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\newtheorem{theorem}{Theorem}
\newtheorem{definition}{Definition}
\newtheorem{lemma}{Lemma}
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\begin{document}
\begin{theorem}
let  x \in  \bigtextl{G}  \quad such that \quad     \ \vert \bigtextl{E}_{\frac{\bigtextl{G}}{\mathbb{R}_2}}^2 ( x \mathbb{R}_2 ) \vert  =\mathcall{P} ,  \mathcall{P} a \quad  opime \quad  where  \quad \mathbb{R}_2 =\mathbb{R}_2 (\bigtextl{G}  ).Then\quad  for \quad all \quad y \in   \bigtextl{G} with\quad \bigtextl{E}_{\frac{\bigtextl{G}}{\mathbb{R}_2}}^2 ( x \mathbb{R}_2 )=\bigtextl{E}_{\frac{\bigtextl{G}}{\mathbb{R}_2}}^2 ( y \mathbb{R}_2 ) \quad  
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\end{theorem}
\begin{proof}
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\end{proof}
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\end{document}