\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{t41\_fdiff\_2 (TMb7j3BxFwpH2znbDEmjhziXTezatYqTpmt)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\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 $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ k2\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v5\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_fcont\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}(((r1\_tarski~\\
(k2\_rcomp\_1~X0~X1)~(k1\_relset\_1~k1\_numbers~X2)){\unicdcdcdhd}((r2\_fdiff\_1~\\
X2~(k2\_rcomp\_1~X0~X1)){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~k1\_numbers){\unicdbdjdcd}\\
(\preoh (X3 \in k2\_rcomp\_1~X0~X1){\unicdcdcdhd}(r1\_xxreal\_0~(k1\_fdiff\_1~X2~X3)~k6\_numbers))))){\unicdbdjdcd}\\
(v5\_valued\_0~(k2\_partfun1~k1\_numbers~k1\_numbers~X2~(k2\_rcomp\_1~\\
X0~X1))))))\end{array}
\label{hyp:ehjdpfchpgmgmgfg}
\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}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}(((r1\_tarski~\\
(k2\_rcomp\_1~X0~X1)~(k1\_relset\_1~k1\_numbers~X2)){\unicdcdcdhd}(v1\_fcont\_1~(\\
k2\_partfun1~k1\_numbers~k1\_numbers~X2~(k2\_rcomp\_1~X0~X1)))){\unicdbdjdcd}((\\
(\preoh v5\_valued\_0~(k2\_partfun1~k1\_numbers~k1\_numbers~X2~(k2\_rcomp\_1~\\
X0~X1))){\unicdcdcdhd}(\preoh v6\_valued\_0~(k2\_partfun1~k1\_numbers~k1\_numbers~X2~\\
(k2\_rcomp\_1~X0~X1)))){\unicdcdcdid}(v3\_rcomp\_1~(k2\_relset\_1~k1\_numbers~(k2\_partfun1~\\
k1\_numbers~k1\_numbers~X2~(k2\_rcomp\_1~X0~X1))))))))\end{array}
\label{hyp:ehcdddpfggdgpgogehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}(((r1\_tarski~\\
(k2\_rcomp\_1~X0~X1)~(k1\_relset\_1~k1\_numbers~X2)){\unicdcdcdhd}((r2\_fdiff\_1~\\
X2~(k2\_rcomp\_1~X0~X1)){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~k1\_numbers){\unicdbdjdcd}\\
(\preoh (X3 \in k2\_rcomp\_1~X0~X1){\unicdcdcdhd}(r1\_xxreal\_0~k6\_numbers~(k1\_fdiff\_1~\\
X2~X3)))))){\unicdbdjdcd}(v6\_valued\_0~(k2\_partfun1~k1\_numbers~k1\_numbers~\\
X2~(k2\_rcomp\_1~X0~X1))))))\end{array}
\label{hyp:ehbdadpfchpgmgmgfg}
\end{equation}
\begin{theorem}\label{thm:ehedbdpfggegjgggggpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}(((r1\_tarski~\\
(k2\_rcomp\_1~X0~X1)~(k1\_relset\_1~k1\_numbers~X2)){\unicdcdcdhd}(r2\_fdiff\_1~X2~\\
(k2\_rcomp\_1~X0~X1))){\unicdbdjdcd}((({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~k1\_numbers){\unicdcdcdhd}\\
((X3 \in k2\_rcomp\_1~X0~X1){\unicdcdcdhd}(r1\_xxreal\_0~(k1\_fdiff\_1~X2~X3)~k6\_numbers))){\unicdcdcdhd}\\
({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~k1\_numbers){\unicdcdcdhd}((X3 \in k2\_rcomp\_1~X0~X1){\unicdcdcdhd}\\
(r1\_xxreal\_0~k6\_numbers~(k1\_fdiff\_1~X2~X3))))){\unicdcdcdid}(v3\_rcomp\_1~(\\
k2\_relset\_1~k1\_numbers~(k2\_partfun1~k1\_numbers~k1\_numbers~X2~\\
(k2\_rcomp\_1~X0~X1))))))))\end{array}$$
\end{theorem}
\end{document}
