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 ad_simple_path_bounded_card :
forall (l : list ad) (last x : ad) (d : D),
CG_path last d (x :: l) ->
ad_list_stutters (x :: l) = false -> length (x :: l) <= S (MapCard _ cg).