#[global]
Instance Decidable_ge_Z : forall (x y : Z), DecidableClass.Decidable (x >= y)%Z := {
  Decidable_spec := Z.geb_ge x y
}.

Lemma bi_induction (P : Z -> Prop) : Proper (eq ==> iff) P -> P 0 -> (forall x, P x <-> P (succ x)) -> forall z, P z.