(* surjectivité de iad_conv *)

Definition iad_conv_prop (p : positive) : Prop :=
  (exists q : positive, p = iad_conv_aux_0 q) \/
  (exists q : positive, p = iad_conv_aux_1 q) \/
  (exists q : positive, (exists r : positive, p = iad_conv_aux_2 q r)).

Lemma iad_conv_surj_4 : forall p : positive, iad_conv_prop p /\ iad_conv_prop (xO p) /\ iad_conv_prop (xI p).