\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{t41\_afproj (TMHxAesBoy4AD7S5FPi14QeGMXGJCXu56pN)}
\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 $ k14\_afproj : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_incsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k13\_afproj : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ u3\_incsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ r1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ 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~(k14\_afproj~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_incsp\_1~(k14\_afproj~X0))){\unicdbdjdcd}({\unicdcdaddd} X3 .  (m1\_subset\_1~\\
X3~(u2\_incsp\_1~(k14\_afproj~X0))){\unicdcdcdhd}((r1\_incsp\_1~(k14\_afproj~X0)~\\
X1~X3){\unicdcdcdhd}(r1\_incsp\_1~(k14\_afproj~X0)~X2~X3)))))\end{array}
\label{hyp:ehedadpfbgggahchpgkg}
\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~(k14\_afproj~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_incsp\_1~(k13\_afproj~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u2\_incsp\_1~(k14\_afproj~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(u2\_incsp\_1~(k13\_afproj~X0))){\unicdbdjdcd}(((X2=X1){\unicdcdcdhd}(X4=k4\_tarski~X3~np\_\_2)){\unicdbdjdcd}\\
((r1\_incsp\_1~(k14\_afproj~X0)~X1~X3){\unicdbdjded}(r1\_incsp\_1~(k13\_afproj~X0)~\\
X2~X4)))))))\end{array}
\label{hyp:ehddhdpfbgggahchpgkg}
\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~(u2\_incsp\_1~(k14\_afproj~X0))){\unicdbdjdcd}(m1\_subset\_1~\\
(k4\_tarski~X1~np\_\_2)~(u2\_incsp\_1~(k13\_afproj~X0))))\end{array}
\label{hyp:ehcdfdpfbgggahchpgkg}
\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~(k14\_afproj~X0))){\unicdbdjdcd}(m1\_subset\_1~\\
X1~(u1\_incsp\_1~(k13\_afproj~X0))))\end{array}
\label{hyp:ehcdcdpfbgggahchpgkg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((m1\_subset\_1~X2~X0){\unicdcdcdhd}(m1\_subset\_1~X3~X1)))){\unicdbdjdcd}\\
(k1\_domain\_1~X0~X1~X2~X3=k4\_tarski~X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfegpgngbgjgogpfbd}
\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))){\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}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(u2\_incsp\_1~(k13\_afproj~X0))){\unicdbdjdcd}(\preoh (r1\_incsp\_1~(k13\_afproj~X0)~\\
X1~X3){\unicdcdcdhd}((r1\_incsp\_1~(k13\_afproj~X0)~X1~X4){\unicdcdcdhd}((r1\_incsp\_1~(k13\_afproj~\\
X0)~X2~X3){\unicdcdcdhd}((r1\_incsp\_1~(k13\_afproj~X0)~X2~X4){\unicdcdcdhd}((X1{\unicdcdgdad}X2){\unicdcdcdhd}(X3{\unicdcdgdad}X4))))))))))\end{array}
\label{hyp:mgfdgdpfbgggahchpgkg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_incsp\_1}~{X0}})}{\unicdbdjdcd}{({\preoh{{{v1\_xboole\_0}~{({{u2\_incsp\_1}~{X0}})}}}})}}}\label{hyp:egehpffhcdpfjgogdgdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_incsp\_1}~{X0}})}{\unicdbdjdcd}{({\preoh{{{v1\_xboole\_0}~{({{u1\_incsp\_1}~{X0}})}}}})}}}\label{hyp:egehpffhbdpfjgogdgdhahpfbd}
\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}\\
((v1\_incsp\_1~(k14\_afproj~X0)){\unicdcdcdhd}(l1\_incsp\_1~(k14\_afproj~X0)))\end{array}
\label{hyp:egehpflgbdedpfbgggahchpgkg}
\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}\\
((v1\_incsp\_1~(k13\_afproj~X0)){\unicdcdcdhd}(l1\_incsp\_1~(k13\_afproj~X0)))\end{array}
\label{hyp:egehpflgbdddpfbgggahchpgkg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_incsp\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_incsp\_1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u2\_incsp\_1~X0)){\unicdbdjdcd}((r1\_incsp\_1~\\
X0~X1~X2){\unicdbdjded}(k1\_domain\_1~(u1\_incsp\_1~X0)~(u2\_incsp\_1~X0)~X1~X2 \in u3\_incsp\_1~\\
X0))))\end{array}
\label{hyp:egbdpfjgogdgdhahpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedbdpfbgggahchpgkg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}(l1\_analoaf~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_incsp\_1~(k14\_afproj~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_incsp\_1~(k14\_afproj~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u2\_incsp\_1~(k13\_afproj~X0))){\unicdbdjdcd}(\preoh (X1{\unicdcdgdad}X2){\unicdcdcdhd}((k1\_domain\_1~(u1\_incsp\_1~\\
(k14\_afproj~X0))~(u2\_incsp\_1~(k13\_afproj~X0))~X1~X3 \in u3\_incsp\_1~\\
(k13\_afproj~X0)){\unicdcdcdhd}((k1\_domain\_1~(u1\_incsp\_1~(k14\_afproj~X0))~\\
(u2\_incsp\_1~(k13\_afproj~X0))~X2~X3 \in u3\_incsp\_1~(k13\_afproj~X0)){\unicdcdcdhd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u2\_incsp\_1~(k14\_afproj~X0))){\unicdbdjdcd}(X3{\unicdcdgdad}\\
k4\_tarski~X4~np\_\_2))))))))\end{array}$$
\end{theorem}
\end{document}
