Section PositiveInductionPrinciple.
Variable P : positive -> Prop.

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)).