\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{l39\_realset2 (TMWuvoAaeRRWeXDR3eUdLRJtsqKjmMsgD7Y)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ k6\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ c4\_\_realset2 : {\iota}$ be given.
Let $ k6\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ c5\_\_realset2 : {\iota}$ be given.
Let $ c7\_\_realset2 : {\iota}$ be given.
Let $ r1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}}$ be given.
Let $ k4\_realset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ c11\_\_realset2 : {\iota}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ g2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ l2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((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))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~X0){\unicdbdjdcd}(((X0=k6\_subset\_1~c4\_\_realset2~(k6\_domain\_1~c4\_\_realset2~\\
c5\_\_realset2)){\unicdcdcdhd}(X2=c7\_\_realset2)){\unicdbdjdcd}((\preoh v2\_struct\_0~(g2\_algstr\_0~\\
X0~X1~X2)){\unicdcdcdhd}((v13\_algstr\_0~(g2\_algstr\_0~X0~X1~X2)){\unicdcdcdhd}((v2\_rlvect\_1~\\
(g2\_algstr\_0~X0~X1~X2)){\unicdcdcdhd}((v3\_rlvect\_1~(g2\_algstr\_0~X0~X1~X2)){\unicdcdcdhd}\\
((v4\_rlvect\_1~(g2\_algstr\_0~X0~X1~X2)){\unicdcdcdhd}(l2\_algstr\_0~(g2\_algstr\_0~\\
X0~X1~X2))))))))))\end{array}
\label{hyp:mgddfdpfchfgbgmgdhfgehcd}
\end{equation}
Assume the following.
\begin{equation}
{{c4\_\_realset2}={np\_\_2}}\label{hyp:egfgpfdgedpfpfchfgbgmgdhfgehcd}
\end{equation}
\begin{theorem}\label{thm:mgddjdpfchfgbgmgdhfgehcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~X0))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~X0){\unicdbdjdcd}(((X0=k6\_subset\_1~c4\_\_realset2~(k6\_domain\_1~c4\_\_realset2~\\
c5\_\_realset2)){\unicdcdcdhd}((X2=c7\_\_realset2){\unicdcdcdhd}(r1\_funct\_2~(k2\_zfmisc\_1~\\
X0~X0)~X0~(k2\_zfmisc\_1~(k6\_subset\_1~c4\_\_realset2~(k6\_domain\_1~\\
c4\_\_realset2~c5\_\_realset2))~(k6\_subset\_1~c4\_\_realset2~(k6\_domain\_1~\\
c4\_\_realset2~c5\_\_realset2)))~(k6\_subset\_1~c4\_\_realset2~(k6\_domain\_1~\\
c4\_\_realset2~c5\_\_realset2))~X1~(k4\_realset1~c4\_\_realset2~c5\_\_realset2~\\
c11\_\_realset2)))){\unicdbdjdcd}((\preoh v2\_struct\_0~(g2\_algstr\_0~X0~X1~X2)){\unicdcdcdhd}((\\
v13\_algstr\_0~(g2\_algstr\_0~X0~X1~X2)){\unicdcdcdhd}((v2\_rlvect\_1~(g2\_algstr\_0~\\
X0~X1~X2)){\unicdcdcdhd}((v3\_rlvect\_1~(g2\_algstr\_0~X0~X1~X2)){\unicdcdcdhd}((v4\_rlvect\_1~\\
(g2\_algstr\_0~X0~X1~X2)){\unicdcdcdhd}(l2\_algstr\_0~(g2\_algstr\_0~X0~X1~X2))))))))))\end{array}$$
\end{theorem}
\end{document}
