\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{t36\_polyform (TMG9U7rv4VNFtcixMf9W6P1turZtjyz8Ssv)}
\maketitle
Let $ v2\_polyform : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_polyform : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_polyform : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_polyform : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_int\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k11\_polyform : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_vectsp\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_bspace : {\iota}$ be given.
Let $ k17\_polyform : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_bspace : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_vectsp\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k7\_bspace : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_matrlin : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v13\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v9\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v10\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v11\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ k8\_polyform : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ l1\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v6\_struct\_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 $ l6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k1\_card\_1}~{({{k9\_bspace}~{X0}})}}={{k1\_card\_1}~{X0}}}}\label{hyp:ehedbdpfcgdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_finset\_1~X0){\unicdbdjdcd}(m1\_vectsp\_7~(k9\_bspace~X0)~k2\_bspace~\\
(k7\_bspace~X0))\end{array}
\label{hyp:ehedadpfcgdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_finset\_1}~{X0}})}{\unicdbdjdcd}{({{{k5\_card\_1}~{X0}}={{k1\_card\_1}~{X0}}})}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_finset\_1~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~(k7\_bspace~X0)){\unicdcdcdhd}\\
(v1\_matrlin~(k7\_bspace~X0)~k2\_bspace))\end{array}
\label{hyp:ggdgfdpfcgdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v2\_struct\_0~(k7\_bspace~X0)){\unicdcdcdhd}((v13\_algstr\_0~(k7\_bspace~\\
X0)){\unicdcdcdhd}((v8\_vectsp\_1~(k7\_bspace~X0)~k2\_bspace){\unicdcdcdhd}((v9\_vectsp\_1~\\
(k7\_bspace~X0)~k2\_bspace){\unicdcdcdhd}((v10\_vectsp\_1~(k7\_bspace~X0)~k2\_bspace){\unicdcdcdhd}\\
((v11\_vectsp\_1~(k7\_bspace~X0)~k2\_bspace){\unicdcdcdhd}((v2\_rlvect\_1~(k7\_bspace~\\
X0)){\unicdcdcdhd}((v3\_rlvect\_1~(k7\_bspace~X0)){\unicdcdcdhd}(v4\_rlvect\_1~(k7\_bspace~\\
X0)))))))))\end{array}
\label{hyp:ggdgbdpfcgdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v2\_polyform~X0){\unicdcdcdhd}((v3\_polyform~X0){\unicdcdcdhd}\\
((v4\_polyform~X0){\unicdcdcdhd}(l1\_polyform~X0)))){\unicdcdcdhd}(v1\_int\_1~X1)){\unicdbdjdcd}(v1\_finset\_1~\\
(k8\_polyform~X0~X1))\end{array}
\label{hyp:egehpflgidpfahpgmgjhggpgchng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v2\_struct\_0~(k7\_bspace~X0)){\unicdcdcdhd}(l1\_vectsp\_1~(k7\_bspace~\\
X0)~k2\_bspace)\end{array}
\label{hyp:egehpflghdpfcgdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(\preoh v2\_struct\_0~k2\_bspace){\unicdcdcdhd}((\preoh v6\_struct\_0~k2\_bspace){\unicdcdcdhd}((v13\_algstr\_0~\\
k2\_bspace){\unicdcdcdhd}((v33\_algstr\_0~k2\_bspace){\unicdcdcdhd}((v3\_group\_1~k2\_bspace){\unicdcdcdhd}\\
((v5\_group\_1~k2\_bspace){\unicdcdcdhd}((v4\_vectsp\_1~k2\_bspace){\unicdcdcdhd}((v5\_vectsp\_1~\\
k2\_bspace){\unicdcdcdhd}((v2\_rlvect\_1~k2\_bspace){\unicdcdcdhd}((v3\_rlvect\_1~k2\_bspace){\unicdcdcdhd}\\
((v4\_rlvect\_1~k2\_bspace){\unicdcdcdhd}(l6\_algstr\_0~k2\_bspace)))))))))))\end{array}
\label{hyp:egehpflgcdpfcgdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~X0){\unicdcdcdhd}\\
((v13\_algstr\_0~X0){\unicdcdcdhd}((v33\_algstr\_0~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v5\_group\_1~\\
X0){\unicdcdcdhd}((v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}\\
((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~X0)))))))))))){\unicdcdcdhd}\\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v8\_vectsp\_1~X1~X0){\unicdcdcdhd}\\
((v9\_vectsp\_1~X1~X0){\unicdcdcdhd}((v10\_vectsp\_1~X1~X0){\unicdcdcdhd}((v11\_vectsp\_1~X1~\\
X0){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}\\
(l1\_vectsp\_1~X1~X0))))))))))){\unicdbdjdcd}(v7\_ordinal1~(k1\_vectsp\_9~X0~X1))\end{array}
\label{hyp:egehpflgbdpfghfgdgehdhahpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_polyform~X0){\unicdcdcdhd}((v3\_polyform~X0){\unicdcdcdhd}((v4\_polyform~\\
X0){\unicdcdcdhd}(l1\_polyform~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_int\_1~X1){\unicdbdjdcd}(k11\_polyform~\\
X0~X1=k5\_card\_1~(k8\_polyform~X0~X1)))\end{array}
\label{hyp:egidpfahpgmgjhggpgchng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v33\_algstr\_0~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v5\_group\_1~X0){\unicdcdcdhd}(\\
(v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~\\
X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~X0)))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v8\_vectsp\_1~X1~X0){\unicdcdcdhd}\\
((v9\_vectsp\_1~X1~X0){\unicdcdcdhd}((v10\_vectsp\_1~X1~X0){\unicdcdcdhd}((v11\_vectsp\_1~X1~\\
X0){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}\\
(l1\_vectsp\_1~X1~X0)))))))))){\unicdbdjdcd}((v1\_matrlin~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v7\_ordinal1~X2){\unicdbdjdcd}((X2=k1\_vectsp\_9~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  (m1\_vectsp\_7~\\
X3~X0~X1){\unicdbdjdcd}(X2=k1\_card\_1~X3))))))\end{array}
\label{hyp:egbdpfghfgdgehdhahpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_polyform~X0){\unicdcdcdhd}((v3\_polyform~X0){\unicdcdcdhd}((v4\_polyform~\\
X0){\unicdcdcdhd}(l1\_polyform~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_int\_1~X1){\unicdbdjdcd}(k17\_polyform~\\
X0~X1=k7\_bspace~(k8\_polyform~X0~X1)))\end{array}
\label{hyp:egbdedpfahpgmgjhggpgchng}
\end{equation}
\begin{theorem}\label{thm:ehddgdpfahpgmgjhggpgchng}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_polyform~X0){\unicdcdcdhd}((v3\_polyform~X0){\unicdcdcdhd}((v4\_polyform~\\
X0){\unicdcdcdhd}(l1\_polyform~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_int\_1~X1){\unicdbdjdcd}(k11\_polyform~\\
X0~X1=k1\_vectsp\_9~k2\_bspace~(k17\_polyform~X0~X1)))\end{array}$$
\end{theorem}
\end{document}
