\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{t10\_fdiff\_2 (TMbnr3C41YMeTN53bmkCpyTDKaewcc24eLv)}
\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 $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_fdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_fcont\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_fdiff\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_fdiff\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~\\
X1){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}(\preoh (r1\_fcont\_1~X2~X0){\unicdcdcdhd}\\
((k1\_seq\_1~X2~X0{\unicdcdgdad}X1){\unicdcdcdhd}(({\unicdcdaddd} X3 .  (m1\_rcomp\_1~X3~X0){\unicdcdcdhd}(r1\_tarski~\\
X3~(k1\_relset\_1~k1\_numbers~X2))){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_rcomp\_1~X3~X0){\unicdbdjdcd}\\
(\preoh (r1\_tarski~X3~(k1\_relset\_1~k1\_numbers~X2)){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~k1\_numbers){\unicdbdjdcd}(\preoh (X4 \in X3){\unicdcdcdhd}(k1\_seq\_1~X2~X4=X1))))))))))\end{array}
\label{hyp:ehhdpfggdgpgogehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~X1)){\unicdbdjded}(r1\_tarski~\\
X0~X1)\end{array}
\label{hyp:ehddpfdhfhcgdhfgeh}
\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}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}((r1\_fdiff\_1~\\
X0~X1){\unicdbdjdcd}(r1\_fcont\_1~X0~X1)))\end{array}
\label{hyp:ehcdedpfggegjgggggpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((r1\_tarski~X0~X1){\unicdcdcdhd}(r1\_tarski~\\
X1~X2)){\unicdbdjdcd}(r1\_tarski~X0~X2)\end{array}
\label{hyp:ehbdpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{r1\_tarski}~{X0}}~{X0}}}}\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfehbgchdhlgjg}
\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}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}((r1\_fdiff\_1~\\
X0~X1){\unicdbdjded}({\unicdcdaddd} X2 .  (m1\_rcomp\_1~X2~X1){\unicdcdcdhd}((r1\_tarski~X2~(k1\_relset\_1~\\
k1\_numbers~X0)){\unicdcdcdhd}({\unicdcdaddd} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v3\_fdiff\_1~X3){\unicdcdcdhd}\\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers))))){\unicdcdcdhd}\\
({\unicdcdaddd} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}((v2\_fdiff\_1~X4){\unicdcdcdhd}(m1\_subset\_1~\\
X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers))))){\unicdcdcdhd}({\unicdcdadad} X5 .  \\
(m1\_subset\_1~X5~k1\_numbers){\unicdbdjdcd}((X5 \in X2){\unicdbdjdcd}(k9\_real\_1~(k1\_seq\_1~X0~\\
X5)~(k1\_seq\_1~X0~X1)=k7\_real\_1~(k1\_seq\_1~X3~(k9\_real\_1~X5~X1))~(\\
k1\_seq\_1~X4~(k9\_real\_1~X5~X1)))))))))))\end{array}
\label{hyp:egedpfggegjgggggpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjded}{({{X0} \in {k1\_numbers}})}}}\label{hyp:egbdpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgbdpfihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehbdadpfggegjgggggpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}(\preoh (k1\_seq\_1~\\
X2~X0{\unicdcdgdad}X1){\unicdcdcdhd}((r1\_fdiff\_1~X2~X0){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_rcomp\_1~X3~X0){\unicdbdjdcd}\\
(\preoh (r1\_tarski~X3~(k1\_relset\_1~k1\_numbers~X2)){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~k1\_numbers){\unicdbdjdcd}(\preoh (X4 \in X3){\unicdcdcdhd}(k1\_seq\_1~X2~X4=X1)))))))))\end{array}$$
\end{theorem}
\end{document}
