\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{t17\_gr\_cy\_2 (TMEvLUwL2t5Vr8tHDzAAVEctmD2ebquXwcD)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_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 $ v1\_gr\_cy\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k7\_group\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r2\_group\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_group\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_gr\_cy\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k7\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_card\_1 : {{\iota}{\unicdbdjdcd}{o}}$ 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}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_group\_1~\\
X1){\unicdcdcdhd}((v3\_group\_1~X1){\unicdcdcdhd}(l3\_algstr\_0~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~\\
X2){\unicdcdcdhd}((v2\_group\_1~X2){\unicdcdcdhd}((v3\_group\_1~X2){\unicdcdcdhd}(l3\_algstr\_0~X2)))){\unicdbdjdcd}\\
(((r1\_group\_6~X0~X1){\unicdcdcdhd}(r1\_group\_6~X1~X2)){\unicdbdjdcd}(r1\_group\_6~X0~X2))))\end{array}
\label{hyp:ehgdhdpfhgchpgfhahpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v8\_struct\_0~X0){\unicdcdcdhd}((v15\_algstr\_0~\\
X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v1\_gr\_cy\_1~X0){\unicdcdcdhd}(l3\_algstr\_0~\\
X0))))))){\unicdbdjdcd}(r2\_group\_6~(k4\_gr\_cy\_1~(k7\_group\_1~X0))~X0)\end{array}
\label{hyp:ehbdfdpfhgchpfdgjhpfcd}
\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){\unicdbdjdcd}(r2\_group\_6~X1~\\
X0))\end{array}
\label{hyp:dhjhngngfgehchjhpfchcdpfhgchpgfhahpfgd}
\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 .  ((v8\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}(k7\_group\_1~\\
X0=k7\_struct\_0~X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflghdpfhgchpgfhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(\preoh v1\_xboole\_0~X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~\\
(k4\_gr\_cy\_1~X0)){\unicdcdcdhd}((v8\_struct\_0~(k4\_gr\_cy\_1~X0)){\unicdcdcdhd}((v15\_algstr\_0~\\
(k4\_gr\_cy\_1~X0)){\unicdcdcdhd}((v2\_group\_1~(k4\_gr\_cy\_1~X0)){\unicdcdcdhd}(v3\_group\_1~\\
(k4\_gr\_cy\_1~X0))))))\end{array}
\label{hyp:ggdghdpfhgchpfdgjhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v8\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~\\
X0))){\unicdbdjdcd}((\preoh v1\_xboole\_0~(k7\_struct\_0~X0)){\unicdcdcdhd}(v7\_ordinal1~(k7\_struct\_0~\\
X0)))\end{array}
\label{hyp:ggdgbdidpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v8\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}((v7\_ordinal1~\\
(k7\_struct\_0~X0)){\unicdcdcdhd}(v1\_card\_1~(k7\_struct\_0~X0)))\end{array}
\label{hyp:ggdgbdhdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l3\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgddpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(\preoh v1\_xboole\_0~X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~\\
(k4\_gr\_cy\_1~X0)){\unicdcdcdhd}((v15\_algstr\_0~(k4\_gr\_cy\_1~X0)){\unicdcdcdhd}(l3\_algstr\_0~\\
(k4\_gr\_cy\_1~X0))))\end{array}
\label{hyp:egehpflgedpfhgchpfdgjhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdhdpfhgchpfdgjhpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v8\_struct\_0~X0){\unicdcdcdhd}((v15\_algstr\_0~\\
X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v1\_gr\_cy\_1~X0){\unicdcdcdhd}(l3\_algstr\_0~\\
X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v8\_struct\_0~X1){\unicdcdcdhd}\\
((v15\_algstr\_0~X1){\unicdcdcdhd}((v2\_group\_1~X1){\unicdcdcdhd}((v3\_group\_1~X1){\unicdcdcdhd}((v1\_gr\_cy\_1~\\
X1){\unicdcdcdhd}(l3\_algstr\_0~X1))))))){\unicdbdjdcd}((k7\_group\_1~X1=k7\_group\_1~X0){\unicdbdjdcd}\\
(r2\_group\_6~X1~X0)))\end{array}$$
\end{theorem}
\end{document}
