\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{t16\_c0sp1 (TMJbD7aNPQHnsR7QwD764MNrU4VZ7skHygM)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_group\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_c0sp1 : {{\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 $ np\_\_1 : {\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 $ 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 $ v2\_funcsdom : {{\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 $ l1\_funcsdom : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_c0sp1 : {{\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 $ k1\_numbers : {\iota}$ be given.
Let $ k1\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v4\_c0sp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_c0sp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ g1\_funcsdom : {{\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 $ k5\_c0sp1 : {{\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 $ 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 $ v4\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l4\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_struct\_0 : {{\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 $ k12\_funcsdom : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funcsdom : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_c0sp1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l5\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l4\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_funcsdom : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_funcsdom : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_funcsdom : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_funcsdom : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_funcsdom : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u3\_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\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_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}((v5\_rlvect\_1~X0){\unicdcdcdhd}\\
((v6\_rlvect\_1~X0){\unicdcdcdhd}((v7\_rlvect\_1~X0){\unicdcdcdhd}((v2\_funcsdom~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}((v5\_group\_1~X0){\unicdcdcdhd}((v1\_vectsp\_1~X0){\unicdcdcdhd}((v3\_vectsp\_1~X0){\unicdcdcdhd}(\\
l1\_funcsdom~X0)))))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_c0sp1~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 .  (m1\_subset\_1~X4~k1\_numbers){\unicdbdjdcd}(\\
(X2=X3){\unicdbdjdcd}(k1\_rlvect\_1~X1~X2~X4=k1\_rlvect\_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:ehidpfdgaddhahbd}
\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}((v2\_funcsdom~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}((v5\_group\_1~X0){\unicdcdcdhd}((v1\_vectsp\_1~X0){\unicdcdcdhd}((v3\_vectsp\_1~X0){\unicdcdcdhd}(\\
l1\_funcsdom~X0)))))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))){\unicdbdjdcd}(((v4\_c0sp1~X1~X0){\unicdcdcdhd}(v3\_c0sp1~X1~X0)){\unicdbdjdcd}((v1\_xboole\_0~\\
X1){\unicdcdcdid}(m2\_c0sp1~(g1\_funcsdom~X1~(k2\_c0sp1~X0~X1)~(k1\_c0sp1~X0~X1)~\\
(k5\_c0sp1~X0~X1)~(k4\_c0sp1~X0~X1)~(k3\_c0sp1~X0~X1))~X0))))\end{array}
\label{hyp:ehgdpfdgaddhahbd}
\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 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v4\_vectsp\_1~X0){\unicdcdcdhd}(l4\_algstr\_0~\\
X0))){\unicdbdjdcd}(k1\_group\_1~X0=k5\_struct\_0~X0)\end{array}
\label{hyp:jgfggdpfghfgdgehdhahpfbd}
\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~k1\_numbers~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X3~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~k1\_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\_funcsdom~X0~\\
X1~X2~X3~X4~X5=g1\_funcsdom~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:ggchfgfgpfhgbdpfggfhogdgdhegpgng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v13\_algstr\_0~(k12\_funcsdom~X0)){\unicdcdcdhd}((v3\_group\_1~(k12\_funcsdom~\\
X0)){\unicdcdcdhd}((v5\_group\_1~(k12\_funcsdom~X0)){\unicdcdcdhd}((v1\_vectsp\_1~(k12\_funcsdom~\\
X0)){\unicdcdcdhd}((v3\_vectsp\_1~(k12\_funcsdom~X0)){\unicdcdcdhd}((v2\_rlvect\_1~(k12\_funcsdom~\\
X0)){\unicdcdcdhd}((v3\_rlvect\_1~(k12\_funcsdom~X0)){\unicdcdcdhd}((v4\_rlvect\_1~(k12\_funcsdom~\\
X0)){\unicdcdcdhd}((v5\_rlvect\_1~(k12\_funcsdom~X0)){\unicdcdcdhd}((v6\_rlvect\_1~(k12\_funcsdom~\\
X0)){\unicdcdcdhd}((v7\_rlvect\_1~(k12\_funcsdom~X0)){\unicdcdcdhd}((v1\_funcsdom~(k12\_funcsdom~\\
X0)){\unicdcdcdhd}(v2\_funcsdom~(k12\_funcsdom~X0)))))))))))))\end{array}
\label{hyp:ggdggdpfggfhogdgdhegpgng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v2\_struct\_0~(k12\_funcsdom~X0)){\unicdcdcdhd}(v1\_funcsdom~(k12\_funcsdom~\\
X0))\end{array}
\label{hyp:ggdgfdpfggfhogdgdhegpgng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((\preoh v1\_xboole\_0~(k6\_c0sp1~X0)){\unicdcdcdhd}\\
((v3\_c0sp1~(k6\_c0sp1~X0)~(k12\_funcsdom~X0)){\unicdcdcdhd}(v4\_c0sp1~(k6\_c0sp1~\\
X0)~(k12\_funcsdom~X0))))\end{array}
\label{hyp:ggdgddpfdgaddhahbd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k1\_numbers}}}}\label{hyp:ggdgbdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l6\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{({{l2\_algstr\_0}~{X0}})}{\unicdcdcdhd}{({{l5\_algstr\_0}~{X0}})}})}}}\label{hyp:egehpfmggdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l5\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{({{l4\_algstr\_0}~{X0}})}{\unicdcdcdhd}{({{l4\_struct\_0}~{X0}})}})}}}\label{hyp:egehpfmgfdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l4\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{({{l3\_struct\_0}~{X0}})}{\unicdcdcdhd}{({{l3\_algstr\_0}~{X0}})}})}}}\label{hyp:egehpfmgedpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_funcsdom}~{X0}})}{\unicdbdjdcd}{({{({{l6\_algstr\_0}~{X0}})}{\unicdcdcdhd}{({{l1\_rlvect\_1}~{X0}})}})}}}\label{hyp:egehpfmgbdpfggfhogdgdhegpgng}
\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 .  m2\_funct\_2~(k9\_funcsdom~X0)~X0~k1\_numbers~(k9\_funct\_2~\\
X0~k1\_numbers)\end{array}
\label{hyp:egehpflgjdpfggfhogdgdhegpgng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  m2\_funct\_2~(k8\_funcsdom~X0)~X0~k1\_numbers~(k9\_funct\_2~\\
X0~k1\_numbers)\end{array}
\label{hyp:egehpflgidpfggfhogdgdhegpgng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_funct\_1~(k7\_funcsdom~X0)){\unicdcdcdhd}((v1\_funct\_2~(k7\_funcsdom~\\
X0)~(k2\_zfmisc\_1~k1\_numbers~(k9\_funct\_2~X0~k1\_numbers))~(k9\_funct\_2~\\
X0~k1\_numbers)){\unicdcdcdhd}(m1\_subset\_1~(k7\_funcsdom~X0)~(k1\_zfmisc\_1~(\\
k2\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~(k9\_funct\_2~X0~k1\_numbers))~\\
(k9\_funct\_2~X0~k1\_numbers)))))\end{array}
\label{hyp:egehpflghdpfggfhogdgdhegpgng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_funct\_1~(k6\_funcsdom~X0)){\unicdcdcdhd}((v1\_funct\_2~(k6\_funcsdom~\\
X0)~(k2\_zfmisc\_1~(k9\_funct\_2~X0~k1\_numbers)~(k9\_funct\_2~X0~k1\_numbers))~\\
(k9\_funct\_2~X0~k1\_numbers)){\unicdcdcdhd}(m1\_subset\_1~(k6\_funcsdom~X0)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k9\_funct\_2~X0~k1\_numbers)~(k9\_funct\_2~\\
X0~k1\_numbers))~(k9\_funct\_2~X0~k1\_numbers)))))\end{array}
\label{hyp:egehpflggdpfggfhogdgdhegpgng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((\preoh v1\_xboole\_0~(k6\_c0sp1~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~(k6\_c0sp1~X0)~(k1\_zfmisc\_1~(u1\_struct\_0~(k12\_funcsdom~\\
X0)))))\end{array}
\label{hyp:egehpflggdpfdgaddhahbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_funct\_1~(k5\_funcsdom~X0)){\unicdcdcdhd}((v1\_funct\_2~(k5\_funcsdom~\\
X0)~(k2\_zfmisc\_1~(k9\_funct\_2~X0~k1\_numbers)~(k9\_funct\_2~X0~k1\_numbers))~\\
(k9\_funct\_2~X0~k1\_numbers)){\unicdcdcdhd}(m1\_subset\_1~(k5\_funcsdom~X0)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k9\_funct\_2~X0~k1\_numbers)~(k9\_funct\_2~\\
X0~k1\_numbers))~(k9\_funct\_2~X0~k1\_numbers)))))\end{array}
\label{hyp:egehpflgfdpfggfhogdgdhegpgng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_funcsdom~(k12\_funcsdom~X0)){\unicdcdcdhd}(l1\_funcsdom~(k12\_funcsdom~\\
X0))\end{array}
\label{hyp:egehpflgbdcdpfggfhogdgdhegpgng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  k12\_funcsdom~X0=g1\_funcsdom~(k9\_funct\_2~X0~k1\_numbers)~\\
(k6\_funcsdom~X0)~(k5\_funcsdom~X0)~(k7\_funcsdom~X0)~(k9\_funcsdom~\\
X0)~(k8\_funcsdom~X0)\end{array}
\label{hyp:egidpfggfhogdgdhegpgng}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l3\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{{k5\_struct\_0}~{X0}}={{u3\_struct\_0}~{X0}}})}}}\label{hyp:eghdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k9\_funcsdom}~{X0}}={{{{k8\_funcop\_1}~{k5\_numbers}}~{X0}}~{np\_\_1}}}}\label{hyp:egfdpfggfhogdgdhegpgng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}(k7\_c0sp1~X0=g1\_funcsdom~(k6\_c0sp1~\\
X0)~(k2\_c0sp1~(k12\_funcsdom~X0)~(k6\_c0sp1~X0))~(k1\_c0sp1~(k12\_funcsdom~\\
X0)~(k6\_c0sp1~X0))~(k5\_c0sp1~(k12\_funcsdom~X0)~(k6\_c0sp1~X0))~(\\
k4\_c0sp1~(k12\_funcsdom~X0)~(k6\_c0sp1~X0))~(k3\_c0sp1~(k12\_funcsdom~\\
X0)~(k6\_c0sp1~X0)))\end{array}
\label{hyp:egbdedpfdgaddhahbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l4\_algstr\_0~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v5\_group\_1~\\
X0){\unicdcdcdhd}(v3\_vectsp\_1~X0))){\unicdbdjdcd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(v4\_vectsp\_1~X0)))\end{array}
\label{hyp:dgdgcdpfghfgdgehdhahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_funcsdom~X0){\unicdbdjdcd}((v1\_funcsdom~X0){\unicdbdjdcd}(X0=g1\_funcsdom~\\
(u1\_struct\_0~X0)~(u2\_algstr\_0~X0)~(u1\_algstr\_0~X0)~(u1\_rlvect\_1~\\
X0)~(u3\_struct\_0~X0)~(u2\_struct\_0~X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdpfggfhogdgdhegpgng}
\end{equation}
\begin{theorem}\label{thm:ehbdgdpfdgaddhahbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}(k1\_group\_1~(k7\_c0sp1~X0)=k8\_funcop\_1~\\
k5\_numbers~X0~np\_\_1)\end{array}$$
\end{theorem}
\end{document}
