(** * Study of initial point w.r.t. [succ] (if any). *)

Definition initial n := forall m, n ~= S m.

Lemma bi_induction_pred : forall A : t -> Prop, Proper (eq==>iff) A -> A 0 -> (forall n, A n -> A (S n)) -> (forall n, A n -> A (P n)) -> forall n, A n.