(** The graph is presented as a finite map from nodes (of type [positive])
  to the lists of their successors. *)

Definition node: Type := positive.Definition graph: Type := PTree.t (list node).Definition t := positive.Definition leb (x y: t): bool := if plt y x then false else true.

(* Specifications: *)
Theorem leb_total : forall x y, is_true (leb x y) \/ is_true (leb y x).