proposition: Lemma pos_add_no_neutral p q : q + p <> p.
proof: Proof. revert q. induction p as [ |p IHp|p IHp]; intros [ |q|q]. 1,3: apply x0_neq_xH. 1: apply x1_neq_xH. 1,3: apply x1_neq_x0. 2,4: apply x0_neq_x1. 1,2: intro H; apply (IHp q). 1: apply x0_inj, H. apply x1_inj, H. Qed.
imports: Basics.Overture Basics.Tactics Pos.Core