\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{t8\_cc0sp1 (TMGrK81xE5bEbmcMRjDAp4k6fF1Ejxt8bKn)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_cc0sp1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
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\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_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 $ v2\_cfuncdom : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_cfuncdom : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_cc0sp1 : {{\iota}{\unicdbdjdcd}{{\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 $ k3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k8\_group\_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 $ k1\_group\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_c0sp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_cc0sp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ g1\_cfuncdom : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k2\_c0sp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_c0sp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_cc0sp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_c0sp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_c0sp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ m1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k2\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ 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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_numbers : {\iota}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k8\_cfuncdom : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_cfuncdom : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_cc0sp1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ l2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_cfuncdom : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_cfuncdom : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_cfuncdom : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_cfuncdom : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_cfuncdom : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_algstr\_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 $ u3\_struct\_0 : {{\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\_group\_1~X0){\unicdcdcdhd}(\\
(v5\_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}((v2\_cfuncdom~X0){\unicdcdcdhd}\\
(l1\_cfuncdom~X0)))))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_cc0sp1~X1~X0){\unicdbdjdcd}\\
(({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (\\
m1\_subset\_1~X3~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
(((X2=X4){\unicdcdcdhd}(X3=X5)){\unicdbdjdcd}(k3\_rlvect\_1~X1~X2~X3=k3\_rlvect\_1~X0~X4~X5)))))){\unicdcdcdhd}\\
(({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (\\
m1\_subset\_1~X3~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
(((X2=X4){\unicdcdcdhd}(X3=X5)){\unicdbdjdcd}(k8\_group\_1~X1~X2~X3=k8\_group\_1~X0~X4~X5)))))){\unicdcdcdhd}\\
(({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (\\
m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (v1\_xcmplx\_0~X4){\unicdbdjdcd}\\
((X2=X3){\unicdbdjdcd}(k1\_clvect\_1~X1~X2~X4=k1\_clvect\_1~X0~X3~X4))))){\unicdcdcdhd}((k1\_group\_1~\\
X1=k1\_group\_1~X0){\unicdcdcdhd}(k4\_struct\_0~X1=k4\_struct\_0~X0))))))\end{array}
\label{hyp:ehddpfdgdgaddhahbd}
\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\_group\_1~X0){\unicdcdcdhd}(\\
(v5\_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}((v2\_cfuncdom~X0){\unicdcdcdhd}\\
(l1\_cfuncdom~X0)))))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
((v3\_c0sp1~X1~X0){\unicdcdcdhd}((v1\_cc0sp1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0)))))){\unicdbdjdcd}(m1\_cc0sp1~(g1\_cfuncdom~X1~(k2\_c0sp1~X0~\\
X1)~(k1\_c0sp1~X0~X1)~(k1\_cc0sp1~X0~X1)~(k4\_c0sp1~X0~X1)~(k3\_c0sp1~\\
X0~X1))~X0))\end{array}
\label{hyp:ehcdpfdgdgaddhahbd}
\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 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m1\_funct\_2~\\
X2~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_funct\_2~X3~X0~X1~X2){\unicdbdjded}(m1\_subset\_1~X3~\\
X2))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X2~X0)){\unicdbdjdcd}(k8\_funcop\_1~X0~X1~X2=k2\_funcop\_1~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgidpfggfhogdgpgahpfbd}
\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 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
(((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~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}\\
((m1\_subset\_1~X4~X0){\unicdcdcdhd}(m1\_subset\_1~X5~X0))))){\unicdbdjdcd}({\unicdcdadad} X6 .  {\unicdcdadad} X7 .  \\
{\unicdcdadad} X8 .  {\unicdcdadad} X9 .  {\unicdcdadad} X10 .  {\unicdcdadad} X11 .  (g1\_cfuncdom~X0~\\
X1~X2~X3~X4~X5=g1\_cfuncdom~X6~X7~X8~X9~X10~X11){\unicdbdjdcd}((X0=X6){\unicdcdcdhd}((X1=X7){\unicdcdcdhd}\\
((X2=X8){\unicdcdcdhd}((X3=X9){\unicdcdcdhd}((X4=X10){\unicdcdcdhd}(X5=X11)))))))\end{array}
\label{hyp:ggchfgfgpfhgbdpfdgggfhogdgegpgng}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((v13\_algstr\_0~(k8\_cfuncdom~X0)){\unicdcdcdhd}\\
((v2\_rlvect\_1~(k8\_cfuncdom~X0)){\unicdcdcdhd}((v3\_rlvect\_1~(k8\_cfuncdom~\\
X0)){\unicdcdcdhd}((v4\_rlvect\_1~(k8\_cfuncdom~X0)){\unicdcdcdhd}((v2\_clvect\_1~(k8\_cfuncdom~\\
X0)){\unicdcdcdhd}((v3\_clvect\_1~(k8\_cfuncdom~X0)){\unicdcdcdhd}((v4\_clvect\_1~(k8\_cfuncdom~\\
X0)){\unicdcdcdhd}((v3\_group\_1~(k8\_cfuncdom~X0)){\unicdcdcdhd}((v5\_group\_1~(k8\_cfuncdom~\\
X0)){\unicdcdcdhd}((v1\_vectsp\_1~(k8\_cfuncdom~X0)){\unicdcdcdhd}((v3\_vectsp\_1~(k8\_cfuncdom~\\
X0)){\unicdcdcdhd}((v1\_cfuncdom~(k8\_cfuncdom~X0)){\unicdcdcdhd}(v2\_cfuncdom~(k8\_cfuncdom~\\
X0))))))))))))))\end{array}
\label{hyp:ggdggdpfdgggfhogdgegpgng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~(k8\_cfuncdom~X0)){\unicdcdcdhd}\\
(v1\_cfuncdom~(k8\_cfuncdom~X0)))\end{array}
\label{hyp:ggdgedpfdgggfhogdgegpgng}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k2\_numbers}}}}\label{hyp:ggdgcdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((\preoh v1\_xboole\_0~(k2\_cc0sp1~X0)){\unicdcdcdhd}\\
((v3\_c0sp1~(k2\_cc0sp1~X0)~(k8\_cfuncdom~X0)){\unicdcdcdhd}(v1\_cc0sp1~(k2\_cc0sp1~\\
X0)~(k8\_cfuncdom~X0))))\end{array}
\label{hyp:ggdgcdpfdgdgaddhahbd}
\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){\unicdbdjdcd}(m1\_subset\_1~X2~X0))\end{array}
\label{hyp:egehpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{({{l2\_struct\_0}~{X0}})}{\unicdcdcdhd}{({{l1\_algstr\_0}~{X0}})}})}}}\label{hyp:egehpfmgcdpfbgmghgdhehchpfad}
\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\_cfuncdom}~{X0}})}{\unicdbdjdcd}{({{({{l6\_algstr\_0}~{X0}})}{\unicdcdcdhd}{({{l1\_clvect\_1}~{X0}})}})}}}\label{hyp:egehpfmgbdpfdgggfhogdgegpgng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}(m1\_funct\_2~(k9\_funct\_2~\\
X0~X1)~X0~X1)\end{array}
\label{hyp:egehpflgjdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((v1\_cfuncdom~(k8\_cfuncdom~X0)){\unicdcdcdhd}\\
(l1\_cfuncdom~(k8\_cfuncdom~X0)))\end{array}
\label{hyp:egehpflgidpfdgggfhogdgegpgng}
\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}~{k5\_numbers}}~{({{k1\_zfmisc\_1}~{k1\_numbers}})}}\label{hyp:egehpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}(m2\_funct\_2~(k5\_cfuncdom~X0)~X0~\\
k2\_numbers~(k9\_funct\_2~X0~k2\_numbers))\end{array}
\label{hyp:egehpflgfdpfdgggfhogdgegpgng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}(m2\_funct\_2~(k4\_cfuncdom~X0)~X0~\\
k2\_numbers~(k9\_funct\_2~X0~k2\_numbers))\end{array}
\label{hyp:egehpflgedpfdgggfhogdgegpgng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((v1\_funct\_1~(k3\_cfuncdom~X0)){\unicdcdcdhd}\\
((v1\_funct\_2~(k3\_cfuncdom~X0)~(k2\_zfmisc\_1~k2\_numbers~(k9\_funct\_2~\\
X0~k2\_numbers))~(k9\_funct\_2~X0~k2\_numbers)){\unicdcdcdhd}(m1\_subset\_1~(k3\_cfuncdom~\\
X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~k2\_numbers~(k9\_funct\_2~\\
X0~k2\_numbers))~(k9\_funct\_2~X0~k2\_numbers))))))\end{array}
\label{hyp:egehpflgddpfdgggfhogdgegpgng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((v1\_funct\_1~(k2\_cfuncdom~X0)){\unicdcdcdhd}\\
((v1\_funct\_2~(k2\_cfuncdom~X0)~(k2\_zfmisc\_1~(k9\_funct\_2~X0~k2\_numbers)~\\
(k9\_funct\_2~X0~k2\_numbers))~(k9\_funct\_2~X0~k2\_numbers)){\unicdcdcdhd}(m1\_subset\_1~\\
(k2\_cfuncdom~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k9\_funct\_2~\\
X0~k2\_numbers)~(k9\_funct\_2~X0~k2\_numbers))~(k9\_funct\_2~X0~k2\_numbers))))))\end{array}
\label{hyp:egehpflgcdpfdgggfhogdgegpgng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((\preoh v1\_xboole\_0~(k2\_cc0sp1~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~(k2\_cc0sp1~X0)~(k1\_zfmisc\_1~(u1\_struct\_0~(k8\_cfuncdom~\\
X0)))))\end{array}
\label{hyp:egehpflgcdpfdgdgaddhahbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((v1\_funct\_1~(k1\_cfuncdom~X0)){\unicdcdcdhd}\\
((v1\_funct\_2~(k1\_cfuncdom~X0)~(k2\_zfmisc\_1~(k9\_funct\_2~X0~k2\_numbers)~\\
(k9\_funct\_2~X0~k2\_numbers))~(k9\_funct\_2~X0~k2\_numbers)){\unicdcdcdhd}(m1\_subset\_1~\\
(k1\_cfuncdom~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k9\_funct\_2~\\
X0~k2\_numbers)~(k9\_funct\_2~X0~k2\_numbers))~(k9\_funct\_2~X0~k2\_numbers))))))\end{array}
\label{hyp:egehpflgbdpfdgggfhogdgegpgng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}(k8\_cfuncdom~X0=g1\_cfuncdom~(k9\_funct\_2~\\
X0~k2\_numbers)~(k2\_cfuncdom~X0)~(k1\_cfuncdom~X0)~(k3\_cfuncdom~\\
X0)~(k5\_cfuncdom~X0)~(k4\_cfuncdom~X0))\end{array}
\label{hyp:egidpfdgggfhogdgegpgng}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{{k4\_struct\_0}~{X0}}={{u2\_struct\_0}~{X0}}})}}}\label{hyp:eggdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}(k3\_cc0sp1~X0=g1\_cfuncdom~(k2\_cc0sp1~\\
X0)~(k2\_c0sp1~(k8\_cfuncdom~X0)~(k2\_cc0sp1~X0))~(k1\_c0sp1~(k8\_cfuncdom~\\
X0)~(k2\_cc0sp1~X0))~(k1\_cc0sp1~(k8\_cfuncdom~X0)~(k2\_cc0sp1~X0))~\\
(k4\_c0sp1~(k8\_cfuncdom~X0)~(k2\_cc0sp1~X0))~(k3\_c0sp1~(k8\_cfuncdom~\\
X0)~(k2\_cc0sp1~X0)))\end{array}
\label{hyp:eggdpfdgdgaddhahbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}(k4\_cfuncdom~X0=k8\_funcop\_1~k1\_numbers~\\
X0~k6\_numbers)\end{array}
\label{hyp:egedpfdgggfhogdgegpgng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v1\_xboole\_0~X1))\end{array}
\label{hyp:dgdgbdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_cfuncdom~X0){\unicdbdjdcd}((v1\_cfuncdom~X0){\unicdbdjdcd}(X0=g1\_cfuncdom~\\
(u1\_struct\_0~X0)~(u2\_algstr\_0~X0)~(u1\_algstr\_0~X0)~(u1\_clvect\_1~\\
X0)~(u3\_struct\_0~X0)~(u2\_struct\_0~X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdpfdgggfhogdgegpgng}
\end{equation}
\begin{theorem}\label{thm:ehidpfdgdgaddhahbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}(k4\_struct\_0~(k3\_cc0sp1~X0)=k8\_funcop\_1~\\
k5\_numbers~X0~k6\_numbers)\end{array}$$
\end{theorem}
\end{document}
