\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{t1\_csspace2 (TMcmNQFgfznB24brGiHZqCGF5iUazGbScsh)}
\maketitle
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k18\_csspace : {\iota}$ be given.
Let $ k11\_csspace : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ k5\_numbers : {\iota}$ be given.
Let $ k2\_numbers : {\iota}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_series\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k20\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k55\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_csspace : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_comseq\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k19\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k2\_comseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_csspace : {\iota}$ be given.
Let $ k1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_series\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_clvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k25\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k4\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k31\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k5\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k46\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k12\_csspace : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k11\_comseq\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ g1\_csspace : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k10\_csspace : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_csspace : {\iota}$ be given.
Let $ k8\_csspace : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_csspace : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k17\_csspace : {\iota}$ be given.
Let $ v1\_csspace : {{\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 $ v1\_clvect\_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 $ l1\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_csspace : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u2\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_clvect\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_csspace : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~k18\_csspace)){\unicdbdjded}(((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k2\_numbers){\unicdcdcdhd}(m1\_subset\_1~X0~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k2\_numbers))))){\unicdcdcdhd}(v1\_series\_1~\\
(k20\_valued\_1~k5\_numbers~k1\_numbers~k1\_numbers~(k55\_valued\_1~\\
k5\_numbers~k2\_numbers~(k2\_csspace~X0))~(k55\_valued\_1~k5\_numbers~\\
k2\_numbers~(k2\_csspace~X0)))))\end{array}
\label{hyp:mgjdpfdgdhdhahbgdgfgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~k18\_csspace)){\unicdbdjded}(((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k2\_numbers){\unicdcdcdhd}(m1\_subset\_1~X0~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k2\_numbers))))){\unicdcdcdhd}(v2\_comseq\_3~\\
(k19\_valued\_1~k5\_numbers~k2\_numbers~k2\_numbers~(k2\_csspace~X0)~\\
(k2\_comseq\_2~k5\_numbers~(k2\_csspace~X0)))))\end{array}
\label{hyp:mgbdjdpfdgdhdhahbgdgfgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~k18\_csspace)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~k18\_csspace)){\unicdbdjdcd}(k12\_csspace~k18\_csspace~\\
X0~X1=k11\_comseq\_3~(k19\_valued\_1~k5\_numbers~k2\_numbers~k2\_numbers~\\
(k2\_csspace~X0)~(k2\_comseq\_2~k5\_numbers~(k2\_csspace~X1)))))\end{array}
\label{hyp:mgbdhdpfdgdhdhahbgdgfgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~k18\_csspace)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~k18\_csspace)){\unicdbdjdcd}(v1\_series\_1~(k20\_valued\_1~\\
k5\_numbers~k1\_numbers~k1\_numbers~(k55\_valued\_1~k5\_numbers~k2\_numbers~\\
(k2\_csspace~X0))~(k55\_valued\_1~k5\_numbers~k2\_numbers~(k2\_csspace~\\
X1)))))\end{array}
\label{hyp:mgbdgdpfdgdhdhahbgdgfgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~k18\_csspace)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~k18\_csspace)){\unicdbdjdcd}(k5\_algstr\_0~k18\_csspace~\\
X0~X1=k46\_valued\_1~k5\_numbers~k2\_numbers~k2\_numbers~(k2\_csspace~\\
X0)~(k2\_csspace~X1)))\end{array}
\label{hyp:mgbdfdpfdgdhdhahbgdgfgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~k18\_csspace)){\unicdbdjdcd}((k4\_algstr\_0~\\
k18\_csspace~X0=k31\_valued\_1~k5\_numbers~k2\_numbers~(k2\_csspace~\\
X0)){\unicdcdcdhd}(r2\_funct\_2~k5\_numbers~k2\_numbers~(k2\_csspace~(k4\_algstr\_0~\\
k18\_csspace~X0))~(k31\_valued\_1~k5\_numbers~k2\_numbers~(k2\_csspace~\\
X0))))\end{array}
\label{hyp:mgbdedpfdgdhdhahbgdgfgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xcmplx\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
k18\_csspace)){\unicdbdjdcd}(k1\_clvect\_1~k18\_csspace~X1~X0=k25\_valued\_1~k5\_numbers~\\
k2\_numbers~(k2\_csspace~X1)~X0))\end{array}
\label{hyp:mgbdddpfdgdhdhahbgdgfgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~k18\_csspace)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~k18\_csspace)){\unicdbdjdcd}(k1\_algstr\_0~k18\_csspace~\\
X0~X1=k1\_series\_1~k2\_numbers~(k2\_csspace~X0)~(k2\_csspace~X1)))\end{array}
\label{hyp:mgbdcdpfdgdhdhahbgdgfgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~k18\_csspace)){\unicdbdjdcd}(X0=k2\_csspace~\\
X0)\end{array}
\label{hyp:mgbdbdpfdgdhdhahbgdgfgcd}
\end{equation}
Assume the following.
\begin{equation}
{{{k4\_struct\_0}~{k18\_csspace}}={k6\_csspace}}\label{hyp:mgbdadpfdgdhdhahbgdgfgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((m1\_subset\_1~\\
X1~X0){\unicdcdcdhd}(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~\\
X0))))){\unicdcdcdhd}(((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(k2\_zfmisc\_1~k2\_numbers~\\
X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~\\
k2\_numbers~X0)~X0))))){\unicdcdcdhd}((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~(k2\_zfmisc\_1~\\
X0~X0)~k2\_numbers){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0)~k2\_numbers)))))))){\unicdbdjdcd}({\unicdcdadad} X5 .  {\unicdcdadad} X6 .  \\
{\unicdcdadad} X7 .  {\unicdcdadad} X8 .  {\unicdcdadad} X9 .  (g1\_csspace~X0~X1~X2~X3~X4=g1\_csspace~\\
X5~X6~X7~X8~X9){\unicdbdjdcd}((X0=X5){\unicdcdcdhd}((X1=X6){\unicdcdcdhd}((X2=X7){\unicdcdcdhd}((X3=X8){\unicdcdcdhd}(X4=X9))))))\end{array}
\label{hyp:ggchfgfgpfhgbdpfdgdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(\preoh v2\_struct\_0~(g1\_csspace~k11\_csspace~(k10\_csspace~k7\_csspace~\\
k11\_csspace)~(k8\_csspace~k7\_csspace~k11\_csspace)~(k9\_csspace~\\
k7\_csspace~k11\_csspace)~k17\_csspace)){\unicdcdcdhd}(v1\_csspace~(g1\_csspace~\\
k11\_csspace~(k10\_csspace~k7\_csspace~k11\_csspace)~(k8\_csspace~\\
k7\_csspace~k11\_csspace)~(k9\_csspace~k7\_csspace~k11\_csspace)~\\
k17\_csspace))\end{array}
\label{hyp:ggdgedpfdgdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(\preoh v2\_struct\_0~k7\_csspace){\unicdcdcdhd}((v13\_algstr\_0~k7\_csspace){\unicdcdcdhd}((v2\_rlvect\_1~\\
k7\_csspace){\unicdcdcdhd}((v3\_rlvect\_1~k7\_csspace){\unicdcdcdhd}((v4\_rlvect\_1~k7\_csspace){\unicdcdcdhd}\\
((v1\_clvect\_1~k7\_csspace){\unicdcdcdhd}((v2\_clvect\_1~k7\_csspace){\unicdcdcdhd}((v3\_clvect\_1~\\
k7\_csspace){\unicdcdcdhd}((v4\_clvect\_1~k7\_csspace){\unicdcdcdhd}(v5\_clvect\_1~k7\_csspace)))))))))\end{array}
\label{hyp:ggdgcdpfdgdhdhahbgdgfg}
\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}((v2\_clvect\_1~\\
X0){\unicdcdcdhd}((v3\_clvect\_1~X0){\unicdcdcdhd}((v4\_clvect\_1~X0){\unicdcdcdhd}((v5\_clvect\_1~X0){\unicdcdcdhd}\\
(l1\_clvect\_1~X0)))))))))){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0)))){\unicdbdjdcd}((v1\_funct\_1~(k9\_csspace~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(k9\_csspace~\\
X0~X1)~(k2\_zfmisc\_1~k2\_numbers~X1)~X1){\unicdcdcdhd}(m1\_subset\_1~(k9\_csspace~\\
X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~k2\_numbers~X1)~X1)))))\end{array}
\label{hyp:egehpflgjdpfdgdhdhahbgdgfg}
\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}((v2\_clvect\_1~\\
X0){\unicdcdcdhd}((v3\_clvect\_1~X0){\unicdcdcdhd}((v4\_clvect\_1~X0){\unicdcdcdhd}((v5\_clvect\_1~X0){\unicdcdcdhd}\\
(l1\_clvect\_1~X0)))))))))){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0)))){\unicdbdjdcd}((v1\_funct\_1~(k8\_csspace~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(k8\_csspace~\\
X0~X1)~(k2\_zfmisc\_1~X1~X1)~X1){\unicdcdcdhd}(m1\_subset\_1~(k8\_csspace~X0~X1)~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X1~X1)~X1)))))\end{array}
\label{hyp:egehpflgidpfdgdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(\preoh v2\_struct\_0~k7\_csspace){\unicdcdcdhd}((v1\_clvect\_1~k7\_csspace){\unicdcdcdhd}(l1\_clvect\_1~\\
k7\_csspace))\end{array}
\label{hyp:egehpflghdpfdgdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v2\_struct\_0}~{k18\_csspace}}}})}{\unicdcdcdhd}{({{l1\_csspace}~{k18\_csspace}})}}\label{hyp:egehpflgbdidpfdgdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k17\_csspace){\unicdcdcdhd}((v1\_funct\_2~k17\_csspace~(k2\_zfmisc\_1~\\
k11\_csspace~k11\_csspace)~k2\_numbers){\unicdcdcdhd}(m1\_subset\_1~k17\_csspace~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~k11\_csspace~k11\_csspace)~\\
k2\_numbers))))\end{array}
\label{hyp:egehpflgbdhdpfdgdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k11\_csspace}}~{({{k1\_zfmisc\_1}~{({{u1\_struct\_0}~{k7\_csspace}})}})}}\label{hyp:egehpflgbdbdpfdgdhdhahbgdgfg}
\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}((v2\_clvect\_1~\\
X0){\unicdcdcdhd}((v3\_clvect\_1~X0){\unicdcdcdhd}((v4\_clvect\_1~X0){\unicdcdcdhd}((v5\_clvect\_1~X0){\unicdcdcdhd}\\
(l1\_clvect\_1~X0)))))))))){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0)))){\unicdbdjdcd}(m1\_subset\_1~(k10\_csspace~X0~X1)~X1)\end{array}
\label{hyp:egehpflgbdadpfdgdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}k18\_csspace=g1\_csspace~k11\_csspace~(k10\_csspace~k7\_csspace~\\
k11\_csspace)~(k8\_csspace~k7\_csspace~k11\_csspace)~(k9\_csspace~\\
k7\_csspace~k11\_csspace)~k17\_csspace\end{array}
\label{hyp:egbdidpfdgdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_csspace~X0){\unicdbdjdcd}((v1\_csspace~X0){\unicdbdjdcd}(X0=g1\_csspace~\\
(u1\_struct\_0~X0)~(u2\_struct\_0~X0)~(u1\_algstr\_0~X0)~(u1\_clvect\_1~\\
X0)~(u1\_csspace~X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdpfdgdhdhahbgdgfg}
\end{equation}
\begin{theorem}\label{thm:ehbdpfdgdhdhahbgdgfgcd}
$$\begin{array}{c}(u1\_struct\_0~k18\_csspace=k11\_csspace){\unicdcdcdhd}(({\unicdcdadad} X0 .  (m1\_subset\_1~\\
X0~(u1\_struct\_0~k18\_csspace)){\unicdbdjded}(((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~\\
X0~k5\_numbers~k2\_numbers){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k5\_numbers~k2\_numbers))))){\unicdcdcdhd}(v1\_series\_1~(k20\_valued\_1~k5\_numbers~\\
k1\_numbers~k1\_numbers~(k55\_valued\_1~k5\_numbers~k2\_numbers~(k2\_csspace~\\
X0))~(k55\_valued\_1~k5\_numbers~k2\_numbers~(k2\_csspace~X0)))))){\unicdcdcdhd}\\
(({\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~k18\_csspace)){\unicdbdjded}(((\\
v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k2\_numbers){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k2\_numbers))))){\unicdcdcdhd}(v2\_comseq\_3~\\
(k19\_valued\_1~k5\_numbers~k2\_numbers~k2\_numbers~(k2\_csspace~X0)~\\
(k2\_comseq\_2~k5\_numbers~(k2\_csspace~X0)))))){\unicdcdcdhd}((k4\_struct\_0~\\
k18\_csspace=k6\_csspace){\unicdcdcdhd}(({\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~\\
k18\_csspace)){\unicdbdjdcd}(X0=k2\_csspace~X0)){\unicdcdcdhd}(({\unicdcdadad} X0 .  (m1\_subset\_1~\\
X0~(u1\_struct\_0~k18\_csspace)){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
k18\_csspace)){\unicdbdjdcd}(k1\_algstr\_0~k18\_csspace~X0~X1=k1\_series\_1~k2\_numbers~\\
(k2\_csspace~X0)~(k2\_csspace~X1)))){\unicdcdcdhd}(({\unicdcdadad} X0 .  (v1\_xcmplx\_0~\\
X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~k18\_csspace)){\unicdbdjdcd}\\
(k1\_clvect\_1~k18\_csspace~X1~X0=k25\_valued\_1~k5\_numbers~k2\_numbers~\\
(k2\_csspace~X1)~X0))){\unicdcdcdhd}(({\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~\\
k18\_csspace)){\unicdbdjdcd}((k4\_algstr\_0~k18\_csspace~X0=k31\_valued\_1~k5\_numbers~\\
k2\_numbers~(k2\_csspace~X0)){\unicdcdcdhd}(r2\_funct\_2~k5\_numbers~k2\_numbers~\\
(k2\_csspace~(k4\_algstr\_0~k18\_csspace~X0))~(k31\_valued\_1~k5\_numbers~\\
k2\_numbers~(k2\_csspace~X0))))){\unicdcdcdhd}(({\unicdcdadad} X0 .  (m1\_subset\_1~X0~\\
(u1\_struct\_0~k18\_csspace)){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
k18\_csspace)){\unicdbdjdcd}(k5\_algstr\_0~k18\_csspace~X0~X1=k46\_valued\_1~k5\_numbers~\\
k2\_numbers~k2\_numbers~(k2\_csspace~X0)~(k2\_csspace~X1)))){\unicdcdcdhd}({\unicdcdadad} X0 .  \\
(m1\_subset\_1~X0~(u1\_struct\_0~k18\_csspace)){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~k18\_csspace)){\unicdbdjdcd}((v1\_series\_1~(k20\_valued\_1~k5\_numbers~\\
k1\_numbers~k1\_numbers~(k55\_valued\_1~k5\_numbers~k2\_numbers~(k2\_csspace~\\
X0))~(k55\_valued\_1~k5\_numbers~k2\_numbers~(k2\_csspace~X1)))){\unicdcdcdhd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~k18\_csspace)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~k18\_csspace)){\unicdbdjdcd}(k12\_csspace~k18\_csspace~\\
X2~X3=k11\_comseq\_3~(k19\_valued\_1~k5\_numbers~k2\_numbers~k2\_numbers~\\
(k2\_csspace~X2)~(k2\_comseq\_2~k5\_numbers~(k2\_csspace~X3)))))))))))))))))\end{array}$$
\end{theorem}
\end{document}
