apply ltM_nonrefl with (1 := os).
Qed.

(* Specifications: *)
Lemma eqT_not_ltT : forall x y : Term A n, ltT x y -> ~ eqT x y.
unfold eqT, ltT, not in |- *; simpl in |- *; intros x y H Q;
absurd (ltM (T2M x) (T2M y)); auto; rewrite Q; auto.
Theorem ltT_not_refl : forall x : Term A n, ~ ltT x x.
intros x; unfold ltT in |- *; apply ltM_nonrefl with (1 := os).