\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{l9\_collsp (TMc24hboGEGJJcgsRvtHmFzfjufW3M1kgwE)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ c4\_\_collsp : {\iota}$ be given.
Let $ k4\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ u1\_collsp : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ np\_\_1 : {\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 $ k6\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ k3\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\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 $ c3\_\_collsp : {\iota}$ be given.
Let $ c2\_\_collsp : {\iota}$ be given.
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}((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 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~X0)){\unicdbdjdcd}\\
(k6\_domain\_1~X0~X1=k1\_tarski~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfegpgngbgjgogpfbd}
\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 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(\\
(m1\_subset\_1~X3~X0){\unicdcdcdhd}((m1\_subset\_1~X4~X1){\unicdcdcdhd}(m1\_subset\_1~X5~X2)))))){\unicdbdjdcd}\\
(k4\_domain\_1~X0~X1~X2~X3~X4~X5=k3\_xtuple\_0~X3~X4~X5)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfegpgngbgjgogpfbd}
\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}
{{\unicdcdadad} X0 .  {\preoh{{{v1\_xboole\_0}~{({{k1\_tarski}~{X0}})}}}}}\label{hyp:ggdgcdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdaddd} X1 .  {{{m1\_subset\_1}~{X1}}~{X0}}}}\label{hyp:fgihjgdhehfgogdgfgpfngbdpfdhfhcgdhfgehpfbd}
\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}~{c4\_\_collsp}}}})}{\unicdcdcdhd}{({{l1\_collsp}~{c4\_\_collsp}})}}\label{hyp:egehpfdgedpfpfdgpgmgmgdhah}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_collsp}~{c3\_\_collsp}}~{c2\_\_collsp}}\label{hyp:egehpfdgddpfpfdgpgmgmgdhah}
\end{equation}
Assume the following.
\begin{equation}
{{c4\_\_collsp}={{{g1\_collsp}~{c2\_\_collsp}}~{c3\_\_collsp}}}\label{hyp:egfgpfdgedpfpfdgpgmgmgdhah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}c3\_\_collsp=k1\_tarski~(k4\_domain\_1~k5\_numbers~k5\_numbers~k5\_numbers~\\
np\_\_1~np\_\_1~np\_\_1)\end{array}
\label{hyp:egfgpfdgddpfpfdgpgmgmgdhah}
\end{equation}
Assume the following.
\begin{equation}
{{c2\_\_collsp}={{{k6\_domain\_1}~{k5\_numbers}}~{np\_\_1}}}\label{hyp:egfgpfdgcdpfpfdgpgmgmgdhah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (X1=k1\_tarski~X0){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X1){\unicdbdjded}\\
(X2=X0))\end{array}
\label{hyp:egbdpfehbgchdhlgjg}
\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:mgjdpfdgpgmgmgdhah}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~c4\_\_collsp)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~c4\_\_collsp)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~c4\_\_collsp)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
c4\_\_collsp)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~c4\_\_collsp)){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~c4\_\_collsp)){\unicdbdjdcd}(((\preoh (\\
X0{\unicdcdgdad}X1){\unicdcdcdhd}((X0{\unicdcdgdad}X2){\unicdcdcdhd}(X1{\unicdcdgdad}X2))){\unicdbdjdcd}(k4\_domain\_1~(u1\_struct\_0~c4\_\_collsp)~\\
(u1\_struct\_0~c4\_\_collsp)~(u1\_struct\_0~c4\_\_collsp)~X0~X1~X2 \in u1\_collsp~\\
c4\_\_collsp)){\unicdcdcdhd}(((k4\_domain\_1~(u1\_struct\_0~c4\_\_collsp)~(u1\_struct\_0~\\
c4\_\_collsp)~(u1\_struct\_0~c4\_\_collsp)~X0~X1~X3 \in u1\_collsp~c4\_\_collsp){\unicdcdcdhd}\\
((k4\_domain\_1~(u1\_struct\_0~c4\_\_collsp)~(u1\_struct\_0~c4\_\_collsp)~\\
(u1\_struct\_0~c4\_\_collsp)~X0~X1~X4 \in u1\_collsp~c4\_\_collsp){\unicdcdcdhd}(k4\_domain\_1~\\
(u1\_struct\_0~c4\_\_collsp)~(u1\_struct\_0~c4\_\_collsp)~(u1\_struct\_0~\\
c4\_\_collsp)~X0~X1~X5 \in u1\_collsp~c4\_\_collsp))){\unicdbdjdcd}((X0=X1){\unicdcdcdid}(k4\_domain\_1~\\
(u1\_struct\_0~c4\_\_collsp)~(u1\_struct\_0~c4\_\_collsp)~(u1\_struct\_0~\\
c4\_\_collsp)~X3~X4~X5 \in u1\_collsp~c4\_\_collsp)))))))))\end{array}$$
\end{theorem}
\end{document}
