\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{l29\_realset2 (TMNAsDo3v5bM9Y9sLmNBxMPTPunP3Cn1GnY)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ c4\_\_realset2 : {\iota}$ be given.
Let $ k1\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_realset2 : {\iota}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_numbers : {\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 $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_funct\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
{{np\_\_2}={{{k2\_tarski}~{k1\_xboole\_0}}~{np\_\_1}}}\label{hyp:ehfdadpfdgbgchegpfbd}
\end{equation}
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}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((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}((m1\_subset\_1~X2~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X3~X0))){\unicdbdjdcd}(k5\_binop\_1~X0~X1~X2~X3=k1\_binop\_1~X1~X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfcgjgogpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{{{k1\_funct\_7}~{np\_\_1}}~{np\_\_2}}={np\_\_1}}\label{hyp:mggdpfchfgbgmgdhfgehcd}
\end{equation}
Assume the following.
\begin{equation}
{{{{k1\_funct\_7}~{k6\_numbers}}~{np\_\_2}}={k6\_numbers}}\label{hyp:mgfdpfchfgbgmgdhfgehcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}k5\_binop\_1~np\_\_2~k1\_realset2~(k1\_funct\_7~np\_\_1~np\_\_2)~(k1\_funct\_7~\\
np\_\_1~np\_\_2)=k1\_funct\_7~k6\_numbers~np\_\_2\end{array}
\label{hyp:mgbdfdpfchfgbgmgdhfgehcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}k5\_binop\_1~np\_\_2~k1\_realset2~(k1\_funct\_7~np\_\_1~np\_\_2)~(k1\_funct\_7~\\
k6\_numbers~np\_\_2)=k1\_funct\_7~np\_\_1~np\_\_2\end{array}
\label{hyp:mgbdedpfchfgbgmgdhfgehcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}k5\_binop\_1~np\_\_2~k1\_realset2~(k1\_funct\_7~k6\_numbers~np\_\_2)~(k1\_funct\_7~\\
np\_\_1~np\_\_2)=k1\_funct\_7~np\_\_1~np\_\_2\end{array}
\label{hyp:mgbdddpfchfgbgmgdhfgehcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}k5\_binop\_1~np\_\_2~k1\_realset2~(k1\_funct\_7~k6\_numbers~np\_\_2)~(k1\_funct\_7~\\
k6\_numbers~np\_\_2)=k1\_funct\_7~k6\_numbers~np\_\_2\end{array}
\label{hyp:mgbdcdpfchfgbgmgdhfgehcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {\preoh{{{v1\_xboole\_0}~{({{{k2\_tarski}~{X0}}~{X1}})}}}}}}\label{hyp:ggdgddpfihcgpgpgmgfgpfad}
\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}
{{c4\_\_realset2}={np\_\_2}}\label{hyp:egfgpfdgedpfpfchfgbgmgdhfgehcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X2=k2\_tarski~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(X3 \in X2){\unicdbdjded}((X3=X0){\unicdcdcdid}(X3=X1)))\end{array}
\label{hyp:egcdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k2\_tarski}~{X0}}~{X1}}={{{k2\_tarski}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfehbgchdhlgjg}
\end{equation}
\begin{theorem}\label{thm:mgcdjdpfchfgbgmgdhfgehcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~c4\_\_realset2){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~c4\_\_realset2){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~c4\_\_realset2){\unicdbdjdcd}\\
(k1\_binop\_1~k1\_realset2~(k1\_binop\_1~k1\_realset2~X0~X1)~X2=k1\_binop\_1~\\
k1\_realset2~X0~(k1\_binop\_1~k1\_realset2~X1~X2))))\end{array}$$
\end{theorem}
\end{document}
