(* 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_1 :
forall p : positive, iad_conv_prop p -> iad_conv_prop (xO (xI p)).