proposition: Lemma Even_Odd_ind (P Q : nat -> Prop) : (forall n, Even n -> Q n -> P (S n)) -> Q 0 -> (forall n, Odd n -> P n -> Q (S n)) -> forall n, Even n -> Q n.
proof: Proof. intros HSE H0 HSO n HE%Even_alt_Even. apply Even_alt_Odd_alt_ind with P; try assumption. - intros m HSE'%Even_alt_Even; auto. - intros m HSO'%Odd_alt_Odd; auto. Qed.
imports: NAxioms NProperties OrdersFacts DecidableClass