\documentclass{article}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\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{t10\_lfuzzy\_1 (TMcu32vLf2iY86aTNe4msWFgN2iGHmxzSZX)}
\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 $ v2\_lfuzzy\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k2\_fuzzy\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_lfuzzy\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_fuzzy\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v5\_relat\_1~X2~(k1\_rcomp\_1~k6\_numbers~np\_\_1)){\unicdcdcdhd}(\\
(v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(k2\_zfmisc\_1~X0~X1)~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)~\\
k1\_numbers)))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v5\_relat\_1~X3~(k1\_rcomp\_1~k6\_numbers~\\
np\_\_1)){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(k2\_zfmisc\_1~X0~X1)~\\
k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1)~k1\_numbers)))))){\unicdbdjdcd}(r2\_relset\_1~(k2\_zfmisc\_1~X1~X0)~k1\_numbers~\\
(k2\_fuzzy\_4~X1~X0~(k2\_fuzzy\_1~(k2\_zfmisc\_1~X0~X1)~X2~X3))~(k2\_fuzzy\_1~\\
(k2\_zfmisc\_1~X1~X0)~(k2\_fuzzy\_4~X1~X0~X2)~(k2\_fuzzy\_4~X1~X0~X3))))))\end{array}
\label{hyp:ehhdpfggfhkhkhjhpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}((r2\_relset\_1~X0~X1~X2~X3){\unicdbdjded}(X2=X3))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchcdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(((v5\_relat\_1~\\
X1~(k1\_rcomp\_1~k6\_numbers~np\_\_1)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~\\
X1~X0~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~\\
k1\_numbers)))))){\unicdcdcdhd}((v5\_relat\_1~X2~(k1\_rcomp\_1~k6\_numbers~np\_\_1)){\unicdcdcdhd}\\
((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~X0~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k1\_numbers)))))))){\unicdbdjdcd}(k2\_lfuzzy\_1~\\
X0~X1~X2=k2\_fuzzy\_1~X0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfmgggfhkhkhjhpfbd}
\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)){\unicdbdjdcd}\\
(\preoh v1\_xboole\_0~(k2\_zfmisc\_1~X0~X1))\end{array}
\label{hyp:ggdgbdadpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~\\
X1){\unicdcdcdhd}((v5\_relat\_1~X2~(k1\_rcomp\_1~k6\_numbers~np\_\_1)){\unicdcdcdhd}((v1\_funct\_1~\\
X2){\unicdcdcdhd}((v1\_funct\_2~X2~(k2\_zfmisc\_1~X1~X0)~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X1~X0)~k1\_numbers)))))))){\unicdbdjdcd}\\
((v5\_relat\_1~(k2\_fuzzy\_4~X0~X1~X2)~(k1\_rcomp\_1~k6\_numbers~np\_\_1)){\unicdcdcdhd}\\
((v1\_funct\_1~(k2\_fuzzy\_4~X0~X1~X2)){\unicdcdcdhd}((v1\_funct\_2~(k2\_fuzzy\_4~\\
X0~X1~X2)~(k2\_zfmisc\_1~X0~X1)~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~(k2\_fuzzy\_4~\\
X0~X1~X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)~k1\_numbers))))))\end{array}
\label{hyp:egehpflgcdpfggfhkhkhjhpfed}
\end{equation}
Assume the following.
\begin{equation}
\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}((v2\_lfuzzy\_1~X1~X0){\unicdbdjded}(r2\_relset\_1~\\
(k2\_zfmisc\_1~X0~X0)~k1\_numbers~(k2\_fuzzy\_4~X0~X0~X1)~X1)))\end{array}
\label{hyp:egedpfmgggfhkhkhjhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdadpfmgggfhkhkhjhpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v5\_relat\_1~X1~(k1\_rcomp\_1~\\
k6\_numbers~np\_\_1)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k2\_zfmisc\_1~\\
X0~X0)~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0)~k1\_numbers)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v5\_relat\_1~\\
X2~(k1\_rcomp\_1~k6\_numbers~np\_\_1)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~(k2\_zfmisc\_1~X0~X0)~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~k1\_numbers)))))){\unicdbdjdcd}(((v2\_lfuzzy\_1~\\
X1~X0){\unicdcdcdhd}(v2\_lfuzzy\_1~X2~X0)){\unicdbdjdcd}(r2\_relset\_1~(k2\_zfmisc\_1~X0~X0)~k1\_numbers~\\
(k2\_fuzzy\_4~X0~X0~(k2\_lfuzzy\_1~(k2\_zfmisc\_1~X0~X0)~X1~X2))~(k2\_lfuzzy\_1~\\
(k2\_zfmisc\_1~X0~X0)~X1~X2)))))\end{array}$$
\end{theorem}
\end{document}
