(** A more general induction principle on non-negative numbers using [Z.lt]. *)

(* Specifications: *)
Lemma Zlt_0_rec :
forall P:Z -> Type,
(forall x:Z, (forall y:Z, 0 <= y < x -> P y) -> 0 <= x -> P x) ->
forall x:Z, 0 <= x -> P x.
Lemma Z_lt_induction :
forall P:Z -> Prop,
(forall x:Z, (forall y:Z, 0 <= y < x -> P y) -> P x) ->
forall x:Z, 0 <= x -> P x.