intros n; elim n; simpl in |- *; auto with arith.
intros n' Rec m; case m; simpl in |- *; auto with arith.
intros m'; elim (Rec m'); intros H'0; case H'0; clear H'0; intros H'0 H'1;
rewrite H'0; auto with arith.
Qed.

Theorem minus_inv_lt_aux : forall n m : nat, n - m = 0 -> n - S m = 0.
intros n; elim n; simpl in |- *; auto with arith.