\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{t9\_incproj (TML374FhCXFyDPCAahFpF1KMCoM7mondJSk)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_collsp : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_collsp : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_collsp : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_collsp : {{\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 $ k3\_incproj : {{\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.
Let $ m1\_incproj : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_collsp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_collsp~X0){\unicdcdcdhd}((v3\_collsp~X0){\unicdcdcdhd}\\
((v4\_collsp~X0){\unicdcdcdhd}(l1\_collsp~X0))))){\unicdbdjdcd}({\unicdcdaddd} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdcdcdhd}((X1{\unicdcdgdad}X2){\unicdcdcdhd}\\
((X2{\unicdcdgdad}X3){\unicdcdcdhd}(X3{\unicdcdgdad}X1))))))\end{array}
\label{hyp:ehgdpfjgogdgahchpgkg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_collsp~X0){\unicdcdcdhd}((v3\_collsp~X0){\unicdcdcdhd}\\
((v4\_collsp~X0){\unicdcdcdhd}(l1\_collsp~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_incsp\_1~(k3\_incproj~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(u2\_incsp\_1~(k3\_incproj~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_incproj~X4~X0){\unicdbdjdcd}(((X1=X3){\unicdcdcdhd}(X2=X4)){\unicdbdjdcd}((r1\_incsp\_1~\\
(k3\_incproj~X0)~X1~X2){\unicdbdjded}(X3 \in X4)))))))\end{array}
\label{hyp:ehfdpfjgogdgahchpgkg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_collsp~X0){\unicdcdcdhd}((v3\_collsp~X0){\unicdcdcdhd}\\
((v4\_collsp~X0){\unicdcdcdhd}(l1\_collsp~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_incproj~\\
X1~X0){\unicdbdjded}(m1\_subset\_1~X1~(u2\_incsp\_1~(k3\_incproj~X0))))\end{array}
\label{hyp:ehedpfjgogdgahchpgkg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_collsp~X0){\unicdcdcdhd}((v3\_collsp~X0){\unicdcdcdhd}\\
((v4\_collsp~X0){\unicdcdcdhd}(l1\_collsp~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjded}(m1\_subset\_1~X1~(u1\_incsp\_1~(k3\_incproj~\\
X0))))\end{array}
\label{hyp:ehddpfjgogdgahchpgkg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_collsp~X0){\unicdcdcdhd}((v3\_collsp~X0){\unicdcdcdhd}\\
((v4\_collsp~X0){\unicdcdcdhd}(l1\_collsp~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}(\preoh (X1{\unicdcdgdad}X2){\unicdcdcdhd}({\unicdcdadad} X3 .  (m2\_collsp~X3~X0){\unicdbdjdcd}(\preoh (X1 \in X3){\unicdcdcdhd}(X2 \in \\
X3))))))\end{array}
\label{hyp:ehbdfdpfdgpgmgmgdhah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_collsp~X0){\unicdcdcdhd}((v3\_collsp~X0){\unicdcdcdhd}\\
((v4\_collsp~X0){\unicdcdcdhd}(l1\_collsp~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_incproj~\\
X1~X0){\unicdbdjded}(m2\_collsp~X1~X0))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngbdpfjgogdgahchpgkg}
\end{equation}
\begin{theorem}\label{thm:ehjdpfjgogdgahchpgkg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_collsp~X0){\unicdcdcdhd}((v3\_collsp~X0){\unicdcdcdhd}\\
((v4\_collsp~X0){\unicdcdcdhd}(l1\_collsp~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_incsp\_1~(k3\_incproj~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(u1\_incsp\_1~(k3\_incproj~X0))){\unicdbdjdcd}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~(u2\_incsp\_1~\\
(k3\_incproj~X0))){\unicdcdcdhd}((r1\_incsp\_1~(k3\_incproj~X0)~X1~X3){\unicdcdcdhd}(r1\_incsp\_1~\\
(k3\_incproj~X0)~X2~X3)))))\end{array}$$
\end{theorem}
\end{document}
