Section CGConsistent.
Variable P : CGconsistent.
(*s Assuming that [cg] is consistent, we can build a distance d(x,y) as follows: d(x,y) is the length of the shortest path from x to y (or +infty if none). *)

Lemma CG_circuits_non_negative_weight :
forall (x : ad) (d : D) (l : list ad),
CG_path x d (x :: l) -> Dle Dz d = true.