\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{t5\_ndiff\_2 (TMGkcwRQXbVuZdC78bWLNVKCKEFFGxYdy7s)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_normsp\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_normsp\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_normsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_normsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_ndiff\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ m1\_nfcont\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ 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 $ k1\_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 $ k2\_normsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_ndiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v3\_normsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_ndiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_normsp\_1 : {{\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 $ k37\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_normsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k18\_complex1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_normsp\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k7\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_real\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}\\
((v5\_rlvect\_1~X0){\unicdcdcdhd}((v6\_rlvect\_1~X0){\unicdcdcdhd}((v7\_rlvect\_1~X0){\unicdcdcdhd}((v8\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_normsp\_0~X0){\unicdcdcdhd}((v4\_normsp\_0~X0){\unicdcdcdhd}((v2\_normsp\_1~X0){\unicdcdcdhd}\\
(l1\_normsp\_1~X0)))))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((\preoh v7\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((\\
v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}((v5\_rlvect\_1~X1){\unicdcdcdhd}((v6\_rlvect\_1~\\
X1){\unicdcdcdhd}((v7\_rlvect\_1~X1){\unicdcdcdhd}((v8\_rlvect\_1~X1){\unicdcdcdhd}((v3\_normsp\_0~X1){\unicdcdcdhd}\\
((v4\_normsp\_0~X1){\unicdcdcdhd}((v2\_normsp\_1~X1){\unicdcdcdhd}(l1\_normsp\_1~X1)))))))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X1))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_nfcont\_1~X4~X0~X3){\unicdbdjdcd}((r1\_tarski~\\
X4~(k1\_relset\_1~(u1\_struct\_0~X0)~X2)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~\\
X5~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~\\
X1)){\unicdbdjdcd}(({\unicdcdadad} X7 .  ((v2\_relat\_1~X7){\unicdcdcdhd}((v1\_funct\_1~X7){\unicdcdcdhd}((v1\_funct\_2~\\
X7~k5\_numbers~k1\_numbers){\unicdcdcdhd}((v1\_fdiff\_1~X7~k6\_numbers){\unicdcdcdhd}(m1\_subset\_1~\\
X7~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers))))))){\unicdbdjdcd}(\\
{\unicdcdadad} X8 .  ((v1\_funct\_1~X8){\unicdcdcdhd}((v3\_funct\_1~X8){\unicdcdcdhd}((v1\_funct\_2~X8~\\
k5\_numbers~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X8~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k5\_numbers~(u1\_struct\_0~X0))))))){\unicdbdjdcd}(((k2\_relset\_1~(u1\_struct\_0~\\
X0)~X8=k1\_tarski~X3){\unicdcdcdhd}(r1\_tarski~(k2\_relset\_1~(u1\_struct\_0~X0)~\\
(k2\_normsp\_1~X0~(k2\_ndiff\_1~X0~X5~X7)~X8))~X4)){\unicdbdjdcd}((v3\_normsp\_1~(\\
k1\_ndiff\_1~X1~(k3\_normsp\_1~X1~(k8\_funct\_2~k5\_numbers~(u1\_struct\_0~\\
X1)~(u1\_struct\_0~X0)~(k2\_normsp\_1~X0~(k2\_ndiff\_1~X0~X5~X7)~X8)~X2)~\\
(k8\_funct\_2~k5\_numbers~(u1\_struct\_0~X1)~(u1\_struct\_0~X0)~X8~X2))~\\
(k37\_valued\_1~k5\_numbers~k1\_numbers~X7))~X1){\unicdcdcdhd}(X6=k6\_normsp\_1~\\
X1~(k1\_ndiff\_1~X1~(k3\_normsp\_1~X1~(k8\_funct\_2~k5\_numbers~(u1\_struct\_0~\\
X1)~(u1\_struct\_0~X0)~(k2\_normsp\_1~X0~(k2\_ndiff\_1~X0~X5~X7)~X8)~X2)~\\
(k8\_funct\_2~k5\_numbers~(u1\_struct\_0~X1)~(u1\_struct\_0~X0)~X8~X2))~\\
(k37\_valued\_1~k5\_numbers~k1\_numbers~X7))))))){\unicdbdjded}({\unicdcdadad} X7 .  (\\
m1\_subset\_1~X7~k1\_numbers){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~X7~k6\_numbers){\unicdcdcdhd}(\\
{\unicdcdadad} X8 .  (m1\_subset\_1~X8~k1\_numbers){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~X8~k6\_numbers){\unicdcdcdhd}\\
({\unicdcdadad} X9 .  (m1\_subset\_1~X9~k1\_numbers){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~X8~(\\
k18\_complex1~X9)){\unicdcdcdhd}((X9{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}((k3\_rlvect\_1~X0~(k1\_rlvect\_1~\\
X0~X5~X9)~X3 \in X4){\unicdcdcdhd}(r1\_xxreal\_0~X7~(k1\_normsp\_0~X1~(k5\_algstr\_0~X1~\\
(k1\_rlvect\_1~X1~(k5\_algstr\_0~X1~(k7\_partfun1~(u1\_struct\_0~X1)~\\
X2~(k3\_rlvect\_1~X0~(k1\_rlvect\_1~X0~X5~X9)~X3))~(k7\_partfun1~(u1\_struct\_0~\\
X1)~X2~X3))~(k2\_real\_1~X9))~X6)))))))))))))))))))\end{array}
\label{hyp:ehddpfogegjgggggpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}\\
((v5\_rlvect\_1~X0){\unicdcdcdhd}((v6\_rlvect\_1~X0){\unicdcdcdhd}((v7\_rlvect\_1~X0){\unicdcdcdhd}((v8\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_normsp\_0~X0){\unicdcdcdhd}((v4\_normsp\_0~X0){\unicdcdcdhd}((v2\_normsp\_1~X0){\unicdcdcdhd}\\
(l1\_normsp\_1~X0)))))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((\preoh v7\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((\\
v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}((v5\_rlvect\_1~X1){\unicdcdcdhd}((v6\_rlvect\_1~\\
X1){\unicdcdcdhd}((v7\_rlvect\_1~X1){\unicdcdcdhd}((v8\_rlvect\_1~X1){\unicdcdcdhd}((v3\_normsp\_0~X1){\unicdcdcdhd}\\
((v4\_normsp\_0~X1){\unicdcdcdhd}((v2\_normsp\_1~X1){\unicdcdcdhd}(l1\_normsp\_1~X1)))))))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X1))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}((r1\_ndiff\_2~X0~X1~X2~X3~X4){\unicdbdjded}({\unicdcdaddd} X5 .  (m1\_nfcont\_1~X5~X0~\\
X3){\unicdcdcdhd}((r1\_tarski~X5~(k1\_relset\_1~(u1\_struct\_0~X0)~X2)){\unicdcdcdhd}({\unicdcdaddd} X6 .  \\
(m1\_subset\_1~X6~(u1\_struct\_0~X1)){\unicdcdcdhd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~\\
k1\_numbers){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~X7~k6\_numbers){\unicdcdcdhd}({\unicdcdadad} X8 .  (m1\_subset\_1~\\
X8~k1\_numbers){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~X8~k6\_numbers){\unicdcdcdhd}({\unicdcdadad} X9 .  (\\
m1\_subset\_1~X9~k1\_numbers){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~X8~(k18\_complex1~\\
X9)){\unicdcdcdhd}((X9{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}((k3\_rlvect\_1~X0~(k1\_rlvect\_1~X0~X4~X9)~\\
X3 \in X5){\unicdcdcdhd}(r1\_xxreal\_0~X7~(k1\_normsp\_0~X1~(k5\_algstr\_0~X1~(k1\_rlvect\_1~\\
X1~(k5\_algstr\_0~X1~(k7\_partfun1~(u1\_struct\_0~X1)~X2~(k3\_rlvect\_1~\\
X0~(k1\_rlvect\_1~X0~X4~X9)~X3))~(k7\_partfun1~(u1\_struct\_0~X1)~X2~X3))~\\
(k2\_real\_1~X9))~X6)))))))))))))))))))\end{array}
\label{hyp:egddpfogegjgggggpfcd}
\end{equation}
\begin{theorem}\label{thm:ehfdpfogegjgggggpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}\\
((v5\_rlvect\_1~X0){\unicdcdcdhd}((v6\_rlvect\_1~X0){\unicdcdcdhd}((v7\_rlvect\_1~X0){\unicdcdcdhd}((v8\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_normsp\_0~X0){\unicdcdcdhd}((v4\_normsp\_0~X0){\unicdcdcdhd}((v2\_normsp\_1~X0){\unicdcdcdhd}\\
(l1\_normsp\_1~X0)))))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((\preoh v7\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((\\
v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}((v5\_rlvect\_1~X1){\unicdcdcdhd}((v6\_rlvect\_1~\\
X1){\unicdcdcdhd}((v7\_rlvect\_1~X1){\unicdcdcdhd}((v8\_rlvect\_1~X1){\unicdcdcdhd}((v3\_normsp\_0~X1){\unicdcdcdhd}\\
((v4\_normsp\_0~X1){\unicdcdcdhd}((v2\_normsp\_1~X1){\unicdcdcdhd}(l1\_normsp\_1~X1)))))))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X1))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}((r1\_ndiff\_2~X0~X1~X2~X3~X4){\unicdbdjded}({\unicdcdaddd} X5 .  (m1\_nfcont\_1~X5~X0~\\
X3){\unicdcdcdhd}((r1\_tarski~X5~(k1\_relset\_1~(u1\_struct\_0~X0)~X2)){\unicdcdcdhd}({\unicdcdaddd} X6 .  \\
(m1\_subset\_1~X6~(u1\_struct\_0~X1)){\unicdcdcdhd}({\unicdcdadad} X7 .  ((v2\_relat\_1~X7){\unicdcdcdhd}\\
((v1\_funct\_1~X7){\unicdcdcdhd}((v1\_funct\_2~X7~k5\_numbers~k1\_numbers){\unicdcdcdhd}((v1\_fdiff\_1~\\
X7~k6\_numbers){\unicdcdcdhd}(m1\_subset\_1~X7~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~\\
k1\_numbers))))))){\unicdbdjdcd}({\unicdcdadad} X8 .  ((v1\_funct\_1~X8){\unicdcdcdhd}((v3\_funct\_1~\\
X8){\unicdcdcdhd}((v1\_funct\_2~X8~k5\_numbers~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
X8~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(u1\_struct\_0~X0))))))){\unicdbdjdcd}\\
(((k2\_relset\_1~(u1\_struct\_0~X0)~X8=k1\_tarski~X3){\unicdcdcdhd}(r1\_tarski~\\
(k2\_relset\_1~(u1\_struct\_0~X0)~(k2\_normsp\_1~X0~(k2\_ndiff\_1~X0~X4~\\
X7)~X8))~X5)){\unicdbdjdcd}((v3\_normsp\_1~(k1\_ndiff\_1~X1~(k3\_normsp\_1~X1~(k8\_funct\_2~\\
k5\_numbers~(u1\_struct\_0~X1)~(u1\_struct\_0~X0)~(k2\_normsp\_1~X0~(\\
k2\_ndiff\_1~X0~X4~X7)~X8)~X2)~(k8\_funct\_2~k5\_numbers~(u1\_struct\_0~\\
X1)~(u1\_struct\_0~X0)~X8~X2))~(k37\_valued\_1~k5\_numbers~k1\_numbers~\\
X7))~X1){\unicdcdcdhd}(X6=k6\_normsp\_1~X1~(k1\_ndiff\_1~X1~(k3\_normsp\_1~X1~(k8\_funct\_2~\\
k5\_numbers~(u1\_struct\_0~X1)~(u1\_struct\_0~X0)~(k2\_normsp\_1~X0~(\\
k2\_ndiff\_1~X0~X4~X7)~X8)~X2)~(k8\_funct\_2~k5\_numbers~(u1\_struct\_0~\\
X1)~(u1\_struct\_0~X0)~X8~X2))~(k37\_valued\_1~k5\_numbers~k1\_numbers~\\
X7)))))))))))))))\end{array}$$
\end{theorem}
\end{document}
