(* needed to implement Stdlib.Numbers.NatInt.NZBitsSpec *)
Definition shiftl_spec_high a n m (_:0<=m) := shiftl_specif_high a n m.(* needed to implement Stdlib.Numbers.NatInt.NZBitsSpec *)
Definition shiftr_spec a n m (_:0<=m) := shiftr_specif a n m.

Lemma binary_induction (A : nat -> Prop) : A 0 -> (forall n, A n -> A (2 * n)) -> (forall n, A n -> A (2 * n + 1)) -> forall n, A n.