elim (lift_trans_le … HT13 … HT3 ?) -T3 // /3 width=5/
]
qed-.
+
+(* Basic_1: was: lift1_free (right to left) *)
+axiom lifts_lift_trans: ∀T1,T0,des0. ⇧*[des0] T1 ≡ T0 →
+ ∀T2,i0. ⇧[O, i0 + 1] T0 ≡ T2 →
+ ∀des,i. @[i] des ≡ i0 → des + 1 ▭ i + 1 ≡ des0 + 1 →
+ ∃∃T. ⇧[0, i + 1] T1 ≡ T & ⇧*[des] T ≡ T2.