\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{l18\_pdiff\_4 (TMJT6wsHXM7hEn5RpeAwphRVsWYq7m6S3dK)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ m2\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_3 : {\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 $ k11\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r3\_pdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k1\_fdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_pdiff\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ 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 $ v3\_fdiff\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_fdiff\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k9\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_fdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ m1\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
(k11\_finseq\_1~X0~X1~X2=k11\_finseq\_1~X3~X4~X5){\unicdbdjdcd}((X0=X3){\unicdcdcdhd}((X1=X4){\unicdcdcdhd}\\
(X2=X5)))\end{array}
\label{hyp:ehhdidpfggjgogdhfgbhpfbd}
\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 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m2\_finseq\_2~X3~k1\_numbers~(k1\_euclid~np\_\_3)){\unicdbdjdcd}({\unicdcdadad} X4 .  ((\\
v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_euclid~\\
np\_\_3)~k1\_numbers)))){\unicdbdjdcd}(((X3=k11\_finseq\_1~X0~X1~X2){\unicdcdcdhd}(r3\_pdiff\_1~\\
np\_\_3~np\_\_3~X4~X3)){\unicdbdjdcd}(r1\_fdiff\_1~(k1\_pdiff\_2~np\_\_3~np\_\_3~X4~X3)~X2))))))\end{array}
\label{hyp:ehgdpfahegjgggggpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_3){\unicdcdcdhd}(m2\_subset\_1~np\_\_3~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_3~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_3~k1\_numbers))\end{array}
\label{hyp:dhahdgddpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_finseq\_2~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_2~\\
X2~X0~X1){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((m1\_subset\_1~X0~\\
k5\_numbers){\unicdcdcdhd}((m1\_subset\_1~X1~k5\_numbers){\unicdcdcdhd}(((v1\_funct\_1~X2){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_euclid~X0)~k1\_numbers)))){\unicdcdcdhd}\\
(m1\_subset\_1~X3~(k1\_euclid~X0))))){\unicdbdjdcd}((v1\_funct\_1~(k1\_pdiff\_2~\\
X0~X1~X2~X3)){\unicdcdcdhd}(m1\_subset\_1~(k1\_pdiff\_2~X0~X1~X2~X3)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k1\_numbers~k1\_numbers))))\end{array}
\label{hyp:egehpflgbdpfahegjgggggpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{{m1\_finseq\_2}~{({{k1\_euclid}~{X0}})}}~{k1\_numbers}})}}}\label{hyp:egehpflgbdpffgfhdgmgjgeg}
\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}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}((X2=k1\_fdiff\_1~\\
X0~X1){\unicdbdjded}({\unicdcdaddd} X3 .  (m1\_rcomp\_1~X3~X1){\unicdcdcdhd}((r1\_tarski~X3~(k1\_relset\_1~\\
k1\_numbers~X0)){\unicdcdcdhd}({\unicdcdaddd} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}((v3\_fdiff\_1~X4){\unicdcdcdhd}\\
(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers))))){\unicdcdcdhd}\\
({\unicdcdaddd} X5 .  ((v1\_funct\_1~X5){\unicdcdcdhd}((v2\_fdiff\_1~X5){\unicdcdcdhd}(m1\_subset\_1~\\
X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers))))){\unicdcdcdhd}((X2=\\
k1\_seq\_1~X4~np\_\_1){\unicdcdcdhd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~k1\_numbers){\unicdbdjdcd}(\\
(X6 \in X3){\unicdbdjdcd}(k9\_real\_1~(k1\_seq\_1~X0~X6)~(k1\_seq\_1~X0~X1)=k7\_real\_1~\\
(k1\_seq\_1~X4~(k9\_real\_1~X6~X1))~(k1\_seq\_1~X5~(k9\_real\_1~X6~X1))))))))))))))\end{array}
\label{hyp:egfdpfggegjgggggpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgidpfpgchegjgogbgmgbd}
\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:mgbdidpfahegjgggggpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_finseq\_2~X4~k1\_numbers~\\
(k1\_euclid~np\_\_3)){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_funct\_1~X5){\unicdcdcdhd}(m1\_subset\_1~\\
X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_euclid~np\_\_3)~k1\_numbers)))){\unicdbdjdcd}\\
(((X4=k11\_finseq\_1~X0~X1~X2){\unicdcdcdhd}(r3\_pdiff\_1~np\_\_3~np\_\_3~X5~X4)){\unicdbdjdcd}(\\
(X3=k1\_fdiff\_1~(k1\_pdiff\_2~np\_\_3~np\_\_3~X5~X4)~X2){\unicdbdjded}({\unicdcdaddd} X6 .  \\
(m1\_subset\_1~X6~k1\_numbers){\unicdcdcdhd}({\unicdcdaddd} X7 .  (m1\_subset\_1~X7~k1\_numbers){\unicdcdcdhd}\\
({\unicdcdaddd} X8 .  (m1\_subset\_1~X8~k1\_numbers){\unicdcdcdhd}((X4=k11\_finseq\_1~X6~\\
X7~X8){\unicdcdcdhd}({\unicdcdaddd} X9 .  (m1\_rcomp\_1~X9~X8){\unicdcdcdhd}((r1\_tarski~X9~(k1\_relset\_1~\\
k1\_numbers~(k1\_pdiff\_2~np\_\_3~np\_\_3~X5~X4))){\unicdcdcdhd}({\unicdcdaddd} X10 .  ((v1\_funct\_1~\\
X10){\unicdcdcdhd}((v3\_fdiff\_1~X10){\unicdcdcdhd}(m1\_subset\_1~X10~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers))))){\unicdcdcdhd}({\unicdcdaddd} X11 .  ((v1\_funct\_1~X11){\unicdcdcdhd}\\
((v2\_fdiff\_1~X11){\unicdcdcdhd}(m1\_subset\_1~X11~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers))))){\unicdcdcdhd}((X3=k1\_seq\_1~X10~np\_\_1){\unicdcdcdhd}({\unicdcdadad} X12 .  \\
(m1\_subset\_1~X12~k1\_numbers){\unicdbdjdcd}((X12 \in X9){\unicdbdjdcd}(k9\_real\_1~(k1\_seq\_1~\\
(k1\_pdiff\_2~np\_\_3~np\_\_3~X5~X4)~X12)~(k1\_seq\_1~(k1\_pdiff\_2~np\_\_3~\\
np\_\_3~X5~X4)~X8)=k7\_real\_1~(k1\_seq\_1~X10~(k9\_real\_1~X12~X8))~(k1\_seq\_1~\\
X11~(k9\_real\_1~X12~X8)))))))))))))))))))))\end{array}$$
\end{theorem}
\end{document}
