\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{l29\_collsp (TMJo4ox9Mikp6CDrX5mjFrWoVBfQRBo3dWN)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ c9\_\_collsp : {\iota}$ be given.
Let $ r1\_collsp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k8\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_enumset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ k4\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ c8\_\_collsp : {\iota}$ be given.
Let $ c7\_\_collsp : {\iota}$ be given.
Let $ m1\_collsp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ g1\_collsp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_collsp : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_collsp : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_collsp : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_3){\unicdcdcdhd}(m2\_subset\_1~np\_\_3~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_3~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_3~k1\_numbers))\end{array}
\label{hyp:dhahdgddpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_2){\unicdcdcdhd}(m2\_subset\_1~np\_\_2~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_2~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_2~k1\_numbers))\end{array}
\label{hyp:dhahdgcdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_1){\unicdcdcdhd}(m2\_subset\_1~np\_\_1~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_1~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_1~k1\_numbers))\end{array}
\label{hyp:dhahdgbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
((m1\_subset\_1~X1~X0){\unicdcdcdhd}((m1\_subset\_1~X2~X0){\unicdcdcdhd}(m1\_subset\_1~X3~X0)))){\unicdbdjdcd}\\
(k8\_domain\_1~X0~X1~X2~X3=k1\_enumset1~X1~X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgidpfegpgngbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~c9\_\_collsp)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~c9\_\_collsp)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~c9\_\_collsp)){\unicdbdjdcd}((k4\_domain\_1~(u1\_struct\_0~c9\_\_collsp)~\\
(u1\_struct\_0~c9\_\_collsp)~(u1\_struct\_0~c9\_\_collsp)~X0~X1~X2 \in c8\_\_collsp){\unicdbdjded}\\
((\preoh (X0{\unicdcdgdad}X1){\unicdcdcdhd}((X1{\unicdcdgdad}X2){\unicdcdcdhd}(X2{\unicdcdgdad}X0))){\unicdcdcdhd}((X0 \in c7\_\_collsp){\unicdcdcdhd}((X1 \in c7\_\_collsp){\unicdcdcdhd}\\
(X2 \in c7\_\_collsp)))))))\end{array}
\label{hyp:mgcdhdpfdgpgmgmgdhah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_collsp~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  \\
(g1\_collsp~X0~X1=g1\_collsp~X2~X3){\unicdbdjdcd}((X0=X2){\unicdcdcdhd}(X1=X3)))\end{array}
\label{hyp:ggchfgfgpfhgbdpfdgpgmgmgdhah}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k4\_ordinal1}}}})}{\unicdcdcdhd}{({{v3\_ordinal1}~{k4\_ordinal1}})}}\label{hyp:ggdggdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_collsp~X1~X0){\unicdbdjdcd}((v1\_collsp~(g1\_collsp~\\
X0~X1)){\unicdcdcdhd}(l1\_collsp~(g1\_collsp~X0~X1)))\end{array}
\label{hyp:egehpfhgbdpfdgpgmgmgdhah}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v2\_struct\_0}~{c9\_\_collsp}}}})}{\unicdcdcdhd}{({{l1\_collsp}~{c9\_\_collsp}})}}\label{hyp:egehpfdgjdpfpfdgpgmgmgdhah}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_collsp}~{c8\_\_collsp}}~{c7\_\_collsp}}\label{hyp:egehpfdgidpfpfdgpgmgmgdhah}
\end{equation}
Assume the following.
\begin{equation}
{{c9\_\_collsp}={{{g1\_collsp}~{c7\_\_collsp}}~{c8\_\_collsp}}}\label{hyp:egfgpfdgjdpfpfdgpgmgmgdhah}
\end{equation}
Assume the following.
\begin{equation}
{{c7\_\_collsp}={{{{{k8\_domain\_1}~{k5\_numbers}}~{np\_\_1}}~{np\_\_2}}~{np\_\_3}}}\label{hyp:egfgpfdghdpfpfdgpgmgmgdhah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~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}(k4\_domain\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)~X1~X2~X3 \in u1\_collsp~X0)))))\end{array}
\label{hyp:egcdpfdgpgmgmgdhah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (X3=k1\_enumset1~\\
X0~X1~X2){\unicdbdjded}({\unicdcdadad} X4 .  (X4 \in X3){\unicdbdjded}(\preoh (X4{\unicdcdgdad}X0){\unicdcdcdhd}((X4{\unicdcdgdad}X1){\unicdcdcdhd}(X4{\unicdcdgdad}X2))))\end{array}
\label{hyp:egbdpffgogfhngdhfgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_collsp~X0){\unicdbdjdcd}((v1\_collsp~X0){\unicdbdjdcd}(X0=g1\_collsp~(u1\_struct\_0~\\
X0)~(u1\_collsp~X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdpfdgpgmgmgdhah}
\end{equation}
\begin{theorem}\label{thm:mgcdjdpfdgpgmgmgdhah}
$$\begin{array}{c}\preoh {\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~c9\_\_collsp)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~c9\_\_collsp)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~c9\_\_collsp)){\unicdbdjdcd}(r1\_collsp~c9\_\_collsp~X0~X1~X2)))\end{array}$$
\end{theorem}
\end{document}
