(* 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 : forall a : ad, exists b : ad, (exists c : ad, a = iad_conv b c).