proposition: Lemma pred_add: forall n, n <> 0 -> pred n + 1 = n.
proof: Proof. intros n Hn. rewrite add_1_r. exact (succ_pred n Hn). Qed.
imports: Coq.Classes.Morphisms Coq.Classes.Morphisms_Prop Coq.Bool.Bool Coq.Arith.Arith Coq.micromega.Lia Coq.NArith.NArith Coq.ZArith.ZArith bbv.N_Z_nat_conversions bbv.Nomega