proposition: Lemma positive_rect2_red1 : forall P c1 c2 c3 p, positive_rect2 P c1 c2 c3 (xI p) = c1 p (positive_rect2 P c1 c2 c3 (Pos.succ p)) (positive_rect2 P c1 c2 c3 p).
proof: Proof. intros P c1 c2 c3 p. unfold positive_rect2. simpl. rewrite positive_rect2_helper_bool. reflexivity. Qed.
imports: Coq(Lia) CoRN.stdlib_omissions.List Coq.Logic.Eqdep_dec Coq.Setoids.Setoid