\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{l30\_realset2 (TMVXTcpCCpEampSGFYktgWqke9TjjScZgiZ)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ g6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ c4\_\_realset2 : {\iota}$ be given.
Let $ c8\_\_realset2 : {\iota}$ be given.
Let $ c9\_\_realset2 : {\iota}$ be given.
Let $ c7\_\_realset2 : {\iota}$ be given.
Let $ c5\_\_realset2 : {\iota}$ be given.
Let $ l6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v36\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_realset2 : {\iota}$ be given.
Let $ k1\_funct\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_realset2 : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{np\_\_2}}}}\label{hyp:dhahdgcdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}(((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~\\
X0))))){\unicdcdcdhd}(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(k2\_zfmisc\_1~X0~X0)~\\
X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~\\
X0)~X0))))){\unicdcdcdhd}((m1\_subset\_1~X3~X0){\unicdcdcdhd}(m1\_subset\_1~X4~X0))))){\unicdbdjdcd}((\preoh \\
v2\_struct\_0~(g6\_algstr\_0~X0~X1~X2~X3~X4)){\unicdcdcdhd}(v36\_algstr\_0~(g6\_algstr\_0~\\
X0~X1~X2~X3~X4)))\end{array}
\label{hyp:ggdgcdjdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k1\_realset2){\unicdcdcdhd}((v1\_funct\_2~k1\_realset2~(k2\_zfmisc\_1~\\
np\_\_2~np\_\_2)~np\_\_2){\unicdcdcdhd}(m1\_subset\_1~k1\_realset2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~np\_\_2~np\_\_2)~np\_\_2))))\end{array}
\label{hyp:egehpflgbdpfchfgbgmgdhfgehcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{m1\_subset\_1}~{({{{k1\_funct\_7}~{X0}}~{X1}})}}~{X1}}}}\label{hyp:egehpflgbdpfggfhogdgehpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (((v1\_funct\_1~\\
X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~X0))))){\unicdcdcdhd}(((v1\_funct\_1~X2){\unicdcdcdhd}(\\
(v1\_funct\_2~X2~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~X0))))){\unicdcdcdhd}((m1\_subset\_1~X3~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X4~X0)))){\unicdbdjdcd}((v36\_algstr\_0~(g6\_algstr\_0~X0~X1~X2~X3~\\
X4)){\unicdcdcdhd}(l6\_algstr\_0~(g6\_algstr\_0~X0~X1~X2~X3~X4)))\end{array}
\label{hyp:egehpfhggdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~c9\_\_realset2){\unicdcdcdhd}((v1\_funct\_2~c9\_\_realset2~(k2\_zfmisc\_1~\\
c4\_\_realset2~c4\_\_realset2)~c4\_\_realset2){\unicdcdcdhd}(m1\_subset\_1~c9\_\_realset2~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~c4\_\_realset2~c4\_\_realset2)~\\
c4\_\_realset2))))\end{array}
\label{hyp:egehpfdgjdpfpfchfgbgmgdhfgehcd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{c5\_\_realset2}}~{c4\_\_realset2}}\label{hyp:egehpfdgfdpfpfchfgbgmgdhfgehcd}
\end{equation}
Assume the following.
\begin{equation}
{{c9\_\_realset2}={k2\_realset2}}\label{hyp:egfgpfdgjdpfpfchfgbgmgdhfgehcd}
\end{equation}
Assume the following.
\begin{equation}
{{c8\_\_realset2}={k1\_realset2}}\label{hyp:egfgpfdgidpfpfchfgbgmgdhfgehcd}
\end{equation}
Assume the following.
\begin{equation}
{{c7\_\_realset2}={{{k1\_funct\_7}~{np\_\_1}}~{np\_\_2}}}\label{hyp:egfgpfdghdpfpfchfgbgmgdhfgehcd}
\end{equation}
Assume the following.
\begin{equation}
{{c4\_\_realset2}={np\_\_2}}\label{hyp:egfgpfdgedpfpfchfgbgmgdhfgehcd}
\end{equation}
\begin{theorem}\label{thm:mgddadpfchfgbgmgdhfgehcd}
$$\begin{array}{c}(\preoh v2\_struct\_0~(g6\_algstr\_0~c4\_\_realset2~c8\_\_realset2~c9\_\_realset2~\\
c7\_\_realset2~c5\_\_realset2)){\unicdcdcdhd}(l6\_algstr\_0~(g6\_algstr\_0~c4\_\_realset2~\\
c8\_\_realset2~c9\_\_realset2~c7\_\_realset2~c5\_\_realset2))\end{array}$$
\end{theorem}
\end{document}
