intros x; case x; auto; intros p y; case y; auto; simpl in |- *; intros;
apply nat_of_P_mult_morphism.
Qed.

Theorem Qpositive_c_unfold1 :
forall p q n : nat,
S p + S q + S q <= S n ->
Qpositive_c (S p + S q) (S q) (S n) = nR (Qpositive_c (S p) (S q) n).