\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{t44\_fdiff\_2 (TMQZQyXH7QYJtadspxDRmHY9Y7b8z258vcq)}
\maketitle
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_subset\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r2\_fdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_fdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ v3\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v6\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v2\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_fcont\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers)))){\unicdbdjdcd}(((r1\_tarski~(k2\_subset\_1~k1\_numbers)~\\
(k1\_relset\_1~k1\_numbers~X0)){\unicdcdcdhd}((r2\_fdiff\_1~X0~(k2\_subset\_1~k1\_numbers)){\unicdcdcdhd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k1\_numbers){\unicdbdjdcd}(\preoh r1\_xxreal\_0~k6\_numbers~\\
(k1\_fdiff\_1~X0~X1))))){\unicdbdjdcd}((v6\_valued\_0~(k2\_partfun1~k1\_numbers~\\
k1\_numbers~X0~(k2\_subset\_1~k1\_numbers))){\unicdcdcdhd}(v2\_funct\_1~X0)))\end{array}
\label{hyp:ehddidpfggegjgggggpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers)))){\unicdbdjdcd}(((r1\_tarski~(k2\_subset\_1~k1\_numbers)~\\
(k1\_relset\_1~k1\_numbers~X0)){\unicdcdcdhd}((r2\_fdiff\_1~X0~(k2\_subset\_1~k1\_numbers)){\unicdcdcdhd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k1\_numbers){\unicdbdjdcd}(\preoh r1\_xxreal\_0~(k1\_fdiff\_1~\\
X0~X1)~k6\_numbers)))){\unicdbdjdcd}((v5\_valued\_0~(k2\_partfun1~k1\_numbers~\\
k1\_numbers~X0~(k2\_subset\_1~k1\_numbers))){\unicdcdcdhd}(v2\_funct\_1~X0)))\end{array}
\label{hyp:ehddhdpfggegjgggggpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers)))){\unicdbdjdcd}(((r1\_tarski~(k2\_subset\_1~k1\_numbers)~\\
(k1\_relset\_1~k1\_numbers~X0)){\unicdcdcdhd}(v1\_fcont\_1~(k2\_partfun1~k1\_numbers~\\
k1\_numbers~X0~(k2\_subset\_1~k1\_numbers)))){\unicdbdjdcd}(((\preoh v5\_valued\_0~(\\
k2\_partfun1~k1\_numbers~k1\_numbers~X0~(k2\_subset\_1~k1\_numbers))){\unicdcdcdhd}\\
(\preoh v6\_valued\_0~(k2\_partfun1~k1\_numbers~k1\_numbers~X0~(k2\_subset\_1~\\
k1\_numbers)))){\unicdcdcdid}(v3\_rcomp\_1~(k2\_relset\_1~k1\_numbers~X0))))\end{array}
\label{hyp:ehcdgdpfggdgpgogehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}((r2\_fdiff\_1~X1~X0){\unicdbdjdcd}\\
(v1\_fcont\_1~(k2\_partfun1~k1\_numbers~k1\_numbers~X1~X0)))\end{array}
\label{hyp:ehcdfdpfggegjgggggpfbd}
\end{equation}
\begin{theorem}\label{thm:ehededpfggegjgggggpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers)))){\unicdbdjdcd}(((r1\_tarski~(k2\_subset\_1~k1\_numbers)~\\
(k1\_relset\_1~k1\_numbers~X0)){\unicdcdcdhd}(r2\_fdiff\_1~X0~(k2\_subset\_1~k1\_numbers))){\unicdbdjdcd}\\
((({\unicdcdaddd} X1 .  (m1\_subset\_1~X1~k1\_numbers){\unicdcdcdhd}(r1\_xxreal\_0~(k1\_fdiff\_1~\\
X0~X1)~k6\_numbers)){\unicdcdcdhd}({\unicdcdaddd} X1 .  (m1\_subset\_1~X1~k1\_numbers){\unicdcdcdhd}\\
(r1\_xxreal\_0~k6\_numbers~(k1\_fdiff\_1~X0~X1)))){\unicdcdcdid}(v3\_rcomp\_1~(k2\_relset\_1~\\
k1\_numbers~X0))))\end{array}$$
\end{theorem}
\end{document}
