intros a b c; case a; case b; case c; unfold ltT in |- *; simpl in |- *; auto.
intros; apply ltM_plusr with (1 := os); auto.
Qed.

(* Specifications: *)
Theorem T1_is_min_ltT : forall a, ~ ltT a (T1 A1 n).
intros a; case a; unfold ltT in |- *; simpl in |- *; auto.