\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{t14\_incproj (TMVyCeeLyxevmee1ee52AojJpR9oFSDRFDh)}
\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 $ v2\_anproj\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_anproj\_2 : {{\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\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_collsp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ u2\_incsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_incproj : {{\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 $ m1\_incproj : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_collsp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ m2\_collsp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ 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 $ v1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u3\_incsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_incproj : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_incproj : {{\iota}{\unicdbdjdcd}{\iota}}$ 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}({\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 .  {\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 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~X1){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}\\
(X0 \in X1))\end{array}
\label{hyp:ehcdpfdhfhcgdhfgeh}
\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}\\
(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}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~X0)){\unicdbdjdcd}((r1\_collsp~X0~X1~X2~X3){\unicdbdjded}(X3 \in k1\_collsp~X0~\\
X1~X2)))))\end{array}
\label{hyp:ehbdbdpfdgpgmgmgdhah}
\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}
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}((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 .  (l1\_incsp\_1~X0){\unicdbdjdcd}(m1\_subset\_1~(u3\_incsp\_1~X0)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_incsp\_1~X0)~(u2\_incsp\_1~X0))))\end{array}
\label{hyp:egehpffhddpfjgogdgdhahpfbd}
\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 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}({\unicdcdadad} X1 .  (m2\_collsp~X1~\\
X0){\unicdbdjded}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdaddd} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdcdcdhd}((X2{\unicdcdgdad}X3){\unicdcdcdhd}(X1=k1\_collsp~X0~\\
X2~X3)))))\end{array}
\label{hyp:eghdpfdgpgmgmgdhah}
\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:ehbdedpfjgogdgahchpgkg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_collsp~X0){\unicdcdcdhd}((v3\_collsp~X0){\unicdcdcdhd}\\
((v4\_collsp~X0){\unicdcdcdhd}((v2\_anproj\_2~X0){\unicdcdcdhd}((v3\_anproj\_2~X0){\unicdcdcdhd}(l1\_collsp~\\
X0))))))){\unicdbdjdcd}(({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdaddd} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdcdcdhd}((r1\_collsp~X0~\\
X1~X2~X5){\unicdcdcdhd}(r1\_collsp~X0~X3~X4~X5))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u2\_incsp\_1~(k3\_incproj~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(u2\_incsp\_1~(k3\_incproj~X0))){\unicdbdjdcd}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~(u1\_incsp\_1~\\
(k3\_incproj~X0))){\unicdcdcdhd}((r1\_incsp\_1~(k3\_incproj~X0)~X3~X1){\unicdcdcdhd}(r1\_incsp\_1~\\
(k3\_incproj~X0)~X3~X2))))))\end{array}$$
\end{theorem}
\end{document}
