apply lt_le_trans with (n + q).
apply plus_lt_compat_l; try trivial with arith.
apply plus_le_compat_r; try trivial with arith.
Qed.

(* Specifications: *)
Lemma plus_eq_zero : forall a b : nat, a + b = 0 -> a = 0 /\ b = 0.
intros a b H.