Hint Rewrite @fold_append_unwrap @fold_append_unwrap' : cheerios.
Inductive le_pos (p : positive) : positive -> Prop :=
| le_p : le_pos p p
| le_xI : forall p2, le_pos p p2 -> le_pos p (xI p2)
| le_xO : forall p2, le_pos p p2 -> le_pos p (xO p2).
Section PositiveInductionPrinciple.
Variable P : positive -> Prop.

(* Specifications: *)
Lemma strongind_pos_aux :
P xH ->
(forall q, ((forall p, le_pos p q -> P p) -> P (xI q)) /\
((forall p, le_pos p q -> P p) -> P (xO q))) ->
(forall q, (forall p, le_pos p q -> P p)).