\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{l78\_normform (TMFkEjBGWWbP6MfkCxdAn4H84D6myaswed4)}
\maketitle
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_finsub\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_normform : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_normform : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u2\_lattices : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k12\_normform : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_lattices : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_normform : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_setwiseo : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k10\_normform : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k5\_finsub\_1~(k7\_normform~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k5\_finsub\_1~(k7\_normform~\\
X0))){\unicdbdjdcd}(k9\_normform~X0~(k5\_setwiseo~(k7\_normform~X0)~(k9\_normform~\\
X0~X1)~X2)=k9\_normform~X0~(k5\_setwiseo~(k7\_normform~X0)~X1~X2)))\end{array}
\label{hyp:ehededpfogpgchngggpgchng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m2\_subset\_1~X1~(k5\_finsub\_1~(k7\_normform~\\
X0))~(k8\_normform~X0)){\unicdbdjdcd}(k9\_normform~X0~X1=X1)\end{array}
\label{hyp:ehedcdpfogpgchngggpgchng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m2\_subset\_1~X1~(k5\_finsub\_1~(k7\_normform~\\
X0))~(k8\_normform~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~X2~(k5\_finsub\_1~\\
(k7\_normform~X0))~(k8\_normform~X0)){\unicdbdjdcd}(k9\_normform~X0~(k5\_setwiseo~\\
(k7\_normform~X0)~(k10\_normform~X0~X1~X2)~X2)=k9\_normform~X0~X2))\end{array}
\label{hyp:mghdcdpfogpgchngggpgchng}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {\preoh{{{v1\_xboole\_0}~{({{k8\_normform}~{X0}})}}}}}\label{hyp:ggdgddpfogpgchngggpgchng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~X0~X1){\unicdbdjdcd}(m1\_subset\_1~X2~X0))\end{array}
\label{hyp:egehpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k5\_finsub\_1~(k7\_normform~\\
X0))){\unicdbdjdcd}(m2\_subset\_1~(k9\_normform~X0~X1)~(k5\_finsub\_1~(k7\_normform~\\
X0))~(k8\_normform~X0))\end{array}
\label{hyp:egehpflgjdpfogpgchngggpgchng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  m1\_subset\_1~(k8\_normform~X0)~(k1\_zfmisc\_1~(k5\_finsub\_1~\\
(k7\_normform~X0)))\end{array}
\label{hyp:egehpflgidpfogpgchngggpgchng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_lattices~(k12\_normform~X0)){\unicdcdcdhd}(l3\_lattices~(k12\_normform~\\
X0))\end{array}
\label{hyp:egehpflgbdcdpfogpgchngggpgchng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_subset\_1~X1~(k5\_finsub\_1~\\
(k7\_normform~X0))){\unicdcdcdhd}(m1\_subset\_1~X2~(k5\_finsub\_1~(k7\_normform~\\
X0)))){\unicdbdjdcd}(m1\_subset\_1~(k10\_normform~X0~X1~X2)~(k5\_finsub\_1~(k7\_normform~\\
X0)))\end{array}
\label{hyp:egehpflgbdadpfogpgchngggpgchng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v3\_lattices~X1){\unicdcdcdhd}(l3\_lattices~X1)){\unicdbdjdcd}(\\
(X1=k12\_normform~X0){\unicdbdjded}((u1\_struct\_0~X1=k8\_normform~X0){\unicdcdcdhd}({\unicdcdadad} X2 .  \\
(m2\_subset\_1~X2~(k5\_finsub\_1~(k7\_normform~X0))~(k8\_normform~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m2\_subset\_1~X3~(k5\_finsub\_1~(k7\_normform~X0))~(k8\_normform~\\
X0)){\unicdbdjdcd}((k1\_binop\_1~(u2\_lattices~X1)~X2~X3=k9\_normform~X0~(k5\_setwiseo~\\
(k7\_normform~X0)~X2~X3)){\unicdcdcdhd}(k1\_binop\_1~(u1\_lattices~X1)~X2~X3=k9\_normform~\\
X0~(k10\_normform~X0~X2~X3)))))))\end{array}
\label{hyp:egbdcdpfogpgchngggpgchng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v1\_xboole\_0~X1))\end{array}
\label{hyp:dgdgbdpfdhfhcgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:mghdidpfogpgchngggpgchng}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m2\_subset\_1~X1~(k5\_finsub\_1~(k7\_normform~\\
X0))~(k8\_normform~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~X2~(k5\_finsub\_1~\\
(k7\_normform~X0))~(k8\_normform~X0)){\unicdbdjdcd}(k1\_binop\_1~(u2\_lattices~\\
(k12\_normform~X0))~(k1\_binop\_1~(u1\_lattices~(k12\_normform~X0))~\\
X1~X2)~X2=X2))\end{array}$$
\end{theorem}
\end{document}
