revert x y.
induction d.
simpl.
intros.
destruct x...
inversion H.
simpl.
intros.
destruct x.
destruct y...
elimtype False.
apply le_Sn_n with d...
rewrite H1.
apply le_minus.
destruct y.
elimtype False.
apply le_Sn_n with d.
rewrite <- H1.
apply le_minus.
apply eq_S.
apply IHd...
Qed.

Lemma lt_not_eq x y: (x < y -> x <> y)%nat.