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

Lemma pos_div_eucl_eq a b : 0 < b -> let (q, r) := pos_div_eucl a b in pos a = q * b + r.