proposition: Theorem S_predn : forall m : nat, m <> 0 -> S (pred m) = m.
proof: Proof. intros. case (O_or_S m). intro. case s. intros. rewrite <- e. rewrite <- pred_Sn with (n := x). trivial. intro. apply False_ind. apply H. apply sym_eq. assumption. Qed.
imports: Coq(Lia)