(*s Properties of the range of the graph *)

Definition cg_range := DMerge D.

Lemma cg_add_out_of_range_1 : forall (cg : CGraph1) (x y : ad) (d : D), (forall (x0 : ad) (d0 : D) (l : list ad), CG_path cg x0 d0 (x0 :: l) -> Dle Dz d0 = true) -> in_dom D x (cg_range cg) = false -> Neqb y x = false -> forall (x0 : ad) (d0 : D) (l : list ad), CG_path (CG_add cg x y d) x0 d0 (x0 :: l) -> Dle Dz d0 = true.