\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{t20\_pdiff\_3 (TMVgXcWEDG5fWDjFEFtidTbPfnBjQ7rynLi)}
\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\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ m2\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m1\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_pdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r4\_pdiff\_3 : {{\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 $ k1\_pdiff\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_pdiff\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v2\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_fdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ v3\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ v2\_comseq\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k20\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k37\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k47\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k8\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k5\_pdiff\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_seq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_fdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r3\_pdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k11\_pdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_card\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_finseq\_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 $ m1\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v6\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\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 .  (m2\_finseq\_2~X2~k1\_numbers~(k1\_euclid~\\
np\_\_2)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k1\_euclid~np\_\_2)~k1\_numbers)))){\unicdbdjdcd}(((X2=k10\_finseq\_1~\\
X0~X1){\unicdcdcdhd}(r4\_pdiff\_3~X3~X2)){\unicdbdjdcd}(k5\_pdiff\_3~X3~X2=k1\_fdiff\_1~(k1\_pdiff\_2~\\
np\_\_2~np\_\_2~(k1\_pdiff\_3~np\_\_2~np\_\_2~X3)~X2)~X1)))))\end{array}
\label{hyp:ehidpfahegjgggggpfdd}
\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\_euclid~np\_\_2)~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_2~X1~\\
k1\_numbers~(k1\_euclid~np\_\_2)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_rcomp\_1~X2~(k1\_seq\_1~\\
(k1\_pdiff\_1~np\_\_2~np\_\_2)~X1)){\unicdbdjdcd}(((r3\_pdiff\_1~np\_\_2~np\_\_2~X0~X1){\unicdcdcdhd}\\
(r1\_tarski~X2~(k1\_relset\_1~k1\_numbers~(k1\_pdiff\_2~np\_\_2~np\_\_2~\\
X0~X1)))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v2\_relat\_1~X3){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~\\
X3~k5\_numbers~k1\_numbers){\unicdcdcdhd}((v1\_fdiff\_1~X3~k6\_numbers){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers))))))){\unicdbdjdcd}(\\
{\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}((v3\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~\\
k5\_numbers~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k5\_numbers~k1\_numbers)))))){\unicdbdjdcd}(((k2\_relset\_1~k1\_numbers~X4=k1\_tarski~\\
(k1\_seq\_1~(k1\_pdiff\_1~np\_\_2~np\_\_2)~X1)){\unicdcdcdhd}(r1\_tarski~(k2\_relset\_1~\\
k1\_numbers~(k3\_valued\_1~k5\_numbers~k1\_numbers~k1\_numbers~X3~X4))~\\
X2)){\unicdbdjdcd}((v2\_comseq\_2~(k20\_valued\_1~k5\_numbers~k1\_numbers~k1\_numbers~\\
(k37\_valued\_1~k5\_numbers~k1\_numbers~X3)~(k47\_valued\_1~k5\_numbers~\\
k1\_numbers~k1\_numbers~(k8\_funct\_2~k5\_numbers~k1\_numbers~k1\_numbers~\\
(k3\_valued\_1~k5\_numbers~k1\_numbers~k1\_numbers~X3~X4)~(k1\_pdiff\_2~\\
np\_\_2~np\_\_2~X0~X1))~(k8\_funct\_2~k5\_numbers~k1\_numbers~k1\_numbers~\\
X4~(k1\_pdiff\_2~np\_\_2~np\_\_2~X0~X1))))){\unicdcdcdhd}(k11\_pdiff\_1~np\_\_2~np\_\_2~\\
X0~X1=k2\_seq\_2~(k20\_valued\_1~k5\_numbers~k1\_numbers~k1\_numbers~\\
(k37\_valued\_1~k5\_numbers~k1\_numbers~X3)~(k47\_valued\_1~k5\_numbers~\\
k1\_numbers~k1\_numbers~(k8\_funct\_2~k5\_numbers~k1\_numbers~k1\_numbers~\\
(k3\_valued\_1~k5\_numbers~k1\_numbers~k1\_numbers~X3~X4)~(k1\_pdiff\_2~\\
np\_\_2~np\_\_2~X0~X1))~(k8\_funct\_2~k5\_numbers~k1\_numbers~k1\_numbers~\\
X4~(k1\_pdiff\_2~np\_\_2~np\_\_2~X0~X1))))))))))))\end{array}
\label{hyp:ehbdidpfahegjgggggpfcd}
\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 .  (m2\_finseq\_2~X2~k1\_numbers~(k1\_euclid~\\
np\_\_2)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k1\_euclid~np\_\_2)~k1\_numbers)))){\unicdbdjdcd}(((X2=k10\_finseq\_1~\\
X0~X1){\unicdcdcdhd}(r3\_pdiff\_1~np\_\_2~np\_\_2~X3~X2)){\unicdbdjdcd}(k11\_pdiff\_1~np\_\_2~np\_\_2~\\
X3~X2=k1\_fdiff\_1~(k1\_pdiff\_2~np\_\_2~np\_\_2~X3~X2)~X1)))))\end{array}
\label{hyp:ehbdedpfahegjgggggpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_finseq\_2~X0~k1\_numbers~(k1\_euclid~np\_\_2)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_funct\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(\\
k1\_euclid~np\_\_2)~k1\_numbers)))){\unicdbdjdcd}((r4\_pdiff\_3~X1~X0){\unicdbdjded}(r3\_pdiff\_1~\\
np\_\_2~np\_\_2~(k1\_pdiff\_3~np\_\_2~np\_\_2~X1)~X0)))\end{array}
\label{hyp:ehbdcdpfahegjgggggpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v3\_card\_1~X1~np\_\_2){\unicdcdcdhd}\\
(m2\_finseq\_1~X1~X0)){\unicdbdjdcd}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~X0){\unicdcdcdhd}({\unicdcdaddd} X3 .  \\
(m1\_subset\_1~X3~X0){\unicdcdcdhd}(X1=k10\_finseq\_1~X2~X3))))\end{array}
\label{hyp:ehbdadadpfggjgogdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_2){\unicdcdcdhd}(m2\_subset\_1~np\_\_2~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_2~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_2~k1\_numbers))\end{array}
\label{hyp:dhahdgcdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{np\_\_2}}}}\label{hyp:dhahdgcdpfcgpgpgmgfg}
\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}
{{v6\_membered}~{k4\_ordinal1}}\label{hyp:ggdggdpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k1\_numbers}}}}\label{hyp:ggdgbdpfogfhngcgfgchdh}
\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){\unicdbdjdcd}(m2\_finseq\_1~X2~X0))\end{array}
\label{hyp:egehpfngcdpfggjgogdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_subset\_1~X0~k5\_numbers){\unicdcdcdhd}\\
(((\preoh v1\_xboole\_0~X1){\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~X1)~\\
k1\_numbers)))))){\unicdbdjdcd}((v1\_funct\_1~(k1\_pdiff\_3~X0~X1~X2)){\unicdcdcdhd}((v1\_funct\_2~\\
(k1\_pdiff\_3~X0~X1~X2)~(k1\_euclid~X1)~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~\\
(k1\_pdiff\_3~X0~X1~X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_euclid~X1)~\\
k1\_numbers)))))\end{array}
\label{hyp:egehpflgbdpfahegjgggggpfdd}
\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 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_euclid~\\
X0)){\unicdbdjdcd}(v3\_card\_1~X1~X0))\end{array}
\label{hyp:dgdgbdpffgfhdgmgjgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v6\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
(v7\_ordinal1~X1))\end{array}
\label{hyp:dgdgbdhdpfngfgngcgfgchfgeg}
\end{equation}
\begin{theorem}\label{thm:ehcdadpfahegjgggggpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k1\_euclid~np\_\_2)~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_2~X1~\\
k1\_numbers~(k1\_euclid~np\_\_2)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_rcomp\_1~X2~(k1\_seq\_1~\\
(k1\_pdiff\_1~np\_\_2~np\_\_2)~X1)){\unicdbdjdcd}(((r4\_pdiff\_3~X0~X1){\unicdcdcdhd}(r1\_tarski~\\
X2~(k1\_relset\_1~k1\_numbers~(k1\_pdiff\_2~np\_\_2~np\_\_2~(k1\_pdiff\_3~\\
np\_\_2~np\_\_2~X0)~X1)))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v2\_relat\_1~X3){\unicdcdcdhd}((v1\_funct\_1~\\
X3){\unicdcdcdhd}((v1\_funct\_2~X3~k5\_numbers~k1\_numbers){\unicdcdcdhd}((v1\_fdiff\_1~X3~k6\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers))))))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}((v3\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~\\
X4~k5\_numbers~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k5\_numbers~k1\_numbers)))))){\unicdbdjdcd}(((k2\_relset\_1~k1\_numbers~X4=k1\_tarski~\\
(k1\_seq\_1~(k1\_pdiff\_1~np\_\_2~np\_\_2)~X1)){\unicdcdcdhd}(r1\_tarski~(k2\_relset\_1~\\
k1\_numbers~(k3\_valued\_1~k5\_numbers~k1\_numbers~k1\_numbers~X3~X4))~\\
X2)){\unicdbdjdcd}((v2\_comseq\_2~(k20\_valued\_1~k5\_numbers~k1\_numbers~k1\_numbers~\\
(k37\_valued\_1~k5\_numbers~k1\_numbers~X3)~(k47\_valued\_1~k5\_numbers~\\
k1\_numbers~k1\_numbers~(k8\_funct\_2~k5\_numbers~k1\_numbers~k1\_numbers~\\
(k3\_valued\_1~k5\_numbers~k1\_numbers~k1\_numbers~X3~X4)~(k1\_pdiff\_2~\\
np\_\_2~np\_\_2~(k1\_pdiff\_3~np\_\_2~np\_\_2~X0)~X1))~(k8\_funct\_2~k5\_numbers~\\
k1\_numbers~k1\_numbers~X4~(k1\_pdiff\_2~np\_\_2~np\_\_2~(k1\_pdiff\_3~np\_\_2~\\
np\_\_2~X0)~X1))))){\unicdcdcdhd}(k5\_pdiff\_3~X0~X1=k2\_seq\_2~(k20\_valued\_1~k5\_numbers~\\
k1\_numbers~k1\_numbers~(k37\_valued\_1~k5\_numbers~k1\_numbers~X3)~\\
(k47\_valued\_1~k5\_numbers~k1\_numbers~k1\_numbers~(k8\_funct\_2~k5\_numbers~\\
k1\_numbers~k1\_numbers~(k3\_valued\_1~k5\_numbers~k1\_numbers~k1\_numbers~\\
X3~X4)~(k1\_pdiff\_2~np\_\_2~np\_\_2~(k1\_pdiff\_3~np\_\_2~np\_\_2~X0)~X1))~(\\
k8\_funct\_2~k5\_numbers~k1\_numbers~k1\_numbers~X4~(k1\_pdiff\_2~np\_\_2~\\
np\_\_2~(k1\_pdiff\_3~np\_\_2~np\_\_2~X0)~X1))))))))))))\end{array}$$
\end{theorem}
\end{document}
