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Let $G$ be a Chevalley--Demazure group scheme with a root system $\\Phi\\ne A_1$ and $E$ its elementary subgroup. Let $R$ be a ring and $I$ an ideal of $R$. Assume additionally that $R$ has no residue fields of 2 elements if $\\Phi=C_2$ or $G_2$.\n  Theorem. Let $g\\in G(R[X],XR[X])$. Suppose that for every maximal ideal $\\m$ of $R$ the image of $g$ under the localization homomorphism at $\\m$ belongs to $E(R_\\m[X],IR_\\m[X])$. 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