proposition: Lemma natInj : forall n m : nat, ntoN n = ntoN m -> n = m.
proof: Proof. fix 1. intro n. case n. simple destruct m. trivial. simpl in |- *. intros. cut (Z <> SUCC (ntoN n0)). intros. case H0. assumption. discriminate. simple destruct m. simpl in |- *. intros. cut (SUCC (ntoN n0) <> Z). intros. case H0. assumption. discriminate. simpl in |- *. intros. cut (n0 = n1). intros. rewrite H0. trivial. apply (natInj n0 n1). injection H; trivial. Qed.
imports: Acc_and_Inf