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

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.