\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{t24\_groeb\_1 (TMQnbE7uEMYXMRTaMBHfXd7VcLzGjShny8R)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k15\_pre\_poly : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_bagorder : {{\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 $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v33\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_vectsp\_1 : {{\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 $ l6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k11\_polynom1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r2\_groeb\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ v1\_polynom1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_rewrite1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_polyred : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k7\_polynom1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_groeb\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k7\_ideal\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v3\_ordinal1 : {{\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\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l4\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v9\_rewrite1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_partfun1~\\
X1~(k15\_pre\_poly~X0)){\unicdcdcdhd}((v1\_relat\_2~X1){\unicdcdcdhd}((v4\_relat\_2~X1){\unicdcdcdhd}((v6\_relat\_2~\\
X1){\unicdcdcdhd}((v8\_relat\_2~X1){\unicdcdcdhd}((v2\_bagorder~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k15\_pre\_poly~X0)~(k15\_pre\_poly~X0)))))))))){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((\preoh v6\_struct\_0~X2){\unicdcdcdhd}((v13\_algstr\_0~\\
X2){\unicdcdcdhd}((v33\_algstr\_0~X2){\unicdcdcdhd}((v3\_group\_1~X2){\unicdcdcdhd}((v5\_group\_1~X2){\unicdcdcdhd}(\\
(v4\_vectsp\_1~X2){\unicdcdcdhd}((v5\_vectsp\_1~X2){\unicdcdcdhd}((v2\_rlvect\_1~X2){\unicdcdcdhd}((v3\_rlvect\_1~\\
X2){\unicdcdcdhd}((v4\_rlvect\_1~X2){\unicdcdcdhd}(l6\_algstr\_0~X2)))))))))))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(k15\_pre\_poly~X0)~(u1\_struct\_0~\\
X2)){\unicdcdcdhd}((v1\_polynom1~X3~(k15\_pre\_poly~X0)~X2){\unicdcdcdhd}(m1\_subset\_1~X3~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~(k15\_pre\_poly~X0)~(u1\_struct\_0~X2))))))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k11\_polynom1~X0~X2))))){\unicdbdjdcd}((r1\_groeb\_1~X0~X1~X2~X4){\unicdbdjdcd}\\
((X3 \in k7\_ideal\_1~(k11\_polynom1~X0~X2)~X4){\unicdbdjded}(r1\_rewrite1~(k3\_polyred~\\
X0~X1~X2~X4)~X3~(k7\_polynom1~X0~X2))))))))\end{array}
\label{hyp:ehcdddpfhgchpgfgcgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\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}
{{\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}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_partfun1~X1~(k15\_pre\_poly~\\
X0)){\unicdcdcdhd}((v1\_relat\_2~X1){\unicdcdcdhd}((v4\_relat\_2~X1){\unicdcdcdhd}((v6\_relat\_2~X1){\unicdcdcdhd}((\\
v8\_relat\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k15\_pre\_poly~\\
X0)~(k15\_pre\_poly~X0))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v7\_struct\_0~X2){\unicdcdcdhd}\\
((v13\_algstr\_0~X2){\unicdcdcdhd}((v33\_algstr\_0~X2){\unicdcdcdhd}((v3\_group\_1~X2){\unicdcdcdhd}((v5\_group\_1~\\
X2){\unicdcdcdhd}((v4\_vectsp\_1~X2){\unicdcdcdhd}((v5\_vectsp\_1~X2){\unicdcdcdhd}((v3\_rlvect\_1~X2){\unicdcdcdhd}\\
((v4\_rlvect\_1~X2){\unicdcdcdhd}(l6\_algstr\_0~X2)))))))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(u1\_struct\_0~(k11\_polynom1~X0~X2)))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~(k1\_zfmisc\_1~(u1\_struct\_0~(k11\_polynom1~X0~X2)))){\unicdbdjdcd}\\
((r2\_groeb\_1~X0~X1~X2~X3~X4){\unicdbdjded}((k7\_ideal\_1~(k11\_polynom1~X0~X2)~X3=\\
X4){\unicdcdcdhd}(v9\_rewrite1~(k3\_polyred~X0~X1~X2~X3))))))))\end{array}
\label{hyp:egedpfhgchpgfgcgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_partfun1~X1~(k15\_pre\_poly~\\
X0)){\unicdcdcdhd}((v1\_relat\_2~X1){\unicdcdcdhd}((v4\_relat\_2~X1){\unicdcdcdhd}((v6\_relat\_2~X1){\unicdcdcdhd}((\\
v8\_relat\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k15\_pre\_poly~\\
X0)~(k15\_pre\_poly~X0))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v7\_struct\_0~X2){\unicdcdcdhd}\\
((v13\_algstr\_0~X2){\unicdcdcdhd}((v33\_algstr\_0~X2){\unicdcdcdhd}((v3\_group\_1~X2){\unicdcdcdhd}((v5\_group\_1~\\
X2){\unicdcdcdhd}((v4\_vectsp\_1~X2){\unicdcdcdhd}((v5\_vectsp\_1~X2){\unicdcdcdhd}((v3\_rlvect\_1~X2){\unicdcdcdhd}\\
((v4\_rlvect\_1~X2){\unicdcdcdhd}(l6\_algstr\_0~X2)))))))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(u1\_struct\_0~(k11\_polynom1~X0~X2)))){\unicdbdjdcd}((r1\_groeb\_1~\\
X0~X1~X2~X3){\unicdbdjded}(v9\_rewrite1~(k3\_polyred~X0~X1~X2~X3))))))\end{array}
\label{hyp:egddpfhgchpgfgcgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
(v3\_ordinal1~X1))\end{array}
\label{hyp:dgdgfdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l4\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{({\preoh{{{v6\_struct\_0}~{X0}}}})}{\unicdbdjdcd}{({\preoh{{{v7\_struct\_0}~{X0}}}})}})}}}\label{hyp:dgdgddpfdhehchfhdgehpfad}
\end{equation}
\begin{theorem}\label{thm:ehcdedpfhgchpgfgcgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_partfun1~\\
X1~(k15\_pre\_poly~X0)){\unicdcdcdhd}((v1\_relat\_2~X1){\unicdcdcdhd}((v4\_relat\_2~X1){\unicdcdcdhd}((v6\_relat\_2~\\
X1){\unicdcdcdhd}((v8\_relat\_2~X1){\unicdcdcdhd}((v2\_bagorder~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k15\_pre\_poly~X0)~(k15\_pre\_poly~X0)))))))))){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((\preoh v6\_struct\_0~X2){\unicdcdcdhd}((v13\_algstr\_0~\\
X2){\unicdcdcdhd}((v33\_algstr\_0~X2){\unicdcdcdhd}((v3\_group\_1~X2){\unicdcdcdhd}((v5\_group\_1~X2){\unicdcdcdhd}(\\
(v4\_vectsp\_1~X2){\unicdcdcdhd}((v5\_vectsp\_1~X2){\unicdcdcdhd}((v2\_rlvect\_1~X2){\unicdcdcdhd}((v3\_rlvect\_1~\\
X2){\unicdcdcdhd}((v4\_rlvect\_1~X2){\unicdcdcdhd}(l6\_algstr\_0~X2)))))))))))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(u1\_struct\_0~(k11\_polynom1~X0~X2)))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k11\_polynom1~X0~X2))))){\unicdbdjdcd}((r2\_groeb\_1~X0~X1~X2~X4~\\
X3){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_funct\_1~X5){\unicdcdcdhd}((v1\_funct\_2~X5~(k15\_pre\_poly~\\
X0)~(u1\_struct\_0~X2)){\unicdcdcdhd}((v1\_polynom1~X5~(k15\_pre\_poly~X0)~X2){\unicdcdcdhd}\\
(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k15\_pre\_poly~X0)~(\\
u1\_struct\_0~X2))))))){\unicdbdjdcd}((X5 \in X3){\unicdbdjdcd}(r1\_rewrite1~(k3\_polyred~X0~\\
X1~X2~X4)~X5~(k7\_polynom1~X0~X2)))))))))\end{array}$$
\end{theorem}
\end{document}
