#[global]
Instance Decidable_eq_nat : forall (x y : nat), Decidable (eq x y) := {
  Decidable_spec := Nat.eqb_eq x y
}.#[global]
Instance Decidable_le_nat : forall (x y : nat), Decidable (x <= y) := {
  Decidable_spec := Nat.leb_le x y
}.

Lemma pow_succ_r a b : 0<=b -> a^(S b) = a * a^b.