\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{t1\_fuzzy\_2 (TMPHyVqnhWeiLKBmGd7DvZDwHkFsrXgUNVT)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ k1\_numbers : {\iota}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k4\_fuzzy\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_fuzzy\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_0 : {\iota}$ be given.
Let $ k7\_rfunct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_funct\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{\preoh{{({{X0} \in {X1}})}}}{\unicdcdcdhd}{({{v1\_xboole\_0}~{X1}})}}}}\label{hyp:ehhdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((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}((r1\_xxreal\_0~\\
(k1\_seq\_1~(k4\_fuzzy\_1~X0)~X1)~(k1\_seq\_1~X2~X1)){\unicdcdcdhd}(r1\_xxreal\_0~(\\
k1\_seq\_1~X2~X1)~(k1\_seq\_1~(k5\_fuzzy\_1~X0)~X1)))))\end{array}
\label{hyp:ehbdgdpfggfhkhkhjhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{np\_\_0}}\label{hyp:dhahdgadpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k7\_rfunct\_1}~{X0}}~{X1}}={{{k4\_funct\_3}~{X0}}~{X1}}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflghdpfchggfhogdgehpfbd}
\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 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v3\_valued\_0~\\
X0))){\unicdbdjdcd}(k1\_seq\_1~X0~X1=k1\_funct\_1~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{v3\_membered}~{k1\_numbers}}\label{hyp:ggdgddpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((v5\_relat\_1~(k5\_fuzzy\_1~X0)~(k1\_rcomp\_1~\\
k6\_numbers~np\_\_1)){\unicdcdcdhd}((v1\_funct\_1~(k5\_fuzzy\_1~X0)){\unicdcdcdhd}((v1\_funct\_2~\\
(k5\_fuzzy\_1~X0)~X0~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~(k5\_fuzzy\_1~X0)~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k1\_numbers))))))\end{array}
\label{hyp:egehpflgfdpfggfhkhkhjhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((v5\_relat\_1~(k4\_fuzzy\_1~X0)~(k1\_rcomp\_1~\\
k6\_numbers~np\_\_1)){\unicdcdcdhd}((v1\_funct\_1~(k4\_fuzzy\_1~X0)){\unicdcdcdhd}((v1\_funct\_2~\\
(k4\_fuzzy\_1~X0)~X0~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~(k4\_fuzzy\_1~X0)~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k1\_numbers))))))\end{array}
\label{hyp:egehpflgedpfggfhkhkhjhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_relat\_1~(k4\_funct\_3~X0~X1)){\unicdcdcdhd}(v1\_funct\_1~\\
(k4\_funct\_3~X0~X1))\end{array}
\label{hyp:egehpflgedpfggfhogdgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({\preoh{{{v1\_xboole\_0}~{X0}}}})}{\unicdbdjdcd}{({{{k5\_fuzzy\_1}~{X0}}={{{k7\_rfunct\_1}~{X0}}~{X0}}})}}}\label{hyp:eghdpfggfhkhkhjhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}(k4\_fuzzy\_1~X0=k7\_rfunct\_1~k1\_xboole\_0~\\
X0)\end{array}
\label{hyp:eggdpfggfhkhkhjhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~\\
X2)){\unicdbdjdcd}((X2=k4\_funct\_3~X0~X1){\unicdbdjded}((k9\_xtuple\_0~X2=X1){\unicdcdcdhd}({\unicdcdadad} X3 .  \\
(X3 \in X1){\unicdbdjdcd}(((X3 \in X0){\unicdbdjdcd}(k1\_funct\_1~X2~X3=np\_\_1)){\unicdcdcdhd}((\preoh X3 \in X0){\unicdbdjdcd}(k1\_funct\_1~\\
X2~X3=k1\_xboole\_0))))))\end{array}
\label{hyp:egddpfggfhogdgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v3\_membered~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(v3\_valued\_0~X2))\end{array}
\label{hyp:dgdgbdidpfghbgmgfhfgegpfad}
\end{equation}
\begin{theorem}\label{thm:ehbdpfggfhkhkhjhpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v5\_relat\_1~X2~(k1\_rcomp\_1~k6\_numbers~np\_\_1)){\unicdcdcdhd}(\\
(v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~X0~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k1\_numbers)))))){\unicdbdjdcd}((r1\_xxreal\_0~\\
k6\_numbers~(k1\_seq\_1~X2~X1)){\unicdcdcdhd}(r1\_xxreal\_0~(k1\_seq\_1~X2~X1)~np\_\_1))))\end{array}$$
\end{theorem}
\end{document}
