\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{t40\_ncfcont1 (TMYaS6YDd6GfsgVaJqZ3xwJbk4o2wqcUQnS)}
\maketitle
Let $ v2\_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 $ v3\_normsp\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_normsp\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_clvect\_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 $ 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 $ r3\_ncfcont1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ r2\_nfcont\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_normsp\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_vfunct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v9\_clvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_comseq\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_normsp\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_seq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_normsp\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_clvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_vfunct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k8\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k10\_complex1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_complex1 : {\iota}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ l1\_normsp\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_normsp\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_numbers : {\iota}$ be given.
Let $ k4\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_normsp\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_normsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_normsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v3\_normsp\_0~X0){\unicdcdcdhd}\\
((v4\_normsp\_0~X0){\unicdcdcdhd}((v2\_clvect\_1~X0){\unicdcdcdhd}((v3\_clvect\_1~X0){\unicdcdcdhd}((v4\_clvect\_1~\\
X0){\unicdcdcdhd}((v5\_clvect\_1~X0){\unicdcdcdhd}((v8\_clvect\_1~X0){\unicdcdcdhd}(l2\_clvect\_1~X0))))))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~k5\_numbers~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(u1\_struct\_0~\\
X0)))))){\unicdbdjdcd}((v9\_clvect\_1~X1~X0){\unicdbdjdcd}((v2\_comseq\_2~(k4\_normsp\_0~X0~\\
X1)){\unicdcdcdhd}(k2\_seq\_2~(k4\_normsp\_0~X0~X1)=k1\_normsp\_0~X0~(k7\_clvect\_1~\\
X0~X1)))))\end{array}
\label{hyp:ehedadpfdgmgpgahcgbgogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v3\_normsp\_0~X0){\unicdcdcdhd}\\
((v4\_normsp\_0~X0){\unicdcdcdhd}((v2\_clvect\_1~X0){\unicdcdcdhd}((v3\_clvect\_1~X0){\unicdcdcdhd}((v4\_clvect\_1~\\
X0){\unicdcdcdhd}((v5\_clvect\_1~X0){\unicdcdcdhd}((v8\_clvect\_1~X0){\unicdcdcdhd}(l2\_clvect\_1~X0))))))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((\preoh v2\_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~X1)~(u1\_struct\_0~X0))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  (v1\_xcmplx\_0~X4){\unicdbdjdcd}((r3\_ncfcont1~\\
X1~X0~X2~X3){\unicdbdjdcd}(r3\_ncfcont1~X1~X0~(k2\_vfunct\_2~(u1\_struct\_0~X1)~X0~\\
X2~X4)~X3))))))\end{array}
\label{hyp:ehddhdpfogdgggdgpgogehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v3\_normsp\_0~X0){\unicdcdcdhd}\\
((v4\_normsp\_0~X0){\unicdcdcdhd}((v2\_clvect\_1~X0){\unicdcdcdhd}((v3\_clvect\_1~X0){\unicdcdcdhd}((v4\_clvect\_1~\\
X0){\unicdcdcdhd}((v5\_clvect\_1~X0){\unicdcdcdhd}((v8\_clvect\_1~X0){\unicdcdcdhd}(l2\_clvect\_1~X0))))))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((\preoh v2\_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~X1)~(u1\_struct\_0~X0))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~\\
X3){\unicdcdcdhd}((v1\_funct\_2~X3~k5\_numbers~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(u1\_struct\_0~X1)))))){\unicdbdjdcd}\\
((r1\_tarski~(k2\_relset\_1~(u1\_struct\_0~X1)~X3)~(k1\_relset\_1~(u1\_struct\_0~\\
X1)~X2)){\unicdbdjdcd}((r2\_funct\_2~k5\_numbers~k1\_numbers~(k4\_normsp\_0~X0~(\\
k8\_funct\_2~k5\_numbers~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)~X3~X2))~\\
(k8\_funct\_2~k5\_numbers~k1\_numbers~(u1\_struct\_0~X1)~X3~(k3\_normsp\_0~\\
(u1\_struct\_0~X1)~X0~X2))){\unicdcdcdhd}(r2\_funct\_2~k5\_numbers~(u1\_struct\_0~\\
X0)~(k5\_vfunct\_1~k5\_numbers~X0~(k8\_funct\_2~k5\_numbers~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X1)~X3~X2))~(k8\_funct\_2~k5\_numbers~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X1)~X3~(k5\_vfunct\_1~(u1\_struct\_0~X1)~X0~X2))))))))\end{array}
\label{hyp:ehddbdpfogdgggdgpgogehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((v13\_algstr\_0~X1){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~\\
X1){\unicdcdcdhd}((v3\_normsp\_0~X1){\unicdcdcdhd}((v4\_normsp\_0~X1){\unicdcdcdhd}((v2\_clvect\_1~X1){\unicdcdcdhd}\\
((v3\_clvect\_1~X1){\unicdcdcdhd}((v4\_clvect\_1~X1){\unicdcdcdhd}((v5\_clvect\_1~X1){\unicdcdcdhd}((v8\_clvect\_1~\\
X1){\unicdcdcdhd}(l2\_clvect\_1~X1))))))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~\\
X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~(u1\_struct\_0~\\
X1))))){\unicdbdjdcd}(r2\_relset\_1~X0~(u1\_struct\_0~X1)~(k5\_vfunct\_1~X0~X1~X2)~\\
(k2\_vfunct\_2~X0~X1~X2~(k10\_complex1~k6\_complex1)))))\end{array}
\label{hyp:ehcdddpfghggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v3\_normsp\_0~X0){\unicdcdcdhd}\\
((v4\_normsp\_0~X0){\unicdcdcdhd}((v2\_clvect\_1~X0){\unicdcdcdhd}((v3\_clvect\_1~X0){\unicdcdcdhd}((v4\_clvect\_1~\\
X0){\unicdcdcdhd}((v5\_clvect\_1~X0){\unicdcdcdhd}((v8\_clvect\_1~X0){\unicdcdcdhd}(l2\_clvect\_1~X0))))))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~k5\_numbers~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(u1\_struct\_0~\\
X0)))))){\unicdbdjdcd}((v9\_clvect\_1~X1~X0){\unicdbdjdcd}(v2\_comseq\_2~(k4\_normsp\_0~X0~X1))))\end{array}
\label{hyp:ehbdbdhdpfdgmgghfgdgehpfbd}
\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 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((v1\_funct\_1~X2){\unicdcdcdhd}\\
((v1\_funct\_2~X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1))))){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~X0~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)))))){\unicdbdjdcd}((r2\_funct\_2~X0~X1~X2~\\
X3){\unicdbdjded}(X2=X3))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchcdpfggfhogdgehpfcd}
\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 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(((\preoh v2\_struct\_0~\\
X1){\unicdcdcdhd}(l1\_normsp\_0~X1)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~(u1\_struct\_0~X1))))))){\unicdbdjdcd}(k3\_normsp\_0~X0~X1~X2=\\
k2\_normsp\_0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfogpgchngdhahpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v4\_relat\_1~X1~X0)){\unicdbdjdcd}(\\
k1\_relset\_1~X0~X1=k9\_xtuple\_0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_numbers){\unicdbdjdcd}(k10\_complex1~X0=k4\_xcmplx\_0~\\
X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdadpfdgpgngahmgfgihbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(u1\_struct\_0~X0))\end{array}
\label{hyp:ggdgcdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_membered}~{k2\_numbers}}\label{hyp:ggdgbdpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgcdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_normsp\_0}~{X0}})}{\unicdbdjdcd}{({{({{l1\_normsp\_0}~{X0}})}{\unicdcdcdhd}{({{l2\_struct\_0}~{X0}})}})}}}\label{hyp:egehpfmgcdpfogpgchngdhahpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_clvect\_1}~{X0}})}{\unicdbdjdcd}{({{({{l1\_clvect\_1}~{X0}})}{\unicdcdcdhd}{({{l2\_normsp\_0}~{X0}})}})}}}\label{hyp:egehpfmgcdpfdgmgghfgdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_normsp\_1}~{X0}})}{\unicdbdjdcd}{({{({{l1\_rlvect\_1}~{X0}})}{\unicdcdcdhd}{({{l2\_normsp\_0}~{X0}})}})}}}\label{hyp:egehpfmgbdpfogpgchngdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_clvect\_1}~{X0}})}{\unicdbdjdcd}{({{l2\_algstr\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfdgmgghfgdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~\\
X2){\unicdcdcdhd}(((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~X0~X2){\unicdcdcdhd}(m1\_subset\_1~X3~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X2))))){\unicdcdcdhd}((v1\_relat\_1~X4){\unicdcdcdhd}((v5\_relat\_1~\\
X4~X1){\unicdcdcdhd}(v1\_funct\_1~X4))))){\unicdbdjdcd}((v1\_funct\_1~(k8\_funct\_2~X0~X1~X2~X3~\\
X4)){\unicdcdcdhd}((v1\_funct\_2~(k8\_funct\_2~X0~X1~X2~X3~X4)~X0~X1){\unicdcdcdhd}(m1\_subset\_1~\\
(k8\_funct\_2~X0~X1~X2~X3~X4)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)))))\end{array}
\label{hyp:egehpflgidpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k6\_complex1}}~{k2\_numbers}}\label{hyp:egehpflggdpfdgpgngahmgfgihbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(((\preoh v2\_struct\_0~\\
X1){\unicdcdcdhd}(l2\_algstr\_0~X1)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~(u1\_struct\_0~X1))))))){\unicdbdjdcd}((v1\_funct\_1~(k5\_vfunct\_1~\\
X0~X1~X2)){\unicdcdcdhd}(m1\_subset\_1~(k5\_vfunct\_1~X0~X1~X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~(u1\_struct\_0~X1)))))\end{array}
\label{hyp:egehpflgfdpfghggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xcmplx\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xcmplx\_0}~{({{k4\_xcmplx\_0}~{X0}})}})}}}\label{hyp:egehpflgedpfihdgngahmgihpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_normsp\_0~X0)){\unicdcdcdhd}\\
((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~k5\_numbers~(u1\_struct\_0~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(u1\_struct\_0~\\
X0))))))){\unicdbdjdcd}((v1\_funct\_1~(k4\_normsp\_0~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(k4\_normsp\_0~\\
X0~X1)~k5\_numbers~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~(k4\_normsp\_0~X0~X1)~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers)))))\end{array}
\label{hyp:egehpflgedpfogpgchngdhahpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(((\preoh v2\_struct\_0~\\
X1){\unicdcdcdhd}(l1\_normsp\_0~X1)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~(u1\_struct\_0~X1))))))){\unicdbdjdcd}((v1\_funct\_1~(k3\_normsp\_0~\\
X0~X1~X2)){\unicdcdcdhd}(m1\_subset\_1~(k3\_normsp\_0~X0~X1~X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~k1\_numbers))))\end{array}
\label{hyp:egehpflgddpfogpgchngdhahpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}(\\
(v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}((v3\_normsp\_0~X1){\unicdcdcdhd}((v4\_normsp\_0~\\
X1){\unicdcdcdhd}((v2\_clvect\_1~X1){\unicdcdcdhd}((v3\_clvect\_1~X1){\unicdcdcdhd}((v4\_clvect\_1~X1){\unicdcdcdhd}\\
((v5\_clvect\_1~X1){\unicdcdcdhd}((v8\_clvect\_1~X1){\unicdcdcdhd}(l2\_clvect\_1~X1))))))))))))){\unicdcdcdhd}\\
(((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~(u1\_struct\_0~X1))))){\unicdcdcdhd}(v1\_xcmplx\_0~X3)))){\unicdbdjdcd}((v1\_funct\_1~(k2\_vfunct\_2~\\
X0~X1~X2~X3)){\unicdcdcdhd}(m1\_subset\_1~(k2\_vfunct\_2~X0~X1~X2~X3)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~(u1\_struct\_0~X1)))))\end{array}
\label{hyp:egehpflgcdpfghggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_normsp\_0~X0)){\unicdcdcdhd}\\
((v1\_relat\_1~X1){\unicdcdcdhd}((v5\_relat\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(v1\_funct\_1~\\
X1)))){\unicdbdjdcd}((v1\_relat\_1~(k2\_normsp\_0~X0~X1)){\unicdcdcdhd}(v1\_funct\_1~(k2\_normsp\_0~\\
X0~X1)))\end{array}
\label{hyp:egehpflgcdpfogpgchngdhahpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_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}((v13\_algstr\_0~X1){\unicdcdcdhd}((v2\_rlvect\_1~\\
X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}((v3\_normsp\_0~X1){\unicdcdcdhd}\\
((v4\_normsp\_0~X1){\unicdcdcdhd}((v2\_clvect\_1~X1){\unicdcdcdhd}((v3\_clvect\_1~X1){\unicdcdcdhd}((v4\_clvect\_1~\\
X1){\unicdcdcdhd}((v5\_clvect\_1~X1){\unicdcdcdhd}((v8\_clvect\_1~X1){\unicdcdcdhd}(l2\_clvect\_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}((r3\_ncfcont1~X0~X1~X2~X3){\unicdbdjded}((X3 \in k1\_relset\_1~\\
(u1\_struct\_0~X0)~X2){\unicdcdcdhd}({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~\\
X4~k5\_numbers~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k5\_numbers~(u1\_struct\_0~X0)))))){\unicdbdjdcd}(((r1\_tarski~\\
(k2\_relset\_1~(u1\_struct\_0~X0)~X4)~(k1\_relset\_1~(u1\_struct\_0~X0)~\\
X2)){\unicdcdcdhd}((v3\_normsp\_1~X4~X0){\unicdcdcdhd}(k6\_normsp\_1~X0~X4=X3))){\unicdbdjdcd}((v9\_clvect\_1~\\
(k8\_funct\_2~k5\_numbers~(u1\_struct\_0~X1)~(u1\_struct\_0~X0)~X4~X2)~\\
X1){\unicdcdcdhd}(k7\_partfun1~(u1\_struct\_0~X1)~X2~X3=k7\_clvect\_1~X1~(k8\_funct\_2~\\
k5\_numbers~(u1\_struct\_0~X1)~(u1\_struct\_0~X0)~X4~X2))))))))))\end{array}
\label{hyp:eghdpfogdgggdgpgogehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v5\_relat\_1~X1~X0){\unicdcdcdhd}(\\
v1\_funct\_1~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  (X2 \in k9\_xtuple\_0~X1){\unicdbdjdcd}(k7\_partfun1~\\
X0~X1~X2=k1\_funct\_1~X1~X2))\end{array}
\label{hyp:eggdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_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 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}((r2\_nfcont\_1~X0~X1~X2){\unicdbdjded}((X2 \in k1\_relset\_1~(\\
u1\_struct\_0~X0)~X1){\unicdcdcdhd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~\\
X3~k5\_numbers~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k5\_numbers~(u1\_struct\_0~X0)))))){\unicdbdjdcd}(((r1\_tarski~\\
(k2\_relset\_1~(u1\_struct\_0~X0)~X3)~(k1\_relset\_1~(u1\_struct\_0~X0)~\\
X1)){\unicdcdcdhd}((v3\_normsp\_1~X3~X0){\unicdcdcdhd}(k6\_normsp\_1~X0~X3=X2))){\unicdbdjdcd}((v2\_comseq\_2~\\
(k8\_funct\_2~k5\_numbers~k1\_numbers~(u1\_struct\_0~X0)~X3~X1)){\unicdcdcdhd}(k7\_partfun1~\\
k1\_numbers~X1~X2=k2\_seq\_2~(k8\_funct\_2~k5\_numbers~k1\_numbers~(\\
u1\_struct\_0~X0)~X3~X1)))))))))\end{array}
\label{hyp:eggdpfogggdgpgogehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
(l1\_normsp\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~(u1\_struct\_0~X1))))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v1\_funct\_1~X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~\\
k1\_numbers)))){\unicdbdjdcd}((X3=k3\_normsp\_0~X0~X1~X2){\unicdbdjded}((k9\_xtuple\_0~X3=\\
k9\_xtuple\_0~X2){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~X0){\unicdbdjdcd}((X4 \in k9\_xtuple\_0~\\
X3){\unicdbdjdcd}(k1\_funct\_1~X3~X4=k1\_normsp\_0~X1~(k7\_partfun1~(u1\_struct\_0~\\
X1)~X2~X4)))))))))\end{array}
\label{hyp:egddpfogpgchngdhahpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}(v5\_relat\_1~X2~X1))\end{array}
\label{hyp:dgdgcdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(v1\_relat\_1~X2)\end{array}
\label{hyp:dgdgbdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
(v1\_xcmplx\_0~X1))\end{array}
\label{hyp:dgdgbdcdpfngfgngcgfgchfgeg}
\end{equation}
\begin{theorem}\label{thm:ehedadpfogdgggdgpgogehbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v3\_normsp\_0~X0){\unicdcdcdhd}\\
((v4\_normsp\_0~X0){\unicdcdcdhd}((v2\_clvect\_1~X0){\unicdcdcdhd}((v3\_clvect\_1~X0){\unicdcdcdhd}((v4\_clvect\_1~\\
X0){\unicdcdcdhd}((v5\_clvect\_1~X0){\unicdcdcdhd}((v8\_clvect\_1~X0){\unicdcdcdhd}(l2\_clvect\_1~X0))))))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v2\_rlvect\_1~\\
X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}((v5\_rlvect\_1~X1){\unicdcdcdhd}\\
((v6\_rlvect\_1~X1){\unicdcdcdhd}((v7\_rlvect\_1~X1){\unicdcdcdhd}((v8\_rlvect\_1~X1){\unicdcdcdhd}((v3\_normsp\_0~\\
X1){\unicdcdcdhd}((v4\_normsp\_0~X1){\unicdcdcdhd}((v2\_normsp\_1~X1){\unicdcdcdhd}(l1\_normsp\_1~X1))))))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X1)~(u1\_struct\_0~X0))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~X1)){\unicdbdjdcd}((r3\_ncfcont1~X1~X0~X2~X3){\unicdbdjdcd}((r2\_nfcont\_1~\\
X1~(k3\_normsp\_0~(u1\_struct\_0~X1)~X0~X2)~X3){\unicdcdcdhd}(r3\_ncfcont1~X1~X0~(\\
k5\_vfunct\_1~(u1\_struct\_0~X1)~X0~X2)~X3))))))\end{array}$$
\end{theorem}
\end{document}
