Section CGNoBadCycles.
Variable
no_bad_cycles :
forall (x : ad) (d : D) (l : list ad),
CG_path x d (x :: l) -> Dle Dz d = true.
(*s The edges are in the domain of the graph *)
(*s The length of a path without repetition is less than the cardinal of the map representing the graph *)

Lemma CG_path_app_1 :
forall (l1 l2 : list ad) (last x : ad) (d1 d2 : D),
CG_path last d2 (x :: l2) ->
CG_path x d1 l1 -> CG_path last (Dplus d2 d1) (l1 ++ l2).