\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{l68\_afproj (TMd9VnG3cvWEfkVy1C26Hiq1hi6dQ4Vinoi)}
\maketitle
Let $ v7\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_diraf : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_analoaf : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k13\_afproj : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_incsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}(l1\_analoaf~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_incsp\_1~(k13\_afproj~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_incsp\_1~(k13\_afproj~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_incsp\_1~(k13\_afproj~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(u1\_incsp\_1~(k13\_afproj~X0))){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_incsp\_1~\\
(k13\_afproj~X0))){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u2\_incsp\_1~(k13\_afproj~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~(u2\_incsp\_1~(k13\_afproj~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X8 .  (m1\_subset\_1~X8~(u2\_incsp\_1~(k13\_afproj~X0))){\unicdbdjdcd}({\unicdcdadad} X9 .  \\
(m1\_subset\_1~X9~(u2\_incsp\_1~(k13\_afproj~X0))){\unicdbdjdcd}(\preoh (r1\_incsp\_1~\\
(k13\_afproj~X0)~X1~X6){\unicdcdcdhd}((r1\_incsp\_1~(k13\_afproj~X0)~X2~X6){\unicdcdcdhd}((r1\_incsp\_1~\\
(k13\_afproj~X0)~X3~X7){\unicdcdcdhd}((r1\_incsp\_1~(k13\_afproj~X0)~X4~X7){\unicdcdcdhd}((r1\_incsp\_1~\\
(k13\_afproj~X0)~X5~X6){\unicdcdcdhd}((r1\_incsp\_1~(k13\_afproj~X0)~X5~X7){\unicdcdcdhd}((r1\_incsp\_1~\\
(k13\_afproj~X0)~X1~X8){\unicdcdcdhd}((r1\_incsp\_1~(k13\_afproj~X0)~X3~X8){\unicdcdcdhd}((r1\_incsp\_1~\\
(k13\_afproj~X0)~X2~X9){\unicdcdcdhd}((r1\_incsp\_1~(k13\_afproj~X0)~X4~X9){\unicdcdcdhd}((\preoh \\
r1\_incsp\_1~(k13\_afproj~X0)~X5~X8){\unicdcdcdhd}((\preoh r1\_incsp\_1~(k13\_afproj~X0)~\\
X5~X9){\unicdcdcdhd}((X6{\unicdcdgdad}X7){\unicdcdcdhd}((\preoh m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdcdcdhd}((m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdadad} X10 .  (m1\_subset\_1~X10~(u1\_incsp\_1~\\
(k13\_afproj~X0))){\unicdbdjdcd}(\preoh (r1\_incsp\_1~(k13\_afproj~X0)~X10~X8){\unicdcdcdhd}(r1\_incsp\_1~\\
(k13\_afproj~X0)~X10~X9)))))))))))))))))))))))))))\end{array}
\label{hyp:mggdhdpfbgggahchpgkg}
\end{equation}
\begin{theorem}\label{thm:mggdidpfbgggahchpgkg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}(l1\_analoaf~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_incsp\_1~(k13\_afproj~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_incsp\_1~(k13\_afproj~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_incsp\_1~(k13\_afproj~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(u1\_incsp\_1~(k13\_afproj~X0))){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_incsp\_1~\\
(k13\_afproj~X0))){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u2\_incsp\_1~(k13\_afproj~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~(u2\_incsp\_1~(k13\_afproj~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X8 .  (m1\_subset\_1~X8~(u2\_incsp\_1~(k13\_afproj~X0))){\unicdbdjdcd}({\unicdcdadad} X9 .  \\
(m1\_subset\_1~X9~(u2\_incsp\_1~(k13\_afproj~X0))){\unicdbdjdcd}(\preoh (r1\_incsp\_1~\\
(k13\_afproj~X0)~X1~X6){\unicdcdcdhd}((r1\_incsp\_1~(k13\_afproj~X0)~X2~X6){\unicdcdcdhd}((r1\_incsp\_1~\\
(k13\_afproj~X0)~X3~X7){\unicdcdcdhd}((r1\_incsp\_1~(k13\_afproj~X0)~X4~X7){\unicdcdcdhd}((r1\_incsp\_1~\\
(k13\_afproj~X0)~X5~X6){\unicdcdcdhd}((r1\_incsp\_1~(k13\_afproj~X0)~X5~X7){\unicdcdcdhd}((r1\_incsp\_1~\\
(k13\_afproj~X0)~X1~X8){\unicdcdcdhd}((r1\_incsp\_1~(k13\_afproj~X0)~X3~X8){\unicdcdcdhd}((r1\_incsp\_1~\\
(k13\_afproj~X0)~X2~X9){\unicdcdcdhd}((r1\_incsp\_1~(k13\_afproj~X0)~X4~X9){\unicdcdcdhd}((\preoh \\
r1\_incsp\_1~(k13\_afproj~X0)~X5~X8){\unicdcdcdhd}((\preoh r1\_incsp\_1~(k13\_afproj~X0)~\\
X5~X9){\unicdcdcdhd}((X6{\unicdcdgdad}X7){\unicdcdcdhd}((\preoh m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdcdcdhd}((\preoh (\preoh m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdcdcdhd}((\preoh m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdcdcdhd}((\preoh \\
m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdcdcdhd}(\preoh m1\_subset\_1~X4~(u1\_struct\_0~\\
X0))))){\unicdcdcdhd}({\unicdcdadad} X10 .  (m1\_subset\_1~X10~(u1\_incsp\_1~(k13\_afproj~\\
X0))){\unicdbdjdcd}(\preoh (r1\_incsp\_1~(k13\_afproj~X0)~X10~X8){\unicdcdcdhd}(r1\_incsp\_1~(k13\_afproj~\\
X0)~X10~X9)))))))))))))))))))))))))))\end{array}$$
\end{theorem}
\end{document}
