proposition: Lemma nat_ind3 (P : nat -> Prop) : P 0 -> P 1 -> P 2 -> (forall i:nat, P i -> P (3 + i)) -> forall n:nat, P n.
proof: Proof. intros H0 H1 H2 HS n. assert (H :P n /\ P (S n) /\ P (S (S n))). induction n. split;auto. destruct IHn as [Hn [HSn HSSn]];repeat split;auto. - apply HS;auto. - tauto. Qed.
imports: Arith