simple induction x; simple induction y.
intros; right; try trivial.
intros.
absurd (0 <> 0); auto with arith.
right; auto.
simpl in |- *.
elim orb_sym; simpl in |- *; intros.
left; replace n with 0.
try trivial.
apply sym_equal; apply zerob_true_elim; try trivial.
Qed.

Lemma zerob_pred_false :
forall n : nat, zerob (pred n) = false -> zerob n = false.