(*s Definition of simple paths : paths without repetition *)

Definition CG_simple_path (last : ad) (d : D) (l : list ad) :=
  and_sp (CG_path last d l) (ad_list_stutters l = false).

Lemma ad_simple_path_dec : forall x y : ad, {l : list ad & {d : D & CG_simple_path y d (x :: l)}} + {(forall (l : list ad) (d : D), CG_simple_path y d (x :: l) -> False)}.