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.

(* Specifications: *)
Lemma le_ne_lt x y: x <= y -> x <> y -> x < y.
Lemma lt_not_eq x y: (x < y -> x <> y)%nat.
Lemma sqrd_plus x y: sqrd x + sqrd y <= sqrd (x + y).
Proof with auto with arith.