\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{t17\_projred1 (TMW8Gi3gJLH5nGY7SxiM9CRTVu8MKCxRKeb)}
\maketitle
Let $ v6\_incsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_incproj : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_incproj : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_incproj : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_incproj : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_incproj : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u2\_incsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v6\_incsp\_1~X0){\unicdcdcdhd}((v1\_incproj~X0){\unicdcdcdhd}((v2\_incproj~X0){\unicdcdcdhd}\\
((v3\_incproj~X0){\unicdcdcdhd}((v4\_incproj~X0){\unicdcdcdhd}((v8\_incproj~X0){\unicdcdcdhd}(l1\_incsp\_1~\\
X0))))))){\unicdbdjdcd}({\unicdcdaddd} X1 .  (m1\_subset\_1~X1~(u1\_incsp\_1~X0)){\unicdcdcdhd}({\unicdcdaddd} X2 .  \\
(m1\_subset\_1~X2~(u1\_incsp\_1~X0)){\unicdcdcdhd}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~\\
(u1\_incsp\_1~X0)){\unicdcdcdhd}({\unicdcdaddd} X4 .  (m1\_subset\_1~X4~(u1\_incsp\_1~X0)){\unicdcdcdhd}\\
({\unicdcdaddd} X5 .  (m1\_subset\_1~X5~(u2\_incsp\_1~X0)){\unicdcdcdhd}((r1\_incsp\_1~X0~\\
X1~X5){\unicdcdcdhd}((r1\_incsp\_1~X0~X2~X5){\unicdcdcdhd}((r1\_incsp\_1~X0~X3~X5){\unicdcdcdhd}((r1\_incsp\_1~\\
X0~X4~X5){\unicdcdcdhd}(r2\_zfmisc\_1~X1~X2~X3~X4))))))))))\end{array}
\label{hyp:ehbdgdpfahchpgkgchfgegbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v6\_incsp\_1~X0){\unicdcdcdhd}((v1\_incproj~X0){\unicdcdcdhd}((v2\_incproj~X0){\unicdcdcdhd}\\
((v3\_incproj~X0){\unicdcdcdhd}((v4\_incproj~X0){\unicdcdcdhd}(l1\_incsp\_1~X0)))))){\unicdbdjdcd}(({\unicdcdaddd} X1 .  \\
(m1\_subset\_1~X1~(u2\_incsp\_1~X0)){\unicdcdcdhd}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~\\
(u1\_incsp\_1~X0)){\unicdcdcdhd}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~(u1\_incsp\_1~X0)){\unicdcdcdhd}\\
({\unicdcdaddd} X4 .  (m1\_subset\_1~X4~(u1\_incsp\_1~X0)){\unicdcdcdhd}({\unicdcdaddd} X5 .  (m1\_subset\_1~\\
X5~(u1\_incsp\_1~X0)){\unicdcdcdhd}((r1\_incsp\_1~X0~X2~X1){\unicdcdcdhd}((r1\_incsp\_1~X0~X3~X1){\unicdcdcdhd}\\
((r1\_incsp\_1~X0~X4~X1){\unicdcdcdhd}((r1\_incsp\_1~X0~X5~X1){\unicdcdcdhd}(r2\_zfmisc\_1~X2~X3~\\
X4~X5)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u2\_incsp\_1~X0)){\unicdbdjdcd}\\
({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~(u1\_incsp\_1~X0)){\unicdcdcdhd}({\unicdcdaddd} X3 .  (m1\_subset\_1~\\
X3~(u1\_incsp\_1~X0)){\unicdcdcdhd}({\unicdcdaddd} X4 .  (m1\_subset\_1~X4~(u1\_incsp\_1~X0)){\unicdcdcdhd}\\
({\unicdcdaddd} X5 .  (m1\_subset\_1~X5~(u1\_incsp\_1~X0)){\unicdcdcdhd}((r1\_incsp\_1~X0~\\
X2~X1){\unicdcdcdhd}((r1\_incsp\_1~X0~X3~X1){\unicdcdcdhd}((r1\_incsp\_1~X0~X4~X1){\unicdcdcdhd}((r1\_incsp\_1~\\
X0~X5~X1){\unicdcdcdhd}(r2\_zfmisc\_1~X2~X3~X4~X5)))))))))))\end{array}
\label{hyp:ehbdddpfahchpgkgchfgegbd}
\end{equation}
\begin{theorem}\label{thm:ehbdhdpfahchpgkgchfgegbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v6\_incsp\_1~X0){\unicdcdcdhd}((v1\_incproj~X0){\unicdcdcdhd}((v2\_incproj~X0){\unicdcdcdhd}\\
((v3\_incproj~X0){\unicdcdcdhd}((v4\_incproj~X0){\unicdcdcdhd}((v8\_incproj~X0){\unicdcdcdhd}(l1\_incsp\_1~\\
X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u2\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdaddd} X2 .  \\
(m1\_subset\_1~X2~(u1\_incsp\_1~X0)){\unicdcdcdhd}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~\\
(u1\_incsp\_1~X0)){\unicdcdcdhd}({\unicdcdaddd} X4 .  (m1\_subset\_1~X4~(u1\_incsp\_1~X0)){\unicdcdcdhd}\\
({\unicdcdaddd} X5 .  (m1\_subset\_1~X5~(u1\_incsp\_1~X0)){\unicdcdcdhd}((r1\_incsp\_1~X0~\\
X2~X1){\unicdcdcdhd}((r1\_incsp\_1~X0~X3~X1){\unicdcdcdhd}((r1\_incsp\_1~X0~X4~X1){\unicdcdcdhd}((r1\_incsp\_1~\\
X0~X5~X1){\unicdcdcdhd}(r2\_zfmisc\_1~X2~X3~X4~X5))))))))))\end{array}$$
\end{theorem}
\end{document}
