(*s Adding a lis of adresses connected to [root] with weight $0$ *)
Fixpoint CG_add_root (root : ad) (cg : CGraph1) (l : list ad) {struct l} :
CGraph1 :=
match l with
| nil => cg
| x :: l' => CG_add_root root (CG_add cg root x Dz) l'
end.

Lemma CG_add_root_rooted_4 :
forall (l : list ad) (cg : CGraph1) (root a : ad),
in_dom _ a (CG_add_root root cg l) = true ->
{a = root} + {in_dom _ a cg = true}.