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Lemma Par_open_tm_wrt_co_preservation: forall G D B1 B2 c, Par G D (open_tm_wrt_co B1 (g_Var_f c)) B2 -> exists B', B2 = open_tm_wrt_co B' (g_Var_f c) /\ Par G D (open_tm_wrt_co B1 (g_Var_f c)) (open_tm_wrt_co B' (g_Var_f c)).