proposition: Lemma lem_2_1 : forall n : nat, Nat.Even n \/ Nat.Even (n + 1).
proof: Proof. hauto using (@Coq.Arith.PeanoNat.Nat.Even_succ, @Coq.Arith.PeanoNat.Nat.add_1_r, @Coq.Arith.PeanoNat.Nat.Even_or_Odd). Qed.
imports: Hammer(Tactics) Arith