(k2\_funcsdom~X0~k1\_numbers~k1\_numbers~\\
(k9\_funct\_2~X0~k1\_numbers)~(k7\_funcsdom~X0)~(k1\_domain\_1~k1\_numbers~\\
(k9\_funct\_2~X0~k1\_numbers)~X8~X1))~(k2\_funcsdom~X0~k1\_numbers~k1\_numbers~\\
(k9\_funct\_2~X0~k1\_numbers)~(k7\_funcsdom~X0)~(k1\_domain\_1~k1\_numbers~\\
(k9\_funct\_2~X0~k1\_numbers)~X9~X2)))~(k2\_funcsdom~X0~k1\_numbers~\\
k1\_numbers~(k9\_funct\_2~X0~k1\_numbers)~(k7\_funcsdom~X0)~(k1\_domain\_1~\\
k1\_numbers~(k9\_funct\_2~X0~k1\_numbers)~X10~X3))))))))))))))))))\end{array}
\label{hyp:ehbdddpfbgogahchpgkgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
({\unicdcdaddd} X2 .  (m2\_funct\_2~X2~X0~k1\_numbers~(k9\_funct\_2~X0~k1\_numbers)){\unicdcdcdhd}\\
((k3\_funct\_2~X0~k1\_numbers~X2~X1=np\_\_1){\unicdcdcdhd}({\unicdcdadad} X3 .  (X3 \in X0){\unicdbdjdcd}\\
((X3=X1){\unicdcdcdid}(k1\_funct\_1~X2~X3=k6\_numbers))))))\end{array}
\label{hyp:ehbdadpfbgogahchpgkgpfcd}
\end{equation}
\begin{theorem}\label{thm:ehbdedpfbgogahchpgkgpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~X0){\unicdbdjdcd}\\
(\preoh (X0=k8\_domain\_1~X0~X1~X2~X3){\unicdcdcdhd}((X1{\unicdcdgdad}X2){\unicdcdcdhd}((X1{\unicdcdgdad}X3){\unicdcdcdhd}((X2{\unicdcdgdad}X3){\unicdcdcdhd}(\\
{\unicdcdadad} X4 .  (m2\_funct\_2~X4~X0~k1\_numbers~(k9\_funct\_2~X0~k1\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  (m2\_funct\_2~X5~X0~k1\_numbers~(k9\_funct\_2~X0~k1\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X6 .  (m2\_funct\_2~X6~X0~k1\_numbers~(k9\_funct\_2~X0~k1\_numbers)){\unicdbdjdcd}\\
({\unicdcdaddd} X7 .  (m2\_funct\_2~X7~X0~k1\_numbers~(k9\_funct\_2~X0~k1\_numbers)){\unicdcdcdhd}\\
({\unicdcdadad} X8 .  (m1\_subset\_1~X8~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X9 .  (m1\_subset\_1~\\
X9~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X10 .  (m1\_subset\_1~X10~k1\_numbers){\unicdbdjdcd}(\preoh \\
r2\_funct\_2~X0~k1\_numbers~X7~(k1\_funcsdom~X0~k1\_numbers~(k5\_funcsdom~\\
X0)~(k1\_funcsdom~X0~k1\_numbers~(k5\_funcsdom~X0)~(k2\_funcsdom~X0~\\
k1\_numbers~k1\_numbers~(k9\_funct\_2~X0~k1\_numbers)~(k7\_funcsdom~\\
X0)~(k1\_domain\_1~k1\_numbers~(k9\_funct\_2~X0~k1\_numbers)~X8~X4))~\\
(k2\_funcsdom~X0~k1\_numbers~k1\_numbers~(k9\_funct\_2~X0~k1\_numbers)~\\
(k7\_funcsdom~X0)~(k1\_domain\_1~k1\_numbers~(k9\_funct\_2~X0~k1\_numbers)~\\
X9~X5)))~(k2\_funcsdom~X0~k1\_numbers~k1\_numbers~(k9\_funct\_2~X0~k1\_numbers)~\\
(k7\_funcsdom~X0)~(k1\_domain\_1~k1\_numbers~(k9\_funct\_2~X0~k1\_numbers)~\\
X10~X6))))))))))))))))))\end{array}$$
\end{theorem}
\end{document}
