\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{t2\_incproj (TMRS2XeDgdxVotopiUs86QG7GQ4ijtzpcDV)}
\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 $ u1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_incproj : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_incsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_incproj : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u3\_incsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_incproj : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ g1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_incproj : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
{\unicdcdadad} X4 .  {\unicdcdadad} X5 .  (g1\_incsp\_1~X0~X1~X2=g1\_incsp\_1~X3~X4~X5){\unicdbdjdcd}\\
((X0=X3){\unicdcdcdhd}((X1=X4){\unicdcdcdhd}(X2=X5))))\end{array}
\label{hyp:ggchfgfgpfhgbdpfjgogdgdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(u1\_struct\_0~X0))\end{array}
\label{hyp:ggdgcdpfdhehchfhdgehpfad}
\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}(v1\_incsp\_1~(k3\_incproj~\\
X0))\end{array}
\label{hyp:ggdgcdpfjgogdgahchpgkg}
\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}(\preoh v1\_xboole\_0~(k1\_incproj~\\
X0))\end{array}
\label{hyp:ggdgbdpfjgogdgahchpgkg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_collsp}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfdgpgmgmgdhah}
\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}(l1\_incsp\_1~(k3\_incproj~\\
X0))\end{array}
\label{hyp:egehpflgddpfjgogdgahchpgkg}
\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}(m1\_subset\_1~(k2\_incproj~\\
X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(k1\_incproj~X0))))\end{array}
\label{hyp:egehpflgcdpfjgogdgahchpgkg}
\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}(k3\_incproj~X0=g1\_incsp\_1~\\
(u1\_struct\_0~X0)~(k1\_incproj~X0)~(k2\_incproj~X0))\end{array}
\label{hyp:egddpfjgogdgahchpgkg}
\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}(k1\_incproj~X0=ReplSep~(\\
toset~({\uniddcgcg} X1 : \iota .  m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))))~\\
({\uniddcgcg} X1 : \iota .  m1\_incproj~X1~X0)~({\uniddcgcg} X1 : \iota .  X1))\end{array}
\label{hyp:egbdpfjgogdgahchpgkg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_incsp\_1~X0){\unicdbdjdcd}((v1\_incsp\_1~X0){\unicdbdjdcd}(X0=g1\_incsp\_1~\\
(u1\_incsp\_1~X0)~(u2\_incsp\_1~X0)~(u3\_incsp\_1~X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdpfjgogdgdhahpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdpfjgogdgahchpgkg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_collsp~X0){\unicdcdcdhd}((v3\_collsp~X0){\unicdcdcdhd}\\
((v4\_collsp~X0){\unicdcdcdhd}(l1\_collsp~X0))))){\unicdbdjdcd}((u1\_incsp\_1~(k3\_incproj~\\
X0)=u1\_struct\_0~X0){\unicdcdcdhd}((u2\_incsp\_1~(k3\_incproj~X0)=k1\_incproj~\\
X0){\unicdcdcdhd}(u3\_incsp\_1~(k3\_incproj~X0)=k2\_incproj~X0)))\end{array}$$
\end{theorem}
\end{document}
