\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{t43\_afproj (TMFDacBg7vrJCeBP9BSwa1MvmVvSpUdw6W8)}
\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 $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_incsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k13\_afproj : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_aff\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_aff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\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 $ k5\_afproj : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r5\_aff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X0 \in X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X2))){\unicdbdjdcd}(m1\_subset\_1~X0~X2)\end{array}
\label{hyp:ehedpfdhfhcgdhfgeh}
\end{equation}
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~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_incsp\_1~(k13\_afproj~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u2\_incsp\_1~(k13\_afproj~X0))){\unicdbdjdcd}(((v1\_aff\_1~X1~\\
X0){\unicdcdcdhd}((X2=k5\_afproj~X0~X1){\unicdcdcdhd}(X3=k4\_tarski~X1~np\_\_1))){\unicdbdjdcd}(r1\_incsp\_1~\\
(k13\_afproj~X0)~X2~X3)))))\end{array}
\label{hyp:ehddadpfbgggahchpgkg}
\end{equation}
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\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_incsp\_1~(k13\_afproj~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(u2\_incsp\_1~(k13\_afproj~X0))){\unicdbdjdcd}(((X1=X3){\unicdcdcdhd}(k4\_tarski~X2~np\_\_1=\\
X4)){\unicdbdjdcd}((r1\_incsp\_1~(k13\_afproj~X0)~X3~X4){\unicdbdjded}((v1\_aff\_1~X2~X0){\unicdcdcdhd}(X1 \in \\
X2))))))))\end{array}
\label{hyp:ehcdgdpfbgggahchpgkg}
\end{equation}
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~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
(\preoh (v1\_aff\_4~X1~X0){\unicdcdcdhd}((v1\_aff\_1~X2~X0){\unicdcdcdhd}((v1\_aff\_1~X3~X0){\unicdcdcdhd}((r1\_tarski~\\
X2~X1){\unicdcdcdhd}((r1\_tarski~X3~X1){\unicdcdcdhd}((\preoh r5\_aff\_1~X0~X2~X3){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (X4 \in X2){\unicdcdcdhd}(X4 \in X3))))))))))))\end{array}
\label{hyp:ehcdcdpfbgggggpfed}
\end{equation}
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))){\unicdbdjded}(\preoh \\
(\preoh m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}(\preoh (X1=k5\_afproj~X0~X2){\unicdcdcdhd}(v1\_aff\_1~\\
X2~X0)))))\end{array}
\label{hyp:ehcdadpfbgggahchpgkg}
\end{equation}
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~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
(((v1\_aff\_1~X1~X0){\unicdcdcdhd}(v1\_aff\_1~X2~X0)){\unicdbdjdcd}((k5\_afproj~X0~X1=k5\_afproj~\\
X0~X2){\unicdbdjded}(r5\_aff\_1~X0~X1~X2)))))\end{array}
\label{hyp:ehbdbdpfbgggahchpgkg}
\end{equation}
\begin{theorem}\label{thm:ehedddpfbgggahchpgkg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}(l1\_analoaf~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u2\_incsp\_1~(k13\_afproj~X0))){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
(m1\_subset\_1~X5~(u2\_incsp\_1~(k13\_afproj~X0))){\unicdbdjdcd}(\preoh (v1\_aff\_4~X1~\\
X0){\unicdcdcdhd}((v1\_aff\_1~X2~X0){\unicdcdcdhd}((v1\_aff\_1~X3~X0){\unicdcdcdhd}((r1\_tarski~X2~X1){\unicdcdcdhd}((\\
r1\_tarski~X3~X1){\unicdcdcdhd}((X4=k4\_tarski~X2~np\_\_1){\unicdcdcdhd}((X5=k4\_tarski~X3~np\_\_1){\unicdcdcdhd}\\
({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u1\_incsp\_1~(k13\_afproj~X0))){\unicdbdjdcd}(\preoh \\
(r1\_incsp\_1~(k13\_afproj~X0)~X6~X4){\unicdcdcdhd}(r1\_incsp\_1~(k13\_afproj~X0)~\\
X6~X5)))))))))))))))\end{array}$$
\end{theorem}
\end{document}
