\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{t63\_pdiff\_9 (TMK7ajpz3yXTSf1vUe4yuYegJouWnkgQA8z)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_pdiff\_7 : {{\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 $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ r3\_pdiff\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ r1\_pdiff\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_pdiff\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ r2\_pdiff\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m2\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k12\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_euclid : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k17\_complex1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_binop\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_pdiff\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k11\_binop\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k3\_pdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r4\_pdiff\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k2\_pdiff\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ r2\_pdiff\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ r1\_pdiff\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k1\_pdiff\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k8\_pdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m2\_subset\_1~X0~k1\_numbers~k5\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m2\_subset\_1~X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k1\_euclid~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((\\
v1\_funct\_1~X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_euclid~\\
X0)~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~\\
X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_euclid~X0)~(k1\_euclid~np\_\_1))))){\unicdbdjdcd}\\
(((r2\_relset\_1~(k1\_euclid~X0)~(k1\_euclid~np\_\_1)~(k3\_pdiff\_1~X0~\\
X3)~X4){\unicdcdcdhd}((v1\_pdiff\_7~X2~X0){\unicdcdcdhd}((r1\_xxreal\_0~np\_\_1~X1){\unicdcdcdhd}((r1\_xxreal\_0~\\
X1~X0){\unicdcdcdhd}(r3\_pdiff\_9~X0~X2~X1~X3))))){\unicdbdjdcd}((r1\_pdiff\_9~X0~X2~(k3\_pdiff\_9~\\
X0~X2~X1~X3)){\unicdbdjded}(r4\_pdiff\_7~X0~np\_\_1~(k2\_pdiff\_7~X0~np\_\_1~X1~X4~X2)~X2)))))))\end{array}
\label{hyp:ehgdcdpfahegjgggggpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m2\_subset\_1~X0~k1\_numbers~k5\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m2\_subset\_1~X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k1\_euclid~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((\\
v1\_funct\_1~X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_euclid~\\
X0)~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~\\
X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_euclid~X0)~(k1\_euclid~np\_\_1))))){\unicdbdjdcd}\\
(((r2\_relset\_1~(k1\_euclid~X0)~(k1\_euclid~np\_\_1)~(k3\_pdiff\_1~X0~\\
X3)~X4){\unicdcdcdhd}((v1\_pdiff\_7~X2~X0){\unicdcdcdhd}((r1\_xxreal\_0~np\_\_1~X1){\unicdcdcdhd}(r1\_xxreal\_0~\\
X1~X0)))){\unicdbdjdcd}((r3\_pdiff\_9~X0~X2~X1~X3){\unicdbdjded}(r2\_pdiff\_7~X0~np\_\_1~X1~X4~X2)))))))\end{array}
\label{hyp:ehgdbdpfahegjgggggpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m2\_subset\_1~X0~k1\_numbers~k5\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k1\_euclid~X0)~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~\\
X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_euclid~X0)~\\
(k1\_euclid~np\_\_1))))){\unicdbdjdcd}((r2\_relset\_1~(k1\_euclid~X0)~(k1\_euclid~\\
np\_\_1)~(k3\_pdiff\_1~X0~X2)~X3){\unicdbdjdcd}(((r1\_tarski~X1~(k1\_relset\_1~(k1\_euclid~\\
X0)~X2)){\unicdcdcdhd}(r2\_pdiff\_9~X1~X0~X2)){\unicdbdjded}(r1\_pdiff\_6~X1~np\_\_1~X0~X3)))))\end{array}
\label{hyp:ehfdddpfahegjgggggpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_funct\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(\\
k1\_euclid~X0)~k1\_numbers)))){\unicdbdjdcd}(k1\_relset\_1~(k1\_euclid~X0)~(k3\_pdiff\_1~\\
X0~X1)=k1\_relset\_1~(k1\_euclid~X0)~X1))\end{array}
\label{hyp:ehddpfahegjgggggpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m2\_subset\_1~X0~k1\_numbers~k5\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m2\_subset\_1~X1~k1\_numbers~k5\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(k1\_euclid~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v1\_funct\_1~X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(\\
k1\_euclid~X0)~(k1\_euclid~X1))))){\unicdbdjdcd}(((v1\_pdiff\_7~X2~X0){\unicdcdcdhd}(r1\_tarski~\\
X2~(k1\_relset\_1~(k1\_euclid~X0)~X3))){\unicdbdjdcd}(({\unicdcdadad} X4 .  (m2\_subset\_1~\\
X4~k1\_numbers~k5\_numbers){\unicdbdjdcd}(((r1\_xxreal\_0~np\_\_1~X4){\unicdcdcdhd}(r1\_xxreal\_0~\\
X4~X0)){\unicdbdjdcd}((r2\_pdiff\_7~X0~X1~X4~X3~X2){\unicdcdcdhd}(r4\_pdiff\_7~X0~X1~(k2\_pdiff\_7~\\
X0~X1~X4~X3~X2)~X2)))){\unicdbdjded}((r1\_pdiff\_6~X2~X1~X0~X3){\unicdcdcdhd}({\unicdcdadad} X4 .  (m2\_finseq\_2~\\
X4~k1\_numbers~(k1\_euclid~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~k1\_numbers){\unicdbdjdcd}\\
(\preoh (X4 \in X2){\unicdcdcdhd}((\preoh r1\_xxreal\_0~X5~k6\_numbers){\unicdcdcdhd}({\unicdcdadad} X6 .  (m1\_subset\_1~\\
X6~k1\_numbers){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~X6~k6\_numbers){\unicdcdcdhd}({\unicdcdadad} X7 .  (\\
m2\_finseq\_2~X7~k1\_numbers~(k1\_euclid~X0)){\unicdbdjdcd}((X7 \in X2){\unicdbdjdcd}((r1\_xxreal\_0~\\
X6~(k12\_euclid~(k8\_euclid~X0~X7~X4))){\unicdcdcdid}({\unicdcdadad} X8 .  (m2\_finseq\_2~\\
X8~k1\_numbers~(k1\_euclid~X0)){\unicdbdjdcd}(r1\_xxreal\_0~(k12\_euclid~(k8\_euclid~\\
X1~(k1\_pdiff\_6~X0~X1~(k8\_pdiff\_1~X0~X1~X3~X7)~X8)~(k1\_pdiff\_6~X0~X1~\\
(k8\_pdiff\_1~X0~X1~X3~X4)~X8)))~(k11\_binop\_2~X5~(k12\_euclid~X8)))))))))))))))))))\end{array}
\label{hyp:ehcdgdpfahegjgggggpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_1){\unicdcdcdhd}(m2\_subset\_1~np\_\_1~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_1~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_1~k1\_numbers))\end{array}
\label{hyp:dhahdgbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{np\_\_1}}}}\label{hyp:dhahdgbdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}((r2\_relset\_1~X0~X1~X2~X3){\unicdbdjded}(X2=X3))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchcdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~X0~X1){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfdhfhcgdhfgehpfbd}
\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 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m2\_subset\_1~X0~k1\_numbers~k5\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k1\_euclid~X0)~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_euclid~X0)~(k1\_euclid~\\
np\_\_1))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_finseq\_2~X3~k1\_numbers~(k1\_euclid~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_finseq\_2~X4~k1\_numbers~(k1\_euclid~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  (m2\_finseq\_2~X5~k1\_numbers~(k1\_euclid~X0)){\unicdbdjdcd}((r2\_relset\_1~\\
(k1\_euclid~X0)~(k1\_euclid~np\_\_1)~(k3\_pdiff\_1~X0~X1)~X2){\unicdbdjdcd}(k17\_complex1~\\
(k10\_binop\_2~(k1\_seq\_1~(k1\_pdiff\_7~X0~X1~X3)~X5)~(k1\_seq\_1~(k1\_pdiff\_7~\\
X0~X1~X4)~X5))=k12\_euclid~(k8\_euclid~np\_\_1~(k1\_pdiff\_6~X0~np\_\_1~\\
(k8\_pdiff\_1~X0~np\_\_1~X2~X3)~X5)~(k1\_pdiff\_6~X0~np\_\_1~(k8\_pdiff\_1~\\
X0~np\_\_1~X2~X4)~X5)))))))))\end{array}
\label{hyp:mghdcdpfahegjgggggpfjd}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k4\_ordinal1}}}})}{\unicdcdcdhd}{({{v3\_ordinal1}~{k4\_ordinal1}})}}\label{hyp:ggdggdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k1\_numbers}}}}\label{hyp:ggdgbdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k5\_numbers}}~{({{k1\_zfmisc\_1}~{k1\_numbers}})}}\label{hyp:egehpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v7\_ordinal1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_euclid~X0)~k1\_numbers))))){\unicdbdjdcd}\\
((v1\_funct\_1~(k3\_pdiff\_1~X0~X1)){\unicdcdcdhd}(m1\_subset\_1~(k3\_pdiff\_1~X0~\\
X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_euclid~X0)~(k1\_euclid~np\_\_1)))))\end{array}
\label{hyp:egehpflgddpfahegjgggggpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgidpfpgchegjgogbgmgbd}
\end{equation}
\begin{theorem}\label{thm:ehgdddpfahegjgggggpfjd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m2\_subset\_1~X0~k1\_numbers~k5\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_euclid~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(\\
k1\_euclid~X0)~k1\_numbers)))){\unicdbdjdcd}(((v1\_pdiff\_7~X1~X0){\unicdcdcdhd}(r1\_tarski~\\
X1~(k1\_relset\_1~(k1\_euclid~X0)~X2))){\unicdbdjdcd}(({\unicdcdadad} X3 .  (m2\_subset\_1~\\
X3~k1\_numbers~k5\_numbers){\unicdbdjdcd}(((r1\_xxreal\_0~np\_\_1~X3){\unicdcdcdhd}(r1\_xxreal\_0~\\
X3~X0)){\unicdbdjdcd}((r3\_pdiff\_9~X0~X1~X3~X2){\unicdcdcdhd}(r1\_pdiff\_9~X0~X1~(k3\_pdiff\_9~\\
X0~X1~X3~X2))))){\unicdbdjded}((r2\_pdiff\_9~X1~X0~X2){\unicdcdcdhd}({\unicdcdadad} X3 .  (m2\_finseq\_2~\\
X3~k1\_numbers~(k1\_euclid~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k1\_numbers){\unicdbdjdcd}\\
(\preoh (X3 \in X1){\unicdcdcdhd}((\preoh r1\_xxreal\_0~X4~k6\_numbers){\unicdcdcdhd}({\unicdcdadad} X5 .  (m1\_subset\_1~\\
X5~k1\_numbers){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~X5~k6\_numbers){\unicdcdcdhd}({\unicdcdadad} X6 .  (\\
m2\_finseq\_2~X6~k1\_numbers~(k1\_euclid~X0)){\unicdbdjdcd}((X6 \in X1){\unicdbdjdcd}((r1\_xxreal\_0~\\
X5~(k12\_euclid~(k8\_euclid~X0~X6~X3))){\unicdcdcdid}({\unicdcdadad} X7 .  (m2\_finseq\_2~\\
X7~k1\_numbers~(k1\_euclid~X0)){\unicdbdjdcd}(r1\_xxreal\_0~(k17\_complex1~(k10\_binop\_2~\\
(k1\_seq\_1~(k1\_pdiff\_7~X0~X2~X6)~X7)~(k1\_seq\_1~(k1\_pdiff\_7~X0~X2~X3)~\\
X7)))~(k11\_binop\_2~X4~(k12\_euclid~X7))))))))))))))))))\end{array}$$
\end{theorem}
\end{document}
