\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\_cc0sp2 (TMWGJELyAsbia4y4mW3BLiizisjwQ8gSttF)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_cc0sp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_cc0sp2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_cfuncdom : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v13\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_cfuncdom : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_cfuncdom : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_c0sp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_cc0sp1 : {{\iota}{\unicdbdjdcd}{{\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 $ g1\_cfuncdom : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k2\_c0sp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_c0sp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_cc0sp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_c0sp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_c0sp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_cfuncdom : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_cc0sp2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}(\\
(v5\_group\_1~X0){\unicdcdcdhd}((v1\_vectsp\_1~X0){\unicdcdcdhd}((v3\_vectsp\_1~X0){\unicdcdcdhd}((v2\_clvect\_1~\\
X0){\unicdcdcdhd}((v3\_clvect\_1~X0){\unicdcdcdhd}((v4\_clvect\_1~X0){\unicdcdcdhd}((v2\_cfuncdom~X0){\unicdcdcdhd}\\
(l1\_cfuncdom~X0)))))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
((v3\_c0sp1~X1~X0){\unicdcdcdhd}((v1\_cc0sp1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0)))))){\unicdbdjdcd}(m1\_cc0sp1~(g1\_cfuncdom~X1~(k2\_c0sp1~X0~\\
X1)~(k1\_c0sp1~X0~X1)~(k1\_cc0sp1~X0~X1)~(k4\_c0sp1~X0~X1)~(k3\_c0sp1~\\
X0~X1))~X0))\end{array}
\label{hyp:ehcdpfdgdgaddhahbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((v13\_algstr\_0~(k8\_cfuncdom~X0)){\unicdcdcdhd}\\
((v2\_rlvect\_1~(k8\_cfuncdom~X0)){\unicdcdcdhd}((v3\_rlvect\_1~(k8\_cfuncdom~\\
X0)){\unicdcdcdhd}((v4\_rlvect\_1~(k8\_cfuncdom~X0)){\unicdcdcdhd}((v2\_clvect\_1~(k8\_cfuncdom~\\
X0)){\unicdcdcdhd}((v3\_clvect\_1~(k8\_cfuncdom~X0)){\unicdcdcdhd}((v4\_clvect\_1~(k8\_cfuncdom~\\
X0)){\unicdcdcdhd}((v3\_group\_1~(k8\_cfuncdom~X0)){\unicdcdcdhd}((v5\_group\_1~(k8\_cfuncdom~\\
X0)){\unicdcdcdhd}((v1\_vectsp\_1~(k8\_cfuncdom~X0)){\unicdcdcdhd}((v3\_vectsp\_1~(k8\_cfuncdom~\\
X0)){\unicdcdcdhd}((v1\_cfuncdom~(k8\_cfuncdom~X0)){\unicdcdcdhd}(v2\_cfuncdom~(k8\_cfuncdom~\\
X0))))))))))))))\end{array}
\label{hyp:ggdggdpfdgggfhogdgegpgng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~(k8\_cfuncdom~X0)){\unicdcdcdhd}\\
(v1\_cfuncdom~(k8\_cfuncdom~X0)))\end{array}
\label{hyp:ggdgedpfdgggfhogdgegpgng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}((v3\_c0sp1~(k2\_cc0sp2~X0)~(k8\_cfuncdom~(u1\_struct\_0~X0))){\unicdcdcdhd}\\
(v1\_cc0sp1~(k2\_cc0sp2~X0)~(k8\_cfuncdom~(u1\_struct\_0~X0))))\end{array}
\label{hyp:ggdgddpfdgdgaddhahcd}
\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\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}(\preoh v1\_xboole\_0~(k2\_cc0sp2~X0))\end{array}
\label{hyp:ggdgcdpfdgdgaddhahcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_pre\_topc}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfahchfgpfehpgahdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((v1\_cfuncdom~(k8\_cfuncdom~X0)){\unicdcdcdhd}\\
(l1\_cfuncdom~(k8\_cfuncdom~X0)))\end{array}
\label{hyp:egehpflgidpfdgggfhogdgegpgng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}(m1\_subset\_1~(k2\_cc0sp2~X0)~(k1\_zfmisc\_1~(u1\_struct\_0~\\
(k8\_cfuncdom~(u1\_struct\_0~X0)))))\end{array}
\label{hyp:egehpflgcdpfdgdgaddhahcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}(k3\_cc0sp2~X0=g1\_cfuncdom~(k2\_cc0sp2~X0)~(k2\_c0sp1~(k8\_cfuncdom~\\
(u1\_struct\_0~X0))~(k2\_cc0sp2~X0))~(k1\_c0sp1~(k8\_cfuncdom~(u1\_struct\_0~\\
X0))~(k2\_cc0sp2~X0))~(k1\_cc0sp1~(k8\_cfuncdom~(u1\_struct\_0~X0))~\\
(k2\_cc0sp2~X0))~(k4\_c0sp1~(k8\_cfuncdom~(u1\_struct\_0~X0))~(k2\_cc0sp2~\\
X0))~(k3\_c0sp1~(k8\_cfuncdom~(u1\_struct\_0~X0))~(k2\_cc0sp2~X0)))\end{array}
\label{hyp:egedpfdgdgaddhahcd}
\end{equation}
\begin{theorem}\label{thm:ehjdpfdgdgaddhahcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}(m1\_cc0sp1~(k3\_cc0sp2~X0)~(k8\_cfuncdom~(u1\_struct\_0~X0)))\end{array}$$
\end{theorem}
\end{document}
