#[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 strong_induction_le (A : nat -> Prop) : A 0 -> (forall n, (forall m, m <= n -> A m) -> A (S n)) -> forall n, A n.