proposition: Lemma S_O : forall n : nat, S n <> 0.
proof: Proof. intro n. red in |- *. intro H. generalize O_S. intro H0. red in H0. apply H0 with n. apply sym_eq. exact H. Qed.
imports: Coq.Arith.Peano_dec Coq.Relations.Relations CoRN.logic.CLogic Coq(Lia)