\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{t71\_group\_6 (TMa9vsKDBwJsiDQBh2arH63TPfJapUySG2G)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v15\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r2\_group\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_group\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_group\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k8\_group\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_group\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_group\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_group\_2 : {{\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\_group\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m1\_subset\_1 : {{\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.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdbdjdcd}(v3\_funct\_2~(k8\_group\_6~X0~(k6\_group\_2~\\
X0))~(u1\_struct\_0~X0)~(u1\_struct\_0~(k5\_group\_6~X0~(k6\_group\_2~\\
X0))))\end{array}
\label{hyp:ehgdfdpfhgchpgfhahpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v15\_algstr\_0~X0){\unicdcdcdhd}\\
((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}(l3\_algstr\_0~X0))))){\unicdcdcdhd}((\preoh \\
v2\_struct\_0~X1){\unicdcdcdhd}((v15\_algstr\_0~X1){\unicdcdcdhd}((v2\_group\_1~X1){\unicdcdcdhd}((v3\_group\_1~\\
X1){\unicdcdcdhd}(l3\_algstr\_0~X1)))))){\unicdbdjdcd}((r2\_group\_6~X0~X1){\unicdbdjded}(r1\_group\_6~X0~\\
X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchcdpfhgchpgfhahpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}\\
((v3\_group\_1~X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdcdcdhd}((v1\_group\_3~X1~X0){\unicdcdcdhd}(m1\_group\_2~\\
X1~X0))){\unicdbdjdcd}((v1\_funct\_1~(k8\_group\_6~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(k8\_group\_6~\\
X0~X1)~(u1\_struct\_0~X0)~(u1\_struct\_0~(k5\_group\_6~X0~X1))){\unicdcdcdhd}(v1\_group\_6~\\
(k8\_group\_6~X0~X1)~X0~(k5\_group\_6~X0~X1))))\end{array}
\label{hyp:ggdgjdpfhgchpgfhahpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}\\
((v3\_group\_1~X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdcdcdhd}((v1\_group\_3~X1~X0){\unicdcdcdhd}(m1\_group\_2~\\
X1~X0))){\unicdbdjdcd}((v2\_group\_1~(k5\_group\_6~X0~X1)){\unicdcdcdhd}(v3\_group\_1~(k5\_group\_6~\\
X0~X1)))\end{array}
\label{hyp:ggdggdpfhgchpgfhahpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}\\
((v3\_group\_1~X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdcdcdhd}((v1\_group\_3~X1~X0){\unicdcdcdhd}(m1\_group\_2~\\
X1~X0))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k5\_group\_6~X0~X1)){\unicdcdcdhd}(v15\_algstr\_0~(k5\_group\_6~\\
X0~X1)))\end{array}
\label{hyp:ggdgfdpfhgchpgfhahpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdbdjdcd}((v15\_algstr\_0~(k6\_group\_2~X0)){\unicdcdcdhd}(v1\_group\_3~\\
(k6\_group\_2~X0)~X0))\end{array}
\label{hyp:ggdgbdpfhgchpgfhahpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}\\
((v3\_group\_1~X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdcdcdhd}((v1\_group\_3~X1~X0){\unicdcdcdhd}(m1\_group\_2~\\
X1~X0))){\unicdbdjdcd}((v1\_funct\_1~(k8\_group\_6~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(k8\_group\_6~\\
X0~X1)~(u1\_struct\_0~X0)~(u1\_struct\_0~(k5\_group\_6~X0~X1))){\unicdcdcdhd}(m1\_subset\_1~\\
(k8\_group\_6~X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~\\
(u1\_struct\_0~(k5\_group\_6~X0~X1)))))))\end{array}
\label{hyp:egehpflgidpfhgchpgfhahpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdbdjdcd}((v15\_algstr\_0~(k6\_group\_2~X0)){\unicdcdcdhd}(m1\_group\_2~\\
(k6\_group\_2~X0)~X0))\end{array}
\label{hyp:egehpflggdpfhgchpgfhahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}\\
((v3\_group\_1~X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdcdcdhd}((v1\_group\_3~X1~X0){\unicdcdcdhd}(m1\_group\_2~\\
X1~X0))){\unicdbdjdcd}(l3\_algstr\_0~(k5\_group\_6~X0~X1))\end{array}
\label{hyp:egehpflgfdpfhgchpgfhahpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_group\_1~\\
X1){\unicdcdcdhd}((v3\_group\_1~X1){\unicdcdcdhd}(l3\_algstr\_0~X1)))){\unicdbdjdcd}((r1\_group\_6~X0~X1){\unicdbdjded}\\
({\unicdcdaddd} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~X0)~\\
(u1\_struct\_0~X1)){\unicdcdcdhd}((v1\_group\_6~X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1))))))){\unicdcdcdhd}(v3\_funct\_2~\\
X2~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)))))\end{array}
\label{hyp:egbdbdpfhgchpgfhahpfgd}
\end{equation}
\begin{theorem}\label{thm:ehhdbdpfhgchpgfhahpfgd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v15\_algstr\_0~X0){\unicdcdcdhd}((v2\_group\_1~\\
X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}(l3\_algstr\_0~X0))))){\unicdbdjdcd}(r2\_group\_6~X0~(k5\_group\_6~\\
X0~(k6\_group\_2~X0)))\end{array}$$
\end{theorem}
\end{document}
