\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{t38\_clopban4 (TMHqAZ4WSraWZh57C8JUNs7uJv6sw3GzEAT)}
\maketitle
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\_normsp\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_normsp\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_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 $ v5\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_cfuncdom : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_clopban2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_clopban2 : {{\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 $ v25\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k7\_clopban4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_struct\_0 : {{\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\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l4\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_cfuncdom : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ 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\_normsp\_0~X0){\unicdcdcdhd}\\
((v4\_normsp\_0~X0){\unicdcdcdhd}((v3\_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}\\
((v5\_clvect\_1~X0){\unicdcdcdhd}((v8\_clvect\_1~X0){\unicdcdcdhd}((v2\_cfuncdom~X0){\unicdcdcdhd}((v5\_clopban2~\\
X0){\unicdcdcdhd}(l1\_clopban2~X0)))))))))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}((k6\_algstr\_0~X0~(k7\_clopban4~X0~X1)~(k7\_clopban4~\\
X0~(k4\_algstr\_0~X0~X1))=k5\_struct\_0~X0){\unicdcdcdhd}(k6\_algstr\_0~X0~(k7\_clopban4~\\
X0~(k4\_algstr\_0~X0~X1))~(k7\_clopban4~X0~X1)=k5\_struct\_0~X0)))\end{array}
\label{hyp:ehddhdpfdgmgpgahcgbgoged}
\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 .  {{({{l1\_clopban2}~{X0}})}{\unicdbdjdcd}{({{({{l1\_cfuncdom}~{X0}})}{\unicdcdcdhd}{({{l2\_clvect\_1}~{X0}})}})}}}\label{hyp:egehpfmgbdpfdgmgpgahcgbgogcd}
\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 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\_normsp\_0~\\
X0){\unicdcdcdhd}((v4\_normsp\_0~X0){\unicdcdcdhd}((v3\_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}((v5\_clvect\_1~X0){\unicdcdcdhd}((v8\_clvect\_1~X0){\unicdcdcdhd}((v2\_cfuncdom~X0){\unicdcdcdhd}\\
((v5\_clopban2~X0){\unicdcdcdhd}(l1\_clopban2~X0)))))))))))))))))){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(u1\_struct\_0~X0))){\unicdbdjdcd}(m1\_subset\_1~(k7\_clopban4~X0~X1)~(u1\_struct\_0~\\
X0))\end{array}
\label{hyp:egehpflghdpfdgmgpgahcgbgoged}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l2\_algstr\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~\\
X0))){\unicdbdjdcd}(m1\_subset\_1~(k4\_algstr\_0~X0~X1)~(u1\_struct\_0~X0))\end{array}
\label{hyp:egehpflgedpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v4\_vectsp\_1~\\
X0){\unicdcdcdhd}(l4\_algstr\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}((v25\_algstr\_0~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}((X2=k9\_algstr\_0~X0~X1){\unicdbdjded}((k6\_algstr\_0~X0~X1~X2=k5\_struct\_0~\\
X0){\unicdcdcdhd}(k6\_algstr\_0~X0~X2~X1=k5\_struct\_0~X0))))))\end{array}
\label{hyp:egidpfmgpgahcgbgogpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v4\_vectsp\_1~\\
X0){\unicdcdcdhd}(l4\_algstr\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}((v25\_algstr\_0~X1~X0){\unicdbdjded}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((k6\_algstr\_0~X0~X1~X2=k5\_struct\_0~X0){\unicdcdcdhd}(k6\_algstr\_0~X0~X2~\\
X1=k5\_struct\_0~X0)))))\end{array}
\label{hyp:egedpfmgpgahcgbgogpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_clopban2~X0){\unicdbdjdcd}(((\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\_normsp\_0~X0){\unicdcdcdhd}((v4\_normsp\_0~X0){\unicdcdcdhd}((v2\_clvect\_1~X0){\unicdcdcdhd}((v3\_clvect\_1~\\
X0){\unicdcdcdhd}((v4\_clvect\_1~X0){\unicdcdcdhd}((v5\_clvect\_1~X0){\unicdcdcdhd}((v8\_clvect\_1~X0){\unicdcdcdhd}\\
((v3\_group\_1~X0){\unicdcdcdhd}((v1\_vectsp\_1~X0){\unicdcdcdhd}((v3\_vectsp\_1~X0){\unicdcdcdhd}((v2\_cfuncdom~\\
X0){\unicdcdcdhd}(v5\_clopban2~X0))))))))))))))))){\unicdbdjdcd}((\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\_normsp\_0~X0){\unicdcdcdhd}((v4\_normsp\_0~X0){\unicdcdcdhd}((v2\_clvect\_1~X0){\unicdcdcdhd}\\
((v3\_clvect\_1~X0){\unicdcdcdhd}((v4\_clvect\_1~X0){\unicdcdcdhd}((v5\_clvect\_1~X0){\unicdcdcdhd}((v8\_clvect\_1~\\
X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v1\_vectsp\_1~X0){\unicdcdcdhd}((v3\_vectsp\_1~X0){\unicdcdcdhd}(\\
(v4\_vectsp\_1~X0){\unicdcdcdhd}((v2\_cfuncdom~X0){\unicdcdcdhd}(v5\_clopban2~X0)))))))))))))))))))\end{array}
\label{hyp:dgdgddpfdgmgpgahcgbgogdd}
\end{equation}
\begin{theorem}\label{thm:ehddidpfdgmgpgahcgbgoged}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v3\_normsp\_0~X0){\unicdcdcdhd}\\
((v4\_normsp\_0~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v1\_vectsp\_1~X0){\unicdcdcdhd}((v3\_vectsp\_1~\\
X0){\unicdcdcdhd}((v2\_clvect\_1~X0){\unicdcdcdhd}((v3\_clvect\_1~X0){\unicdcdcdhd}((v4\_clvect\_1~X0){\unicdcdcdhd}\\
((v5\_clvect\_1~X0){\unicdcdcdhd}((v8\_clvect\_1~X0){\unicdcdcdhd}((v2\_cfuncdom~X0){\unicdcdcdhd}((v5\_clopban2~\\
X0){\unicdcdcdhd}(l1\_clopban2~X0)))))))))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}((v25\_algstr\_0~(k7\_clopban4~X0~X1)~X0){\unicdcdcdhd}(\\
(k9\_algstr\_0~X0~(k7\_clopban4~X0~X1)=k7\_clopban4~X0~(k4\_algstr\_0~\\
X0~X1)){\unicdcdcdhd}((v25\_algstr\_0~(k7\_clopban4~X0~(k4\_algstr\_0~X0~X1))~X0){\unicdcdcdhd}\\
(k9\_algstr\_0~X0~(k7\_clopban4~X0~(k4\_algstr\_0~X0~X1))=k7\_clopban4~\\
X0~X1)))))\end{array}$$
\end{theorem}
\end{document}
