\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{t28\_clopban4 (TMVd8GVSE7C5oDqVjSRfZAVCDRKa1JhZ34E)}
\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 $ v3\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_vectsp\_1 : {{\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 $ v2\_cfuncdom : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_clopban2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_clopban2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k4\_series\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_sin\_cos : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_normsp\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_numbers : {\iota}$ be given.
Let $ k3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_clvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_complex1 : {\iota}$ be given.
Let $ k5\_complex1 : {\iota}$ be given.
Let $ k10\_complex1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_complex1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_complex1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k8\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k17\_complex1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_clopban1 : {{\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 $ k1\_normsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_bhsp\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_clopban4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_series\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k13\_complex1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\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\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ l2\_normsp\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_normsp\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_cfuncdom : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\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}((v3\_group\_1~X0){\unicdcdcdhd}(\\
(v1\_vectsp\_1~X0){\unicdcdcdhd}((v3\_vectsp\_1~X0){\unicdcdcdhd}((v2\_cfuncdom~X0){\unicdcdcdhd}((v5\_clopban2~\\
X0){\unicdcdcdhd}(l1\_clopban2~X0)))))))))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~k2\_numbers){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~k2\_numbers){\unicdbdjdcd}\\
((k3\_rlvect\_1~X0~X1~X2=k3\_rlvect\_1~X0~X2~X1){\unicdcdcdhd}((k3\_rlvect\_1~X0~(\\
k3\_rlvect\_1~X0~X1~X2)~X3=k3\_rlvect\_1~X0~X1~(k3\_rlvect\_1~X0~X2~X3)){\unicdcdcdhd}\\
((k3\_rlvect\_1~X0~X1~(k4\_struct\_0~X0)=X1){\unicdcdcdhd}(({\unicdcdaddd} X6 .  (m1\_subset\_1~\\
X6~(u1\_struct\_0~X0)){\unicdcdcdhd}(k3\_rlvect\_1~X0~X1~X6=k4\_struct\_0~X0)){\unicdcdcdhd}(\\
(k6\_algstr\_0~X0~(k6\_algstr\_0~X0~X1~X2)~X3=k6\_algstr\_0~X0~X1~(k6\_algstr\_0~\\
X0~X2~X3)){\unicdcdcdhd}((k1\_clvect\_1~X0~X1~k6\_complex1=X1){\unicdcdcdhd}((k1\_clvect\_1~\\
X0~X1~k5\_complex1=k4\_struct\_0~X0){\unicdcdcdhd}((k1\_clvect\_1~X0~(k4\_struct\_0~\\
X0)~X4=k4\_struct\_0~X0){\unicdcdcdhd}((k1\_clvect\_1~X0~X1~(k10\_complex1~k6\_complex1)=\\
k4\_algstr\_0~X0~X1){\unicdcdcdhd}((k6\_algstr\_0~X0~X1~(k5\_struct\_0~X0)=X1){\unicdcdcdhd}(\\
(k6\_algstr\_0~X0~(k5\_struct\_0~X0)~X1=X1){\unicdcdcdhd}((k6\_algstr\_0~X0~X1~(k3\_rlvect\_1~\\
X0~X2~X3)=k3\_rlvect\_1~X0~(k6\_algstr\_0~X0~X1~X2)~(k6\_algstr\_0~X0~X1~\\
X3)){\unicdcdcdhd}((k6\_algstr\_0~X0~(k3\_rlvect\_1~X0~X2~X3)~X1=k3\_rlvect\_1~X0~\\
(k6\_algstr\_0~X0~X2~X1)~(k6\_algstr\_0~X0~X3~X1)){\unicdcdcdhd}((k1\_clvect\_1~X0~\\
(k6\_algstr\_0~X0~X1~X2)~X4=k6\_algstr\_0~X0~(k1\_clvect\_1~X0~X1~X4)~X2){\unicdcdcdhd}\\
((k1\_clvect\_1~X0~(k3\_rlvect\_1~X0~X1~X2)~X4=k3\_rlvect\_1~X0~(k1\_clvect\_1~\\
X0~X1~X4)~(k1\_clvect\_1~X0~X2~X4)){\unicdcdcdhd}((k1\_clvect\_1~X0~X1~(k8\_complex1~\\
X4~X5)=k3\_rlvect\_1~X0~(k1\_clvect\_1~X0~X1~X4)~(k1\_clvect\_1~X0~X1~X5)){\unicdcdcdhd}\\
((k1\_clvect\_1~X0~X1~(k9\_complex1~X4~X5)=k1\_clvect\_1~X0~(k1\_clvect\_1~\\
X0~X1~X5)~X4){\unicdcdcdhd}((k1\_clvect\_1~X0~(k6\_algstr\_0~X0~X1~X2)~(k9\_complex1~\\
X4~X5)=k6\_algstr\_0~X0~(k1\_clvect\_1~X0~X1~X4)~(k1\_clvect\_1~X0~X2~X5)){\unicdcdcdhd}\\
((k1\_clvect\_1~X0~(k6\_algstr\_0~X0~X1~X2)~X4=k6\_algstr\_0~X0~X1~(k1\_clvect\_1~\\
X0~X2~X4)){\unicdcdcdhd}((k6\_algstr\_0~X0~(k4\_struct\_0~X0)~X1=k4\_struct\_0~X0){\unicdcdcdhd}\\
((k6\_algstr\_0~X0~X1~(k4\_struct\_0~X0)=k4\_struct\_0~X0){\unicdcdcdhd}((k6\_algstr\_0~\\
X0~X1~(k5\_algstr\_0~X0~X2~X3)=k5\_algstr\_0~X0~(k6\_algstr\_0~X0~X1~X2)~\\
(k6\_algstr\_0~X0~X1~X3)){\unicdcdcdhd}((k6\_algstr\_0~X0~(k5\_algstr\_0~X0~X2~X3)~\\
X1=k5\_algstr\_0~X0~(k6\_algstr\_0~X0~X2~X1)~(k6\_algstr\_0~X0~X3~X1)){\unicdcdcdhd}\\
((k5\_algstr\_0~X0~(k3\_rlvect\_1~X0~X1~X2)~X3=k3\_rlvect\_1~X0~X1~(k5\_algstr\_0~\\
X0~X2~X3)){\unicdcdcdhd}((k3\_rlvect\_1~X0~(k5\_algstr\_0~X0~X1~X2)~X3=k5\_algstr\_0~\\
X0~X1~(k5\_algstr\_0~X0~X2~X3)){\unicdcdcdhd}((k5\_algstr\_0~X0~(k5\_algstr\_0~X0~X1~\\
X2)~X3=k5\_algstr\_0~X0~X1~(k3\_rlvect\_1~X0~X2~X3)){\unicdcdcdhd}((k3\_rlvect\_1~\\
X0~X1~X2=k3\_rlvect\_1~X0~(k5\_algstr\_0~X0~X1~X3)~(k3\_rlvect\_1~X0~X3~\\
X2)){\unicdcdcdhd}((k5\_algstr\_0~X0~X1~X2=k3\_rlvect\_1~X0~(k5\_algstr\_0~X0~X1~X3)~\\
(k5\_algstr\_0~X0~X3~X2)){\unicdcdcdhd}((X1=k3\_rlvect\_1~X0~(k5\_algstr\_0~X0~X1~\\
X2)~X2){\unicdcdcdhd}((X1=k5\_algstr\_0~X0~X2~(k5\_algstr\_0~X0~X2~X1)){\unicdcdcdhd}(((k1\_normsp\_0~\\
X0~X1=k6\_numbers){\unicdbdjdcd}(X1=k4\_struct\_0~X0)){\unicdcdcdhd}(((X1=k4\_struct\_0~X0){\unicdbdjdcd}\\
(k1\_normsp\_0~X0~X1=k6\_numbers)){\unicdcdcdhd}((k1\_normsp\_0~X0~(k1\_clvect\_1~\\
X0~X1~X4)=k8\_real\_1~(k17\_complex1~X4)~(k1\_normsp\_0~X0~X1)){\unicdcdcdhd}((r1\_xxreal\_0~\\
(k1\_normsp\_0~X0~(k3\_rlvect\_1~X0~X1~X2))~(k7\_real\_1~(k1\_normsp\_0~\\
X0~X1)~(k1\_normsp\_0~X0~X2))){\unicdcdcdhd}((r1\_xxreal\_0~(k1\_normsp\_0~X0~(k6\_algstr\_0~\\
X0~X1~X2))~(k8\_real\_1~(k1\_normsp\_0~X0~X1)~(k1\_normsp\_0~X0~X2))){\unicdcdcdhd}\\
((k1\_normsp\_0~X0~(k5\_struct\_0~X0)=np\_\_1){\unicdcdcdhd}(v3\_clopban1~X0))))))))))))))))))))))))))))))))))))))))))\end{array}
\label{hyp:ehddidpfdgmgpgahcgbgogdd}
\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}((v3\_group\_1~X0){\unicdcdcdhd}((v1\_vectsp\_1~X0){\unicdcdcdhd}((v3\_vectsp\_1~\\
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}((v2\_cfuncdom~X0){\unicdcdcdhd}((v5\_clopban2~\\
X0){\unicdcdcdhd}(l1\_clopban2~X0)))))))))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~X2~k1\_numbers~k5\_numbers){\unicdbdjdcd}\\
((r1\_xxreal\_0~(k1\_normsp\_0~X0~(k1\_normsp\_1~X0~(k1\_bhsp\_4~X0~(k1\_clopban4~\\
X0~X1))~X2))~(k1\_seq\_1~(k3\_series\_1~(k4\_sin\_cos~(k1\_normsp\_0~X0~\\
X1)))~X2)){\unicdcdcdhd}((r1\_xxreal\_0~(k1\_seq\_1~(k3\_series\_1~(k4\_sin\_cos~\\
(k1\_normsp\_0~X0~X1)))~X2)~(k4\_series\_1~(k4\_sin\_cos~(k1\_normsp\_0~\\
X0~X1)))){\unicdcdcdhd}(r1\_xxreal\_0~(k1\_normsp\_0~X0~(k1\_normsp\_1~X0~(k1\_bhsp\_4~\\
X0~(k1\_clopban4~X0~X1))~X2))~(k4\_series\_1~(k4\_sin\_cos~(k1\_normsp\_0~\\
X0~X1))))))))\end{array}
\label{hyp:ehcdhdpfdgmgpgahcgbgoged}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k1\_xboole\_0}}~{k4\_ordinal1}}\label{hyp:ehbdpfogfhngfgchbgmgdh}
\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}((v3\_group\_1~X0){\unicdcdcdhd}((v1\_vectsp\_1~X0){\unicdcdcdhd}((v3\_vectsp\_1~\\
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}((v2\_cfuncdom~X0){\unicdcdcdhd}((v5\_clopban2~\\
X0){\unicdcdcdhd}(l1\_clopban2~X0)))))))))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~X2~k1\_numbers~k5\_numbers){\unicdbdjdcd}\\
((k1\_normsp\_1~X0~(k1\_clopban4~X0~X1)~(k2\_nat\_1~X2~np\_\_1)=k6\_algstr\_0~\\
X0~(k1\_clvect\_1~X0~X1~(k13\_complex1~k6\_complex1~(k2\_nat\_1~X2~np\_\_1)))~\\
(k1\_normsp\_1~X0~(k1\_clopban4~X0~X1)~X2)){\unicdcdcdhd}((k1\_normsp\_1~X0~(k1\_clopban4~\\
X0~X1)~k6\_numbers=k5\_struct\_0~X0){\unicdcdcdhd}(r1\_xxreal\_0~(k1\_normsp\_0~\\
X0~(k1\_normsp\_1~X0~(k1\_clopban4~X0~X1)~X2))~(k1\_seq\_1~(k4\_sin\_cos~\\
(k1\_normsp\_0~X0~X1))~X2))))))\end{array}
\label{hyp:ehbdddpfdgmgpgahcgbgoged}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\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 v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_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)))))){\unicdcdcdhd}(m1\_subset\_1~X2~k5\_numbers))){\unicdbdjdcd}(k1\_normsp\_1~X0~X1~X2=\\
k1\_funct\_1~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfogpgchngdhahpfbd}
\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\_0}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfogpgchngdhahpfad}
\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}
{{\unicdcdadad} X0 .  {{({{l1\_clopban2}~{X0}})}{\unicdbdjdcd}{({{({{l1\_cfuncdom}~{X0}})}{\unicdcdcdhd}{({{l2\_clvect\_1}~{X0}})}})}}}\label{hyp:egehpfmgbdpfdgmgpgahcgbgogcd}
\end{equation}
Assume the following.
\begin{equation}
{{{{m2\_subset\_1}~{k6\_numbers}}~{k1\_numbers}}~{k5\_numbers}}\label{hyp:egehpflggdpfogfhngcgfgchdh}
\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 .  (((\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}((v3\_group\_1~X0){\unicdcdcdhd}((v1\_vectsp\_1~X0){\unicdcdcdhd}(\\
(v3\_vectsp\_1~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}((v2\_cfuncdom~X0){\unicdcdcdhd}\\
((v5\_clopban2~X0){\unicdcdcdhd}(l1\_clopban2~X0)))))))))))))))))){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(u1\_struct\_0~X0))){\unicdbdjdcd}((v1\_funct\_1~(k1\_clopban4~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~\\
(k1\_clopban4~X0~X1)~k5\_numbers~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
(k1\_clopban4~X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(u1\_struct\_0~\\
X0))))))\end{array}
\label{hyp:egehpflgbdpfdgmgpgahcgbgoged}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_algstr\_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~(k1\_bhsp\_4~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(k1\_bhsp\_4~\\
X0~X1)~k5\_numbers~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~(k1\_bhsp\_4~X0~\\
X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(u1\_struct\_0~X0))))))\end{array}
\label{hyp:egehpflgbdpfcgigdhahpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_algstr\_0~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}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~k5\_numbers~\\
(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k5\_numbers~(u1\_struct\_0~X0)))))){\unicdbdjdcd}((X2=k1\_bhsp\_4~X0~X1){\unicdbdjded}((k1\_normsp\_1~\\
X0~X2~k6\_numbers=k1\_normsp\_1~X0~X1~k6\_numbers){\unicdcdcdhd}({\unicdcdadad} X3 .  (m2\_subset\_1~\\
X3~k1\_numbers~k5\_numbers){\unicdbdjdcd}(k1\_normsp\_1~X0~X2~(k2\_nat\_1~X3~np\_\_1)=\\
k1\_algstr\_0~X0~(k1\_normsp\_1~X0~X2~X3)~(k1\_normsp\_1~X0~X1~(k2\_nat\_1~\\
X3~np\_\_1))))))))\end{array}
\label{hyp:egbdpfcgigdhahpfed}
\end{equation}
\begin{theorem}\label{thm:ehcdidpfdgmgpgahcgbgoged}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v3\_normsp\_0~X0){\unicdcdcdhd}\\
((v4\_normsp\_0~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v1\_vectsp\_1~X0){\unicdcdcdhd}((v3\_vectsp\_1~\\
X0){\unicdcdcdhd}((v2\_clvect\_1~X0){\unicdcdcdhd}((v3\_clvect\_1~X0){\unicdcdcdhd}((v4\_clvect\_1~X0){\unicdcdcdhd}\\
((v5\_clvect\_1~X0){\unicdcdcdhd}((v8\_clvect\_1~X0){\unicdcdcdhd}((v2\_cfuncdom~X0){\unicdcdcdhd}((v5\_clopban2~\\
X0){\unicdcdcdhd}(l1\_clopban2~X0)))))))))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(r1\_xxreal\_0~np\_\_1~(k4\_series\_1~(k4\_sin\_cos~\\
(k1\_normsp\_0~X0~X1)))))\end{array}$$
\end{theorem}
\end{document}
