\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{l53\_lfuzzy\_1 (TMZu2aUvrmKiWhPoVETmUyZYC4RAvmH5Y3L)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ np\_\_1 : {\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\_numbers : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_lfuzzy\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_lfuzzy\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k12\_lattice3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k7\_lfuzzy\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k9\_lfuzzy\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 : \iota{\unicdbdjdcd}\iota{\unicdbdjdcd}\iota .  {\unicdcdadad} X2 : \iota{\unicdbdjdcd}\iota{\unicdbdjdcd}\iota .  {\unicdcdadad} X3 : \\
\iota{\unicdbdjdcd}o .  {\unicdcdadad} X4 : \iota{\unicdbdjdcd}o .  {\unicdcdadad} X5 .  {\unicdcdadad} X6 .  ({\unicdcdadad} X7 .  \\
(m1\_subset\_1~X7~X6){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_subset\_1~X8~X5){\unicdbdjdcd}(((X4~X7){\unicdcdcdhd}\\
(X3~X8)){\unicdbdjdcd}(X2~X7~X8=X1~X7~X8)))){\unicdbdjdcd}(k1\_yellow\_0~X0~(ReplSep~(toset~\\
({\uniddcgcg} X7 : \iota .  m1\_subset\_1~X7~X6))~({\uniddcgcg} X7 : \iota .  X4~X7)~({\uniddcgcg} X7 : \iota .  \\
k1\_yellow\_0~X0~(ReplSep~(toset~({\uniddcgcg} X8 : \iota .  m1\_subset\_1~X8~X5))~\\
({\uniddcgcg} X8 : \iota .  X3~X8)~({\uniddcgcg} X8 : \iota .  X2~X7~X8))))=k1\_yellow\_0~X0~(ReplSep~\\
(toset~({\uniddcgcg} X7 : \iota .  m1\_subset\_1~X7~X5))~({\uniddcgcg} X7 : \iota .  X3~X7)~({\uniddcgcg} X7 : \\
\iota .  k1\_yellow\_0~X0~(ReplSep~(toset~({\uniddcgcg} X8 : \iota .  m1\_subset\_1~X8~\\
X6))~({\uniddcgcg} X8 : \iota .  X4~X8)~({\uniddcgcg} X8 : \iota .  X1~X8~X7)))))\end{array}
\label{hyp:dhfdpfmgggfhkhkhjhpfad}
\end{equation}
\begin{theorem}\label{thm:mgfdddpfmgggfhkhkhjhpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v5\_relat\_1~X1~(k1\_rcomp\_1~\\
k6\_numbers~np\_\_1)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k2\_zfmisc\_1~\\
X0~X0)~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0)~k1\_numbers)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(u1\_struct\_0~(k4\_lfuzzy\_0~(k2\_zfmisc\_1~X0~X0))))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~X0){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~X0){\unicdbdjdcd}\\
(k1\_yellow\_0~(k1\_lfuzzy\_0~(k1\_rcomp\_1~k6\_numbers~np\_\_1))~(ReplSep~\\
(toset~({\uniddcgcg} X5 : \iota .  m1\_subset\_1~X5~X0))~({\uniddcgcg} X5 : \iota .  True)~({\uniddcgcg} X5 : \\
\iota .  k1\_yellow\_0~(k1\_lfuzzy\_0~(k1\_rcomp\_1~k6\_numbers~np\_\_1))~\\
(ReplSep~(toset~({\uniddcgcg} X6 : \iota .  m1\_subset\_1~X6~(u1\_struct\_0~(k4\_lfuzzy\_0~\\
(k2\_zfmisc\_1~X0~X0)))))~({\uniddcgcg} X6 : \iota .  X6 \in X2)~({\uniddcgcg} X6 : \iota .  k12\_lattice3~\\
(k1\_lfuzzy\_0~(k1\_rcomp\_1~k6\_numbers~np\_\_1))~(k7\_lfuzzy\_0~(k2\_zfmisc\_1~\\
X0~X0)~X1~(k1\_domain\_1~X0~X0~X3~X5))~(k9\_lfuzzy\_0~(k2\_zfmisc\_1~X0~\\
X0)~X6~(k1\_domain\_1~X0~X0~X5~X4))))))=k1\_yellow\_0~(k1\_lfuzzy\_0~\\
(k1\_rcomp\_1~k6\_numbers~np\_\_1))~(ReplSep~(toset~({\uniddcgcg} X5 : \iota .  m1\_subset\_1~\\
X5~(u1\_struct\_0~(k4\_lfuzzy\_0~(k2\_zfmisc\_1~X0~X0)))))~({\uniddcgcg} X5 : \\
\iota .  X5 \in X2)~({\uniddcgcg} X5 : \iota .  k1\_yellow\_0~(k1\_lfuzzy\_0~(k1\_rcomp\_1~\\
k6\_numbers~np\_\_1))~(ReplSep~(toset~({\uniddcgcg} X6 : \iota .  m1\_subset\_1~X6~\\
X0))~({\uniddcgcg} X6 : \iota .  True)~({\uniddcgcg} X6 : \iota .  k12\_lattice3~(k1\_lfuzzy\_0~\\
(k1\_rcomp\_1~k6\_numbers~np\_\_1))~(k7\_lfuzzy\_0~(k2\_zfmisc\_1~X0~X0)~\\
X1~(k1\_domain\_1~X0~X0~X3~X6))~(k9\_lfuzzy\_0~(k2\_zfmisc\_1~X0~X0)~X5~\\
(k1\_domain\_1~X0~X0~X6~X4)))))))))))\end{array}$$
\end{theorem}
\end{document}
