(** The following induction principle is useful for reasoning about, e.g., Fibonacci numbers *)
Variable A : N.t -> Prop.
Hypothesis A_wd : Proper (N.eq==>iff) A.

Theorem pair_induction :
A 0 -> A 1 ->
(forall n, A n -> A (S n) -> A (S (S n))) -> forall n, A n.