simplify.reflexivity.
qed.
-(* da spostare in nat/order *)
-theorem S_pred: \forall n:nat.lt O n \to eq nat n (S (pred n)).
-intro.elim n.apply False_ind.exact not_le_Sn_O O H.
-apply eq_f.apply pred_Sn.
-qed.
(*
theorem symmetric_Ztimes : symmetric Z Ztimes.