\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{l44\_c0sp2 (TMdYqqhGJDZzZmv9Zdo4SSChWanavWf4JhD)}
\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\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k12\_funcsdom : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_c0sp2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ v5\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_real\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ 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 $ v1\_funcsdom : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_funcsdom : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~(k12\_funcsdom~X0)){\unicdcdcdhd}\\
((v13\_algstr\_0~(k12\_funcsdom~X0)){\unicdcdcdhd}((v2\_rlvect\_1~(k12\_funcsdom~\\
X0)){\unicdcdcdhd}((v3\_rlvect\_1~(k12\_funcsdom~X0)){\unicdcdcdhd}((v4\_rlvect\_1~(k12\_funcsdom~\\
X0)){\unicdcdcdhd}((v5\_rlvect\_1~(k12\_funcsdom~X0)){\unicdcdcdhd}((v6\_rlvect\_1~(k12\_funcsdom~\\
X0)){\unicdcdcdhd}((v7\_rlvect\_1~(k12\_funcsdom~X0)){\unicdcdcdhd}((v8\_rlvect\_1~(k12\_funcsdom~\\
X0)){\unicdcdcdhd}(l1\_rlvect\_1~(k12\_funcsdom~X0)))))))))))\end{array}
\label{hyp:ehhdpfdgaddhahbd}
\end{equation}
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}((v5\_rlvect\_1~X0){\unicdcdcdhd}\\
((v6\_rlvect\_1~X0){\unicdcdcdhd}((v7\_rlvect\_1~X0){\unicdcdcdhd}((v8\_rlvect\_1~X0){\unicdcdcdhd}(l1\_rlvect\_1~\\
X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
(k4\_algstr\_0~X0~X1=k1\_rlvect\_1~X0~X1~(k1\_real\_1~np\_\_1)))\end{array}
\label{hyp:ehbdgdpfchmgghfgdgehpfbd}
\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 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (\\
m1\_subset\_1~X2~(u1\_struct\_0~(k12\_funcsdom~(u1\_struct\_0~X0)))){\unicdbdjdcd}\\
((X2 \in k6\_c0sp2~X0){\unicdbdjdcd}(k1\_rlvect\_1~(k12\_funcsdom~(u1\_struct\_0~X0))~\\
X2~X1 \in k6\_c0sp2~X0))))\end{array}
\label{hyp:mgedddpfdgaddhahcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v13\_algstr\_0~(k12\_funcsdom~X0)){\unicdcdcdhd}((v3\_group\_1~(k12\_funcsdom~\\
X0)){\unicdcdcdhd}((v5\_group\_1~(k12\_funcsdom~X0)){\unicdcdcdhd}((v1\_vectsp\_1~(k12\_funcsdom~\\
X0)){\unicdcdcdhd}((v3\_vectsp\_1~(k12\_funcsdom~X0)){\unicdcdcdhd}((v2\_rlvect\_1~(k12\_funcsdom~\\
X0)){\unicdcdcdhd}((v3\_rlvect\_1~(k12\_funcsdom~X0)){\unicdcdcdhd}((v4\_rlvect\_1~(k12\_funcsdom~\\
X0)){\unicdcdcdhd}((v5\_rlvect\_1~(k12\_funcsdom~X0)){\unicdcdcdhd}((v6\_rlvect\_1~(k12\_funcsdom~\\
X0)){\unicdcdcdhd}((v7\_rlvect\_1~(k12\_funcsdom~X0)){\unicdcdcdhd}((v1\_funcsdom~(k12\_funcsdom~\\
X0)){\unicdcdcdhd}(v2\_funcsdom~(k12\_funcsdom~X0)))))))))))))\end{array}
\label{hyp:ggdggdpfggfhogdgdhegpgng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v2\_struct\_0~(k12\_funcsdom~X0)){\unicdcdcdhd}(v1\_funcsdom~(k12\_funcsdom~\\
X0))\end{array}
\label{hyp:ggdgfdpfggfhogdgdhegpgng}
\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}
{{\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 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}(m1\_subset\_1~(k1\_real\_1~\\
X0)~k1\_numbers)\end{array}
\label{hyp:egehpflgbdpfchfgbgmgpfbd}
\end{equation}
\begin{theorem}\label{thm:mgededpfdgaddhahcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k12\_funcsdom~\\
(u1\_struct\_0~X0)))){\unicdbdjdcd}((X1 \in k6\_c0sp2~X0){\unicdbdjdcd}(k4\_algstr\_0~(k12\_funcsdom~\\
(u1\_struct\_0~X0))~X1 \in k6\_c0sp2~X0)))\end{array}$$
\end{theorem}
\end{document}
