\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{t56\_normform (TMYXtwjhBGG33unJTwhDP2B3PGApHS7gjLZ)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k12\_normform : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_finsub\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_normform : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_normform : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v3\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ k9\_normform : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_setwiseo : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u1\_lattices : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_normform : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  k1\_xboole\_0 \in ReplSep~(toset~({\uniddcgcg} X1 : \iota .  m1\_subset\_1~\\
X1~(k5\_finsub\_1~(k7\_normform~X0))))~({\uniddcgcg} X1 : \iota .  {\unicdcdadad} X2 .  (\\
m2\_subset\_1~X2~(k2\_zfmisc\_1~(k5\_finsub\_1~X0)~(k5\_finsub\_1~X0))~\\
(k7\_normform~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_subset\_1~X3~(k2\_zfmisc\_1~(\\
k5\_finsub\_1~X0)~(k5\_finsub\_1~X0))~(k7\_normform~X0)){\unicdbdjdcd}(((X2 \in X1){\unicdcdcdhd}\\
((X3 \in X1){\unicdcdcdhd}(r1\_normform~(k5\_finsub\_1~X0)~(k5\_finsub\_1~X0)~X2~X3))){\unicdbdjdcd}\\
(X2=X3))))~({\uniddcgcg} X1 : \iota .  X1)\end{array}
\label{hyp:mgedcdpfogpgchngggpgchng}
\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 .  k8\_normform~X0=ReplSep~(toset~({\uniddcgcg} X1 : \iota .  m1\_subset\_1~\\
X1~(k5\_finsub\_1~(k7\_normform~X0))))~({\uniddcgcg} X1 : \iota .  {\unicdcdadad} X2 .  (\\
m2\_subset\_1~X2~(k2\_zfmisc\_1~(k5\_finsub\_1~X0)~(k5\_finsub\_1~X0))~\\
(k7\_normform~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_subset\_1~X3~(k2\_zfmisc\_1~(\\
k5\_finsub\_1~X0)~(k5\_finsub\_1~X0))~(k7\_normform~X0)){\unicdbdjdcd}(((X2 \in X1){\unicdcdcdhd}\\
((X3 \in X1){\unicdcdcdhd}(r1\_normform~(k5\_finsub\_1~X0)~(k5\_finsub\_1~X0)~X2~X3))){\unicdbdjdcd}\\
(X2=X3))))~({\uniddcgcg} X1 : \iota .  X1)\end{array}
\label{hyp:egjdpfogpgchngggpgchng}
\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}
\begin{theorem}\label{thm:ehfdgdpfogpgchngggpgchng}
${{\unicdcdadad} X0 .  {{{m1\_subset\_1}~{k1\_xboole\_0}}~{({{u1\_struct\_0}~{({{k12\_normform}~{X0}})}})}}}$.
\end{theorem}
\end{document}
