Module NZDomainProp (Import NZ:NZDomainSig').
Include NZBaseProp NZ.
(** * Relationship between points thanks to [succ] and [pred]. *)
(** For any two points, one is an iterated successor of the other. *)
(** Generalized version of [pred_succ] when iterating *)
(** From a given point, all others are iterated successors or iterated predecessors. *)
(** In particular, all points are either iterated successors of [0] or iterated predecessors of [0] (or both). *)
(** * Study of initial point w.r.t. [succ] (if any). *)
Definition initial n := forall m, n ~= S m.
(** ... then all other points are descendant of it. *)

Lemma initial_ancestor : forall m, exists p, m == (S^p) init.